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NAVAL POSTGRADUATE SCHOOL
" Monterey, California
The Viability of Acoustic Tomography in
Monitoring the Circulation of
Monterey Bay
by
James H. Miller, Laura L. Ehret,
Robert C. Dees and Theresa M. Rowan
October 1989 to December 1989
Approved for public release; distribution unlimited.
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Monterey Bay Aquarium Research Institute
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H.™ I CA 93W 101 NAVAL POSTGRADUATE SCHOOL
MON.cru-f ^ Monterey, CA
Rear Admiral R.W. West, Jr. H. Shull
Superintendent ProvoSt
This report was prepared for the Monterey Bay Aquarium Research Institute
(MBARI) and funded by MBARI, the Office of Naval Research, and the Naval
Postgraduate School Research Council.
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l Title (include Security Classification) The Viability of Acoustic Tomography in Monitoring the Circulation of
>lonterey Bay
2 Personal Author(s) James H. Miller, Laura L. Ehret, Robert C. Dees, and Theresa M. Rowan
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echnical Report
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From Oct 88 To Dec 89
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[December 29^ 1989 200
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Acoustic Tomography, Underwater Acoustics
9 Abstract (continue on reverse if necessary and identify by block number
This report presents the results of a fifteen month study on the viability of acoustic tomography in
nonitoring the circulation of Monterey Bay, California. The basis for ocean acoustic tomography is the
neasurement of travel times of coded acoustic signals between the transceivers. The sound speed field and
urrent structure can be inferred from the fluctuations in the travel times. However, the extreme bathymetry
if the Monterey Submarine Canyon complicates the acoustic transmissions in the Bay. The study
•onsisted of an experiment and a computer modeling effort. The experiment consisted of transmitting
omography signals in the Bay for four days. The signals were received with a sonobuoy-based telemetry
ystem. The experimental effort showed multipath arrivals that were stable and resolvable. The modeling
effort involved the use of 2-D and 3-D ray tracing computer programs. The programs had difficulty in
nodeling the effects of Monterey Bay's extreme bathymetry making the multipath identification challenging.
Progress is expected with the augmentation of the ray tracing programs with Gaussian beam and time front
)ostprocessors.
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ames H. Miller
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Unclassified
Abstract
This report presents the results of a fifteen month study on the viability of
acoustic tomography in monitoring the circulation of Monterey Bay, Cal-
ifornia. The basis for ocean acoustic tomography is the measurement of
travel times of coded acoustic signals between the transceivers. The sound
speed field and current structure can be inferred from the fluctuations in the
travel times. However, the extreme bathymetry of the Monterey Submarine
Canyon complicates the acoustic transmissions in the Bay. The study con-
sisted of an experiment and a computer modeling effort. The experiment
consisted of transmitting tomography signals in the Bay for four days. The
signals were received with a sonobuoy-based telemetry system. The exper-
imental effort showed multipath arrivals that were stable and resolvable.
The modeling effort involved the use of 2-D and 3-D ray tracing computer
programs. The programs had difficulty in modeling the effects of Monterey
Bay's extreme bathymetry making the multipath identification challenging.
Progress is expected with the augmentation of the ray tracing programs with
Gaussian beam and time front postprocessors.
DUD'EYWOXLIBFV
NAV, <= SrGRADUAT *CHOOL
MOh.a-wf CA 9394o- 101
Contents
1 Introduction 11
1.1 The Original Concept 12
1.2 Results of the study 13
1.3 Report Overview 16
2 Background 17
2.1 Ocean Acoustic Tomography 17
2.1.1 The Forward Problems IS
2.1.2 The Inverse Problem 21
2.1.3 Discussion 22
2.2 Monterey Bay 23
2.2.1 Bathymetry 23
2.2.2 Geology and Sediments 2G
2.2.3 Currents 30
2.2.4 Temperature and Salinity Variations 33
2.2.5 Tides 35
2.2.G Surface Waves 35
2.2.7 Internal Waves and Canyon Currents 37
3 Experimental Effort 43
3.1 Experiment Objectives 43
3.1.1 Location and Description 44
3. 1.2 Receiver Placement 46
3.2 Equipment 47
3.2.1 Transmitter 47
3.2.2 Receivers 49
3.2 3 Acoustic Data Recording 40
3.2.4 NDBC Wave Measurement and ARGOS buoys .... 51
3.2.5 Sound Speed Profile Measurement 54
3.2.6 Acoustic Doppler Current Profiler 55
3.3 Summary of the Experimental Procedure 55
3.4 Signal Processing 56
34.1 Signal design 56
3.4.2 Signal demodulation and correlation system 60
3.4.3 Travel time estimation 64
3.4.4 Summary of signal processing 66
3.5 Experimental Results 67
351 General Summary of Data 67
35.2 Station J Data 69
3.53 Analysis of Arrival Time Fluctuations at Surface Wave
Frequencies 74
3.54 Analysis of Arrival Time Fluctuations at Internal Wave
Frequencies 81
3 5 5 Summary of experimental results 81
4 Modeling Effort 8G
4.1 The Multiple Profile Ray-Tracing Program 86
4.1.1 Description 8G
4.1.2 Program Flow 87
4.1.3 MPP Input/Output 93
4.2 3-D Ray Tracing with HARPO ' 109
4.2.1 Hamiltoiuan Ray Tracing 110
4.2.2 Application Ill
o
Conclusions 11G
A MPP Data 118
A 1 Bathymetry Data for Receiver Locations 118
A. 2 MPP Ray Traces and Stick Plots 125
B Chronologic Summary of Events in the 1988 Monterey Bay
Experiment 142
B.l 12 December 1988 142
B.2 13 December 1988 142
B.3 14 December 1988 144
B.4 15 December 1988 144
B.5 10 December 1988 145
B.G Data Disposition 140
C Maximal-length Sequences and the Fast Hadamard Trans-
form 147
C.l Introduction 147
C2 Generating the M-sequence 148
C.3 The Hadamard Matrix 150
C.4 Input and Output Vector Order Permutation 152
C5 The Fast Hadamard Transform 154
C.6 Using the Reverse Code 156
C7 Correlation Procedure 156
C8 Example 158
C.9 Summary 158
D Additional Data for Station J 160
D.l Hadamard Transformed Acoustic Signal 160
D.2 Arrival Time and Surface Wave Spectra 187
Initial Distribution List 199
List of Figures
1.1 Possible Monterey Bay tomography transceiver locations. . . 14
1.2 An example of the multipaths between tomography source
and receiver in Monterey Bay 15
2.1 (top) Several transmitters (T) and receivers (R) give many
ray paths as viewed from above, (bottom) Each slice may con-
tain numerous eigenrays connecting the transmitters and re-
ceivers. This diagram is from a 1983 experiment near Bermuda. 19
2.2 Monterey Bay. California 24
2.3 Distribution of sediment types in Monterey Bay 26
2.4 Offshore surficial geologic map of Monterey Bay 29
2.5 Monterey Bay seasonal current patterns , 32
2.6 Mean temperature and salinity variation at the mouth of
Monterey Bay (station 3) and CalCOFI station during 1950-
19G2 34
2.7 Monterey Bay tidal pattern 3C
2.8 North Monterey Bay buoy, December 1987, wave energy data. 3S
2.9 North Monterey Bay buoy. December 1987. wave energy spec-
tra graph 39
2.10 Temperature distribution at (a) high and (b) low internal
tide, Monterey Canyon axis, 13-14 September 1979 41
3.1 Monterey Bay showing the positions of the tomography source
and receivers (positions marked with •). The source is at
station A while all others are receivers. The shore station is
marked with A 45
3.2 The 224 Hz resonant tomography source and mooring config-
uration 48
3.3 Modified AN/SSQ-57 sonobuoy as used in the Monterey Bay
Acoustic Tomography Experiment. The hydrophone rests on
the bottom to eliminate motion 50
3.4 Sonobuoy data recording system located in the van. This sys-
tem receives the sonobuoy radio transmission, demodulates it
for the acoustic signal, and records that signal on videotape
using pulse code modulation 52
3.5 Comparison of resolved and unresolved pulses 57
3.6 Quadrature demodulation and digitization performed in the
Monterey Bay Acoustic Tomography Experiment 61
3.7 Diagram of tomography signal data flow for 'real time' digi-
tization and code correlation 63
3.8 Two dimensional ray path predicted using MPP. This eigen-
ray connects the source at Station A to the receiver at Station
J 70
3.9 Sound speed profile from near Station J. Note that any ray
path will be refracted downward. The trace has two lines, one
as the CTD goes down and the other as it is brought back to
the surface 72
3.10 Sound speed profile from near mid-Bay. This profile is typical
of the profiles found in deep water at the time of the experi-
ment and very close to the profile used in MPP for eigenray
prediction 73
3.11 Received acoustic signal after Hadamard transforming for
maximal-length sequence from Station J. 14DEC88 1855 to
1957 PST. Each line is 31 seconds of data coherently aver-
aged to one 1.9375 second period. The earliest period is in
the foreground and the latest is at the back 75
3.12 Arrival time estimate for Station J from 1855 to 1924 PST
on 14Dec88. The fast fluctuations in arrival time are due
to surface waves changing the path length. Lower frequency
oscillations from other causes are also seen 76
3.13 Arrival time estimate for Station J from 1925 to 1955 PST
on 14Dec88. The fast fluctuations in arrival time are due
to surface waves changing the path length. Lower frequency
oscillations from other causes are also seen 77
3.14 Arrival time power spectrum for Station J. Spectrum from
2.2 hours of arrival times series. 1855 to 2107 14 Dec88 PST. 7fJ
3.15 Surface wave power spectrum in Monterey Bay at 2000 PST
on 14 Dec88 as taken from the NDBC wave measuring buoy
southwest of Santa Cruz 80
3. 16 Arrival time data for Station J lowpass filtered to 0. 00258 Hz
(Period = 64 minutes) 82
3.17 Arrival time data for Station J lowpass filtered to 0.00258 Hz
(Period = 6.4 minutes) 83
3.18 Arrival time data for Station J lowpass filtered to 0.00258 Hz
(Period = 6.4 minutes). High amplitude after 0400 is due to
low SNR during storm 84
3.19 Arrival time data for Station J lowpass filtered to 0.00258 Hz
(Period = 6.4 minutes) 85
4.1 MPP block diagram with input and output files 88
4.2 Receiver hydrophone locations for ray tracing 94
4.3 Typical December sound speed profile for Monterey Bay. ... 98
4.4 A model of the bathymetry of Monterey Bay region 113
4.5 Planar view of rays calculated from Station J towards the
tomography transmitter 114
4.6 Top view of rays calculated from Station J towards the to-
mography transmitter 115
A.l Ray trace for receiver location 1 126
A. 2 Stick plot for receiver location 1 127
A. 3 Ray trace for receiver location 2 128
A. 4 Stick plot for receiver location 2 129
A. 5 Ray trace for receiver location 4 130
A. 6 Stick plot for receiver location 4 131
A. 7 Ray trace for receiver location 5 132
A. 8 Stick plot for receiver location 5 133
A. 9 Ray trace for receiver location 7 134
A. 10 Stick plot for receiver location 7 135
A.ll Ray trace for receiver location 8 136
A. 12 Stick plot for receiver location 8 137
A. 13 Ray trace for receiver location 13 138
A. 14 Stick plot for receiver location 13 139
A. 15 Ray trace for receiver location 17 140
A. 16 Stick plot for receiver location 17 141
CI Shift register realization 149
C.2 Indices formed from matrix octal equivalents 153
C.3 Basic Fast Hadamard Transform element for cascading addi-
tions and the full diagram for an eight point FHT 157
D.l Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 1317 to 1419 14DEC88. High
ambient noise at the start is from the R/V Point Sur after
deploying buoy 161
D.2 Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 1419to 1521 14DEC88 162
D.3 Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 1521 to 1623 14DEC88 163
D.4 Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 1623 to 1725 14DEC88 164
D.5 Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 1725 to 1827 14DEC88 165
D.6 Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 1827 to 1929 14DEC88. Signal
cutoff is due to tape change 166
D.7 Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J. 1957 to 2059 14DEC88. The pre-
vious hour is included as Figure 12 on page 58. Note that the
arrival structure is shifted for data from a new tape 107
D.8 Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 2059 to 2201 14DEC88 168
D.9 Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J. 2201 to 2303 14DEC88 169
D.10 Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J. 2303 14DEC88 to 0005 15DEC88. 170
D.ll Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 0005 to 0107 15DEC88. Note that
computer generated time scale is extended past 0000 for con-
venience in processing. The reason for signal cutoff is that
the end of the tape was reached 171
D.12 Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J. 0052 to 0154 15DEC88. Note that
the arrival structure is shifted because of the start of a new
tape 172
D.13 Tomographic signal, coherently averaged 16 timesthen mag-
nitude squared. Station J, 0154 to 0256 15DEC88 173
D.14 Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 0256 to 0358 15DEC88 174
D.15 Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 0358 to 0500 15DEC88. High
scattering and ambient noise were present at this time be-
cause of high winds (the worst windstorm of the year to hit
the central California coast) 175
D.16 Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 0500 to 0602 15DEC88. High
ambient noise and high scattering continue from windstorm. . 176
D.17 Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 0602 to 0704 15DEC88. The rea-
son for signal cutoff is that the end of the tape was reached. . 177
D.18 Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J. 0647 to 0749 15DEC88. The rea-
son for the increased amplitude is unknown. Note that the
arrival structure is shifted at the start of the new tape. . . . 178
D.19 Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 0749 to 0851 15DEC88 179
D. 20 Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 0851 to 0953 15DEC88 180
D.21 Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 0953 to 1055 15DEC88 181
D.22 Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J. 1055 to 1157 15DEC88 182
D.23 Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J. 1157 to 1259 15DEC88. The rea-
son for the signal cutoff is that the end of the tape was reached. 183
D.24 Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 1226 to 1328 15DEC88. Note that
the arrival structure is shifted at the start of the new tape. . 184
D.25 Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J. 1328 to 1430 15DEC88 185
D.26 Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J. 1430 to 1532 15DEC88. Signal
cutoff is due to buov failure 18C
D. 27 Arrival time power spectrum for Station J. Spectrum from
2.2 hours of Arrival Time Series, 2001 to 2213 14DEC88 PST. 188
D.28 Surface wave power spectrum in Monterey Bay. Data is from
the NDBC buoy southwest of Santa Cruz, 2100 14DEC88 PST. 189
D. 29 Arrival time power spectrum for Station J. Spectrum from
2.2 hours of Arrival Time Series, 2107 to 2319 14DEC88 PST. 190
D.30 Surface wave power spectrum in Monterey Bay. Data is from
the NDBC buoy southwest of Santa Cruz, 2200 14DEC88 PST. 191
D.31 Arrival time power spectrum for Station J. Spectrum from
2.2 hours of Arrival Time Series, 2213 14DEC88 to 0005
15DEC88 PST 192
D.32 Surface wave power spectrum in Monterey Bay. Data is from
the NDBC buoy southwest of Santa Cruz, 2300 14DEC88 PST. 193
D.33 Arrival time power spectrum for Station J. This spectrum
was generated using the segmented FFT method on the data
from an entire 6 hour tape (the maximum length time series
without tape-to-tape synchronization) 194
List of Tables
2.1 Up and down-canyon reversal cycle data for Monterey Canyon. 40
2.2 Up and down-canyon reversal cycle data for Carmel Canyon. 42
4.1 Position, range and depth of simulation receivers 95
4.2 December sound speed profile values for Monterey Bay region. 99
4.3 Eigenray information for site 16 based on change of source
placement 101
4.4 Eigenray information for sites 1,2,4,5,7,8 and 13 102
4.5 Eigenray information for site 17 107
A.l Bathymetry data for receiver locations 1, 2, and 3 119
A. 2 Bathymetry data for receiver locations 4, 5, and 6 120
A. 3 Bathymetry data for receiver locations 7. 8, and 9 121
A. 4 Bathymetry data for receiver locations 10, 11, and 12 122
A. 5 Bathymetry data for receiver locations 13. 14, and 15 123
A. 6 Bathymetry data for receiver locations 16 and 17 124
C.l Shift register contents when generating M-sequence 149
C.2 Re-ordering of input and output vectors 155
10
Chapter 1
Introduction
This report presents the results of a fifteen month study on the viability of
acoustic tomography in monitoring the circulation of Monterey Bay, Cali-
fornia. It is envisioned that the Bay could be surrounded by shore-linked
acoustic transceivers that would transmit and receive coded acoustic signals.
Ocean acoustic tomography uses the fluctuations of measured travel times
from a number acoustic multipaths though an ocean body. These travel
time fluctuations can be 'inverted" to provide an estimate of the interven-
ing sound speed structure (and hence density) and current structure.
Acoustic tomography has been used with success in deep ocean environ-
ments where bottom bathymetry has been not a factor. However, applying
it to an ocean body like Monterey Bay with its Submarine Canyon intro-
duces a number of questions. These questions deal with the character of
acoustic transmissions in the Bay. Namely, for acoustic tomography to be
viable, four questions must be answered affirmatively:
1. Are the acoustic arrivals strong enough to accurately estimate their
arrival time'7
2. Are the acoustic arrivals resolvable from one another?
3. Are the acoustic arrivals stable over time?
4. Are the arrivals identifiable (i.e. comparable) with computer-modeled
arrivals7
This study attempts to answer the above questions through two efforts:
experiment and computer modeling. The experiment involved the trans-
mission of acoustic signals from a source off of Point Sur to a number of
11
receivers on the northern shelf of Monterey Bay. The computer modeling
effort used two acoustic ray tracing programs to simulate the multipath
arrival structure of the received acoustic signals.
1.1 The Original Concept
The presence in Monterey Bay of MBARI and five other institutions with
strong oceanography programs provides a unique opportunity for a long-
term interdisciplinary study of the biology and physics of a coastal envi-
ronment. This tomography system is intended to be a core measurement
system which, with ancillary measurements colocated at the hard-wired to-
mographic transceivers, would provide a real-time view of the circulation and
density structure within the Bay. Data from the relatively sparse spot mea-
surements and integrated tomographic data will be assimilated into dynam-
ical models to provide an interpolated and displayable view of the physical
properties (e.g., velocity and thermal structure at selected depths) spanning
the measurement domain. These physical models further provide the basis
for incorporating biological variables to study (and display) a wide range of
physical and biological processes.
The state-of-the-art in ocean acoustic tomography and in associated
signal processing and data storage technology has advanced to the point
where we can think about the long-term (five year) imaging of the complete
oceanogaphic structure of Monterey Bay.
Recently, much progress has been made in data assimilation, the process
of integrating data into a dynamical model of the circulation of both large
and small scale oceanographic systems. With the measurements available
from acoustic tomography and other traditional oceanographic instruments,
dynamic models of Monterey Bay could be verified. Acoustic tomography
could provide the boundary conditions for the open end of the Bay and
verification of the models as time progressed.
The Monterey Bay is a unique location in which to conduct ocean acous-
tic tomography. The semi-circular geometry of the Bay enables acoustic
transceivers to be placed around the Bay near enough to shore to be linked
by an underwater cable. The more coverage in angle around the Bay, the
better resolved are the oceanographic features. The transceivers would not
be data-storage limited as data could be sent up the cable to shore. They
would not be power limited as power could come from shore down the cable.
The Monterey Bay tomography system would include a number of tomo-
12
graphic transceivers placed at the bottom surrounding the bay near shore.
The shore substations would be linked to the main data collection station
via either land lines or RF telemetry links. An example tomographic sys-
tem is shown in Figure 1.1. It consists of eight transceivers placed on the
periphery of the bay between the depths of 25 to 100 meters. An additional
transceiver has been placed near the mouth of the Bay. An array consisting
of J transceivers has J • (J — 1) horizontal paths across the volume of in-
terest. This includes a two-way path between each transceiver. In addition,
depending on the acoustic conditions, there are a number K vertical multi-
paths for each horizontal path as illustrated in Figure 1.2. An estimate of
the average number of usable multipaths for Monterey Bay is three. There-
fore, the total number, Ar, of individual acoustic paths through the Bay is
N = J ■ (J — 1) • K or 168 paths through Monterey Bay for the array pictured
in Figure 1.1.
Ongoing oceanographic studies on Monterey Bay could be integrated
into the tomography system. A primary forcing mechanism for circulation
of the Bay is the oceanic currents at the mouth of the Bay. Planned hydro-
graphic, constituent and current measurements by MBARI, NPS, and other
institutions will be extremely useful for this purpose. In addition to the in
situ measurements, satellite AYIIRR (Advanced Very High Resolution Ra-
diometer) thermal maps could be integrated routinely with the tomography.
The system could be a focal point for research on the Bay to foster coop-
eration and improve the communication between the various oceanographic
institutions around the Bay.
1.2 Results of the study
As mentioned above, the viablity of acoustic tomography in monitoring the
circulation of an ocean body like Monterey Bay depends on four character-
istics of the acoustic arrivals:
1. signal-to-noise ratio,
2. resolvability,
3. stability, and
4. identifiability.
This study has looked at each of the above necessary characteristics with
a two-pronged study: an experiment and modeling with a ray-tracing com-
13
Figure 1.1: Possible Monterey Bay tomography transceiver locations.
\A
22.5 30.0 37.5
RANGE (KM)
60.
Figure 1.2: An example of the multipaths between tomography source and
receiver in Monterey Bay.
15
puter program. A experiment was held in Monterey Bay in December, 1988
in which a single tomography source off Point Sur transmitted to a number
of receivers in the northern part of the Bay. The modeling effort involved
the use of two acoustic ray-tracing programs that attempted to model the
multipath arrival structure.
The results of this study support the feasibility of acoustic tomography in
Monterey Bay. The Monterey Bay Acoustic Tomography Experiment of De-
cember 1988 showed strong acoustic arrivals that were mostly resolved and
stable over the cross-canyon paths for the 3 day experiment. However, one
important piece of the puzzle is still missing: the identification of multipath
arrivals measured in the experiment. The MPP (Multiple Profile Program)
2-D ray tracing program was able to identify a few eigenrays (rays connect-
ing source and receiver). The HARPO (HAmiltonian Ray Program for the
Ocean) 3-D ray tracing program has not been able to find any eigenrays. The
inability of these programs to model the acoustic propagation in Monterey
Bay stems from the extreme bathymetry of the Bay. These eigenrays exist
because the experiment measured them. The lack is not in the existence
of stable, resolvable arrivals but in our ability to model them correctly. In
the next few months, as part of another feasibility study for the Norwegian-
Barents Sea Tomography Experiment. HARPO capabilities will be increased
with the addition of Gaussian beam and time front post-processing routines.
These routines eliminate the need for modeling eigenrays and should be able
to identify the arrivals measured in the Monterey Bay Experiment.
1.3 Report Overview
This report into five chapters including this introduction. Chapter 2 provides
a background on Monterey Bay including oceanography, bathymetry, and
geology. Chapter 3 describes the experiment carried out in Monterey Bay in
December. 198l>. Chapter 4 describes the work to date on modeling acoustic
propagation in Monterey Bay. Chapter 5 lists our conclusions about the
feasibility of an acoustic tomography system in Monterey Bay.
1G
Chapter 2
Background
2.1 Ocean Acoustic Tomography
''Ocean acoustic tomography is a technique for observing the dynamic be-
havior of ocean processes by measuring the changes in travel time of acoustic
signals transmitted over a number of ocean paths." [1] The word tomography
is derived from two Greek roots meaning ''to slice" and "to look at." Ocean
acoustic tomography uses sound energy to look at a "slice" of the ocean by
measuring the travel time of signals propagating through the water. Sound
speed in the ocean is a function of salinity, pressure, and temperature. As
acoustic energy travels along its path, its rate of travel varies with these
quantities as well as with the speed and direction of any currents. Math-
ematical inverse methods are applied to these travel time fluctuations to
estimate the variation of these dynamic ocean variables.
Ocean acoustic tomography was originally proposed by Munk and Wuil-
sch in 1977. In 1979. they presented methods for inverting the data to
estimate the sound speed field. [3] This procedure is similar to the proce-
dure used in medical x-ray tomography where the measuring signal travels
in a straight line from transmitter to receiver. Ocean acoustic tomogra-
phy may have energy traveling along several curving paths with different
travel times and from one transmitter to several receivers simultaneously,
as shown in Figure 2.1. Thus, with several sound sources and receivers, the
amount of data collected grows multiplicatively rather than additively (as in
point sampling). The sound speed fluctuations along the entire path affect
the travel time of a signal. Because of this integrating characteristic of the
travel time, small inhomogeneities will have a negligible effect. Sound also
has the advantage of sampling along its path very quickly - approximately
r
1500 meters per second. If transmissions are made in both directions along
a path, the difference in travel time is related to currents along the path.[l]
Ocean acoustic tomography is a valuable tool for monitoring the ocean in-
terior. Its overall system performance can be improved, however, if it is
supplemented by in situ measurements by ships and buoys.
2.1.1 The Forward Problems
Treating the ocean medium as a large, time-varying distortionless filter, the
impulse response of the source-receiver channel is just the sum of the impulse
responses of the individual paths [5]
P
h{i) = 22*6(1 -n) (2.1)
i=i
where P is the number of paths, a, is the amplitude, and r, is the total
travel time along the path. If the transmitted signal is an impulse then
the received signal will be the impulse response. The separate paths can be
predicted from ray theory. The limits placed on the sound speed structure
for ray theory to be valid can be described as: [6]
• The amplitude of the wave must not change appreciably in distances
comparable to a wavelength.
• The speed of sound must not change appreciably in distances compa-
rable to a wavelength.
• The channel depth and source-receiver distance must be large in com-
parison to a wavelength.
If these conditions cannot be met, other methods must be used, and '"full
wave'" or modal solutions can be attempted [6,4].
Density Tomography
The travel time for a ray path can be found by integrating the sound slowness
(inverse speed) over the specific ray path denoted by P, (the ith ray path)[6]
f ds
JP, c(x,y.z,1)
18
R
C(km/s)
E
O
Range (km)
Figure 2.1: (top) Several transmitters (T) and receivers (R) give many ray
paths as viewed from above, (bottom) Each slice may contain numerous
eigenrays connecting the transmitters and receivers. This diagram is from
a 1983 experiment near Bermuda[2].
19
The fluctuations in sound speed can be thought of as perturbations from
some arbitrary base speed c0(z),
c(x,y,z,t) = c0(z) + 6c(x,y,z,t) (2.3)
so that the travel time becomes a constant travel time with a perturbation
f ds
Jpt c0 + 6c(x,y,z,t)
For 6c <C c0, an approximation from the binomial expansion can be used
ds
Ti,0 + 6tx - / — r^T
JP, co(z) M '
o(=) ;
- / —
JP, C0{ =
+
_ 6c(x.y.z,1)\ d$
) V c0(z)
1 6c(x.y,zJ)
P, \c0{ = ) c20(z)
ds (2.5)
The perturbation is[G]
f>c{x,y,z,t)
°n = - / TT\ — (2-6)
Current Tomography
In the above development, the arrival time of an acoustic pulse was assumed
to be only a function of sound speed, a scalar quantity. However, if a current
field exists in the ocean between transceivers, the travel time of a pulse is
in one direction is different from the other direction. If we define At, to be
the difference in the to and fro travel times of the ith ray. then
,= /_A__/^i_ (2.7)
Js, c + u ■ s Js, c - v ■ s
where u is the space varying current field and s is the unit tangent vector
to the ray. Implicit in Equation 2.7 is that the ray path is same for both
directions, a very good approximation.
20
2.1.2 The Inverse Problem
The inverse problem is to determine 6c(x, y, z,t) (u) from 6r,. The travel
time perturbation 6r, (At,) depends on the magnitude of sound speed (cur-
rent) fluctuations and the path of the ray, which determines the water that
is sampled by that ray. Note that this perturbation relation has now been
linearized. Inverse mathematical methods are often used in connection with
geophysical problems where some characteristic is measured by its effect in
perturbing some transmitted signal, rather than direct observation of that
characteristic. There is a large body of information relating to linear and
nonlinear inverse techniques - many of which can be applied to acoustic
tomography inversions. [12]
Briefly, one inverse approach is to discretize Equation 2.6 (we shall con-
centrate on density tomography here), so that
t = Gc (2.8)
where we have assumed that the unknown sound speed perturbation field has
been discretized into a vector c of dimension (ATC x 1) and we have formed
a vector of dimension (Ar* x 1), t, of the known travel time perturbations
of each ray at each receiver. In all realistic ocean acoustic tomography
problems, Arc > Nt, i.e. we have an underdetermined inverse problem with
more unknowns than independent pieces of data. G is the known kernel
matrix of dimension A'( x Arc that has the information about each of the
paths and background sound speed profile. Since G is not square, we cannot
simply say that c = G_1t.
One way to solve Equation 2.8 is to form a quadratic functional that
is sensitive to model (sound speed) estimation error and model smoothness
given by
1(c) = (Gc - t)7W(Gc - t) + AcJSc (2.9)
where W is a weighting matrix which allows us to use different types of
measurements with different levels of confidence and S is a matrix which
smooths the estimate over space. The Lagrange multiplier A determines
how important the error is versus the smoothness of the estimated model.
We now derive the c which minimizes L. First, we expand Eq. (2.9)
(following Liebelt [7] )
1(c) = (cTGT - tT)W(Gc - t) + AcTSc (2.10)
1(c) = crGTWGc - cTGTWt - tTWGc + tTWt + AcTSc (2.11)
21
Because the third term in the preceding equation is a scalar, we can trans-
pose this term to obtain
L(c) = cTGTWGc - 2cTGTWt + tTWt + AcrSc. (2.12)
We next differentiate Eq. (2.12) with respect to the components of c yielding
— = 2GTWGc-2GTWt + 2ASc. (2.13)
dc
Setting the expression above to zero and solving for c we get
c = (GrWG + AS)_1GTWt. (2.14)
The solution given in Eq. 2.14 is analogous to the weighted damped least
squares[8, 9 ,10, 11. 12]. The choice of smoothing matrix 5 and its weight A is
a tradeoff between the resolution and error in the sound speed field estimate.
2.1.3 Discussion
The solution of the the ocean acoustic tomography problem is tied directly to
the "forward" problem. The path of each eigenray between the source and
receiver must be identified before the integral relating time perturbation
to sound speed perturbation can be inverted. This eigenray is normally
considered to be fixed spatially (usually a good approximation) with the
sound speed perturbations acting on this path. Fluctuation in the sound
speed field is the data upon which ocean acoustic tomography depends, but
if the fluctuation is too great, the ray path may become unstable and no
longer reach the receiver. Rays do not arrive as a single point but cover
an area measured by the Fresnel zone size. The size of the Fresnel zone
depends on the sound speed structure and acoustic frequency but for channel
transmission remains fairly constant after 20 kilometers. [4] This size and
knowledge of sound speed fluctuations along the path can be used to estimate
path stability. In summary, ocean acoustic tomography requires a sufficient
understanding of the ocean along the source-receiver path that eigenrays
along which the signal will travel can be predicted. The received signal must
have an ''arrival'" structure which is stable and does not fade or disappear.
The arrival must be identifiable as to its path for the tomographic inversion
to proceed. The transmitted signal must be constructed to facilitate an
accurate estimate of the travel time perturbations and should be resolvable
form other arrivals at very close intervals. Finally, these time perturbations
will be used to estimate the fluctuations in the ocean sound speed field using
inverse methods.
22
2.2 Monterey Bay
Monterey Bay is a semi-enclosed elliptical embayment along the Central
Coast of California between latitudes 36°36.05'iV and 36°58.70'W as de-
scribed in Figure 2.2. Moss Landing is located at the easternmost point
of the bay at longitude 121°47.30'W\ Since the bay is open to the Pacific
Ocean along its western side, we assume an artificial line between Point
Pinos to the south (121°56.20'PV) and Point Santa Cruz along the north
shore (122°01.60'Wr). Based on these positions, the bay is 42 km long and
17.6 km wide from Moss Landing due west to the open bay boundary. The
surface area of the bay is approximately 534 km2, of which 81% is above the
continental shelf while the rest overlies the submarine canyons. [13]
Fresh water enters the bay via the San Lorenzo River, Soquel Creek, Ap-
tos Creek, Pajaro River and Salinas River. These streams have a combined
mean annual discharge of 1.85xl06m3/day with the Salinas River having
the greatest contribution at 55% [14]. Precipitation and river runoff are
normally greatest during the winter rainy season. During the dry months of
May through October, a sand bar blocks the Salinas River, forcing its water
to flow north and discharge through Elkhorn Slough[13].
2.2.1 Bathymetry
Continental Shelf and Slope
The continental shelf is fairly narrow south of Monterey Bay, ranging in
width from less than 1.6 km at Cypress Point on the Monterey Peninsula to
about 14 km at Point Sur. North of the Bay the shelf is wider, ranging from
about 9.3 km to 37 km width south of San Francisco. The shelf in Monterey
Bay is cut by submarine canyons and the shelf bottom slopes toward the
edge of the canyons. The northern bay shelf is approximately 238 km in
area and is at a maximum depth of 90 m at the canyon rim, as compared to
the shelf in the south bay that is 195 km2 and deepens to 180 m[13,15]. The
maximum slope near Seaside is 2%, while offshore of the the Salinas River
it is 1-1.5%[1G].
Between the continental shelf and the deep ocean floor lies the continen-
tal slope with it steeper gradient. According to Shepard[17], the slope in the
greater Monterey Bay area is not consistent. Just south of Monterey Bay
the outer part of the slope is set toward the northeast for 30 km or more.
Further south, the slope spreads over a wide area. North of the bay, the
continental slope is narrower, has an average grade of 10%>, and is marked
23
Figure 2.2: Monterey Bay. California.
24
by a number of submarine canyons.
Submarine Canyons
The most prominent feature of Monterey Bay is the Monterey Submarine
Canyon (MSC), depicted in Figure 2.2, which bisects the fairly symmetrical
bay at Moss Landing. With a volume of 450 km3, MSC has the distinction of
being the largest submarine canyon on the California continental slope[18].
Shepard, Emery, and Dills [17,19] have described the MSC system in con-
siderable detail, so the canyon system specification given in this report is
based on their work.
Monterey Canyon has an axis length of about 94.5 km and ranges in
depth from 18 m to 2925 m where the true canyon ends and the Monterey
Fan-valley begins. The two largest tributaries entering MSC are the Soquel
Submarine Canyon from the north and the Carmel Submarine Canyon from
the south. After the Carmel Canyon juncture, only small tributaries enter
the MSC
The Soquel Canyon joins the MSC at the 915 m depth after dropping at
a rate of 74.% along its 12 km length, giving the appearance of a hanging
valley. The axis of MSC winds and meanders beyond the Soquel Canyon
juncture, especially off of the Monterey Peninsula where the floor is granite.
At the beginning of this granite ridge, at the 1525 m mark, the axis gradient
increases to over 10% or 100 ra/km. The MSC is V-shaped from its head
to past the granite rock, until at an axial depth of 1920 m the canyon floor
becomes more irregular and broader. This is the point where a northern
trough-likp valley enters the MSC.
The trough-shaped valley section of the canyon runs southwest for about
35 km. The walls increase in height along the canyon with the northwest
wall reaching up to 370 m. The southeast wall is the continental slope and
has a number of valleys entering it with heads as deep as 1520 m.
The Carmel Submarine Canyon connects with the MSC at a depth of
2010 m. Carmel Canyon is about 30 km long with an axial slope of 73
m/km. At its 9 m head in Carmel Bay, which may be considered a drowned
river valley, are several tributaries cut into the granite walls along the shore
with no intervening shelf. The head has some portions with gradients as
large as 30%, but the base is smooth, probably due to recent erosion. After
large storms, there are considerable changes in the nature and thickness of
the fill in the head of the canyon.
The V-shaped submarine canyon of Carmel first runs west, then winds
northwest and parallels the coast. It appears to run along a fault in soft rock
that lies between two hard rock masses. The inner portion of the canyon
has an axial slope of 10% with a drop of 550 m and a floor width of about 75
m. It ends as a hanging valley at the Monterey Canyon with no fan-valley
At approximately 122C40'W, the high northwest wall of the MSC drops
down to a low ridge where the southeast wall leaves the continental slope
and a levee forms on top of the wall. The channel then takes a large 24
km meander before returning to its general course only 3 km downstream
from the point where the meander began. A little farther down the channel,
the trough-like portion of the MSC opens up into a modified fan-valley
with convex-upward levees bordering an eroded valley. This fan-valley is
approximately 320 km long and 280 km wide with an axial gradient of
4.8m/km, its apex at a depth of 3050 m and base at 4600 m[20]. The fan
valley eventually opens up into the deep ocean basin of the Pacific.
2.2.2 Geology and Sediments
The coastline depression of Monterey Bay was probably carved out by wave
attack on the relatively soft sedimentary rocks in the center of the Salinas
River Valley trough[21]. The promontories at Soquel Point and Point Pifios
are rocks that were better able to resist the erosional action.
The rivers that empty into Monterey Bay deposit igneous, sedimentary
and metamorphic rocks of the central and southern Coast Ranges. The
igneous rocks are Mesozoic granite, while the metamorphic rocks are of the
Sur Series. Monterey. Pancho Rico. Paso Robles and Aromas Formations
contribute to the Tertiary sedimentary rocks. [21]
The sediment within Monterey Bay is composed of gravel, various sizes
of sand, silt and clay. The following excerpt from a report by Engineering-
Science. Inc., for the Monterey Peninsula Water Pollution Control Agency
[16] provides a succinct description of the Monterey Bay sediment.
The bottom sediments vary in size and composition according
to depth contour, as shown in Figure 2.3. The nearshore bot-
tom and beach consist of coarse and medium sand. The bottom
gradates to fine sand down to a depth of 36 m. The sides and
bottom of the submarine canyon nearshore are characterized by
silt and clay which gradate into gravel and coarse sediments in
the deeper parts. The lower portion of the south bay is semipro-
tected from wave action by the protruding headlands at Point
20
Pinos. This topographical feature, which refracts and dimin-
ishes wave energy, produces a pronounced sorting of coarse and
medium sand particles in the south bay below the Salinas River.
Monterey Canyon with its Soquel and Carmel tributaries is the pre-
dominant feature of the tomography experimental region. MSC's axial
path appears to meander and wind in relationship to hard and soft rock
zones. The tributaries enter the main canyon as hanging valleys with trellis
drainage pattern[17]. There are many large-scale slumps along the walls of
the Monterey Submarine Canyon, indicating a history of undercutting and
erosion[16].
At the head of MSC, directly off Elkhorn Slough, there is only uncon-
solidated sediment. The inner canyon cuts into unconsolidated sediment for
about 8 miles, and along the walls and floor of the canyon for this stretch
is silt and clay. Based on information from Shepard and Dill, the first rock
to appear is Upper Pliocene mudrock at an axial depth of 640 m. The
north wall of MSC beyond this point is Pliocene sedimentary rock which
also comprises the west wall of Soquel Canyon. A box core sample taken in
Soquel Canyon yielded surface mud above rounded pebbles with shells and
fragment of siltstone.[19]
The first granite to appear in Monterey Canyon is an extension of the
Monterey Peninsula formation, and is found only along the south wall where
MSC axis makes a large bend to t lie south. The opposite wall is still sedimen-
tary rock. Beyond the Carmel Canyon junction, the MSC north wall sedi-
mentary rocks include limestone, sandstone, mudstone and Lower Miocene
foraminifora and coccoliths (organic calcareous ooze). The south wall is just
mud. [19]
Based on the Offshore Surficial Geologic Map (Figure 2.4), the Monterey
Canyon beyond Monterey Bay is sandy mud until it becomes mud (silt and
clay) after the granite outcroppings. For most of the receiver locations, the
rays from the acoustic source will initially bounce off of mud, and then a
sandymud bottom, before reaching the canyon(s).[22]
Carmel Submarine Canyon appears to be a seaward extension of the land
canyon, with no continental shelf between the canyon heads and the beach.
The main head begins directly off the mouth of San Jose creek. As expected,
the head fills rapidly with sediment from the creek and is then cleaned out.
This fill appears to undergo continuous change in nature and thickness, but
changes are especially noticeable after a large storm. [19,23]
The Carmel Canyon is narrow, Y-shaped and cut in granite. The steep
Figure 2.3: Distribution of sediment types in Monterey Bay. [16]
28
Figure 2 4: Offshore surficial geologic map of Monterey Bay. [22]
29
rock walls are mostly granite with a smooth base. The floor is sandy or
rocky. Near the juncture to the Monterey Canyon, Carmel Canyon's east
wall is composed of weathered granite, while the west wall has Mid-Miocene
sedimentary rock. [19,23]
2.2.3 Currents
California Current System
Flowing along western North America in a south to southeasterly direction
is the eastern boundary current called the California Current. This current
brings Subarctic water to California, which is low in both temperature and
salinity but high in nutrients. The California Current is wide, shallow and
slow, extending maybe 700-1000 km off the coast, down to a depth less than
500 m, and flows at a speed that is less than 25 cm/sec. [13, 16]
A subsurface current, the California Countercurrent, moves warm and
highly saline Equatorial Pacific water north along the coast from Baja Cal-
ifornia to Cape Mendocino (41°N latitude). The core of this current is at
about the 200 m depth, extending 50-100 km offshore, with a velocity of less
than 22 cm/sec north of 30° N latitude. In the fall or early winter, the Cal-
ifornia Countercurrent surfaces and becomes the Davidson Current. This
surfacing of the current, which occurs somewhere between British Columbia
and Point Conception, now provides for another surface current to move
along the coast inward of the California Current. The Davidson Current,
flowing between 16 and 47 cm/sec, is found as far as 80 km offshore. [13,16]
Associated with the California Current system are three oceanic sea-
sons, designated the Davidson period, the upwelling period and the oceanic
period. These periods appear to be directly affected by wind speed and
direction.
The Davidson period generally occurs between November and February,
when a semi-permanent Pacific high pressure cell weakens, moves southward,
and is replaced by an intermittent low pressure cell. The winds are very light
in the fall, and from the west or southwest in the winter. The Davidson
Current surfaces and is pushed toward the coast, due to the wind direction
and Coriolis force. This water converges along the western North America
coast and then sinks, resulting in nutrient-poor water along the coast. [13]
From about February to July, the winds are strong and blow out of the
north or northwest. The surface water along the shore is carried away from
the coast by the Coriolis force, based on the wind direction. Upwelling occurs
as subsurface water rises to replace the vacated surface water. The water
30
level is generally a little higher away from the shore, where the surface water
has been pushed, rather than close to shore, where the subsurface water
has risen. The upwelled water is cooler but high in salinity and nutrients.
Upwelling occurs at a rate of 0.7-2. 7 m/day and is found as far as 50 km
offshore. [13,16]
At the end of the upwelling period, the regular current pattern collapses
into irregular eddies in connection with the wind abatement. Smethie [13]
indicated that during this oceanic period "... the sea surface slopes down-
ward, isotherms slope upward toward the coast, and the geostrophic current
flows southward." With the irregular eddies, the currents are usually weak
and variable.
Monterey Bay Current Flow
The surface water in Monterey Bay appears to originate from three water
types [14]:
1. recently upwelled water;
2. freshwater from the rivers and streams; and
3. warmer, low-nutrient water which has been warmed at the surface.
The bay currents appear to be regulated by the oceanic seasons. Figure
2.5 illustrates the seasonal surface current flow within Monterey Bay.
Engineering-Science, Inc., in their report to the Monterey Peninsula Wa-
ter Pollution Control Agency [16], indicated that during the upwelling pe-
riod, the bay flow is dominated by the southward flowing offshore current.
They cited Broenkow and Smethie 's [14] conclusion that the offshore waters
enter mostly from the southwest up the Monterey Canyon, separate, and
then flow over the northern and southern continental shelves in the bay.
Clockwise and counterclockwise gyres over the shelves result, with speeds
anywhere from 2.5 to 26 cm/sec, but the predominant flow is north and
northeast. Even through in the oceanic period the currents become irregu-
lar and the wind is light, the bay current continues the pattern established in
the upwelling period, except that irregular eddies from over the north shelf.
The nearshore ocean currents shift from southerly to northerly, and pass
through Monterey Bay as a large, open eddy. However, the bay currents
circulate irregularly and slowly.
Broenkow and Smethie [11] studied and reported on the Monterey Bay
surface circulation and water replenishment during a 27 month period in
31
UPWELLING SEASON
(MAR -AUG )
DAVIDSON CURRENT SEASON
(DEC. -FEB.)
OCEANIC SEASON
(SEP -NOV)
1
IC
NAUTICAL MILES
0 10 20
KILOMETERS
Figure 2.5: Monterey Bay seasonal current patterns. [16]
32
the mid 1970's. As stated earlier, offshore water predominantly enters up
the canyon into the bay, but sometimes flows directly from the west. The
replacement time for the north and south bay waters is between 2 and 14
days, during which time their characteristics can be modified by air tem-
perature at the surface, photosynthesis, sewage outflow and freshwater river
discharge. The water parcels had longer paths near the shoreline, and there-
fore, had longer replenishment times than the water over the canyon. Dur-
ing the period of October 1972 through March 1973, the largest volume
of bay freshwater replenishment occurred in February with an estimate of
86xl06m3. October had the smallest volume at 2xl06m3 During most of
the year the freshwater lens is above the 10m depth mark, except for January
and February when about 1/8 of the freshwater falls to a depth between 10
and 30 m.
2.2.4 Temperature and Salinity Variations
The temperature and salinity within Monterey Bay appear to coincide with
seasonal oceanic periods associated with the California Current system,
amount of river runoff and with variations in the wind. Figure 2.6 shows
the mean variation of temperature and salinity at the mouth of Monterey
Bay, and at a point 40 km south of the bay, during the years 1950-1962. On
any given day the temperature throughout the bay is not uniform, varying
from 1 to 3°C for a particular layer, while the salinity is laterally consistent
[14,16]. The surface waters in the north and south bight areas are generally
warmer in the spring and summer than the mid-bay waters. Also, the max-
imum temperatures often occur after days of southerly winds. The lowest
salinity readings generally occur with the highest temperatures for the year,
or during the period of maximum freshwater runoff. The late upwelling
period yields the highest salinity levels.
Each seasonal oceanic period greatly affects the temperature and salinity
of the Monterey Bay water. In the late fall and early winter, the sinking of
nearshore waters during the Davidson period results in a fairly deep layer
where the temperature is uniform, with little variance in surface water tem-
perature over the entire bay. The 8°C isotherm deepens and all the isotherms
slope deeper towards the coast. Seasonal rainfall, together with large river
runoff, combine to dilute the surface water to measurable depths, which
brings the salinity in this diluted layer down to around 33.4 jj and variable.
Late in the winter the southerly winds die out, and strong northeasterly
winds arise. This is the onset of the upwelling period. [16]
33
16
10
8
34.0
33J2
ColCOfl ttotion locotod 10 km
of fshort ond 40 km south of
Moflttrty Bay
jIfUIaImIj IjUUIoInIoIj
Month
Figure 2.6: Mean temperature and salinity variation at the mouth of Mon-
terey Bay (station 3) and CalCOFI station during 1950-1962.(13]
34
During early upwelling the cool subsurface water replaces the vacated
surface water, bringing the surface temperature down to its lowest yearly
value of around 10 — 11°C The south and north bights are warmer than
the middle of the bay, which lead to a variation of surface temperature by
greater than 3°C The isotherms rise, so the 8°C isotherm is usually above
the 100 m mark during this period. Even with intermittent upwelling in
the summer, the water temperature remains cool; however, the maximum
salinity level occurs near the end of upwelling in the July timeframe. During
the entire upwelling period, the salinity is high because the rising subsurface
water has a high salinity value. [16]
The oceanic period generally takes place from July to November. The
surface temperatures ascend to their warmest yearly values to 13 — 16°C,
but the temperature varies horizontally throughout the bay by 2 — 3°C
The 8°C isotherm drops, and all of the isotherms slope upward toward the
coast. There is usually a sharp thermocline within the first 50 m. Since
the upwelling has ceased during this period, the salinity level first declines
and then levels off, due to the ingress of offshore water that is lower in
salinity. [16].
2.2.5 Tides
The tidal pattern along the west coast of the United States is classified as
a mixed semidiurnal tide. As shown by the tidal curve of Figure 2.7, two
high tides and two low tides occur each day; however, the high tides are of
different heights with respect to each other. The same is true for the two
daily low tides. In Monterey Bay, the tidal range between the lower low tide
and the higher high tide is on the order to 2 m [23], with the tides arriving
in the order of lower low tide, lower high tide, higher low tide and higher
high tide in a 24-hour day cycle.
2.2.6 Surface Waves
The waves that arrive in Monterey Bay hit all points of the shoreline, due
to refraction and defraction of the waves as they wrap around the bay. The
bay experiences two general types of waves. Winter waves occur usually
from November to March and have a short period of 8-10 seconds. These
swells come out of the northwest and are the product of local storms or may
originate from as far away as the Gulf of Alaska. Winter waves severely
erode beaches because the short wave action keeps the beach face saturated
with water and the swash cannot permeate the sand. Instead, this type of
Jmr
TIDE 1
1
1
1
1
13
34
36
41
HOURS
60 73 14
Figure 2.7: Monterey Bay tidal pattern. [23]
wave returns as a backwash, carrying much of the beach sand with it and
depositing the sand on a sand bar at a typical depth of 9 m.
Summer waves have a longer period of 14-16 seconds, arrive at Monterey
Bay from the southwest, originate in the Antarctic region, and have flattened
out due to the long travel time. These waves move the sand bar deposit back
to the shore, so the beach widens. The longer wave action allows the beach
face to dry out a little between waves, so the swash permeates the sand and
there is no backwash to carry the beach away.
Monthly and annual reports on the surface wave and current conditions
along the California coast are distributed through the Coastal Date Infor-
mation Program (CDIP), a cooperative program by the U.S. Army Corps of
Engineers and the California Department of Boating and Waterways [24,25].
The data for these reports are gathered by four types of ocean measuring
equipment:
1. four gage slope array for nearshore direction and energy measurement;
2. surface following buoy for deepwater wave energy measurement;
3. single point gage for nearshore wave energy measurement; and
4. single point gage for deep ocean wave energy measurement.
36
A station of particular interest in connection with the tomography ex-
periment is Station 8, North Monterey Bay buoy, at latitude Z6°b6.9'N ,
longitude 122025.1'W and depth of 320 m. Figure 2.8 and Figure 2.9 are
two pages taken out of the December 1987 report [24]. The data page for a
period of time from 9 December to 19 December 1987, exactly one year prior
to the December 1988 tomography experiment, provides numerical informa-
tion on significant wave height, total amount of wave energy and the percent
of energy per band period. Note the high wave energy level on 16 December
1987, with the greatest energy occuring in the period between 8-14 seconds.
The wave energy spectra of Figure 2.9 visually illustrates this surge. In all
likelihood, a storm passed through the area on this date, kicking up the
waves.
Based on a chart from the CDIP Annual Report [25], the October
through December 1987 period had the highest average wave height. There
was a 58% seasonal probability that the significant wave height would ex-
ceed 2 m, 32% for 3 m and 13% for significant wave heights greater than 4
m.
2.2.7 Internal Waves and Canyon Currents
As defined by Clay and Med win [2G], internal waves "... are volume gravity
waves having their maximum vertical displacement amplitude at a plane
where the density is changing most rapidly with depth or between two wa-
ter masses of different densities." A number of studies [14,23,27,28], have
presented evidence that the Monterey Submarine Canyon commonly has
internal waves of a semidiurnal nature. The results of a conductivity-
temperature-depth (CTD) time series for five stations in the Monterey Canyon
have indicated that these internal tides had heights of 50 m to 120 m [27].
Along the bottom of the Monterey Canyon the currents are strong and
fluctuating, with speeds up to 50 cm/s [14]. These flows are generally in an
upcanyon direction, but in truth they appear to have almost no connection
with the canyon axis. Cross valley flows are a predominant feature along
MSC [23], but there has not been a determination as to the cause of this
phenomenon. Tides and wind direction appear to have no relationship to
the cross currents [23].
Current-meter data (Table 2.1) from MSC provide information on the
internal tide up- and downcanyon reversal cycles. Estimated upcanyon ad-
vance rates for an internal wave in the Monterey Canyon is 25 cm/sec be-
tween 7.5 km and 8.5 km away from the canyon head (depth of 400-375 m),
37
t'ORTH MONTEREY
DAY DUOY
DEC 1987
PERCENT
ENERGY IN BAND
(TOTAL
ENERCY INCLUDES RANCE 2
348-4
SECS)
PST
SIC
HT TOT. EN
SAND
PERIOD LIMITS (SECS)
DAY/TIME
(CM
)
(CM SO)
22*
22-18
18-16
16-14
14-12
12-10
10-8
8-6
6-
4
9
1501
324
4
6577 5
0 3
0 5
9.
1
23 e
25 3
11 4
18 4
7 7
4.
1
9
2100
357
4
7983 0
0 2
0 3
1.
5
25 1
38. 3
14 9
10 7
6 3
3
1
10
0300
238
7
7170 B
0 1
0 1
1.
9
116
30 2
23 0
20 1
7 9
3
3
10
0906
309
3
5979. 7
0 4
0 4
1
4
19 0
30 9
22 2
13 e
6 4
4
0
10
1523
363
2
6246 9
9 2
5. •»
3.
0
14 9
27 7
20 6
9 9
7. 4
2
4
10
2101
490.
2
15016 1
2. 1
16. 3
13.
2
20. 1
13 5
13 2
6 8
7. 3
6.
0
1 1
0300
461.
5
13308 6
0 8
7. 0
19
2
119
12 8
113
17 1
13 9
6
3
1 1
0900
461
7
13322 3
0 4
4 3
14
3
14 3
16 7
21. 3
16 8
8 2
4
1
1 1
1503
470
4
13829 8
1 1
2 3
B.
3
11 9
20 6
24. 8
15 7
9 8
6
0
1 1
21C2
455
9
12990. 1
0. 3
1. 7
e.
3
16. 4
20. 0
20. 4
18. 9
9. 9
4.
3
12
0302
449
5
12626 9
0 2
0 3
2.
1
10 5
36 9
22 3
13 1
7 9
3
0
12
0902
414
0
10714 6
0 3
0 3
1
7
3 8
19 0
34 2
18 1
16 0
7
1
12
2059
471.
4
13891. 1
0 2
0 2
0
4
7. 2
22 2
20. 2
22 6
19 8
7.
6
13
0302
391.
7
9590 0
0 I
0 1
0
2
6. 0
21. 0
23. 4
21 1
19 1
9
3
13
09C2
370
2
8567 1
0 2
0 2
0
3
3 3
10 5
28. 4
21 3
24 2
1 1
8
13
2102
207.
5
2690 8
0 2
0 3
0
3
1 0
11 1
26 1
16 4
17. 0
28
1
14
0302
187
4
2194 2
0 1
0 1
0
3
1 2
12 7
18 2
36 3
16 2
13
2
14
0901
133
5
1113 2
0 1
1 0
1
2
4 5
22 3
13 8
23 3
19 9
14
2
14
2059
140
e
1239 3
0 2
1 6
23
3
114
12 8
28 6
12 8
6 0
3
7
15
0251
136
4
1162 4
0 2
0 6
18
4
26 4
13. 9
7 1
6 3
4 0
23
3
15
0657
220
1
3027. 9
0 3
0 2
3
0
9. 5
7. 4
3 9
1 3
37 6
37
1
16
0255
732
4
33523. 8
0 3
0 3
0
4
2. 5
23 3
41 3
17 4
9 7
4
9
16
0655
597
2
22293 1
0 2
0. 2
0
9
5 4
26 7
28 0
18 9
13 3
7
0
16
150 1
520
0
16897 0
2 1
1 1
0
7
1 9
5. 9
38 e
27 3
13 e
e
e
16
2057
347
e
7559. 9
0 1
0. 1
0
5
1. 6
114
31. 2
30 6
13 9
9
0
18
18
IB
17 0237
17 0857
17 1459
17 2059
0259
1439
2039
309 3 3981 0
294 3 3414. 7
293 4 5091. 9
263 3 4400 3
252 5 3984 2
207 0 2677 9
228 8 3270. 8
0 1
0 I
0 6
0 2
0 1
0 2
0. 7
0 1
0 1
0 3
0 2
0 3
0 3
0 3
0. 2
2. 0 BO 34 4 40 0
18 13 6 32 9 35 3
16 20 1 36 4 20 8
14 15. 8 34 0 23 1
0 2 0 3
0 7 0 3
2. 9 0. 7
19 0259 269 4 4337 2
0 2 10 3
4 3
1 1
0 7
0 9
0 4
38
26
13
28 9
30 8
44. 7
10 1
12 1
13 6
16 8
16 4
26 5
21 6
8 5
11.9
118
1 7
8 9 34 3 26 2 13 9
Figure 2.8:
data. [24]
North Monterey Bay buoy, December 1987, wave energy
38
WAVE ENERGY SPECURA DEC 1987
20 16 12 8
PERIOD SEC
NORTH MONTEREY BAY BUOY
Figure 2.9: North Monterey Bay buoy, December 1987, wave energy spectra
graph. [24]
39
METER POSITION
AVER-
AGE
CYCLE
LENGTH
(hrs)
DIREC-
TION
OF NET
FLOW
AVERAGE SPEED (cm/sec)
DEPTH
(m)
HEIGHT
ABOVE
FLOOR
(m)
UP
DOWN
CROSS
155
•>
3
7.2
down
9.2
10.3
4.0
155
30
4.4
up
8.5
6.7
3.7
357
3
8.8
down
13.8
11.4
5.2
384
3
8.0
up
12.1
13.1
5.6
1061
■n
j
6.5
up
19.7
16.6
15.3
1061
30
6.5
up
20.3
26.0
9.8
1445
8.7
up
13.2
11.1
5.8
1445
30
10.0
Up
13.6
10.0
4.2
Table 2.1: Up and down-canyon reversal cycle data for Monterey Canyon. [23]
and 38 cm/sec from 7.5 km to 2 km up the canyon (375-150 m depth) [28].
Based on small amplitude wave theory, a long wave will increase in height
as it moves into shallow water, but its period will remain constant. As an
internal wave advances up the canyon towards the head, where it is narrow
and shallow, the wave energy may become focused and the wave height
increase, taking on the appearance of an internal tidal bore. This bore
"... is characterized by a rapid increase in temperature at a fixed position,
in which the advancing water forms an abrupt front." An internal bore at
the MSC head has been indicated by thermistor data showing a 3.8°C/hr
temperature change. [27]
Broenkow and Smethie [14] conducted a 24 hr time series study at two
stations near the head of the Monterey Submarine Canyon. They observed
internal tidal oscillations with the same period as the surface tides, but
approximately 180 out of phase. The wave height was 80 m at a depth of
130 m, while at 250 m deep the height of the wave was about 120 m.
The oscillating internal tide produces a volume convergence at flood tide.
During volume convergence, the denser canyon water rises above the rim and
40
150
Figure 2.10: Temperature distribution (°C) at (a) high and (b) low internal
tide, Monterey Canyon axis, 13-14 September 1979. [27]
settles on the shelf. When the internal tide reverses and goes downcanyon,
the dense canyon water on the shelf starts flowing back into the canyon;
however, as a result of mixing, surface heating and inertia, the edge of this
dense water remains behind on the shelf. Figure 2.10 illustrates volume
convergence and divergence for 13 and 14 September 1979. A 20 m thick
lens of 12°C water flowed out of the canyon as the internal tide rose, and
remained on the north shelf when the rest of the dense water fell back into
MSC at tidal reversal. This lens was estimated to affect an area of 26 km2.
Data indicate that the volume convergence is about 240xl06m3/8 hr, which
would put the speed of water crossing the rim of MSC at about 13 cm/s.[27]
Internal waves along Carmel Submarine Canyon appear to follow the
axis, unlike the situation in Monterey Canyon. The currents at 3 and 30
m above the floor showed very similar characteristics. Current-meter data
(Table 2.2) is given for Carmel Canyon's up- and downcanyon reversal cycles
for internal tides. Interestingly, almost all of the northern cross canyon flows
occurred at ebb tide. [23]
41
MEIER POSITION
AVER-
AGE
CYCLE
LENGTH
(hrs)
DIREC-
TION
OF NET
FLOW
AVERAGE SPEED (cm'sec)
DEPTH
(m)
HEIGHT
ABOVE
FLOOR
(m)
UP
DOWN
CROSS
156
3
3.6
down
5.0
7.6
4.0
205
3
4.1
down
12.4
14.5
4.3
34 S
3
5.1
down
15.8
19.5
7.9
1070
3
10.2
down
9.6
15.0
4.4
1445
3
11.7
down
11.3
10.3
5.2
Table 2.2: Up and down-canyon reversal cycle data for Carmel Canyon. [23]
42
Chapter 3
Experimental Effort
3.1 Experiment Objectives
The December, 1988 Monterey Bay Acoustic Tomography Experiment had
four goals:
• Investigate the relation between the frequency-direction spectrum of
surface waves and the spectra of travel time changes in tomography
signals experimentally.
• Investigate the effect of internal waves on tomography signals in a
coastal environment.
•
Investigate the effect of complex three dimensional bathymetry on long
range acoustic propagation.
• Test the first real-time shore-based tomography data acquisition sys-
tem.
The most significant difference between this experiment and other ocean
tomography experiments was in the transmitted signal. For this experi-
ment the signal repeated every 1.9375 seconds, allowing sampling above the
Nyquist frequency of dynamic ocean processes with frequencies below 0.258
Hz, which includes the longer period surface gravity waves. Surface gravity
waves are classified by their period length: fully developed seas - 5 to 12
seconds, swell - 6 to 22 seconds, and surf beat - 1 to 3 minutes[29]. All of
these could have observable effects, depending on their orientation to the
signal path. The signal was also transmitted continuously. In most other
43
experiments the signal is transmitted periodically to reduce the power con-
sumption and amount of data to be recorded. The continuous transmission
permits long period disturbances to be investigated without the aliasing
effects of higher frequency internal waves and surface waves. Aliasing of
high frequency energy to low frequencies could be a problem if only a few,
time-separated transmissions are used. Internal waves and tidal fluctuations
will be of much longer period than the longest swell - periods of 8 minutes
(internal waves in shallow water) to 24 hours are possible.
3.1.1 Location and Description
The tomography experiment extended from a transmitter placed on an un-
named seamount 36 kilometers west of Point Sur to receivers placed along
the north side of Monterey on the continental shelf between Moss Land-
ing and Santa Cruz. This area and the placement of the transmitter and
receivers is detailed in Figure 3.1. Monterey Bay is a semi-enclosed bay
containing a submarine canyon cut into the continental shelf. This canyon
(the largest on the California coast) dominates the bathymetry by cutting
the bay into two roughly equal halves. The continental shelf surrounding
the canyon is fairly smooth with a slope of 1 - 2 percent from shore to a
depth of 90 to 100 meters on the north canyon rim and approximately 180
meters on the south rim. The canyon itself drops sharply from the shelf.
The axis of the canyon is steep with a grade of around 7 percent for most of
its length and ends in a fan valley at a depth of 2925 meters. Several smaller
canyons join the Monterey submarine canyon, most notably the Soquel and
Carmel canyons. See Chapter 2 for more detailed information on Monterey
Bay.
The initial ray tracing done in preparation for the experiment used a
two-dimensional ray-tracing program called Multiple Profile Ray-Tracing
Program (MPP). See Section 4.1 for a description of the two-dimensional
ray tracing results. This program used various sound speed profiles and
took into consideration the bathymetry along planar paths between source
and receiver. The shortcoming of this program is that it neglects horizontal
deflection of acoustic energy. Eigenrays which leave a vertical plane between
source and receiver can be reflected or refracted back to the receiver in such
a complicated environment dominated by rough bathymetry. It is possible
that there are stable raypaths which arrive at the receiver by bouncing off
the submarine canyon walls via three-dimensional paths which are not close
enough to two-dimensional solutions to be identified. See Section 4.2 for a
44
Figure 3.1: Monterey Bay showing the positions of the tomography source
and receivers (positions marked with •). The source is at station A while
all others are receivers. The shore station is marked with A.
45
description of the the three-dimensional ray tracing results to date.
3.1.2 Receiver Placement
The tomography signal receivers for the experiment utilize fixed hydrophones
located on the ocean bottom so that receiver motion would not cause arrival
time fluctuations. The placement of the receiver was dictated by several re-
quirements. First and most important, the paths of the eigenrays must pass
through the water that is of interest in order to sample the sound speed. Sec-
ond, there should be several eigenrays identifiable passing from the source to
the receiver to give vertical resolution. Third, there should be enough sepa-
ration in the arrival times of the rays traveling along different paths for the
received signal to be resolved into distinct arrival times. The area of interest
in this experiment is the Monterey Bay submarine canyon and the edge of
the continental shelf along the north rim of the canyon. In order to sample
the fluctuations due to surface waves, the path should have surface inter-
actions. The greatest effect on the tomography signal should occur when
the ray path is almost perpendicular to the direction of travel of the surface
waves [30]. As can be seen in Figure 3.1, lines connecting the receivers to
the transmitter would spread over an arc of about 45 degrees from north
to northeast relative to the signal transmitter. If the eigenray paths are
planar, then these ray paths would be perpendicular to the expected swell
direction, that is from the west or northwest. Eigenrays and their travel
times were predicted using the program MPP as described in Chapter 4.
All of the raypaths had many surface interactions as a consequence of the
shallow location of the receivers. It should also be noted that moving the
location of the receiver a few meters would give much the same path in deep
water but could significantly change the number of surface interactions in
shallow water.
Internal waves will also have the greatest effect if propagating perpen-
dicular to the path of the ray. The direction of propagation of internal waves
in Monterey Bay is unknown but is expected to vary with orientation with
the submarine canyon rim. Internal tidal bores occur in submarine canyons
and have been observed in Monterey Bay [28]. Internal tides force cold,
dense water over the rim of the canyon[27]. This may be one of the forcing
functions generating the internal waves. All the receivers were positioned
in about 100 meters of water. This was predicted to give several eigenrays
without too many bottom interactions (<10 in most cases) which could se-
riously attenuate the signal. This depth still supports the approximations
46
used in ray theory propagation and sea surface waves are only beginning
to feel the effects of the continental shelf on their motion[30]. The receiver
locations will be designated by letters as are shown in Figure 3.1. Stations
J, L, L-l, and L-2 are located so that eigenrays will have relatively little
travel in the submarine canyon. Their paths cross the canyon and continue
up a fairly gradual slope. Stations G, H, and I require the eigenrays to pass
though the most complex bathymetry along the length of the canyon, which
could lead to complicated arrival time fluctuations. Station E has a path re-
quiring propagation trough 100 to 200 meter water for almost 20 kilometers.
This leads to many surface and bottom interactions which could make the
signal too weak to be received. Position B is the closest station and paths
to B cross the Carmel Canyon but not the Monterey Canyon.
3.2 Equipment
3.2.1 Transmitter
The tomography transmitter is a 224 Hz resonant system controlled by a
microprocessor and powered by batteries. It was modeled after neutrally
buoyant SOFAR floats and is ruggedly designed for deep water use. As
shown in Figure 3.2, it consists of four quarter-wavelength aluminum pipes,
each about two meters long, and each driven at the closed end by a piezoelec-
tric driver. The system has a high Q , limiting the useable signal bandwidth
to 16 Hz when demodulated to baseband. The central tube contains the
batteries, microprocessor, digital to analog converter, amplifier, and clock.
The clock is a low-power quartz clock carefully calibrated with respect to
temperature for very accurate time keeping. The source is held tightly be-
tween a large anchor and glass flotation balls. A tension of about 2,000
pounds with only a 1 meter distance from the anchor is expected to keep
transmitter motion to a minimum. Other experiments with long mooring
distance have measured the position of the transmitter as it moves in the
current [2]. For recovery, two acoustically triggered releases are attached
to a chain led through the eye on the anchor. Only one release need op-
erate for recovery. The transmitter used in this experiment is one of those
used in a 1981 experiment off Bermuda and in several other experiments.
It transmitted a phase-modulated signal continuously for four days at an
approximate source level of 172 dB re 1 microPascal at 1 meter. This same
source has been used for intermittent transmission of signals at up to 185
dB re 1 microPascal at 1 meter. [1,2]
47
30 meters
5 meters
Light and Radio Beacon (for
recovery only)
Glass Spheres
for buoyancy
Signal Generator and
Batteries
Resonant Tubes
Piezoelectric Drivers
Acoustic Releases
Anchor
Ocean Floor Depth 870 meters
Figure 3.2: The 224 Hz resonant tomography source and mooring configu-
ration.
48
3.2.2 Receivers
The acoustic receivers used in the experiment were modified AN/SSQ- 57
sonobuoys configured as shown in Figure 33. The unmodified sonobuoys
have a single omnidirectional hydrophone connected by wire to a VHF ra-
dio transmitter, all powered by a salt-water battery and having a lifetime
of about 8 hours. The buoys as modified used the same hydrophone, ra-
dio transmitter and antenna but had a longer life battery and an anchor
so that they could be used for a longer period. During modification, the
antenna and the buoy electronics package were attached to a building foam
insulation and plywood float which also supported a waterproof battery com-
partment. Panasonic LCL12V38P wheelchair batteries were used to power
the buoy. The battery could power the buoy for up to one week. The buoys
were moored using 15 pound mushroom anchors and about 250 meters of
polypropylene line. The hydrophone wire was attached to the anchor line
so that the hydrophone would rest on the bottom near the anchor. The
sonobuoy electronics packages were modified by Sparton Electronics (man-
ufacturer of the unmodified buoys) and installed in the floats and anchor
systems by Woods Hole Oceanographic Institution personnel.
A total of 11 modified AN/SSQ-57 buoys were prepared, of which there
were several failures. In addition to these, two experimental Moored Inshore
Undersea Warfare (MIUW) buoys, AN/SSQ-58, were deployed. One MIUW
buoy was deployed with a modified AN/SSQ-57 buoy at station B and the
other was deployed alone at station L-l. The data recorded from the MIUW
buoys is probably not useable for tomography inversions as the hydrophone
is suspended in the water below the floating buoy. Shifts in the travel time
of signals received due to buoy motion probably cannot be sorted out from
arrivals due to ocean path fluctuations.
The modified AN/SSQ-57 buoys have an acoustic bandwidth from 10 Hz
to 20 kHz. The AN/SSQ.-58 MIUW buoys have a useable acoustic bandwidth
from 50 Hz to 10 kHz. Both types use an FM radio transmitter with a
transmitted power out of about .5 to 1 watt on any of 31 selectable VHF
channels. [31, 32]
3.2.3 Acoustic Data Recording
The sonobuoys transmit to a receiver in a van located on Huckleberry Hill
during the experiment. Huckleberry Hill on the grounds of the Defense
Language Institute (DLI) at the Presidio of Monterey is one of the highest
unobstructed points on Monterey Peninsula. The antenna on the van is
49
battery
building foam float
hydrophone wire
attached to anchor line
mushroom
anchor
antenna
sonobuoy electronics
approximately
250 meters of line
hydrophone on bottom
Figure 3.3: Modified AN/SSQ-57 sonobuoy as used in the Monterey Bay
Acoustic Tomography Experiment. The hydrophone rests on the bottom to
eliminate motion.
50
about 260 meters above sea level and can receive VHF and UHF radio
signals from Monterey Bay and beyond to a radius of about 60 kilometers,
just over 30 nautical miles. Close along the coast to the south of Point Lobos
there are areas where radio shadows exist but at Point Sur good reception
begins about 10 kilometers off the coast. Good radio communications were
maintained throughout the area of the experiment.
The sonobuoy receiving system, shown in Figure 3.4, consists of a direc-
tional antenna which feeds the received signal through a filter and pream-
plifier to an AN/ARR-72 sonobuoy receiver. The AN/ARR-72 is a multi-
channel sonobuoy receiver used by the U.S. Navy in aircraft. The outputs
from the receiver are routed to a patch panel where they can be connected
to test equipment (for analyzing the signal as it is received) or to the data
recording system.
The recording system uses Yamaha Hi-Fi Stereo videocassette recorders
(YV-1000) which have been modified to record two audio channels, two
digital pulse-code-modulated (PCM) audio channels, and a time code signal
on standard commercial videotapes. In this experiment Maxell XL Hi-Fi
120 videotapes on extended play would record 6 hours of data. One audio
channel on each tape recorded a 7168 Hz synchronization square wave signal
from a signal generator stabilized by a 1 MHz rubidium frequency standard.
This signal is used for accurate demodulation and sampling of the recorded
data. When replayed, the time-code signal displays the hour, minute, and
second that the data was recorded. Data was normally recorded on the two
PCM channels of each recorder but in a few cases the last audio channel was
also used. All channels appear to reproduce the signal adequately, 30 Hz to
20 kHz for the PCM channels, with a slight lowering in frequency. The 7168
Hz recorded signal is shifted to 7160.85 ± 0.05 Hz.
3.2.4 NDBC Wave Measurement and ARGOS buoys
The National Data Buoy Center (NDBC) has operated several types of di-
rectional wave measurement buoys since 1977. The moored buoys collect
surface wave spectrum and direction and are usually equipped with other
meteorological sensors such as thermometers and anemometers to help give
a complete picture of the weather affecting the sea surface. The buoys mea-
sure the surface elevation and wave slope in order to calculate the wave
spectrum and direction. The method has undergone extensive testing and
has been shown to be accurate in most cases[33j. The spectrum coefficients
are calculated using a segmented fast fourier transform on 100 seconds of
51
Antenna
Filter
I
Preamplifier
I
AN/ARR-72
Sonobuoy Receiver
2E
Patch Panel
\
Time Code
Generator
VCR#1
l
m.
VCR #2
I
iz
VCR #3
1MHz
Rubidium Standard
7168 Hz Signal
Generator
Figure 3.4: Sonobuoy data recording system located in the van. This system
receives the sonobuoy radio transmission, demodulates it for the acoustic
signal, and records that signal on videotape using pulse code modulation.
52
data. An average is made of 19 sequential data segments with an overlap
of 49 seconds, giving the data 28 equivalent degrees of freedom. After cor-
recting for various scaling factors resulting from the parabolic windowing
used before the transform, the data is ready for transmission. Once an hour
the data is transmitted by the buoy to the Geostationary Operational Envi-
ronmental Satellite (GOES). From the satellite the data is downlinked and
relayed to NDBC and other users. The data contains information on wave
height and direction as well as the power spectrum from 0.03 to 030 Hz
with 001 Hz resolution. The three meter diameter discus buoy in Monterey
Bay (station 46042) also measures wind speed and direction. The buoy is lo-
cated in deep water (about 2000 meters) southwest of Santa Cruz (36°45'N -
122°235'W). Four free-drifting ARGOS buoys were obtained for additional
data collection. Two of the buoys were designed to measure wave spectra in
much the same way as the NDBC discus buoy. These are designated TMD
by the manufacturer. The other two (designated TZD) suspend a 600 me-
ter thermistor string below them to make temperature measurements. The
buoys were designed and built by Polar Research Laboratory, Incorporated
and utilize the ARGOS system for telemetry. ARGOS is a joint program
of the CNES (the French space agency), NASA, and NOAA. The ARGOS
transmitters are a very simple, small package (< 1 kg) powered by batteries
(approximately 200 milliwatts) and used for many data transmission and
tracking systems. The transmitter sends a message of up to 256 bits once
every minute at 401.650 MHz automatically, whether there is a satellite over-
head or not. Multiplexing occurs at the receiver through random timing of
transmissions as well as through doppler frequency shifting due to satellite
motion - up to 24 kHz for older TIROS low earth orbit satellites and 80 kHz
for newer ones. The location of the transmitter is calculated from doppler
shift measurements made by the satellite. Normal accuracy for location is
about 300 meters. Typical data delivery time is three hours from uplink.
NDBC receives and processes the ARGOS wave buoy data. [34]
The ARGOS buoy measurements were expected to supplement the more
accurate data from the NDBC moored buoy and from other measurements.
The uneven time spacing and random drift pattern of the buoys would de-
crease the expected usefulness of the data. But as it turned out, the data
from the buoys was corrected onboard with erroneous dynamical parame-
ters which involved zeroing wave spectral data less than zero. This erroneous
correction was not recoverable and all data from the ARGOS buoys was lost.
53
3.2.5 Sound Speed Profile Measurement
The vertical structure of the sound speed in the ocean determines to a large
extent the path sound energy will travel through the ocean. Records of
many measurements of the sound speed profile are averaged and kept in
databases in order to predict sound propagation through the oceans and
this type of data was used in the initial ray tracing for this experiment.
Fluctuations around this average profile are caused by numerous different
forces, and to both verify the climatological data and to look for fluctuations
the sound speed profiles at various locations were measured. The speed of
sound in sea water can be found from an empirically derived function of
pressure, salinity, and temperature. The dominant effect in shallow water
is the variation of temperature. The salinity of sea water can be calculated
from the conductivity of the water and the depth (or density) can be found
from the pressure. A set of CTD measurements (conductivity, temperature,
density) can be combined to generate a sound speed profile.
In this experiment a digital, recording, battery-powered CTD measuring
device manufactured by Neil Brown Instruments was used. This system is
powered by a rechargeable battery but is limited by its data storage capac-
ity to about four hours of continuous data collection. After four hours of
recording, the CTD data is transferred via cable to a personal computer
for storage on floppy disks. In addition to CTD measurements the device
measures the transmissivity of light in the water with a low power transmis-
someter. In use, the CTD device is weighted to help it sink quickly while
being lowered by cable from the research vessel. The device could be lowered
at about 45 meters per minute and is usually raised at the same rate. A
battery powered acoustic transmitter is attached to the frame of the CTD
device as a safety precaution. The transmitter "pings" every few seconds
and the received sound registers on a recording fathometer trace. As it nears
the bottom, the bottom reflected signal grows stronger and also appears on
the trace. The distance between the two signal receptions gives the distance
remaining to the bottom and so a collision with the bottom can be avoided.
Several problems are inherent with this device. Because of the limited
vertical speed of the device, consecutive measurements in deep water may be
separated by intervals of 30 to 45 minutes. Drift of the deploying vessel can
easily be greater than one knot (1.8 kilometer/hour) and consecutive mea-
surements might be a kilometer apart. "Yo-yo" measurements, maintaining
position as much as possible, may give adequate information about internal
wave amplitude but frequency and direction will be difficult to determine.
54
3.2.6 Acoustic Doppler Current Profiler
The acoustic doppler current profiler (ADCP) transmits four narrow, 120
kHz beams of sound in pulses from the bottom of the research vessel. The
profiler looks at various time delays of sound scattered back to the trans-
ducers to range gate the signal. By measuring the doppler shift of returned
pulses in four directions and comparing it to the ship's course and speed from
the ship's navigation system, an estimate of the north-south and east- west
water velocity as a function of depth is obtained. Because of the boundary
conditions of internal wave motion, these create a characteristic movement
of the water around the pycnocline related to the horizontal motion caused
by vertical displacement in the internal wave. This may appear in the ADCP
data.
3.3 Summary of the Experimental Procedure
The Research Vessel Point Sur, operated by Moss Landing Marine Labo-
ratories for the National Science Foundation, was used for deployment and
recovery of all equipment as well as a platform for the CTD and ADCP
data measurements. The van located on the hill at DLI began recording
when the first sonobuoys were placed in the water. The plan for the ex-
periment was fairly straightforward, but evolved during the experiment as
weather, equipment, and luck in locating deployed equipment began to af-
fect schedules. The actual chronology of events is given in Appendix A.
The R/V Point Sur was to begin by proceeding south to the seamount and
deploying the tomography signal transmitter. During the transit to the
north rim of the canyon the four drifting ARGOS buoys would be deployed.
Upon reaching the continental shelf at the edge of the submarine canyon,
the modified sonobuoys would be deployed, working from west to east. CTD
measurements were to be made at each station and, after completion of buoy
deployment, the vessel would proceed to different parts of the experiment
area to make CTD "yo-yo" measurements. A "yo-yo" measurement is re-
peated raising and lowering of the CTD to resample the same water column,
hopefully to gain information about internal waves at that position. At the
end of the experiment, 96 hours after the beginning, the equipment would
be recovered, probably in reverse order to the way it was deployed.
55
3.4 Signal Processing
3.4.1 Signal design
System Requirements
The basic task of signal processing in tomography is to receive the tomo-
graphic signal, decompose the received signal into individual eigenray ar-
rivals, and estimate the arrival time of these arrivals. The processing should
assist in improving the signal-to-noise ratio of the received signal if this
can be done without an adverse effect on the received data. Eventually,
the signal-to-noise ratio will limit the accuracy of the estimation of the ar-
rival time. This chapter will discuss the various questions involved in signal
design and processing and the solutions chosen in this experiment.
Signal Resolution
The time separation required of signals traveling along different eigenrays
can be predicted by ray tracing programs such as MPP. The results described
in Chapter 4 give predictions of arrival time separations between consecutive
ray arrivals ranging from 2 to 500 milliseconds, with most separated by more
than 80 milliseconds. In order to separate the closest arrivals, the signal
would have to be less than 2 milliseconds in duration. The tomographic
source that was used in the Monterey Bay experiment has a bandwidth of
only 16 Hz, limiting the shortest pulse that can be efficiently transmitted
to about 62.5 milliseconds (1/16 Hz). Pulses arriving with less than 62.5
milliseconds separation may appear as one pulse of greater amplitude, and
not be resolvable into separate pulses. Figure 3.5 shows an example of such
an arrival. In this experiment, the transmitter bandwidth of 16 Hz limited
the signal to a minimum period of 62.5 milliseconds, even though that could
not resolve all eigenrays into distinct arrivals.
Pulse Compression
A finite length pulse signal is the closest practical equivalent of an impulse
(a signal of infinitesimal length and infinite magnitude) that can be trans-
mitted. The amplitude and length of the pulse are limited by the peak
power and bandwidth, respectively, of the transmitter. An effective method
of boosting the peak amplitude is pulse compression. Pulse compression
has been used extensively in RADAR applications but to a lesser extent
in underwater sound transmission [5]. Simply stated, a long coded signal is
56
Amplitude
Arrival of Two Resolved Pulses
Time
A
Amplitude
Arrival of Two Unresolved Pulses
Time
Figure 35: Comparison of resolved and unresolved pulses. If two pulses
arrive without enough time separation they will interfere with one another.
This figure shows the case where they constructively interfere.
57
transmitted and the received signal is passed through a matched filter which
compresses the long transmission into a short, high energy pulse. One rel-
atively easy technique for doing this is to use maximal-length sequences.
This method uses a phase-modulated carrier signal to transmit a specific
maximal-length code. The autocorrelation of the code with the received sig-
nal produces a single pulse at the point where the code and received signal
match with an increase in amplitude equal to the number of digits in the
code. The width of the pulse is equal to the width of one individual digit
of the code. The length of the code is only limited by the system limita-
tions for which it will be applied so the amplitude gain can be quite large
when compared to the power the transmitter can send in a single pulse. Ap-
pendix B discusses the generation and autocorrelation of the maximal-length
sequences.
Signal Period
The maximal-length sequence consists of a number of digits determined by
the order of the sequence. The code is transmitted continuously, phase
modulating a carrier frequency, for the period of the sequence. If the code
is transmitted at the maximum rate allowed by the bandwidth of the trans-
mitter, the length will be determined as a compromise between two charac-
teristics:
•
•
The shorter the code length, the greater the repetition frequency and
the higher the sampling frequency for ocean data. This determines the
highest frequency which may be observed.
The longer the code, the greater the increase in signal-to-noise ratio of
the signal and the more accurately the arrival time of the signal can
be estimated.
The driving consideration in this experiment is the period of the surface
waves to be investigated - fully developed seas of greater than 5 seconds
period. To sample the fluctuations due to the surface waves at the Nyquist
frequency, the period of the signal must be less than 2.5 seconds. A maximal-
length sequence 31 digits long transmitted at a digit frequency of 16 Hz has
a period of 1.9375 seconds. This length was chosen for the Monterey Bay
experiment. As discussed in Appendix B, the code is generated from a
primitive polynomial. The polynomial for this case is
g(D) = D5 + D2 + \, (3.1)
58
resulting in the (reverse) code
MT = [0000100101100111110001101110101]. (3.2)
This code is mapped from 0,1 to 1,-1 and used to phase modulate a 224
Hz carrier signal. The transmitted signal is given by
s(t) = cos(2nfct + M,0), (3.3)
where fc = 224 Hz and M, is the ith digit in the (mapped) maximal-length
sequence. The power spectrum of this signal has an envelope characterized
by the familiar sin x/x squared function
PU)=(S^P\\ (3-4)
wdf J
where d is the digit period. The envelope is filled by impulse functions
separated by the code repetition frequency. Some advantage can be taken
of this. If 6 is chosen so that
0 = tan*1(v/77) (3.5)
for N equal to the number of digits in the code, the carrier signal will fall
exactly on the envelope and result in the maximum signal-to-noise perfor-
mance after demodulation and pulse compression. [5]
Arrival Time Estimation
The resulting pulse after pulse compression of the maximal-length sequence
is a flat topped pulse of one code digit duration. The estimation of the
arrival time of the pulse must produce two results:
1. Find a characteristic of the received pulse which can be reliably located
on each arrival and the arrival time estimated.
2. Estimate the uncertainty in the arrival time estimate.
Because the signal is transmitted with a finite bandwidth and suffers some
dispersion during its travel, the received signal is rounded at the edges of the
pulse, sometimes so much that it resembles the peak of a Gaussian distribu-
tion curve. One method of finding a consistent point on each pulse arrival is
to correlate the signal again with a square pulse of the same duration as the
signal. For the perfect received flat topped pulse, this is the correlation of
59
two squares, the result is a triangle with the peak at the center of the signal.
In effect, this gives the received signal a sharper peak. Since this processing
is done using discrete points of much greater separation than the expected
uncertainty in the best estimation, the position of the peak is found by in-
terpolation. Various methods such as parabolic fit, Gaussian fit, and cubic
spline are available to fit curves to the discrete points with a separation of
points somewhat less than the expected uncertainty. The time of arrival of
the interpolated (or original) point with the highest magnitude is the arrival
time estimate. If the code is transmitted continuously then the arrival time
is compared to an arbitrary starting point recurring at the code repetition
frequency. The accuracy of the time estimate depends on the bandwidth
of the signal and the received signal-to-noise ratio. The calculation of this
type of non-linear estimate with white Gaussian noise is discussed by Van
Trees[36]. Spindel gives the result as
<*t = \= (3.6)
with at the arrival time uncertainty, B the bandwidth of the signal, and
SNR the signal-to-noise ratio. [5] For 10 dB signal-to-noise ratio and a 16 Hz
bandwidth, this equation gives an uncertainty crt of 3.1 milliseconds.
3.4.2 Signal demodulation and correlation system
Analog Processing
The received acoustic signals from the sonobuoys are recorded on videotape
for storage. This analog or pulse-code-modulated recording is played back
for quadrature demodulation and digitization as shown in Figure 3-6. The
tomography signal is contained in a band 16 Hz above and below the car-
rier frequency of 224 Hz. In order to ensure the proper frequencies and
timing of the tape recordings, the 7168 Hz synchronization signal is used
both to demodulate the signal and to generate an interrupt signal for the
analog to digital converter. An unsynchronized demodulation system must
demodulate the signal without knowing its phase. The received signal can
be represented as
s(t) = A cos(2tt/ci + Mid + <j>) (3.7)
which is the same as the transmitted signal but with an unknown phase
shift cp caused by the delay due to the travel time. Because this phase
is unknown, the signal must be multiplied by both the cosine and sine at
60
7168 Hz
synch, signal
Video Cassette
Recorder
Pulse-Code
Modulation Audio
Decoder
1
1
Time Code
Generator/Search
Unit
Narrowband
analog signal
Data - Synchronous
Quadrature
Demodulator
64 Hz
nterrupt
Signal
In-phase and
Quadrature Signal
Components
Analog to Digital
Converter
Zenith
Z-200 PC
Figure 3.6: Quadrature demodulation and digitization performed in the
Monterey Bay Acoustic Tomography Experiment
61
the carrier frequency to recover all of the magnitude of the signal in the
baseband. Multiplication gives
I(t) = A cos(2tt fct + M,0 + <j>) cos(2:r/c<)
= - [cos(Mt0 + 4) + cos(47r/ct + Mt0 + <f>)]
(3.8)
and
Q(t) = A cos(2?r fct + M.-0 + <f>) cos(2tt fct + -)
A
2
cos(M,0 + <)> - -) + cos(4?r/cf + M.-0 + <j> + ^)
(3.9)
These signals are passed through a low-pass filter to remove their high fre-
quency components and produce the in-phase and quadrature signals
and
ILp{t) = jcos{Mte + <t>)
QLP(t) = ^sm(Mie + <P)
(3-10)
(3.11)
These signals are now baseband and limited by both the input bandpass
and output lowpass filters to 16 Hz bandwidth. Since all the information
is contained at frequencies below 16 Hz, the digital sampling rate for the
signal must be greater than the Nyquist frequency of 32 Hz to avoid aliasing.
The sample rate chosen for the experiment was 64 Hz. This gives a period
between samples of 15.625 milliseconds, or four samples for each digit in the
maximal-length sequence.
Digital System
The conversion from analog to digital data was accomplished with a Zenith
Z-200 PC (6 MHz, 80286 based machine) equipped with a MetraByte DASH
16F data acquisition and control interface board. The mode in which the
DASH 16F was used was to scan 4 channels on receipt of an external inter-
rupt signal and store the 12-bit voltage code in memory via Direct Memory
Access (DMA). During DMA the computer Central Processing Unit (CPU)
is left free to execute other parts of the program. In this manner the code
correlation could be performed in parallel with the analog to digital conver-
sion, resulting in a large processing time savings. A diagram of the operation
62
Analog to Digital + dian- 1> l & Q
Converter L , „ . . n
j chan. 2, 1 & Q
MetraBy te D ASH16F ^ „
64 Hz interrupt
signal
transfer direct to
memory via DMA,
\
\
r >
Upper Section,
RAM Buffer
\
\
N
\
\
r
x
a
Lower Section,
RAM Buffer
transfer to program
for 'real time' processing
Maximal Length
Sequence
Correlation
i
Coherent Averaging
of 16 Sequences
Bernoulli Box
20 MByte
Cartridge
Figure 3.7: Diagram of tomography signal data flow for 'real time' digitiza-
tion and code correlation.
63
is shown in Figure 3.7. The Fast Hadamard Transform described in the Ap-
pendix was used to perform the matched-filtering for the code correlation
with sufficient efficiency to be run concurrently with the digitization. Equiv-
alent programs performing the correlation using Discrete Fourier Transforms
took approximately 300 times as long to perform and could not be used for
"real-time" processing of the recorded data. The in-phase and quadrature
components of the signal are combined after the code correlation and are
stored as magnitude and phase. This results in about 44 kilobytes of data
per channel per minute. This data was stored on 20 megabyte cartridges
with a dual drive Bernoulli Box manufactured by IOMEGA. One six hour
videotape containing two recorded channels of information was converted to
about 17 megabytes of data on each of two cartridges. In addition a coher-
ent average of 16 time periods is conducted and stored. The source code
for FORTRAN programs to conduct the signal digitization and correlation
are contained in Appendix C. The program AMORE was used for the data
conversion with concurrent code correlation and is the program described
in this section. The programs AINPUT and AHAD perform the same op-
erations but in two steps, storing the digitized samples before correlating
for the maximal-length sequence. Both AMORE and AINPUT make use
of library routines provided with the DASH 16F board for controlling the
board, including the interrupt handler for the external interrupt.
3.4.3 Travel time estimation
Eigenray Arrival Selection
An important part of understanding the data was an effective display of the
data. Programs AGRAF4 and AGRAF5, listed in Appendix C, were used to
generate files of magnitude and/or phase for plotting routines in MATLAB
and SURFER. MATLAB is a product of The Mathworks, Inc. of Sherborn,
MA and SURFER is a product of Golden Software, Inc. of Golden, CO.
Both routines generate a plot usually described as a "waterfall" plot. This
plot places one 1.9375 second period of the signal behind another for up to
about 70 lines so that any feature common to all the sequences will stand
out clearly. For the data coherently averaged for sixteen periods, if every
other sequence is skipped, 62 minutes of data can be displayed on a single
plot. From these plots an estimate of the resolution and stability can be
made by eye. The arrival must not disappear (an indication of an unstable
path) and it should not merge or split with another arrival (an indication
that the ray arrivals are not resolved).
64
Interpolation between Signal Points
The points of the received signal are separated by the sample period of
15.625 milliseconds. The points can be interpolated to a smaller separation
by using curve fitting. A cubic spline curve fitting routine adapted from
Press, et al., generates points separated by 0.976 milliseconds[37]. Until this
point all the calculations have been conducted using integer mathematics.
This gives insufficient separation for selecting the highest magnitude point
after interpolation. The interpolation is therefore done with floating point
decimal mathematics in FORTRAN.
Signal-to-Noise Ratio Calculation
Although the point interpolation allows the selection of the time of arrival
of the point of highest highest magnitude to less than a millisecond, the
actual uncertainty is a function of the signal-to-noise ratio. A pessimistic
estimate of the signal-to-noise ratio is made by finding the mean amplitude
of all the points in a 1.9375 second data string, not trying to sort out signal
from noise. The peak magnitude is then divided by this value to obtain a
signal-to- noise ratio.
Methods of Selecting Peak Magnitude
Two different algorithms were used to estimate the arrival time and signal-
to-noise ratio. Both programs could perform coherent averaging of con-
secutive signal periods for up to sixteen periods. This will increase the
signal-to-noise ratio but reduces the sampling rate below what is necessary
for surface wave data. The method could be of use for investigating internal
wave frequency fluctuations. Both programs could also perform a correla-
tion with a square pulse. This correlation results in low-pass filtering of
the data and smooths out fast fluctuations(< 65 milliseconds) as well as
increasing the peak amplitude of features longer than 65 milliseconds. The
noise improvement was very slight and the amplitude gain for arrivals did
not greatly increase the signal-to-noise ratio or estimation accuracy. The
first program, AGONY, is an interactive program which requires the user to
input a window size for the program to search for a peak, a starting position,
and a minimum threshold for the signal-to-noise ratio. If the maximum am-
plitude of the peak found does not exceed the SNR threshold, the program
stops, displays the signal period in question and asks the operator to pick
the peak. The window shifts to take the last peak found as its starting point.
65
The second program, ACRID, was both less flexible and more efficient. The
window for the peak-picking was rigid and the maximum amplitude found
inside the window would be the chosen arrival peak. If the signal-to-noise
threshold was not attained, the previous arrival time would be repeated with
the lower signal-to-noise ratio. The SNR would serve as a flag for a repeated
arrival but would still allow for relatively little noise contamination. Having
a uniform separation of the samples is important for Fast Fourier Transform
analysis and segmented sample power spectrum estimation. Typical window
sizes were about 80 milliseconds to either side of a starting position.
3.4.4 Summary of signal processing
The signal processing system estimates the arrival time perturbations from
the analog recordings through the following procedure:
1. The signal passes through a band-pass filter to remove any out-of-
band noise.
2. The signal is quadrature-demodulated to baseband and low-pass fil-
tered to remove the high frequency components.
3. The signal in-phase and quadrature components are sampled at 64 Hz
and digitized.
4. The Fast Hadamard Transform is used to matched-filter for the maximal-
length sequence code and the result is stored.
5. Given a certain window around an eigenray arrival, the arrival time of
the ray is estimated with respect to an arbitrary code starting position,
and the signal-to-noise ratio is calculated.
6. The geophysical time (clock time) of the data point, time of arrival,
peak magnitude, and signal-to-noise ratio are stored. This stored data
contains the fluctuations due to path length and sound speed pertur-
bations and will be the input data for the tomographic inversion to
estimate the ocean conditions.
66
3.5 Experimental Results
3.5.1 General Summary of Data
Acoustic Data
Approximately 300 hours of acoustic data was recorded on videotapes. This
data varied because of the location of the receivers and inconsistencies in
the operation of the equipment. Ambient noise at all stations was often
stronger than the 224 Hz signal but, after the maximal-length sequence cor-
relation, all sonobuoys which functioned showed some ray arrival signature.
The amplitude of the received signal varied with time but does not appear to
correlate with tidal fluctuations. Interfering acoustic sources were dolphins,
whales, and fishing boats. Of these, only the fishing boats adversely affected
the signal reception. Radio frequency interference occurred to a greater de-
gree than expected, with most channels having some minor interference and
a few having the sonobuoy signal completely blocked for several minutes.
Some of the identified sources of interference were a pocket-pager trans-
mitting station, walkie-talkies used by personnel at the Defense Language
Institute, marine-band radios, vehicle dispatch radios, and the McDonald's
Restaurant radio-intercom for their drive-up window. Most of the interfer-
ence only degraded the signal for short periods and only on a few channels.
The following is a short description by station of the received data from the
time the transmitter was activated:
• Station B - 1710 12DEC to 0250 13DEC This is the shortest path and
has several resolved arrivals. The buoy appears to have broken free
or been dragged away in the early morning of the second day. The
signal-to-noise ratio until then was good.
• Station B-l (MIUW) - 1700 12DEC to 0130 16DEC Several resolved
arrivals are present. The arrival structure appears stable but moves
quickly, apparently due to buoy motion. The fluctuation in arrival
time due to buoy motion probably cannot be sorted out of the motion
due to path and sound speed fluctuations.
•
Station E - 1430 13DEC to 2400 15DEC Only very unstable arrivals
with a low signal-to-noise ratio are present. This path travels through
shallow water for longer than any other path and bottom losses may
have reduced the signal below a useable level.
67
• Station G - 1300 14DEC to 2400 15DEC This stations early data
was lost because of a malfunctioning receiver. The data shows one
fairly stable arrival and several unstable arrivals. This ray path travels
through most of the Monterey Canyon.
• Station H - 1330 13DEC to 2230 15DEC Several unstable arrivals are
present, usually with a low signal-to-noise ratio. Two dimensional ray
tracing may be inadequate to predict the paths of eigenrays which
reach this buoy at the head of Soquel Canyon.
• Station I - 1300 13DEC to 2200 15DEC Usually several arrivals with
good signal-to-noise ratio are present. The arrivals have large magni-
tude fluctuations and the paths seem to be unstable over a period of
hours. Again, the complex bathymetry may lead to unstable three-
dimensional raypaths.
• Station J - 1300 14DEC to 1400 15DEC This ray path has simpler
bathymetry than paths to G, H, and I. After the path crosses the
canyon the path has a steady grade into shallow water. Several re-
solved rays with good signal-to-noise ratio are present. This data
record is short because the first sonobuoy at this position never func-
tioned and the second failed after 25 hours.
• Station L - 1000 13DEC to 2000 14DEC Many arrivals with good
signal- to-noise ratio are present but some of the strongest are some-
times unresolved. This path also had simple bathymetry with a steady
slope into shallow water after crossing the canyon. Poor reproduction
from a faulty PCM encoder may have contributed to loss of signal
at some points. Back up audio tapes will be examined to see if the
recording is better.
• Station L-l (MIUVV) - 1400 14DEC to 1900 15DEC This buoy required
the replacement of a circuit board before it could be deployed. The ray
arrivals varied from two resolved arrivals to many unresolved arrivals.
The shifts due to buoy motion are not as apparent as for station B-l.
• Station L-2 - This buoy failed and was immediately recovered. Data
for Station J will be presented as an example data set.
68
Surface Wave Data
The NDBC moored surface wave buoy operated as designed and hourly re-
ports of the surface wave power spectral density, wave direction, barometric
pressure, and temperature for the entire experiment have been received.
This data will be compared to the data derived from tomography in the
same frequency band. Unfortunately, all the data from the ARGOS drifting
buoys is unusable. The algorithm used in calculating the power spectral
density from the accelerometer inputs uses the lowest frequency information
(0.01 and 0.02 Hz) to calculate a noise correction factor. Somewhere in the
process an error was made and since neither the raw data nor the correction
factor is transmitted or recorded, the correct results cannot be calculated.
The data from the moored NDBC buoy should be sufficient.
Sound Speed Profile and Current Measurements
The data taken during conductivity, temperature , and density (CTD) mea-
surements and by the acoustic Doppler current profiler is being analyzed at
Woods Hole Oceanographic Institution. The sound speed profile results for
two positions near the path to Station J will be presented. The ADCP data
is not ready at the time of writing.
3.5.2 Station J Data
Station J Eigenray Prediction
The bathymetry along a two dimensional slice between the transmitter and
the receiver and the eigenray predicted MPP are shown in Figure 3.5.2
as described in Chapter 4. Although the eigenray was predicted from a
historical sound speed data base, the measured profile in deep water very
nearly matched and the original prediction is probably accurate enough until
a three dimensional prediction can be made. The single eigenray predicted
has few interactions with the surface or bottom before reaching the the shelf
water. Once in the shallow water of the shelf the ray has many reflections.
The number of bounces predicted was seven but a small change in the angle
of the ray could easily double or halve the number of surface interactions in
the last 8 kilometers before the receiver.
69
0.00
7.25
14.50
21.75
29.00
36.25
43.50
50.75
58.00
RANGE (KM)
Figure 3.8: Two dimensional ray path predicted using MPP. This eigenray
connects the source at Station A to the receiver at Station J.
70
Measured Sound Speed Profiles
Sound speed profiles from two positions near the ray path connecting the
transmitter and Station J are shown in Figures 3. 5. 2 and 3.5.2. Figure 3.5.2
shows the profile for shallow water at 36°51.095'N - 122°04.798'Wr, near
Station J. The profile in Figure 3.5.2 is from deep water at 36°32.906'A^ -
122o16.210'W\ near the transmitter. Both profiles show two traces, one for
measurements while the CTD instrument is descending and the other while
its ascending through the water column. The difference between the curves
where the sound speed gradient is steepest is evidence of internal waves.
The difference in depth of a certain sound speed gives a minimum vertical
displacement for the internal wave but gives no information about the period
or actual amplitude of the oscillation. The two points at 30 meters on Figure
3.5.2 are about 4 minutes apart, based on a 30 meter per minute rate for the
CTD. Similarly, in Figure 3.5.2, the 100 meter points were crossed about an
hour apart, based on a 45 meter per minute rate. Analysis of the CTD "yo-
yo" measurements may give information on the deep water, lower frequency
internal waves however no "fast" measurements were made in shallow water.
Using the CTD measurements, the Brunt-Vaisala frequency at the density
gradient can be calculated as
n = J-^ (3.12)
for depth z, density r, and gravitational acceleration g. The Brunt-Vaisala
frequency is the highest where the gradient is greatest. In the case of the
shallow water with the sound speed profile shown in Figure 3.5.2, the min-
imum period (maximum frequency) the gradient will sustain is about 8.3
minutes. The density gradient can support much longer period oscillations
also. [4]
Received Acoustic Signal
The data recorded for Station J only covers 25 hours during the experiment
because of failures in the first and second modified sonobuoys placed there.
The received signal shows three or four ray arrivals throughout the function-
ing span. All of the arrivals fluctuate in strength over time. Shown in Figure
3.11 is an example of the received signal. This plot is the result of coher-
ent averaging of 16 sequences and then only plotting every other averaged
sequence. The data shown covers 62 minutes for each plot and is used for
71
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(m/s)
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00 M9J JJ 1496
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Figure 3.9: Sound speed profile from near Station J. Note that any ray path
will be refracted downward. The trace has two lines, one as the CTD goes
down and the other as it is brought back to the surface.
72
Soundopeed
(M,/S)
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Figure 3.10: Sound speed profile from near mid-Bay. This profile is typical
of the profiles found in deep water at the time of the experiment and very
close to the profile used in MPP for eigenray prediction.
73
determining which arrival to track for the travel time fluctuation data. The
orientation of the plot assists in visually integrating the data to spot char-
acteristics recurring at the code repetition frequency. The remaining plots
for Station J are in Appendix D. Note that the data from different video-
tapes has a new arbitrary starting point for timing the arrival estimations.
This random displacement is unimportant when measuring ocean perturba-
tions with periods somewhat shorter than six hours. If investigation of tidal
frequency phenomenon was a goal of this experiment then some method
of synchronizing the different data sets would be required. The individual
eigenray arrivals can be located (for stable paths) on different tapes by ob-
serving the location of a ray relative to the others. The analysis of one ray
arrival will be shown to demonstrate the data for travel time fluctuations.
In Figure 3.11, the selected arrival has its peak at about 0.85 seconds after
the arbitrary start point as shown on the sequence repetition time scale.
While the signal-to-noise ratio of this arrival varies, there is always enough
so that it can be measured during the 25 hour interval.
Travel Time Fluctuations
The arrival time is estimated by finding the peak of the ray arrival signal.
The absolute travel time is something around 50 seconds and is not mea-
sured. Each cycle of the maximal-length code is the same as the others and
cannot be identified. Moreover, since the fluctuation of the absolute travel
time is the same as the fluctuation in the arrival time as measured from an
arbitrary starting point, only the latter will be measured. The arrival time
estimation vs. time for the selected arrival shown in Figure 12 is shown in
Figures 13 and 14. The uncertainty calculated from the signal-to-noise ratio
is between 2.5 and 4.5 milliseconds for most of the estimates. The perturba-
tions have a peak-to-peak amplitude of about 50 milliseconds. Also visible
are some lower-frequency oscillations.
3.5.3 Analysis of Arrival Time Fluctuations at Surface Wave
Frequencies
The power spectral density of the arrival time fluctuations caused by the sur-
face waves should reflect the power spectral density measured by the NDBC
surface wave measurement buoy. The power spectral density of the arrival
time perturbation was estimated using a segmented Fast Fourier Transform.
The individual segments were chosen to be 64 samples long to match the
frequency resolution of the NDBC data. Approximately 2.2 hours of data
74
Slgnol Magnitude Squared Slot Ion J 1 4DEC88
vO
3
CD
^*\
Cl
sn
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0)
m
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sn
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0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Se quence Rep It It Ion T I me ( seconds)
Figure 3.11: Received acoustic signal after Hadamard transforming for max-
imal-length sequence from Station J, 14DEC88 1855 to 1957 PST. Each line
is 31 seconds of data coherently averaged to one 1.9375 second period. The
earliest period is in the foreground and the latest is at the back.
<b
&
<tf
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Arrival Time Estimate, Station J
14 December 1988
0.90
0.85-
0.80-
0.75-
0.70
18.90
19.00 19.10 19.20
Pacific Standard Time (decimal Hours)
19.30
19.40
Figure 3.12: Arrival time estimate for Station J from 1855 to 1924 PST
on 14Dec88. The fast fluctuations in arrival time are due to surface waves
changing the path length. Lower frequency oscillations from other causes
are also seen.
76
2?
<fl
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A
C
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0.90
Arrival Time Estimate, Station J
14 December 1988
0.85-
0.80
0.75
0.70
19.41
19.51 19.61 19.71
Pacific Standard Time (decimal hours)
19.81
19.91
Figure 3.13: Arrival time estimate for Station J from 1925 to 1955 PST
on 14Dec88. The fast fluctuations in arrival time are due to surface waves
changing the path length. Lower frequency oscillations from other causes
are also seen.
77
points provides 64 segments for 128 degrees of freedom. An example of the
arrival time power spectrum is shown in Figure 3.14. The resolution band-
width is 0.00806 Hz. This value is used to normalize the magnitude so that
other spectra of the same data will have a directly comparable magnitude
although a different resolution bandwidth is used. Note that the segmented
transform method sums (instead of averaging) the result of the FFT's so
that the total power will contribute to the magnitude. [38] The power spec-
trum from surface waves provided by the National Data Buoy Center has
already been described. An example of the wave data is shown in Figure
315. The spectral resolution is 0.01 Hz. Additional sea surface and arrival
time spectra are included in Appendix D. A comparison of the arrival time
and surface wave power spectra immediately shows agreement in the general
shape and frequency distribution with the largest concentration of power in
the long period swell frequency region of 0.07 to 0.09 Hz. The arrival time
spectrum also shows a smaller but still significant peak at about 0.03 Hz.
This is a longer period than is normally observed for sea swell in the Pacific.
This frequency of fluctuation is higher than can be attributed to internal
waves and must be due to a path length change, but either a modulation on
the swell or an extremely long period wave could cause it. A possible expla-
nation is "beating" between two systems of long period swell propagating
in slightly different directions. A source of this surf beat could be swell that
has been reflected or refracted off the shallow water or shoreline along the
north side of the Bay. The arrival time spectrum shows a nearly white noise
floor. This is due in part to the random uncertainty in the estimation of
the arrival estimation. All fluctuations of higher frequency than 0.258 Hz
will spread out the arrival pulse width and lower the signal-to-noise ratio,
contributing to the uncertainty. The spectrum for the surface wave buoy
data does not show this kind of noise. The algorithm for calculating the
wave data calculates a noise correction factor from the two lowest frequency
data points, 0.01 and 0.02 Hz, and applies this to the rest of the data. Since
the accelerometer calculations are most sensitive to noise and least sensitive
to motion at the lower frequencies this is convenient. Unfortunately, the
energy seen by the tomography signal may indicate that "zeroing" the low
frequencies may not always be correct.
78
W5
C
a
o
u
■»-
G.
C/3
0.012
Arrival Time Power Spectrum
Station J 14DEC88 2001 PST
0.05 0.1 0.15
Frequency (Hz)
0.25
Figure 3.14: Arrival time power spectrum for Station J. Spectrum from 2.2
hours of arrival times series, 1855 to 2107 14 Dec88 PST.
79
Sea Surface Spectrum
NDBC Buoy 14Dec88 2000 PST
N
£
E
GJ
u
»~
53
fC
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to
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?0 -
OR -
OC\ -
1S -
m _
l u
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0-
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0.00
0.05 0.10 0.15
Frequency (Hz)
0.20
0.25
Significant Wave Height 4.10 m
Average Period 9.67 sec
Dominant Period 12.50 sec
Dominant Direction 308°N
Figure 3.15: Surface wave power spectrum in Monterey Bay at 2000 PST
on 14 Dec88 as taken from the NDBC wave measuring buoy southwest of
Santa Cruz.
80
3.5.4 Analysis of Arrival Time Fluctuations at Internal Wave
Frequencies
The magnitude of time fluctuations at internal wave frequencies is expected
to be of somewhat lower magnitude than fluctuations due to surface waves.
Figure 3. 5. 2 shows a sound speed difference of only 5 meters per second
across the thermocline, a change of only 0.33%. The surface wave causes a
300 times greater time perturbation for the same amplitude as an internal
wave. To begin analysis of the data, the time perturbation data series was
detrended by subtracting the mean and then low-pass filtered with an 8th
order Chebyshev digital filter to a cutoff frequency of .01 of the original max-
imum digital frequency. Oscillations of period greater than 6.4 minutes pass
through the filter including any perturbations due to internal waves. The
result for Station J is shown in Figures 3.16, 317, 3.18, and 3.19. This data
appears to show the presence of several different frequencies but segmented
FFT methods were unsuccessful in measuring their distribution. It is prob-
able that the the record length before the oscillations become uncorrelated
is not long enough to form a statistically significant group and still have
the frequency resolution necessary to analyze the waveform. Other methods
such as the Prony method, maximum entropy method, or a frequency-time
spectral density may identify these frequencies[37,38].
3.5.5 Summary of experimental results
For the stations analyzed to date, many of the acoustic arrivals are observed
to be resolved and stable. The arrivals shown in Figure 3.11 illustrate a typ-
ical arrival pattern for about an hour. The strong central arrival is present
in the Station J data for the 17 hours that the sonobuoy was operating.
The lowpass-filtered arrival time of that central peak is shown in Figures
3.16, 3.17 and 3.18. A key result is that tidal effects do not destroy the sta-
bility of the multipath arrival that has traversed the Monterey Submarine
Canyon. This result bodes well for the stability of arrivals in a permanent
tomography system in the Bay.
81
Arrival Time Perturbation Station J 14DEC88 1317 - 1855
0.1
0.08-
C/3
0.06
C
o
o
CJ
v.
c
n
0.04
ca
.c
w.
0.02
0-
«
>
"E
o
<
■0.02
-0.04
13
15 16 17
Pacific Standard Time (hours)
19
Figure 3.16: Arrival time data for Station J lowpass filtered to 0.00258 Hz
(Period = 6.4 minutes).
82
0.05
Arrival Time Perturbation Station J 14DEC88 1855 - 15DEC88 0052
T
20 21 22 23
Pacific Standard Time (hours)
Figure 3.17: Arrival time data for Station J lowpass filtered to 0.00258 Hz
(Period = 6.4 minutes).
83
Arrival Time Perturbation Station J 15DEC88 0052 - 0647
0.04
-0.05
2 3 4 5
Pacific Standard Time (hours)
Figure 3 18: Arrival time data for Station J lowpass filtered to 0.00258 Hz
(Period = 6.4 minutes). High amplitude after 0400 is due to low SNR during
storm.
84
Arrival Time Perturbation Station J 15DEC88 0647 - 1226
8 9 10 11
Pacific Standard Time (hours)
13
Figure 3.19: Arrival time data for Station J lowpass filtered to 0.00258 Hz
(Period = 6.4 minutes).
85
Chapter 4
Modeling Effort
4.1 The Multiple Profile Ray-Tracing Program
4.1.1 Description
The analysis tool that was the basis for the selection of receiver locations
in Monterey Bay for the December 1988 tomography experiment is called
the Multiple Profile Ray-Tracing Program (MPP). Originally written as five
separate programs by Ocean Data, Inc., for the Office of Naval Research
[35]. the MPP program has evolved to its present form through extensive
modification by John Spiesberger of the Woods Hole Oceanographic Institu-
tion. This program computes transmission loss and arrival structure for the
eigenrays that it determines will arrive at a fixed receiver, from a source at
a fixed depth. The ocean is modeled with a range-dependent sound speed
profile (SSP). variable bottom depth and bottom reflectivity. Transmission
loss is calculated under a variety of options, including
1. asymptotic treatment of caustics with rms or fully coherent addition
of the two paths in the interference region of the airy functions;
2. surface-image interference at the source; and
3. source and/or receiver vertical directivity patterns.
Output generated, based on a successful finding of eigenrays, are
1. all input data;
2. ray trajectories at arrivals;
86
3. sequential signature groups;
4. precise angle, time and intensity at a limited number of range points
using quadratic interpolation;
5. transmission loss versus range;
6. plot of eigenray path from source to receiver; and
7. stick plot of transmission loss versus arrival time for the eigenrays.
4.1.2 Program Flow
Figure 4.1 is a block diagram of the program flow, with input files shown on
the left side of each routine and output files on the right side of the routine
block. The command file runart is called upon to execute the routines
writefiles2art, mppl, mpp2cout(lst pass), zofth , post63 and mpp2cout(2nd
pass), after an input data file has been created by the user. The routine
nrayfil2 is used to generate the ray tracing and stick plot graphs from binary
data in file TAPE16.DAT and TAPE 20.DAT.
Writefiles2art is a small routine that separates and reformats the user-
generated input data into six different files. These six files are accessed by
the other programs that runart executes. Zofth is another short routine that
plots initial angle versus the depth at which its ray path arrives that the
receiver location (range). Most of these rays do not arrive at the receiver,
i.e., they are beyond the vertical miss allowance. For the simulation, a ray
has to come within a vertical distance of 15m from the receiver, either above
or below. Since the receiver was placed lm below the receiver. Post63 is the
eigenray post-processor routine. It determines the eigenrays' arrival angle at
the receiver, creates file TAPE16.DAT which is used by nrayfil2 to generate
the ray trace graph, and produces a printout enumerating the eigenrays in
three sorted lists, based on increasing travel time, decreasing initial angle
and increasing transmission loss. The function and logical flow of the four
main programs, used to determine and plot the eigenrays at a given receiver
location, will be described in more detail.
Mppl
Mppl is the second routine called by the command file runart. Its purpose
is to determine the sectors within the region between two range-stipulated
input SSPs. These sector determinations are required for calculating ray
87
input.dat —
writcfilcs2art
,-MPPI.DAT
MPP2.DI
MPP2.D2
ZOFTII.DAT
POST63.DAT
* CFPLT.DAT
MPP1.DAT--
MIT2.DI.
PROFIl.E.IMT
QANFII.E.DAT
CONF1I.E.DAT
SPCFI1.E.DAT
TAPF.I4.DAT
TAPE40.DAT
1 mppl
mpp2cout (1st pass)
.MPPl.OUT
PR0F1LE.DAT
QANFILE.DAT
CON4.DAT
CONFlLE.DAT
SPCFILE.DAT
SSP.OUT
TAPE14.DAT
TAPE40.DAT
,-MPP2.01
TAPE6I.DAT
TAPE63.DAT
-TAPE15.DAT
ZOFTII.DAT
TAPEI5.DAT
zoith
ZOFTII.OUT
POST63.DAT
TAPE63.DAT
TAPEI4.DAT
post63
■POST63.0UT
TAPEJ6.DAT
•TAPE17.DAT
MPP2.D2.
TAPEI7.DAT
PROFH.E.DAT
QANFI1.E.DAT
COM"! I.E. DAT
SPCFILE.DAT
TAPE14.DAT
TAPE40.DAT
TAPE16.DAT---
TAPE20.DAT- -
nipp2cout (2nd pass)
" nraylil2
-TAPE20.DAT
MPP2.02
TAPE61.DAT
TAPE63.DAT
TAPE15.DAT
PLOTFILE
ravTile.RAY
ravfile.LEN
NRAYPI.OT
STICKPLOT
ravcoor.dat
Figure 4.1: MPP block diagram with input and output files.
88
paths in mpp2cout. Mppl also uses the input bottom data to assemble the
bottom profile and tabulate the bottom loss as a function of grazing angle
in each of the range domains. If a loss function is specified as "Modified
Rayleigh", the program tabulates it on a variable mesh to yield accurate
values by linear interpolation.
Sectors can be either triangular or rectangular. Rectangular sectors ease
the computational crunching of the ray path determination logic, and speeds
up the computer time. Sector determination begins with a comparison of the
sound speed at the very bottom of the first SSP (sspl) versus the very bottom
of the second SSP (ssp2). If sspl equals ssp2 at the bottom, then a horizontal
line is attached between the two points, and the next higher profile values
for sspl and ssp2 are compared. If the two values are not identical, then
a triangular sector will be specified. Once one sector has been determined
to be a triangle, the entire upper region will be triangularized, even though
all shallow points of the two SSPs may match. The only way to have all
rectangular sectors is to have completely identical SSPs.
Mpp2cout(lst pass)
Mpp2cout(lst pass) is the first half of the eigenray processing programs. The
main program is very small, but it calls seven subroutines that in turn call
other subroutines. The first subroutine, ctll, inputs data and takes care of
initialization. The program then loops through the rest of the subroutines,
until it equals the number of passes that the user's input file stipulated as a
maximum number of passes. The first subroutine in the loop, reset, locates
the sound speed triangular section that encompasses the receiver.
The next subroutine, ctl2, is the longest and accomplishes the most.
After initialization, it determines the initial velocity sector for the ray and
the direction that the ray will go. As the ray travels toward the receiver.
ct!2 computes the ray intersections with sector boundaries (top, bottom and
sides), stores parameters and checks for bottom reflections. Next, it calcu-
lates the spreading factors and performs a check for caustics. If there is a
caustic, it locates the caustic for both curved and straight rays. Continuing,
this subroutine updates the intensity derivatives for bottom reflection, sur-
face reflection, sector crossings and region crossings, and the transmission
loss is then updated. After arrival information is stored, then the ray is
checked to see if it should be cut. The following are reasons to cut a ray:
1. ray has reached maximum range (ray range>target range);
89
2. ray angle too steep (ray has reflected at an angle> 85;
3. max bottom reflections exceeded (as stipulated by the user);
4. max turning events exceeded (the total number of bottom reflections,
bottom horizontals, surface reflections and surface horizontals have
exceeded the maximum number of turning points as stipulated by the
user).
The rays that were not cut are now sorted in increasing angle order by the
subroutine sort61. The second biggest subroutine, iterat, then determines
the relationship of the uncut rays with the receiver at the target range. It
also extrapolates new rays and checks the angle loss tolerance for these new
extrapolated rays. All of the uncut rays have one of the following ray/target
relationships:
1. good bracketted source depth (IDENT=2), where a pair of rays verti-
cally surround the receiver;
2. good diffraction field (IDENT=3), where a pair of rays do not bracket
the source but they appear to be within the receiver's focus or conver-
gence region;
3. badly bracketted source depth (IDENT=4), where a pair of rays fail
the criteria for the above relationships;
4. bad diffraction field (IDENT=5), where the ray pair appear to be
within the receiver's focus, but they are outside of the time tolerance:
5. good bracketted source, two eigenrays (IDENT=6);
6. badly bracketted source, two eigenrays (IDENT=7); and
7. bad signature pair of rays (DENT=8), which is the most common
ray/target relationship, resulting from the ray pair being too close to
each other.
Mpp2cout concludes by calling subroutines clean, which removes the
deletable angles from file TAPE61, and dump63, which prints out the ray
status for all uncut rays. The program then increments the pass number
counter and starts all over again.
90
Mpp2cout(2nd pass)
The second pass of mpp2cout is the eigenray plotting run and is logically very
similar to the first pass of mpp2cout. It is executed after post63. This run
begins with the "good bracketted source" and "good diffraction field" rays
that were first identified in mpp2cout (1st pass) and post-process in post63.
A trace for each of these rays is produced. The following information is
provided in the trace at every surface reflection, bottom reflection, refraction
and caustic along each ray's path:
1. range (km).
2. depth (m),
3. angle (deg),
4. time (sec),
5. loss (dB),
6. number of caustics,
7. arrival number,
8. number of surface horizontals (refractions),
9. number of surface reflections,
10. number of bottom horizontals (refractions),
11. number of bottom reflections, and
12. total number of turning points.
Another main difference between the two passes is that this second pass
generates the file TAPE20.DAT, used by nrayfi!2 to graph the ray plots
and stick plots. For each coordinate on the ray trace, not just the turning
points, TAPE20.DAT stores the range (km), depth (km), angle (radians) and
sound speed (km/sec). In the beginning of this pass, angle values are read in
from file TAPE17.DAT. Otherwise, mpp2cout (2nd pass) goes through the
same logical flow as mpp2cout(lst pass), and is the final eigenray processing
program executed by the command file runart.
91
Nrayfil2
The routine nrayfil2 is called by the user after the command file runart
has executed all of the eigenray-determining programs and eigenrays have
been identified. Since nrayfi!2 is used to generate the ray tracing and stick
plot graphs, there is no reason to execute this routine if there are not any
eigenrays. This routine should be run immediately after the programs exe-
cuted by runart determine one or more successful eigenray(s), or else rename
TAPE16.DAT and TAPE20.DAT files so that they can be accessed later by
nrayfil2.
There are six options that can be accessed in this program : 1. make,
2. inspect, 3. rayplot, 4. stick, 5. add, and 6. delete. "Make" has to
be the first option specified since it generates two files of ray data that is
used by the other options It requires ass input the files TAPE16.DAT and
TAPE20.DAT that were generated for the last executed MPP run. The
output file name, has to be all capitalized and end in. RAY. If, for example,
the user specifies the ray file name as RCVR2.RAY, this "make" option
creates a file with that name and another file with the name RCVR2.LEN.
Both are needed for the other options.
"Inspect" allows the user to inspect the rays and to store all of the ray
coordinates in the file RAYCOORCAT. These ray coordinates are used to
graph the ray trace, and include the values of range, depth, angle and sound
speed for every specified point on the ray trace graph. "Add" allows a new
ray to be added to an existing ray file, while "delete" removes an unwanted
ray from the ray file.
The last two options plot graphs. "Rayplot" will plot the ray trace of
one or more rays, based on the inputted ray file name. For the first ray file
stipulated, a list of all the initial ray angles are displayed on the screen, after
the user has specified the graph dimensions and titles. The user indicates
the ray angle that is to be plotted, and has the option of plotting more rays
on the same graph or stopping. Another ray file can be accessed, and those
angles can be added to the graph with the first ray file angles. The graph
data is placed in the N RAYPLOT file, which is then plotted. The ray traces
in Appendix A. 2 were produced with this option. "Stickplot" graphs the
transmission loss for all the rays that are contained in the user-specified ray
file. The only input options are graph dimensions, graph title and ray file
name.
92
4.1.3 MPP Input/Output
The focus of this effort was to recommend the locations for six receiver
hydrophones that were used in the December, 1988 tomography experiment,
and to provide eigenray and travel time information related to each site. The
recommendations were based on the results from two-dimensional, range
and bathymetry dependent, ray tracing computer simulations for various
locations in and around the bay, as well as a preliminary assessment of the
oceanographic and geo-acoustic environment of the region. This section will
identify the receiver locations that were addressed, the input parameters
used in the MPP computer program, and the results from the simulations.
Simulated Receiver Locations
Seventeen locations for possible receiver hydrophone placement were tested
using the MPP program. These points are on the continental shelf surround-
ing the Monterey Canyon, from southwest of Santa Cruz to Pacific Grove,
excluding the Monterey Seaside nearshore area where a direct ray from the
Point Sur seamount (source location) could not reach. All of these sites are
shallower than 100m, and the hydrophone in the simulation were placed 1
m above the sea floor.
All of these locations were selected for specific reasons. Figure 4.2 de-
lineates the position of these receiver location in the area of Monterey Bay,
while Table 4.1 provides the specific position. Any eigenrays arriving at
receiver numbers 6 and 7 will have traveled through Carmel Canyon the
trough of Monterey Canyon. Sites 4, 8 and 15 are in the general area of
the Monterey Canyon head, where internal waves are at their highest am-
plitudes. Receiver 5 is located on the edge of the south wall of Monterey
Canyon, and was selected for comparison between rays going through the
narrow part of MSC and those that do not. Any eigenrays that receiver 14
would pick up have traveled right down the Monterey Canyon in the granite
wall formation. Locations 3, 9, 10, 12 and 13 surround the Soquel Canyon.
Finally, receiver positions 1, 2,16 and 17 are out of Monterey Bay and would
have eigenrays that traveled through the trough of Monterey Canyon, where
the floor is wider.
Input
For each receiver location of interest, an input file was created that provided
the MPP routines with the following information:
93
Figure 4.2: Receiver hydrophone locations for ray tracing.
91
RCV
NO
LOCATION
LONGI-
TUDE
LATITUDE
RANGE
(km)
DEPTH
(m)
1
SW of Santa Cruz
122°09.60'W
36°53.10'N
59.35
97.76
2
SSW of Santa Cruz
122°05.00'W
36°51.20'N
57.99
90.44
3
Head of Soquel
Canyon
121°57.35'W
36°51.75'N
63.87
90.44
4
\V of Moss Landing,
Monterey Canyon
north wall
121°52.20'W
36°48.65'N
63.49
90.44
5
W of Salinas River
mouth, Monterey-
Canyon south wall
121°54.10'W
36°45.00'N
56.51
90.44
6
N\V of Point Pinos
121'58.35'W
36°39.25'N
44.43
90.44
7
WSW of Point
Pinos
121°59.25'W
36°37.60'N
42.02
50.21
8
\V of Pajaro River
mouth
121°51.00'W
36°50.00'N
67.49
54.00
9
ENE of Soquel
Canyon head
121°54.90'W
36°57.00'N
67.15
4S.38
10
N of Soquel Canyon
head
121C57.40'W
36°52.75'N
68.39
44.72
11
North wall, west of
Soquel Canyon
juncture
122°01.55'\V
36°48.80'N
56.04
90.44
12
North wall, Soquel
Canyon
121°59.65'\V
36°50.25'N
59.72
90.44
13
East side, Soquel
Canyon juncture
121°57.90"W
36°48.65'N
58.53
90.44
14
North wall of
Monterey Canyon,
prior to Soquel
Canyon juncture
121°55.00'W
36°48.25'N
60.36
90.44
15
Near head of
Monterey Canyon
121°50.20'\V
36°47.90'N
64.36
90.44
16
SW of Santa Cruz,
nearshore
122°03.50'W
36°54.50'N
66.20
45.00
17
W of Santa Cruz,
nearshore
122°08.17'W
36°56.50'N
67.47
48.93
Table 4.1: Position, range and depth of simulation receivers.
93
1. range and depth of source;
2. range and depth of receiver;
3. minimum and maximum angle range for the eigenray search;
4. number of initial rays;
5. number of turning points and bottom reflections;
6. sound speed profile (SSP) data;
7. bathymetry data from source location to beyond the receiver location;
and
8. bottom reflectivity values, i.e., loss for a given angle.
MPP sets limits on some of the input variables. For instance, the max-
imum number of initial rays is 80, the maximum number of points in the
SSP is 100, the maximum number of bottom loss domains is five and the
maximum number of bathymetry points is 62. The source an receiver were
placed lm above the floor; other wise, negative initial rays would have been
deleted immediately. All of the individual input files contained exactly the
same information on the source position, SSP, initial rays, turning points
and bottom reflection data. The source and receiver were always placed lm
above the sea floor.
A 15 December 1987 sound speed profile (Figure 4.3), generated by a
computer system called ICAPS [39], was used for both SSP curves in each
individual file. The ICAPS-generated sound speed profiles for an approx-
imate source position (36°21'N, 122°18'W) and a general receiver position
in the bay (36°50'N, 121°51'W) were identical down to a depth of 360 m.
which was the cutoff for the receiver area SSP. The MPP computer rou-
tines triangularize all sectors between two inputted sound speed profiles if
the SSPs do not begin at the same maximum depth, which complicates the
ray tracing calculations and requires much longer processing time. Since it
was advantageous to have rectangular sectors for the SSP region, the deeper
ICAPS SSP (source location) was specified for both the source location and
for spot about 2 km beyond the receiver location. This did put the profile
through the sea and shelf floor in all areas. The exact values used for the
sound speed profile in the MPP computer simulation are specified in Table
4.2. each receiver location's input file contained the following parameters
with associated valued:
96
1. source depth = 831.1 m and source range = 00 km;
2. minimum and maximum angles allowed in eigenray search = -15. 0 to
-10.0,-10.0 to -5.0,-5.0 to 0.0 to 5.0,5.0 to 10.0 and 10.0 to 15.0 degrees
(six separate computer runs);
3. minimum and maximum angles allowed in eigenray search = 31;
4. maximum number of passes allowed for ray search = 100;
5. total number of turning points or reflections allowed = 350;
6. maximum number of bottom reflections =100;
7. number of loss domains = 1; and
8. bottom loss at angles of 0 and 90 degrees = 0.0 dB.
This data facilitated a "best case" simulation in which there was no
bottom loss when rays bounced off the sea floor and canyon walls (total
reflectivity), while allowing for a large number of surface and bottom reflec-
tions.
The range value for each receiver was determined by a computer program
that used the longitude and latitude of both source and receiver positions
to determine the range and bearing from source to receiver. This program
included a correction for search curvature. Table 4.1 gives the range and
depth for all 17 locations.
Bathymetry values along a straight line from source to receiver were
manually extracted from a NOAA ocean bottom contours chart [40]. The
selected depths were generally contour rings of some multiple of 100 fath-
oms. Every once in a while a significant reading (based on the author's
subjectivity) that wasn't a contour ring was included in the bathymetry
data to provide a more relevant and accurate bottom profile. The maxi-
mum number of bathymetric points that could be entered per input file was
62, but none of the files contained more than 50 points. The distance of each
bathymetric point from the source location was calculated by using linear
interpolation between source and receiver positions. All points beyond the
receiver were considered to be at the same depth as the receiver location
for this simulation. The program appeared to prefer this little idiosyncrasy,
but the eigenray results were not affected. The bathymetric data for all 17
receiver hydrophone sites are provided in Appendix A.l.
97
I I
1460 1470 1460 1400 1500
SOUND SPEED (M)
1510
1520
1530
Figure 4.3: Typical December sound speed profile for Monterey Bay.
98
DEPTH (m)
SOUND SPEED
(m's)
DEPTH (m)
SOUND SPEED
(m's)
0.
1509.46
321.
1487.08
16.
1509.40
327.
1486.41
43.
1509.85
357.
1485.00
58.
1500.48
390.
1485.18
65.
1497.5S
43S.
1484.04
68.
1496.60
451.
1483.47
S2.
1494.S2
475.
1483.49
95.
1492.64
600.
14S2.32
116.
1490.60
800.
14S1.S9
12S.
14S9.7S
1000.
14S2.54
150.
14S9.91
1200.
1483.73
169.
1489.18
1500.
1486.26
230.
14S9.26
2000.
1491.44
273.
14S7.77
2500.
1498.67
2S7.
14S8.01
3000.
1506.65
291.
1487.32
3290.
1511.51
303.
1487.53
Table 4.2: December sound speed profile values for Monterey Bay region.
99
Output
More that 100 computer runs were performed to determine possible eigen-
rays with associated travel time and transmission loss for the December
tomography experiment. In a majority of these runs, no eigenrays were
identified. This Monterey Bay experimental region is a particularly tough
area to conduct a tomography experiment due to the wide fluctuations in
the sea floor. The MPP program would drop a ray if it ever exceeded a ±85
deg angle anywhere along its path. Most of the time when a ray hit one of
the steep canyon walls, the ray would bounce off at greater than 85. A few
of the rays exceeded the maximum number of turning points or reflections
that was stipulated in the input file, and thus were dropped along the way
of the ray search.
The MPP program identified rays that either bracketted the receiver
or were within the diffraction field. The bracketing rays were shown to
arrive at the receiver, and will be considered eigenrays. The diffraction field
rays passed through the receiver's focus or convergence zone, but did not
necessarily arrive at the receiver. For this simulation, the maximum vertical
distance that a ray could miss the receiver was stipulated at ±15 m. Of the
58 rays that the program identified, 17 diffraction field rays were outside
of the vertical miss tolerance. These 17 rays are not considered eigenrays
and have been eliminated from post-program analysis. Twenty-six of the
remaining 41 rays arrived at location 17.
Nine locations had no rays arriving at the receiver. These were sites
3, 6, 9, 10, 11, 12, 14, 15 and 16. Five of these positions are in the area
of Soquel Canyon, one was near the head of Monterey Canyon, another
(receiver 14) was at a position selected for its difficult ray path due to the
winding canyon, the seventh was off of Point Pinos in a shallow area, and
the last was in the shallow nearshore area of Santa Cruz. The results for the
other eight receiver spots will be outlined and a table of all eigenrays with
initial angle, arrival angle, travel time and transmission loss will follow the
output discussion.
An interesting result occurred for receiver location 16 when the source
was positioned down the slope in front of the seamount at the 9130 m depth
(which changed the range to 64.0 km), instead of on the top of the seamount
where the source was placed for all of the other simulations. Four eigenrays
in the 0 to -5 range now arrived at receiver 16 when before all rays were
lost. On top of the seamount these initial rays bounced off of the seamount
immediately and were driven upward, eventually to be lost by exceeding
100
TRAVEL TIME
(sec)
INITIAL ANGLE
(degrees)
ARRIVAL
ANGLE
(degrees)
TRANSMISSION
LOSS (dB)
47.0753
-2.8463
-32.0741
93.6
47.4651
-2.9378
-54.3062
94.1
47.4652
-4.6413
-54.3904
94.2
47.4872
-2.9774
55.7486
94.1
Table 4.3: Eigenray information for site 16 based on change of source place-
ment.
the 85 deg angle. However, on the side of the seamount they continued at
downward trace until they refracted up (did not hit the bottom). Table 4.3
provides data on these four eigenrays. For the simulation, the source was
placed on the top of the mount because the author felt that in the actual
experiment, it would be easier to moor the source on the top rather than
at some particular point on the slope of the seamount. This is just one
indication that the eigenray arrivals are very sensitive to both source and
receiver placement.
Because a 16 Hz bandwidth pseudo-random phase-encoded signal of
1.9375 s duration is planned to be used in the December experiment, a
separation of ray arrivals by 1/16 Hz (62.5 ms) is necessary for resolving
those arrivals [5]. Also, the entire bundle of eigenrays must arrive at the
receiver with a total separation time of under 1.9375 s. The description of
the output is based on this requirement.
Receiver Location 1. Receiver 1 was southwest of Santa Cruz on the
continental slope not. far from the canyon edge. Eigenrays would have to
travel along a path that brings them over the deepest but widest part of
Monterey Canyon in this experimental area. Two eigenrays at initial an-
RCVR
TRAVEL
TIME
(sec)
RAY SEPA-
RATION
(sec)
INITIAL
ANGLE
(degrees)
ARRIVAL
ANGLE
(degrees)
TRANS-
MISSION
LOSS (dB)
1
40.0920
40.0920
2.0837
20.1333
98.1
40.1353
0.0433
-3.9048
23.5287
95.9
2
39.3994
39.3994
-14.8056
-17.1602
95.9
4
45.7964
45.7964
-9.5632
-51.3754
95.6
45.9304
0.1340
-5.9567
-28.2386
84.8
45.9312
o.ooos
-5.9841
40.3657
83.5
5
43.4764
43.4764
6.4800
56.6509
97.7
7
28.6596
28.6596
3.6113
41.5440
92.1
28.7173
0.0577
1.7916
6.2005
79.0
29.2176
0.5003
1.7497
55.4856
S9.6
29.2177
0.0001
1.5429
55.105S
90.5
8
49.7370
49.7370
6.4S25
-34.7151
106.0
49.S610
0.1240
6.4969
-39.4762
105.7
49.8610
0.0000
6.4969
-39.5973
105.7
13
39.6526
39.6526
-13.6680
-33.1896
83.7
Table 4.4: Eigenray information for sites 1,2,4,5,7,8 and 13.
gles of 2.0837 and -3.9018 deg were identified (Table 4.4). These two rays
have a fairly clean ray path. After leaving the seamount with one possible
bounce, the rays travel along the sound channel axis track until they hit
the north wall of the Monterey Canyon through at around 31 and 39 km
downrange. They then bounce up and have a turning point refraction before
again bouncing off of the now gentler slope at around the 52.0 km mark.
Either three or four bottom reflections occur before each ray arrives at the
receiver. These ray experience very few bottom bounces that could absorb
some of the sound or change the direction of the rays.
The separation time between the 2.0837 and -3.9048 deg ray is not good
at 43ms. This spacing is below the experiment's separation minimum for
identifying the individual rays. The transmission loss values for both rays
10-2
are in the upper 90 dB. The ray trace and the transmission loss profile
graphs for these rays can be found in Appendix A. 2.
Receiver Location 2. East-southeast of receiver 1 is the site for receiver
2. The simulated hydrophone is placed on a gentle slope a little north of
the main Monterey Canyon wall. Rays arriving at this receiver would travel
across a wide and deep portion of the canyon, similar to the receiver 1 rays.
The north wall rises until at about 39 km downrange of the source, there is
a drop of the sea floor for about 6 km before rising steeply again up to the
continental shelf.
One eigenray was identified by the simulation with a 96 dB transmission
loss. The -14.8056 deg ray initially bounces off of the seamount and refracts
before striking the north wall close to 28 km away from the seamount. It
then reflects off the surface and bounces in the dropped floor of the north
wall before surface reflecting and bouncing its way on the shelf, prior to
arriving at the receiver. It bounces off of the continental shelf six times.
Information on this ray is found in Table 4.4, and the graphs for the ray
trace and transmission loss are located in Appendix A. 2.
Receiver Location 4. Receiver 4 is due west of Moss Landing, situated
on the Monterey Canyon north wall edge. Rays arriving at this location will
pass over Carmel Canyon and the continental shelf before crossing Mon-
terey Canyon. This position is above the narrower and shallower portion of
Monterey Canyon, so it may be a good location for an internal waves study.
Three eigenrays were identified, having transmission losses between 83.5
dB and 95.6 dB, and with good arrival separation between the first two
rays (Table 4.4). A graphical depiction of the ray paths can be found in
Appendix A. 2, along with the transmission loss graph. The arrival time
separation between the last two rays (-5.9567 and -5.9841) of 0.8 ms is too
short for the conditions of the experiment. The ray with the initial angle of
-9.5632 arrives first and is followed in 134ms by ray -5.9567.
The three eigenrays have the same general ray path. Ray - 9.5632 has
one refractive turning point, while the other two rays display one cycle of
refraction (two turning points). All of the rays have a multitude of surface
and bottom bounces as they proceed along the shelf, and they bounce twice
in Monterey Canyon with one refraction between the bounces. Ray -9.5632
has three surface reflections at the end of its path, and the other two rays
have two surface bounces. All of the rays have paths that could be used in
both the internal wave and surface wave studies.
103
Receiver Location 5. Situated on the south edge of the Monterey Canyon,
due west of the Salinas River mouth, is the location for receiver 5. It was
selected to give the tomography experiment a means by which to possi-
bly recognize the effects that traveling through the Monterey Canyon head
would have on an eigenray, such as internal waves or internal bores. The
unfortunate aspect of this location is that the rays have to travel over 16 km
of shallow shelf, which manifests itself in possibly a hundred or more surface
and bottom reflections. The ray trace graph in Appendix B illustrates this
oscillation. Transmission loss plot follows the ray trace. Table 4.4 contains
tabularized data on the two eigenrays.
Ray 6.4800 refracts once on either side of reflecting off the bottom, then
hits high on the side of the Carmel Canyon east wall, before oscillating its
way along the continental shelf. The shelf is sandy, so there will be come
absorption and not the total reflectivity that was simulated. Simulated
transmission loss for the ray is 97.7 dB, but parameters for bottom loss
were not included in the computer input because of the great variation in
the sediment and geology along any one path. It should be expected that
the real world case would have a larger dB loss.
Receiver Location 7. The shallow nearshore region just off of Asilomar
Beach in Pacific Grove is the location for receiver 7. This is the closet posi-
tion to the source-moored seamount in this simulation. The rays pass per-
pendicularly over the Carmel Canyon axis and the wider Monterey Canyon
trough, but a straight path from source to receiver stays clear of the nar-
rower portion of the winding canyon. Since the receiver site is situated on
the shelf at approximately 3 km from the edge of the Carmel Canyon, most
of the rays oscillate between the surface and shelf bottom before completing
the trek to the receiver.
Four eigenrays were identified by the simulation process. Specific values
for these rays are given in Table 4.4. Ray trace and transmission loss graphs
are found in Appendix A. 2. Rays 1.5429 and 1.7497 appear to travel together
because their paths are almost identical and there is only a 01 ms timespan
between them. These two rays refract prior to bouncing off the trough wall
just before the 31 km range. They then reflect off the surface and hit the
Carmel Canyon wall twice before oscillating on the continental shelf.
The first eigenray to arrive at 28.6596 s is the 3.6113 deg initial angle
ray. It first refracts before reflecting off the sea floor, hitting the wall above
the Carmel Canyon, and oscillating along the shelf. It was a slightly weaker
signal at 92 dB loss than the 2-ray pair. Arriving 57.7 ms later but a full
104
1/2 second before the ray pair is initial ray 1.7916. This ray refracts once
before bouncing off of the trough wall, reflecting off the surface, reflecting off
Carmel Canyon west wall, and then refracting and bottom reflecting along
the shelf. Of all the eigenrays identified in this simulation, ray 1.7916 was
the strongest with only a 79 dB loss.
Receiver Location 8. Receiver 8 is positioned due west of the mouth of
the Pajaro River. Rays traveling from the source location to this receiver
would follow nearly the same horizontal path as do the eigenrays to receiver
4, except that site 8 is situated a little further behind location 4 on the
continental shelf. Eigenrays have to pass over Carmel Canyon, not far from
the Monterey Canyon junction, and over the continental shelf before crossing
Monterey Canyon just a little downslope from its head.
The MPP program determined that three eigenrays would be picked up
by receiver 8; however, two of these rays are almost identical. These two
rays (initial angle of 6.4969 deg) will be treated as though they were just
one ray for the rest of the discussion. A comparison of the eigenrays may be
found in Table 4.4 while graphs of the ray trace and transmission loss are
located in Appendix A. 2. Ray 6.4825 makes two refracted-bottom reflected
(RBR) cycles, with bounces at 22.0 nm and 40.5nm, prior to oscillating
on the continental shelf between the surface and shelf floor. This oscillating
portion of the ray path covers 15.5 nm in about 14.2 s. At Monterey Canyon
it bounces off the wall twice, with one refraction within the canyon, before
making 13 surface/bottom reflection cycles just prior to arriving at the hy-
drophone. The other ray (6.4969) follows an almost identical path to ray
6.4825, with its first two bounces at the same location, one refraction within
Monterey Canyon, and the same number of surface and bottom reflections
at the end of its path.
Even though the paths of these two eigenrays are very similar, there
is a good arrival time separation of 124.0 ms between them. Transmission
losses range between 105.7 dB for the slower ray and 106.0 dB for the faster
ray. These rays bounce in an area of Monterey Canyon that should ex-
hibit internal wave effects, plus they have a considerable number of surface
reflections.
Receiver Location 13. The juncture of the Soquel Canyon east wall and
the Monterey Canyon north wall is the location of receiver 13. The straight-
line path from source to receiver is over the section of the Monterey Canyon
that has many winding and meandering turns, and includes the point where
105
Carmel Canyon joins Monterey Canyon. It is not a good prospect for finding
any eigenrays, but fortunately one lone ray, which happened to stay in the
deep sound channel for a long distance after its initial seamount bounce,
was identified by the MPP simulation.
The first time that this ray bounces off any canyon walls is at the 54.79
km mark, not far from the edge of the continental shelf. After hitting the
wall, the ray surface refracts and shelf bounces seven times before it is
picked up by receiver 13. It should be a fairly strong signal at only an 84
dB transmission loss which is received in 39.6526s at an angle of -33.2. The
eigenray data is given in Table 4.4 while the ray trace and dB loss graphs
are in Appendix A. 2.
Receiver Location 17. This last receiver position is located slightly
south of due west of Santa Cruz in the open nearshore shelf area. It was one
of the first sites to be simulated, but the resulting large number of identified
eigenrays oscillating along the continental shelf made a change in receiver
depth a necessity. The rest of the locations were selected based on their
proximity to the canyon edge. The rays which arrive at location 17 travel
about the same course as they would if going to receiver 1, except that they
have longer trek along the shelf.
The ray tracing simulation and eigenray identification at this receiver lo-
cation can be best described as a complete mess. Twenty-six eigenrays were
identified by the MPP program and almost all of them have a tremendous
number of surface reflections and continental shelf bounces before arriving
at the receiver. Needless to say, this would be an extremely complicated
experimental site and probably not a good one for a first time tomography
experiment in these waters.
The ray trace graph in Appendix A. 2 for location 17 only contains a
few representative rays, since graphing all of the rays would annihilate any
possible distinguishing individual lines. All of the stick plots (dB losses) are
on the transmission loss graph following the ray trace graph. Travel time,
transmission loss and arrival angle for each ray are listed in Table 4.5.
The entire package of rays can be categorized in just a few groups. Eight
rays follow an almost identical path of two refractions before bouncing off
of the steep slope above the Monterey Canyon, from a downward approach
at a depth of 780 m and a range of around 44.6 km from the source. They
continue bouncing up the slope and onto the shelf with one or two refractions
and the rest surface reflections. These rays start at angles of-1.6163, -2.0828,
-3.0111, -3.0509, -3.1028.-3.1411, -3.1431 and -3.2418. Rays of -3.6277 and
106
TRAVEL
TIME (sec)
RAY SEPA-
RATION
(sec)
INITIAL
ANGLE
(degrees)
ARRIVAL
ANGLE
(degrees)
TRANS-
MISSION
LOSS (dB)
45.4324
45.4324
-1.1110
5.4710
110.6
45.4508
0.0184
0.3232
-4.6675
100.9
45.5656
0.1148
-3.0111
-19.9961
104.4
45.5825
0.0169
-4.5475
-19.6807
97.7
45.6019
0.0194
-3.9658
-20.3254
91.1
45.6364
0.0345
-3.2418
-23.1483
93.2
45.6641
0.0277
-8.6415
-23.5988
90.5
45.6641
0.0000
-8.7093
-23.5525
S9.5
45.6645
0.0004
4.0027
24.7201
91.1
45.6647
0.0002
-8.7180
24.7281
90.3
45.6656
0.0009
-3.1411
-24.1419
99.6
45.6656
0.0000
-1.6163
-24.1725
99.4
45.6656
0.0000
-3.1431
-24.5613
99.8
45.693S
0.0282
-3.1028
-25.6257
100.8
45.6960
0.0022
-5.3708
-25.7395
100.6
45.72?"
0.0277
-3.0509
27.845S
98.4
45.7567
0.0330
-2.0828
-28.2343
93. S
46.0462
0.2S95
2.1406
39.3321
96.5
46.0939
0.0477
-3.6277
-39.6695
97.0
46.3275
0.2336
-12.5001
-44.7474
93. S
46.9973
0.669S
-6.4559
-60.2335
99.5
47.0004
0.0031
1.7248
-60.4129
99.8
47.0019
0.0015
-6.4516
61.2411
99.6
47.4270
0.4251
-6.39SS
69.1542
100.2
47.4272
0.0002
1.6711
69.1952
100.4
47.6187
0.1915
-6.3534
72.1043
101.5
Table 4.5: Eigenray information for site 17.
1U"
-5.3708 deg are very similar to the first eight with the exceptions that they
bounce off the slope at just a slightly longer range and a few meters more
shallow, and the -5.3708 ray hits at an upward angle. An 11th ray at -4.5475
refracts three times before hitting the slope at about the same spot of the
first group of eight, following the path of the above 10 rays up the slope
with the exception that this ray has three more refractions.
Another set of seven rays (1.6711, 1.7248, 2.1406, -6.3534, -6.3988, -
6-4516 and -6.4559) are very similar to the first group of eight, with two
refractions before bouncing up the slope. The three main differences are
that this second set reflect off the wall at a spot with a slightly shorter
range and lower depth (41.3 km and 950 m), the rays are heading upward
just before their first wall bounce, and that they have many more oscillations
on the shelf than does the first group. With the abundance of reflections,
it is understandable why this group as a whole has the slowest arrival times
to the receiver.
Ray -39658 has two refractions before striking the sloping wall at a
depth of 860m and a range of 42.9 km. It then bounces up the slope with
three refractions and 14 surface reflections. The last three individual and
one group of four rays are different from the preceding 19 rays.
The rays -8.6415, -8.7093, -8.7180 and 4.0027 are grouped together due
to their parallel paths and they arrive as a group in a span of 0.6 ms. These
rays make one refractive turn before colliding with a lower north canyon
wall point at a depth of 1410 m and a range of 32.85 km from the source
on the seamount. They next hit the upper slope at the 53.8 km mark and
300 m depth after one refraction. One more refractive turn remains for this
group prior to 17 surface and bottom oscillations along the shelf.
The last three rays are individuals. The fastest eigenray originates at
an angle of -1.1110 deg, reaches receiver 17 in 45.4324 s, but has the largest
transmission loss at 110. 6 dB. This ray has two refractive turns before strik-
ing the slope at 45.67 km downrange and 734 m deep. It refracts and then
bounces off the shelf area (178 m deep) at a distance of 56.64 km from the
source. It makes three more refracted-bottom reflected (RBR) cycles and
one surface reflection before arriving at its destination. Ray 0.3232 arrives
18.4 ms later and has a somewhat similar path. It has three refractions
prior to colliding with the wall 44.48 km away at a depth of 788 m. The
second bounce occurs at the 59.4 km mark on the shelf in 124m of water.
Seven RBR cycles and one surface reflection complete this ray's path. It
takes another 114.8 ms of time before the third fastest ray (-3.0111) arrives
on the scene.
108
The very last ray to be described should be easily identified in an exper-
imental situation. Arriving at the 46.3275 s time mark, ray -12.5001 follows
the next faster ray by 233.6 ms and is followed by another ray 669.8 ms
later. This is the best separation for the entire 26-ray package. Another in-
teresting fact is that this ray strikes the Monterey Canyon on its south wall
and refracts once in the canyon before one more refraction and a bounce at
50.48km range and 460m depth. It then oscillates along the shallow shelf
with one more refraction but a multitude of surface and bottom reflections.
Looking at the results in Table 4.5, one can begin to understand why
this location would be a bit of a problem in a tomography experiment. The
dB loss ranges from 89.5 dB for ray - 8.7093 to 110.6 dB for the first arriving
ray (-1.1110). There is not enough arrival time separation for most of these
rays, based on 16 Hz bandwidth, except for the following:
1. 114.8 ms between ray 0.3232, arriving at 45.4508 s, and ray - 3.0111;
2. 289.5 ms between ray-2.0828, arriving at 45.7567 s, and ray 2.1406;
3. 233.6 ms between ray-3.6277, arriving at 46.0939 s, and ray- 12.5001;
4. 669.8 ms between ray -12. 5001, arriving at 46.3275 s, and ray - 6.4559;
5. 425.3 ms between ray -6.4516, arriving at 47.0019 s, and ray 1.6711;
and
6. 191.7 ms between ray -6.3988, arriving at 47.4270 s, and ray - 6.3534.
Six adequate arrival time separations with 26 arriving rays does not put this
receiver location on the top of the list for best spots. The condition that
eliminates this location as a recommended receiver site is that the arrival
separation between the first and last eigenray is 2.1863s. The acoustic signal
from the source is of 1.9375s duration, which is the maximum separation
time that will be experimentally allowed for all of the rays arriving at one
location.
4.2 3-D Ray Tracing with HARPO
NOAA'S Hamiltonian Acoustic Ray-tracing Program for the Ocean (HARPO)
is well documented[41]. It has recently been enhanced by Newhall, Lynch,
Chiu, and Daugherty[42]. The program entails a core integration model and
interchangeable models defining distribution of sound speed, current, sea
109
surface, bottom bathymetry, and dispersion relation or Hamiltonian. The
application of HARPO to the Monterey Bay and its canyon centered on
two efforts: IBM conversion of the VAX-originating code from WHOI; and
simulating the complex bathymetry.
4.2.1 Hamiltonian Ray Tracing
Hamiltonian ray tracing requires the sound speed of the ocean to be modeled
as a continuous three-dimensional function. Each raypath is computed by
numerically integrating Hamilton's equations with a different set of initial
conditions. In modeling wave propagation with Hamilton's equations, the
point of view is taken that in a high-frequency limit, waves behave like
particles and travel along rays, according to equations that exactly parallel
those governing changes of position and momentum in mechanical systems.
These ray paths satisfy Fermat's principle, that is, the paths are those for
which the action is stationary for variations in the path. For the wave
equation, one forms a Hamiltonian that gives the dispersion relation for the
wave in question when it is set to zero. Integrating Hamilton's equations
then gives a path which satisfies Fermat's principle.
In Cartesian coordinates, Hamilton's equations take the simple form
. = 1,2,3 (41>
where r is time, H is the Hamiltonian, kt are the wave number components,
and i, are the coordinates of a point on the raypath.
To solve Eq. 4.1 for one of the raypaths, one chooses initial values for the
six quantities x,- and lc, and performs a numerical integration of the system
in Eq. 4.1 of six total differential equations. The integration of Hamilton's
equations is performed using the implicit Adams-Moulton method with a
Runge-Kutta start up. For our case of acoustic waves in the ocean, the
Hamiltonian (which is constant along a ray path) is defined as the dispersion
relation
H{x{, kj) = [u> - k ■ V(xt)]2 - C2{xt)k2 = 0 (4.2)
where V(xt) is the ocean current, C(z,) is the sound speed field, and u> is
the angular wave frequency.
For earth-centered spherical polar coordinates, Hamilton's equations (see
Lighthill) in four dimensions are:
110
dx, _
_ dH
17 -
- w;
dk,
- dH
dr
dx,
dr
dr
=
dH
dkT
(4.3)
de
dr
=
1 dH
r dke
(4.4)
d<f>
dr
=
1 dH
r sin 6 dkj,
(4.5)
dt
dr
=
dH
(4.6)
dkT
17
=
dH ,de , m
—3 — (- ke— + kjsmd—
or dr or
(4.7)
dke
dr
—
I, dH dr , 8<f>,
-r{-oT-kedr- + k*rCOSedT-)
(4.8)
dkt
dr
=
1 i dH ^ flrfr ^
( A:q!)sin6' fc^rcos
rsiny a<p dr
or
(4.9)
d^j
~dl-
=
dH
dt
(4.10)
where r, 8, <fr are the Earth-centered spherical polar coordinates of a point on
the raypath; kr, kg, k$ are the local components of the propagation vector
(a vector whose magnitude
h = y/k? + kl + kl = 2n/\, (4.11)
is the wavenumber. and that points in the wave normal direction) in the r,
6, and d directions; t is the propagation time of the wave packet.
4.2.2 Application
HARPO was used to calculate raypaths in the extreme bathymetry of the
Monterey Bay Canyon. This bathymetry was a focal point of effort in this
application. Sea surface was modeled as a sphere of constant radius; the
current field was set to zero; absorption was calculated as a function of
frequency using a Skretting-Leroy empiricism; a single sound speed profile
based on data from the December '88 Monterey Bay Tomography Experi-
ment (MBTE) was used everywhere. The bottom was defined on a 1 km
by 1 km grid over 122°20' to 121°50'W and 36°23' to 37° N producing a
42 by 65 bathymetric array. The depth values were a result of the union
of the 200 m resolution bathymetry set of Thornton and Burych for north
111
of Pt. Joe and a .5' resolution bathymetric set read from a NOAA depth
chart for south of Pt. Joe. The later was projected on an x,y grid with the
same origin (36°36'N, 122°20'W) and reference location as the Thornton-
Burych data. The two data were then combined using a spine interpolation
routine provided by DISSPLA software. HARPO used this bathymetric
grid to calculate a bi-cubic spline with knots at each grid point. From
the discontinuous behavior of adjacent raypaths, the bottom surface deriva-
tives, as calculated using the splines, were suspected of having an intra-grid
variability analogous to Gibbs phenomena. The bathymetry was modified
using a 1-6-1 filter to remedy this problem. Figure 4.4 shows the resulting
bathymetry.
Raypaths were calculated originating from the location of the transmitter
in for Monterey Bay Tomography Experiment on an underwater knoll at a
depth of 1020.6 m just north of the Pt. Sur area and 35 km off the coast.
Initial azimuth angle was set on a near direct path to receiver J on the shelf
due south of Santa Cruz and 94.2 m in depth. The calculated raypaths were
channeled by the shelf and reflected back into the canyon. As a remedy the
raypaths were then calculated as originating from receiver J on the shelf and
directed toward the transmitter location. Figures 4.5 and 4.6 show a planar
and top view of typical ray paths within Monterey Canyon between Station
J and the transmitter.
A program is available from WHOI that operates in conjunction with
HARPO and calculates eigenrays. This program interpolates launch angles
from previously calculated ray path intersections with receiver depth and
eigenrange (the distance between receiver and transmitter.) The eigenray
program, as it stands, is IBM I/O incompatible and is biased toward direct-
path eigenrays. The Monterey Bay application of HARPO was loaded on
the WHOI VAX 8800 and run with their eigenray program over an ele-
vation range of 27°. No eigenrays were found. At NPS, an effort to use
HARPO alone with a human interpolator proved to be too slow for the
fully three-dimensional Monterey Bay problem. An effort is under way to
develop and/or modify an Gaussian beam/timefront postprocessor for this
application. Future work is likely to be performed on a SUN workstation
which may eliminate the I/O problem.
112
IOSS LANDING
*0
SOURCE
Figure 4.4: A model of the bathymetry of Monterey Bay region.
113
1 MONTEREY BAY CANYON
MODEL = MBJ ,FREQ= 400.000 HZ, AZ =201.054 DEG
EL = 7.20 DEG TO 10.20 DEG, STEP = 1.00 DEG
XMTR HT = -0.09 KM ,LAT - 0.47 DEG, LONG = 0.18 DEG
ACOUSTIC WAVE *** WITH CURRENT *** WITH LOSSES
8
RANGE AT SEA LEVEL (km)
16 24 32 40
48 54
i
a-
Figure 4.5: Planar view of rays calculated from Station J towards the to-
mography transmitter.
11-1
2 REPEAT SAMPLE CASE W/HORIZONTAL PLOT, W/NO PRINT
MODEL = MBJ ,FREQ= 400.000 HZ, AZ =201.054 DEG
EL= 7.20 DEG TO 10.20 DEG, STEP = 1.00 DEG
XMTR HT = -0.09 KM ,LAT = 0.47 DEG, LONG = 0.18 DEG
ACOUSTIC WAVE *** WITH CURRENT *** WITH LOSSES
4
1
H 0
* _£
o
CQ
CQ
2 -3
-4
10 20 30 40
0.18 DEG E. RANGE AT SEA LEVEL (km)
0.00 DEG N.
50
0.00 DEG E.
0.01 DEG N.
Figure 4.6: Top view of rays calculated from Station J towards the tomog-
raphy transmitter.
115
Chapter 5
Conclusions
All results to date have shown that acoustic tomography is a viable technique
for monitoring the circulation of Monterey Bay:
1. Acoustic arrivals were received in the 1988 Monterey Bay Tomography
Experiment that were strong enough to observe the fluctuations due
to surface waves, internal waves, and tides. Lengthening the code in
the future tomography system would provide enough signal-to-noise
ratio for ocean current tomography. Limitations to the code length
due to surface wave-induced Doppler are under study.
2. The acoustic arrivals were mostly resolved for the 16 Hz bandwidth
signal. It is foreseen that a future tomography system in the Bay
would use a much larger bandwidth signal, e.g. 100 Hz. Even with the
shorter distances involved with the proposed tomography array in the
Bay, this larger bandwidth signal would eliminate the small number
of resolution difficulties observed.
3. Stable acoustic arrivals were observed for the entire 4 day experiment
through several tidal cycles for cross-canyon paths. This experimen-
tal result was the most important for demonstrating the viability of
tomography in the Bay.
4. The identification of the multipath arrivals measured in the experi-
ment was attempted with the MPP 2-D and HARPO 3-D ray tracing
programs. MPP found some eigenrays (rays connecting source and
receiver) while HARPO did not find any eigenrays because of the dif-
ficulty in modeling the effect of the extreme bathymetry of the Bay
116
on acoustic propagation. The lack is not in the existence of stable,
resolvable arrivals but in our ability to model them correctly. These
eigenrays exist because the experiment measured them. In the next
few months, as part of another feasibility study for the Norwegian-
Barents Sea Tomography Experiment, HARPO capabilities will be
increased with the addition of Gaussian beam and time front post-
processing routines. These routines will eliminate the need for model-
ing eigenrays and should be able to identify the arrivals measured in
the Monterey Bay Experiment.
11
Appendix A
MPP Data
A.l Bathymetry Data for Receiver Locations
118
RECEIVER LOCATION
1
RECEIVER LOCATION
2
RECEIVER LOCATION
3
Range (km)
Depth (in)
Range (kin)
Depth (in)
Range (km)
Depth (m)
0.0
832.10
0.0
832.16
0.0
832. i6
3.26
826.62
1.09
914.40
0.76
914.40
4.07
914.40
3.75
914.40
4.07
1097.28
7.06
1463.04
6.16
1280.16
5.75
1280.16
17.37
1463.04
6.74
1463.04
6.64
1463.04
18.57
1645.92
9.96
1463.04
7.32
1463.04
21.53
2560.32
12.71
1280.16
12.14
1280.16
21.89
2560.32
14.67
1280.16
15.54
1280.16
23.07
2377.44
17.17
1463.04
18.80
1463.04
24.61
2194.56
19.56
1828.80
20.39
1828.80
25.65
2011.68
21.01
2194.56
22.36
1828.80
27.25
1828.80
21.51
2377.44
23.80
2011.68
27.69
1645.92
23.85
2377.44
27.65
2011.68
30.07
1463.04
25.75
1828.80
29.46
2194.56
35.29
1280.16
26.51
1645.92
30.54
2011.68
37.51
1097.28
29.74
1463.04
32.71
1828.80
40.31
914.40
33.32
1280.16
35.02
2011.68
44.11
731.52
36.07
1097.28
39.31
1828.80
46.68
548.64
37.30
1047.90
39.96
1645.92
51.84
365.76
38.03
1097.28
41.53
1463.04
55.55
182.88
39.60
958.29
42.47
1645.92
59.35
98.76
40.47
1097.28
43.10
1828.80
70.50
98.76
41.01
1280.16
43.43
1828.80
45.41
1280.16
44.10
1463.04
45.99
1325.88
45.65
1097.28
46.45
1280.16
46.95
731.52
47.42
1097.28
48.52
731.52
48.53
731.52
49.52
1097.28
50.34
365.76
50.29
1097.28
51.72
182.88
50.96
914.40
54.87
106.07
51.78
806.50
57.99
91.44
53.00
914.40
70.50
91.44
53.40
54.35
55.30
57.06
61.26
62.89
63.87
70.50
1005.84
914.40
731.52
548.64
365.76
182.88
91.44
91.44
Table A.l: Bathymetry data for receiver locations 1, 2, and 3.
119
RECEIVER LOCATION
4
RECEIVER LOCATION
5
RECEIVER LOCATION
6
Range (km) Depth (in)
Range (km) Depth (m)
Range (km) Depth (m)
0.
0
832.
10
0.
0
832.
10
0.
0
832.
10
0.
54
914.
40
0.
60
914.
40
0.
60
914.
40
3.
30
1097.
28
2.
89
1097.
28
2.
35
1097.
28
5.
19
1280.
16
4.
76
1280.
16
4.
33
1280.
16
6
38
1351.
48
6.
60
1351.
48
6.
76
1351.
48
10
33
1280.
16
10.
01
1280.
16
9.
52
1280.
16
14
25
1252.
73
15.
83
1280.
16
11
85
1126.
54
16
05
1280
16
16.
73
1463.
04
16
34
1280
16
17
04
1463
04
19
16
1463
04
17
14
1463
04
23
54
1463
04
20
57
1280
16
17
68
1556
31
24
67
1645
92
23
06
1280
16
18
40
1463
04
25
61
1828
80
25
98
1828
80
19
54
1280
16
26
24
1828
80
26
74
1828
80
24
41
1280
16
27
78
1463
04
29
28
1280
16
25
80
1645
92
28
73
1280
16
29
91
1097
28
26
65
1645
92
32
33
1280
16
31
83
1097
.28
28
50
1463
04
33
73
1097
28
32
48
914
.40
29
.66
1280
16
35
22
1097
28
34
28
914
.40
30
.17
1280
16
35
71
1280
16
34
75
1097
.28
31
.39
914
40
36
79
1280
16
36
67
1097
.28
33
.77
914
40
38
24
731
52
38
.65
365
.76
34
.31
1097
28
39
68
548
64
39
.62
182
.88
34
.58
1097
28
40
26
365
76
44
.79
107
.90
35
.45
731
52
43
56
182
88
54
.78
91
.44
37
.23
548
64
46
89
118
87
70
.50
91
.44
38
.06
182
88
52
70
104
24
41
.40
91
44
56
.33
182
88
70
.50
91
.44
57
.46
365
76
58
.33
548
64
58
.80
548
64
61
.63
365
76
62
.63
182
88
63
.49
91
.44
70
.50
91
.44
Table A. 2: Bathymetry data for receiver locations 4, 5, and 6.
120
RECEIVER LOCATION
7
RECEIVER LOCATION
8
RECEIVER LOCATION
9
Range (km) Depth (m)
Range (km) Depth (m)
Range (km) Depth (m)
0
.0
824
79
1
.21
1097
28
14
.24
1097
28
18
.97
1280
16
21
.55
1097
28
24
.72
1097
28
26
.38
1280
16
27
67
1645
92
29
34
1463
04
31
11
914
40
32
72
731
52
33
26
731
52
34
01
914
40
34
39
914
40
35
79
548
64
37
13
365
76
37
99
182
88
39
12
91
44
39.
98
73.
15
40.
84
73.
15
41.
91
54.
86
42.
02
51.
21
45.
0
51.
21
0.
0
825.
0.
37
915.
1.
73
1097.
6.
35
1251.
7.
75
1280.
8.
18
1280.
13.
56
1127.
17.
65
1280.
18.
46
1463.
18.
90
1556.
20.
26
1463.
21.
27
1280.
24.
68
1280.
25.
55
1463.
26.
44
1646.
27.
32
1829.
27
91
1829.
28
57
1646.
29
05
1562.
29
39
1463.
30
35
1280.
31
31
1097.
32
19
1097.
33
82
1097.
35
00
915.
35
82
940.
36
18
1097.
36
60
1280.
37
91
1280.
38
57
1097.
38
95
915.
39
28
732.
41
.06
366.
42
.17
229.
44
.56
183.
48
.07
119.
53
.61
104.
56
.41
99.
56
.98
183.
57
.90
366.
59
.08
549.
59
.67
549.
62
.40
366.
63
.06
183.
63
.63
91.
64
.48
75.
67
.33
73.
67
.49
55.
0.
0
824.
79
1.
61
1097.
28
2.
26
1280.
16
17.
30
1280.
16
20.
04
1645.
92
21.
22
1645.
92
22.
62
1463.
04
24.
28
1463.
04
26.
00
1828.
80
27.
29
1828.
80
28.
63
1463.
04
30.
08
1463.
04
30
73
1645.
92
32
39
1645
92
36
21
1463
04
37
07
1280
16
37
.82
1280
16
39
.22
1645
92
40
.45
1645
.92
41
.79
1097
.28
43
.62
1097
.28
45
.18
1645
.92
45
.80
1645
.92
47
.11
1097
.28
48
.17
1097
.28
49
.15
1280
.16
50
.07
1280
.16
52
.29
731
.52
55
.01
731
.52
57
.96
182
.88
59
.41
91
.44
64
.57
73
.15
66
.72
54
.86
67
.15
49
.38
70
.15
49
.38
Table A. 3: Bathymetry data for receiver locations 7, 8, and 9.
121
RECEIVER LOCATION
RECEIVER LOCATION
RECEIVER LOCATION
10
11
12
Range (km)
Depth (m)
Range (km)
Depth (ni)
Range (km)
Depth (m)
0.0
824.79
0.0
832.10
0.0
832.10
1.84
1097.28
0.81
914.40
0.81
914.40
2.43
1280.16
2.81
914.40
2.81
914.40
18.20
1280.16
5.95
1280.16
5.85
1280.16
21.01
1463.04
6.60
1463.04
6.60
1463.04
22.43
1828.80
7.17
1463.04
7.17
1463.04
24.05
1645.92
12.31
1280.16
12.31
1280.16
24.88
1645.92
15.01
1280.16
15.26
1280.16
26.25
2011.68
17.96
1463.04
18.22
1463.04
26.61
2011.68
20.83
2011.68
20.89
2011.68
27.47
1828.80
22.50
2011.68
23.22
2011.68
29.84
1828.80
23.31
2194.56
24.36
2194.56
30.67
2011.68
23.94
2194.56
35.18
2194.56
32.43
2011.68
24.48
2377.44
36.05
2011.68
33.59
1828.80
26.07
2377.44
39.84
2011.68
41.64
1828.80
31.37
2194.56
41.00
1828.80
42.84
1645.92
33.08
2194.56
41.86
1775.76
44.73
1645.92
33.75
2011.68
42.35
1828.80
45.34
1828.80
34.75
1828.80
42.97
1828.80
45.72
1828.80
39.22
1828.80
44.11
1463.04
46.47
1463.04
39.76
2011.68
46.14
1097.28
48.15
1097.28
40.57
2011.68
46.44
914.40
49.42
731.52
41.16
1828.80
47.22
731.52
51.11
731.52
42.84
1828.80
49.31
731.52
52.23
1097.28
44.63
1463.04
50.77
1097.28
52.95
1097.28
45.26
1463.04
51.74
1097.28
53.83
914.40
46.30
1097.28
52.86
914.40
56.26
914.40
47.92
731.52
53.91
731.52
57.64
548.64
49.22
731.52
54.85
548.64
60.56
548.64
50.36
548.64
56.02
365.76
61.50
365.76
53.37
548.64
57.19
182.88
62.16
182.88
54.81
365.76
59.72
91.44
66.63
91.44
55.28
182.88
70.50
91.44
67.18
73.15
56.04
91.44
67.84
54.86
70.50
91.44
68.39
45.72
71.39
45.72
Table A.4: Bathymetry data for receiver locations 10, 11, and 12.
122
RECEIVER LOCATION
RECEIVER LOCATION
RECEIVER LOCATION
13
14
15
Range (km)
Depth (m)
Range (km)
Depth (m)
Range (km)
Depth (m)
0.0
832.10
0.0
832.10
0.0
832.10
0.87
914.40
0.59
914.40
0.54
914.40
3.90
1097.28
3.25
1097.28
2.29
1097.28
5.69
1280.16
5.30
1280.16
4.43
1280.16
6.68
1463.04
6.36
1351.48
6.48
1351.48
7.32
1463.04
10.60
1280.16
9.90
1280.16
11.60
1280.16
13.93
1252.73
11.82
1126.54
16.15
1280.16
16.05
1280.16
15.79
1280.16
19.10
1463.04
17.67
1463.04
16.87
1463.04
19.87
1645.92
18.80
1645.92
18.90
1463.04
20.32
1828.80
19.83
1645.92
19.87
1280.16
20.77
1828.80
21.15
1463.04
23.49
1280.16
21.89
1645.92
21.91
1431.95
25.27
1645.92
23.03
1645.92
23.04
1463.04
27.75
1645.92
23.71
1828.80
24.99
1828.80
28.98
1463.04
24.39
2011.68
26.14
1828.80
29.80
1280.16
24.66
2011.68
27.26
1463.04
30.18
1097.28
25.36
1828.80
28.23
1404.52
31.75
914.40
26.66
1645.92
29.48
1463.04
32.88
731.52
27.31
1645.92
32.05
1463.04
33.20
691.29
28.51
1828.80
34.26
1280.16
33.65
731.52
29.13
2011.68
34.94
1097.28
34.61
1097.28
30.08
2011.68
35.88
1097.28
34.96
1097.28
30.35
1828.80
36.29
1463.04
36.77
914.40
32.25
1645.92
37.00
1463.04
38.51
365.76
38.80
1645.92
37.64
1280.16
39.20
182.88
39.13
1728.22
39.30
1097.28
42.06
102.41
39.62
1645.92
40.13
731.52
53.51
91.44
39.89
1463.04
42.05
548.64
61.87
91.44
40.92
1280.16
42.73
429.77
62.99
182.88
42.14
1280.16
43.45
548.64
63.82
182.88
43.63
1828.80
44.71
731.52
64.36
91.44
43.84
1907.44
47.73
731.52
70.50
91.44
44.03
1828.80
48.52
548.64
44.87
1280.16
49.87
365.76
46.34
914.40
52.03
182.88
46.79
914.40
53.98
182.88
4 8.23
1097.28
55.53
365.76
49.05
1280.16
56.66
548.64
49.32
1280.16
58.47
548.64
51.43
731.52
59.55
182.88
53.19
731.52
60.36
91.44
53.47
914.40
70.50
91.44
54.47
548.64
56.63
182.88
58.53
91.44
70.50
91.44
Table A. 5: Bathymetry data for receiver locations 13, 14, and 15.
123
RECEIVER LOCATION 16
RECEIVER LOCATION 17
Range (km)
Depth (in)
Range (km)
Depth (in)
0.0
825.
0.0
824.79
8.4
1463.
6.60
1097.28
9.0
1463.
8.00
1280.16
14.1
1280.
8.59
1463.04
16.6
1280.
11.65
1463.04
24.2
2378.
14.63
1280.16
25.8
2378.
16.37
1280.16
41.2
958.
19.05
1463.04
42.4
1280.
20.13
1645.92
47.8
1280.
20.93
1828.80
53.5
139.
21.58
2011.68
66.2
46.
22.22
2194.56
70.0
46.
22.87
2377.44
24.90
2377.44
25.76
2194.56
27.80
2011.68
28.82
1828.80
29.68
1645.92
31.40
1463.04
36.39
1280.16
39.24
1097.28
41.71
914.40
45.73
731.52
48.68
548.64
52.39
365.76
56.41
182.88
61.14
91.44
64.14
73.15
66.99
54.86
67.47
49.93
70.47
49.93
Table A. 6: Bathymetry data for receiver locations 16 and 17.
121
A.2 MPP Ray Traces and Stick Plots
125
RECEIVER LOCATION 1: RAY TRACE
15.0
22.5 30.0 37.5
RANGE (KM)
Figure A.l: Ray trace for receiver location 1.
26
RECEIVER LOCATION 1: STICK PLOT
r-
O"
IT)
m a
o °>
►J
2°
CO
TRANSM
3 87 9
CD
0)
to
r-
i r r 1
i i
i i T "
40.00 40.02 40.04 40.06 40.08 40.10 40.12
ARRIVAL TIME (SEC)
40.14 40.16 40.18 40.20
Figure A. 2: Stick plot for receiver location 1.
12-
RECEIVER LOCATION 2: RAY TRACE
0.00
14.50
RANGE (KM)
Figure A. 3: Ray trace for receiver location 2.
128
RECEIVER LOCATION 2: STICK PLOT
c
a2'
m
m o
o °5'
-j
O en'
00
m
co'
en
39.390 39.394
39.390 39.402
ARRIVAL TIME (SEC)
39.406
39.410
Figure A. 4: Stick plot for receiver location 2.
29
RECEIVER LOCATION 4: RAY TRACE
Figure A. 5: Ray trace for receiver location 4.
130
RECEIVER LOCATION 4: STICK PLOT
»o
o
s-
co
CO o>
o °>'
O ©
LO
CO
CO
%*■
n
CD'
09
«o.
45.75 45.77 45.79 45.81 45.83 45.85 45.87 45.89
ARRIVAL TIME (SEC)
45.91
45.93
45.95
Figure A. 6: Stick plot for receiver location 4.
131
RECEIVER LOCATION 5: RAY TRACE
11.4 17.1 22.8 28.5 34.2 39.9
RANGE (KM)
Figure A. 7: Ray trace for receiver location 5.
132
RECEIVER LOCATION 5: STICK PLOT
»fi
o-
S2~
CO o
5 «n
C o>
CO
TRANSM
3 87 9
1
W5_
r-n
i i i i i " '
1 i !
43.470 43.471 43.472 43.473 43.474 43.475 43.476 43.477 43.478 43.479 43.480
ARRIVAL TIME (SEC)
Figure A. 8: Stick plot for receiver location 5.
133
RECEIVER LOCATION 7: RAY TRACE
RANGE (KM)
Figure A. 9: Ray trace for receiver location 7.
13-1
RECEIVER LOCATION 7: STICK PLOT
«o
©
03 <n
s-
m
O ai'
►J
C cj'
GO
CO
GO
< £■
K
H
eo'
28.60 28.67 28.74 28.81 28.88 28.95 29.02
ARRIVAL TIME (SEC)
29.09
29.16 29.23
29.30
Figure A. 10: Stick plot for receiver location 7.
13;
RECEIVER LOCATION 8: RAY TRACE
RANGE (KM)
Figure A. 11: Ray trace for receiver location 8.
136
RECEIVER LOCATION 8: STICK PLOT
tf>
o-
o2"
m
m en
o °>
5 »o
O o
w
CO
1— — ■
TRANSM
3 87 9
1
CO
a
r-n
i
i i i i i i i
i
49.720 49.736 49.752 49.768 49.784 49.800 49.816 49.832 49.848 49.864 49.880
ARRIVAL TIME (SEC)
Figure A. 12: Stick plot for receiver location 8.
13;
RECEIVER LOCATION 13: RAY TRACE
11.8 17.7 23.6 29.5 35.4 41.3
RANGE (KM)
53.1 59.0
Figure A. 13: Ray trace for receiver location 13.
138
RECEIVER LOCATION 13: STICK PLOT
m
o
S-
CO
00 o»
O °
►J
? »fi
O c. '
00
CO
CO
5 6-
C5
39.60 39.61 39.62 39.63 39.64 39.65 39.66 39.67
ARRIVAL TIME (SEC)
39.68 39.69
39.70
Figure A. 14: Stick plot for receiver location 13-
139
RECEIVER LOCATION 17: RAY TRACE
RANGE (KM)
Figure A. 15: Ray trace for receiver location 17.
40
RECEIVER LOCATION 17: STICK PLOT
*n
mat
o-
D2'
CO
CO ai
o °>
O OS
CO
CO
TRANSM
3 87 9
CO
a
r-
M
i
1 i
,
^T"
l i i
i
45.400 45.625 45.850 46.075 46.300 46.525 46.750 46.975 47.200 47.425 47.650
ARRIVAL TIME (SEC)
!
Figure A. 16: Stick plot for receiver location 17
Ml
Appendix B
Chronologic Summary of
Events in the 1988
Monterey Bay Experiment
The following is a summary of the experiment as it happened from the deck
log of R/V Point Sur. All dates and times are in Pacific Standard Time
(PST).
B.l 12 December 1988
0950 R/V Point Sur underway from Moss Landing. Receiver van is in place
on Huckleberry Hill.
1150 Deployed modified AN/SSQ-57 buoy at station B, 36°56.3'N- 122°00.5'\V
1241 Deployed MIUW buoy, station Bl, 36o36.3'N-122o00.2'\V
1705 Deployed transmitter in 870 meters of water 36°23.7'N- 122°17.84'W
2013 CTD measurement 36°23.2'N-122°17.8/W
2204 CTD measurement to 1800 meters 36°31.9'N-122°17.8'W
B.2 13 December 1988
0013 CTD measurement to 155 meters 36o40.4'N-122°04.5'W
142
0105 CTD measurement to 1400 meters 36°40.4'N-122°04.4/W
0230 Lost contact with buoy at station B
0308 CTD measurement to 73 meters 36°48.6'N-122°57.9'W
0357 CTD measurement to 800 meters 36°46.5'N-122°05.6'W
0507 CTD measurement to 800 meters 36°44.7'N-122°13.3'W
0811 Deployed ARGOS wave buoy #6249 at 36°44.3'N-122°13.3'W but re-
covered buoy after no radio signal was received
1033 Deployed modified sonobuoy, station L, 36°52.9'N-122°10.8"VV in 61
fathoms of water
1151 Deployed modified sonobuoy, station J, 36°51.1'N-122o04.8'W in 53
fathoms of water
1157 CTD measurement to 82 meters 36°51.0'N-122°01.5'W
1245 Deployed modified sonobuoy. station I, 36°49.1'N-122°01.5'W in 53
fathoms of water
1339 Deployed modified sonobuoy, station II, 36051.8'N-122057.2'W in 50
fathoms of water
1346 CTD measurement to 73 meters 36°4S.5A' - 121°57.2'W
1452 Deployed modified sonobuoy, station G, 36°48.5Ar - 121°57.9'W in 53
fathoms of water
1558 Deployed modified sonobuoy, station E, 36°48.5A - 121°52.1'W in 45
fathoms of water
1605 CTD measurement to 52 meters 3C°43.6'N-122o00.6'W
1713 Deployed ARGOS waves buoy 36o43.6'N-122o00.6'W
1805 Deployed ARGOS waves buoy 36°43.9'N-122°08.6'W. Because of the
weather forecast for high winds and seas, a decision was made not to
deploy the ARGOS thermistor string buoys.
1900 CTD "yo-yo" measurements to 600 meters 36°44.1'N-122°13.7'W
2200 Stop CTD to reposition - have drifted to 36°43.2'N-122°14.7'W
2245 CTD "yo-yo" measurements to 600 meters 36°44.5'N-122°13.3'W
143
B.3 14 December 1988
0000 Continue CTD "yo-yo" measurements 36°44.7'N-122°14.7'W
0033 Halt CTD to move ship (traffic avoidance)
0052 Resume CTD "yo-yo" to 600 meters 36°14.5'N-122013.3'W
0338 Stop CTD to reposition - have drifted to 36045.9'N-122°16.7/W
0408 CTD "yo-yo" measurements to 600 meters 36044.6'N-122013.5'W
0557 Stop CTD measurements - have drifted to 36°45.2'N-122°14.8'W
0832 Returned to Moss landing to offload 3 ARGOS buoys and 2 personnel.
Remain in port about two hours.
1246 Replace station J modified sonobuoy (replaced with malfunctioning
buoy repaired by changing hydrophone, original J buoy recovered)
1435 Deployed MIUW buoy at station L-l (repaired by splicing power con-
nection in electronics package) 36°55.1'N-122o14.0'W
1528 Deployed modified sonobuoy at station L-2 (repair unsuccessful and
buoy recovered at 1643)
1542 CTD measurement to 80 meters 36°57.6'N-122°17.7'W
1738 CTD measurement to 90 meters 36D52.8'N-122°10.7'W
1854 CTD measurement to 1000 meters 36°42.9'N-122013.7'W
2046 CTD measurement to 1500 meters 36°32.9'N-122°16.7'W
2238 CTD measurement to 800 meters 36°23.6'N-122°17.9'W
B.4 15 December 1988
0055 CTD "yo-yo" measurement to 600 meters 36o39.0'N-122°18.0'W
0411 Stop CTD to reposition - have drifted to 36°39.4'N-122°23.2,W. Winds
exceed 40 knots for much of the night.
0445 CTD "yo-yo" measurements to 600 meters 36°38.8'N-122°18.2'W
141
0617 CTD to 1200 meters
0644 Stop CTD - have drifted to 36°39.2'N-122022.4'W
1138 Recovered ARGOS wave buoy. Begin search for second buoy. Posi-
tions are inexact due to three hour time lag in position report to ship.
Swell height limits buoy visibility to about 700 meters.
1623 Discontinue search for ARGOS buoy.
1853 Recovered MIUW buoy, station L-l
2007 Recovered buoy, station L
2114 Recovered buoy, station J
2148 Recovered buoy, station 1
2226 Recovered buoy, station h
2257 Recovered buoy, station G
2330 Recovered buoy, station E
B.5 16 December 1988
0134 Recovered MIUW buoy, station Bl, Buoy for station B is not in place
0224 Stop search for station B buoy
0335 CTD measurement to SOU meters 36o30.6'N-122°09.7'W
0704 Transmitted release signal to acoustic releases on tomography trans-
mitter, no transponder reply heard.
0805 Leave area of tomography transmitter to look for ARGOS buoy.
1030 Recover ARGOS buoy
1253 Transmitted release signal to acoustic releases, which released the
anchor.
1331 Transmitter on surface
1421 Transmitter recovered
1830 Moored, Moss Landing
145
B.6 Data Disposition
1. CTD and ADCP data to Woods Hole Oceanographic Institution for
Processing.
2. Tomographic acoustic signal recordings to Naval Postgraduate School
for processing.
3. NDBC and ARGOS buoy data to National Data Buoy Center for pro-
cessing.
HG
Appendix C
Maximal- length Sequences
and the Fast Hadamard
Transform
C.l Introduction
Impulsive excitation is an extremely easy and useful mathematical tool for
measuring the impulse response of a system or determining travel time
through a media. The problem is that an impulse is fairly difficult to achieve
physically. As the transmitted pulse approaches an impulse, the required
bandwidth and peak power of the transmitter increase. Impulsive sound
signals can be generated by explosive or implosive sources but these have
uneven frequency distribution energy, and repeatability. Another solution
is to use pseudorandom noise. The period, frequency distribution, and en-
ergy are deterministic and can be tailored to meet system requirements.
The signal can be repeated identically for additional signal processing gain.
Importantly, when sampled and digitized the signal becomes an impulse of
much shorter duration and higher peak power than the original signal. The
method for generating the sequence as well as a fast method for processing
the received signal will be described here.
The pseudorandom noise signal is a binary maximal-length shift register
sequence. The sequence's most important characteristic its autocorrela-
tion, which is constant except at a shift of zero, making the sequence the
equivalent of white noise. The energy at zero is much higher than for each
individual digit, making it easier to estimate the arrival time of the signal.
ir
Other properties of maximal-length sequences (m-sequences) are detailed by
Ziemer and Peterson [43], including a list of polynomials which produce m-
sequences. Not all shift register sequences are of maximal-length, only those
which do not repeat until after 2n-l delays, where n is the number of delays
in the shift register.
As an example the table entry for a maximal-length sequence of degree
three will be developed into a code and a fast method for its autocorrelation
will be examined. Various sources were used. [44, 45, 46]
C.2 Generating the M-sequence
Table 8-5 of Ziemer and Peterson [43] lists only one polynomial for generating
an m-sequence of degree three. The length of the sequence will be seven
digits. The listing in the table is an octal representation of the binary
coefficients of the generating polynomial. Translating to binary this becomes
[13]s — [1011]2. (CI)
The corresponding polynomial is
g(D) = DZ + D+1, (C.2)
where D is a delay of one unit (D is three delays). The shift register register
realization follows directly as shown in Figure C.l.
Loading the initial state is arbitrary since the register will cycle through
all possible combinations before repeating. For an initial state 02 = 1,
a\ = 0, ao = 0, this is one period of the sequence as shown in Table C.l.
The m-sequence is a single column of the register states. The character-
istics of the autocorrelation are unaffected by whether the m- sequence is
read from top to bottom or the reverse, but the method for formulating the
Hadamard demodulation does change. The top to bottom sequence will be
designated the "forward" code,
f 1001110 forward code (c .
' \ 0111001 reverse code. * ' '
In use, the m-sequence digits are transformed by replacing 1 with -1 and
0 with 1. When dealing with the structure and mathematics it is easier to
use 0 and 1 because many people are familiar with binary mathematics and
can more easily adapt to modulo-two mathematics The received signal has
148
a2
*i
— ©-►
a0
Figure C.l: Shift register realization of Eq. C.2
Cycle
a 2
Q]
ao
1
1
0
0
2
0
1
0
3
0
0
1
4
1
0
1
5
1
1
1
6
1
1
0
7
0
1
1
8
1
0
0
Table C.l: Shift register contents when generating M-sequence.
1-19
an unknown time delay and so must be correlated with all possible shifts of
the code. Let the seven shifted sequences form the matrix M:
10 0 1110
0 10 0 111
10 10 0 11
10 0 1
M =
1 1 0
1110 10 0
0 1110 10
.0011101.
(C4)
When this matrix and the code are transformed to + and -l's , multiplying
the signal by the matrix will result in the correlation,
Rsm = MS.
(C.5)
This is the entire goal of the initial signal processing, all that remains is to
develop a fast, efficient algorithm to accomplish this multiplication.
C.3 The Hadamard Matrix
To describe the fast algorithm, it is necessary to introduce the Hadamard
matrix. The Sylvester-type Hadamard Matrix has a recursive form for higher
orders given by
Hi=[l],ff2i ^ Hi
The third degree matrix II is
Hi -Hi
(C6)
H =
1
1
1
1
-1
-1
-1
-]
'
I -1
-]
[ -]
[ -1
-1
. -1
(C.7)
150
or, represented by ones and zeros,
H =
00000000
0 10 10 10 1
0 0 110 0 11
0 110 0 110
1
(C.8)
0 0 0 0 111
0 10 110 10
0 0 11110 0
0 110 10 0 1
One way to form the matrix is by multiplying matrices formed of the binary
'counting' matrix from 0 to 7,
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 u
The matrix M can be factored in the same fashion, but not as simply. Form
the first matrix B from the successive contents of the shift register, but bit
reversed (from right to left)and in reverse order (from bottom to top). The
original order is then preserved by shifting the rows of the matrix to bring
the 3x3 identity matrix to the top,
H = AAT =
0 0 0 0 1111
0 0 110 0 11
0 10 10 10 1
(C.9)
B =
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
1
(CIO)
Form the second matrix C from three shifted versions of the m-sequence
c =
10 0 1110
0 10 0 111
10 10 0 11
(C.ll)
151
It is easy to verify that
BC=M. (C12)
Note that M,B) and C matrices must be expanded by a leading row and/or
column of zeros to be of the proper size. The new matrices will be denoted
with a prime. If mapping matrices can be found such that QA = B' and
A*P — C . then the same matrices will map the Hadamard matrix to the
m- sequence matrix
M' = B'C' = QAA'P = QHP. (C13)
Recall that the correlation for the signal with the output code is given
by multiplication, Eq. C5, which now becomes
Km = M'S1. (C.14)
(S' because the leading zeros must be added. ) Combining Eqs. C.13 and
C.14 results in
R'am = QHPS'. (C.15)
This gives the signal correlation that is required. The initial entry is removed
to change R'sm to Rsm .
C.4 Input and Output Vector Order Permuta-
tion
The matrices P and Q must be found such that QA = B' and AfP = C . A
natural index for each row or column is its equivalent octal value since the
values range from 0 to 7 and do not repeat as shown in Figure C.4.
The permutation matrices will have ones in the following positions:
Q row 0 12 3 4 5 6 7
Q column 0 4 2 16 3 7 5
(C16)
P row 0 5 2 14 6 7 3
P column 0 12 3 4 5 6 7.
These indices are important. With the indices, the matrices do not have
to be constructed. The 'multiplication' by the permutation matrices is ac-
complished by shuffling the order of the signal vector, rather than direct
multiplication, as shown in Figure C.2. Note that no multiplications are
required, only the reordering. For a given code the permutations can be
evaluated once and the result stored as an index array to be applied to each
vector.
152
AT =
A =
0 0 0
0
0 0 1
1
0 1 0
2
0 1 1
3
1 0 0
4
1 0 1
5
1 1 0
6
1 1 1
7
0 0 0 0 1111
0 0 110 0 11
0 10 10 10 1
0 12 3 4 5 6 7
B' =
C =
0 0 0
0
1 0 0
4
0 1 0
2
0 0 1
1
1 1 0
6
0 1 1
3
1 1 1
7
1 0 1
5
0 10 0 1110
0 0 10 0 111
0 10 10 0 11
0 5 2 14 6 7 3
Figure C.2: Indices formed from matrix octal equivalents.
153
C.5 The Fast Hadamard Transform
There exists an efficient method of performing the multiplication by the
Hadamard matrix. If a vector is multiplied by the Hadamard matrix (the
normal Hadamard matrix of {+1, — 1}). The result is a vector of sums of
all the components of the vector with various + and - weighting. Define a
vector V such that
" a
V =
c
d
e
f
9
h
After multiplying this by the Hadamard matrix the vector becomes
(C.17)
HV =
1 1-1-1 1 1-1-1
"a"
6
c
d
e
f
9
.h.
(C.18)
HV =
"a
+
6
+
c
+
d
+
e
+
/
+
9
+
h'
a
-
b
+
c
-
d
+
t
-
/
+
9
-
h
a
+
6
-
c
-
d
+
e
+
/
-
9
-
h
a
-
b
-
c
+
d
+
e
-
/
-
9
+
h
a
+
b
+
c
+
d
-
e
-
/
-
9
-
h
a
-
b
+
c
-
d
-
t
+
/
-
9
+
h
a
+
b
-
c
-
d
-
e
-
/
+
9
+
h
.a
-
b
-
c
+
d
-
e
+
/
+
9
-
h.
(C.19)
When calculating correlations, let a = 0 so that no new information is
added. The zeroth position result is the sum of all the elements of the code
and is therefore equal to the DC pedestal. This pedestal can be removed by
subtracting this sum of all elements, or not, depending on the application.
Compare this result to the result using a flow diagram identical to the pro-
151
P column
Prow
S«
becomes
PS'
0
0
So
Go
1
5
Si
G5
2
2
S2
G2
3
1
S3
Gi
4
4
S4
G4
5
6
s5
G6
6
7
s6
G7
7
3
S7
G3
Orow
O column
F=HPS'
becomes
R=OHPS'
0
0
F0
Ro
1
4
F4
Ri
2
2
F2
R2
3
1
Fi
R3
4
6
F6
R4
5
3
F3
R5
6
7
F7
R6
7
5
F5
R7
Table C.2: Re-ordering of input and output vectors according to the per-
mutation matrices P and Q. For the input vector, let C - PS' and for the
output vector, let F = H PS' ■
155
cedure used with the Fast Fourier Transform, except that all the 'twiddle'
factors are equal to one, Figure C.3.
The result of the Fast Hadamard Transform is the same as for multi-
plication. The algorithm used for the Fast Fourier Transform is trivialized
in this case - there is no bit reversal or multiplication by a phase factor.
Because the method requires only additions, the exact computational speed
increase is difficult to calculate. (The speed improvement for FFT over DFT
is usually calculated by comparing the number of multiplications required)
The 'multiplication' by P and Q has been replaced by reordering, so that
there is no multiplication required. The speed of execution now depends
on other statements in the program as well as the correlation because loop
increments and tests for completion may take as long as the additions.
C.6 Using the Reverse Code
The permutation matrices for the reverse code are found in a slightly dif-
ferent way. The matrix B is found from the contents of the shift register
directly, not bit reversed and in reverse order as for the forward code. The
matrix C is formed by shifting the code to the left (vice right). The permu-
tation indices are determined and used in the same fashion as before.
C.7 Correlation Procedure
The procedure for performing the correlation can now be summarized in five
straightforward steps:
1. Augment the signal vector S by adding a zero in the zeroth position.
2. Permute the vector according to P.
3. Perform the Fast Hadamard Transform.
4. Permute the resulting vector according to Q.
5. Remove the zeroth entry.
15G
Basic Element
B
A + B
A-B
a
b
c
d
e
f
g
h
a+b+c+d+e+f+g+h
a-b+c-d+e-f+g-h
a+b-c-d+e+f-g-h
a-b-c+d+e-f-g+h
a+b+c+d-e-f-g-h
a-b+c-d-e+f-g+h
a+b-c-d-e-f+g+h
a-b-c+d-e+f+g-h
Figure C.3: Basic Fast Hadamard Transform element for cascading additions
and the full diagram for an eight point FHT.
157
C.8 Example
Consider the first and third rows of the m-sequence matrix as input signals:
first third
1001110 1010011
Transform to {— 1,+1}. The result is the signal vector S as would be re-
ceived.
-111-1-1-11 -11-111 -1 -1
Add beginning 0
0-111-1-1-11 o-ll-lll-l-l
Permute according to P
0 111-1-1-1-1 0-11-11-11-1
Perform Fast Hadamard Transform (can be done in this case by comparing
to rows in the Hadamard matrix for a match)
-1 -1 -1 -1 7 -1 -1 -1 -1 7 -1 -1 -1 -1 -1 -1
Permute according to Q
-1 7 -1 -1 -1 -1 -1 -1 -1 -1 -1 7 -1 -1 -1 -1
Remove the zeroth element
7 -1 -1 -1 -1 -1 -1 -1 -1 7 -1 -1 -1 -1
As expected, the correlation produces a peak in the first and third positions,
respectively.
C.9 Summary
When performing the correlation of a signal and the m-sequence using the
Fast Hadamard Transform and a quadrature demodulation system the real
and imaginary components of the signal are correlated separately and later
combined for magnitude and phase. Note that the FHT only works on one
158
sample per digit of the m-sequence in the signal. For improved accuracy in
estimating the arrival time of the impulse, it is valuable to sample at a higher
frequency. This may also allow digital filtering. The sampling frequency
should be an integer multiple of the code clock rate (also known as the
"chip" rate). The data samples should then be decimated into records at
the code clock frequency so that they are again one sample per digit. After
the FHT correlation the data interleaves are recombined to their original
positions. For example, if a code clocked at 16 Hz is sampled at 64 Hz, then
4 separate correlations will have to be performed on each of the in-phase
and quadrature channels. The FHT correlation is still much faster than
using DFT or FFT methods, or matrix multiplies. The result of the FHT
correlation in the case of data sampled at higher than the code clock rate
is not the same as for conventional correlation. In an ideal case, each of
the interleaves will produce an output peak of equal magnitude, resulting
in a 'flat-topped' correlation peak, vice a 'pointy' correlation peak. The
estimation of travel time must look for this shape, rather than the 'point'.
159
Appendix D
Additional Data for Station
J
D.l Hadamard Transformed Acoustic Signal
160
Slgnol Mogn Ltud© Squored StotLon J 1 4DEC88
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Se q u e n c e Re p It It Ion T I me ( seconds)
Figure D.l: Tomographic signal, coherently averaged 16 times then magni-
tude squared. Station J, 1317 to 1419 14DEC88. High ambient noise at the
start is from the R/V Point Sur after deploying buoy.
161
Slgnol Megn Ltudo Squorod Station J 1 4DEC88
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Se quence Rep It It Ion T I me ( seconds)
Figure D.2: Tomographic signal, coherently averaged 16 times then magni-
tude squared. Station J, 1419to 1521 14DEC88.
162
Slgnol Megn Ltud© Squor©d Stotlon J 1 4DEC88
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Se q u e n c e Re pit It Ion T I me ( seconds)
Figure D.3: Tomographic signal, coherently averaged 16 times then magni-
tude squared. Station J, 1521 to 1623 14DEC88.
1C3
Slgnol Mogn Itudo Squared
on J 14DEC88
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Sequence Rep It It Ion Time (seconds)
Figure D.4: Tomographic signal, coherently averaged 16 times then magni-
tude squared. Station J, 1623 to 1725 14DEC88.
164
Slgnol Mogn LtudG Squored Station J 1 4DEC88
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Se quence Re p It It Ion f I me ( seconds)
Figure D.5: Tomographic signal, coherently averaged 16 times then magni-
tude squared. Station J, 1725 to 1827 14DEC88.
1G5
Signal Mognltude SquorGd Slot Ion J 1 4DEC88
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Se q u e n c e Re p It It Ion T Lme ( seconds)
Figure D.6: Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 1827 to 1929 14DEC88. Signal cutoff is due to
tape change.
166
Slgnel MegnLtudo Squofred Slot Ion J 1 4DEC88
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Sequence Rep It It Ion Time (seconds)
Figure D.7: Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 1957 to 2059 14DEC88. The previous hour is
included as Figure 12 on page 58. Note that the arrival structure is shifted
for data from a new tape.
167
Slgnel Mogn Uudo Squerod Station J 1 4DEC88
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Se quence Rep It It Ion T I me ( seconds)
Figure D.8: Tomographic signal, coherently averaged 16 times then magni-
tude squared. Station J, 2059 to 2201 14DEC88.
168
Slgnol Mogn Uudo SqJfcred Slot Ion J 1 4DEC88
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Sequence Rep It It Ion Time (seconds)
Figure D.9: Tomographic signal, coherently averaged 16 times then magni-
tude squared. Station J, 2201 to 2303 14DEC88.
169
Sign el tiegn llud© Sq
Slot Ion J 14DEC88
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Se quence Rep It It Ion T I me ( seconds)
Figure D.10: Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 2303 14DEC88 to 0005 15DEC88.
170
Signal Mogn ItudG Squored Station J 1 4DEC88
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Se quence Rep It It Ion T I me ( seconds)
Figure D.ll: Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 0005 to 0107 15DEC88. Note that computer
generated time scale is extended past 0000 for convenience in processing.
The reason for signal cutoff is that the end of the tape was reached.
171
Slgnol Magnitude Squared Station J 1 5DEC88
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Se q u e n c e Re petition T I me ( seconds)
Figure D.12. Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 0052 to 0154 15DEC88. Note that the arrival
structure is shifted because of the start of a new tape.
172
Slgnol Mogn Itude Squored StotLon J 1 5DEC88
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Sequence Repetition Time (seconds)
Figure D.13: Tomographic signal, coherently averaged 16 timesthen magni-
tude squared. Station J, 0154 to 0256 15DEC88.
173
Signal Mogn Ltude Squared Station J 1 5DEC88
Q-
a>
o
3
a
CO
— I
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Sequence Repetition Time (seconds)
Figure D.14: Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 0256 to 0358 15DEC88.
174
Slgnol Mogn Itude Squared StotLon J 1 5DEC88
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Sequence Repetition Time (seconds)
Figure D.15: Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 0358 to 0500 15DEC88. High scattering and
ambient noise were present at this time because of high winds (the worst
windstorm of the year to hit the central California coast).
ro
Signal Magnitude Squared Station J 1 5DEC88
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Sequence Repetition Time (seconds)
Figure D.16: Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 0500 to 0602 15DEC88. High ambient noise and
high scattering continue from windstorm.
170
Signal Mogn Ltu.de Squared Station J 1 5DEC88
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Se quence Repetition Time (seconds)
Figure D.17: Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 0602 to 0704 15DEC88. The reason for signal
cutoff is that the end of the tape was reached.
Signal Magnitude Squared Ste
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Sequence Repetition Time (seconds)
Figure D.18: Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 0647 to 0749 15DEC88. The reason for the
increased amplitude is unknown. Note that the arrival structure is shifted
at the start of the new tape.
178
Slgnel Magnitude Squared Station J
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Sequence Repetition Time (seconds)
Figure D.19: Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 0749 to 0851 15DEC88.
179
Slgnel Magn Itude Squored Stot
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Se q u e n c e Re petition T I me ( seconds)
Figure D.20: Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 0851 to 0953 15DEC88.
180
Slgnol Magn Itude Squared Station J 1 5DEC88
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Sequence Repetition Time (seconds)
Figure D.21: Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 0953 to 1055 15DEC88.
181
Signal Mognltude Squared Station J 1 5DEC88
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Sequence Repetition Time (seconds)
Figure D.22: Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 1055 to 1157 15DEC88.
18:
Slgnel Mogn Ltude Squared Station J 1 SDEC88
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Sequence Repetition Time (seconds)
Figure D.23: Tomographic signal, coherently averaged 16 times then magni-
tude squared. Station J, 1157 to 1259 15DEC88. The reason for the signal
cutoff is that the end of the tape was reached.
183
Signal Negn Itude Squared Station J 1 5DEC88
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Sequence Repetition Time (seconds)
Figure D.24: Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 1226 to 1328 15DEC88. Note that the arrival
structure is shifted at the start of the new tape.
184
Signet Megn itude Squared Stotlon J 1 5DEC88
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Se que nee Repetition Time (seconds)
Figure D.25: Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 1328 to 1430 15DEC88.
185
Signal Magnitude Squared Station J 1 5DEC88
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
Sequence Repetition Time (seconds)
Figure D.26: Tomographic signal, coherently averaged 16 times then mag-
nitude squared. Station J, 1430 to 1532 15DEC88. Signal cutoff is due to
buov failure.
186
D.2 Arrival Time and Surface Wave Spectra
is;
Arrival Time Power Spectrum
Station J 14DEC88 2107 PST
v.
C
Q
«
u
o
C
o
E
0.1 0.15
Frequency (Hz)
0.25
Figure D.27: Arrival time power spectrum for Station J. Spectrum from 2.2
hours of Arrival Time Series, 2001 to 2213 14DEC88 PST.
188
N
i
5
u
O)
o
<-»
t:
C
CJ
CD
35
30
25
20
15
10
U.00
Sea Surface Spectrum
NDBC Buoy 14DEC88 2100 PST
•
■
■
•
■
■
■
1 "■
0.05 0.10 0.15
Frequency (Hz)
0.20
0.25
Significant Wave Height 3.54 m
Average Period 9.11 sec
Dominant Period 12.50 sec
Dominant Direction 314 N
Figure D.28: Surface wave power spectrum in Monterey Bay. Data is from
the NDBC buoy southwest of Santa Cruz, 2100 14DEC88 PST.
189
Arrival Time Power Spectrum
Station J 14DEC88 2213 PST
K
c
o
C
u
c/5
£
0.01
0.008
0 006
0.004
0.002
0
0
0.05
0.1
0.15
0.2
0.25
Frequency (Hz)
Figure D.29: Arrival time power spectrum for Station J. Spectrum from 2.2
hours of Arrival Time Series, 2107 to 2319 14DEC88 PST.
190
35
| 30
i 25
£ 20-
09
10
0
0.00
Sea Surface Spectrum
NDBC Buoy 14DEC88 2200 PST
0.05 0.10 0.15
Frequency (Hz)
0.20
0.25
Significant Wave Height 4.10 m
Average Period 9.67 sec
Dominant Period 12.50 sec
Dominant Direction 308 N
Figure D.30: Surface wave power spectrum in Monterey Bay. Data is from
the NDBC buoy southwest of Santa Cruz, 2200 14DEC88 PST.
191
Arrival Time Power Spectrum
Station J 14DEC88 2319 PST
C
o
Q
u
o
c
0.25
Frequency (Hz)
Figure D.31: Arrival time power spectrum for Station J. Spectrum from 1.9
hours of Arrival Time Series,2213 14DEC88 to 0005 15DEC88 PST.
192
^^
35
N
a
5
30
6
25
2
20
O*
en
o
u
15
re
VM
J-i
3
10
W
TO
5
0
0.00
Sea Surface Spectrum
NDBC Buoy 14DEC88 2300 PST
0.05
0.10
0.15
0.20
0.25
Frequency (Hz)
Significant Wave Height 3.85 m
Average Period 936 sec
Dominant Period 12.50 sec
Dominant Direction 321 N
Figure D.32: Surface wave power spectrum in Monterey Bay. Data is from
the NDBC buoy southwest of Santa Cruz, 2300 14DEC88 PST.
193
Arrival Time Power Spectrum
Station J 14DEC88 2130 PST
N
CJ
C
o
Q
u
c
CO
CJ
E
0.01
0.008
0.006
0.004
0.002
0.25
Frequency (Hz)
Spectrum from 5.2 hours of Arrival Time Series, 1855
14DEC88 to 0005 15DEC88 PST
Figure D.33: Arrival time power spectrum for Station J. This spectrum was
generated using the segmented FFT method on the data from an entire 6
hour tape (the maximum length time series without tape-to-tape synchro-
nization).
194
Bibliography
[6]
P
[9
[10
Spindel, R.C, "Ocean Acoustic Tomography: A Review," Current
Practices and New Technology in Ocean Engineering, v. 11, pp. 7-13,
1986.
The Ocean Tomography Group, ''A Demonstration of Ocean Acoustic
Tomography," Nature, v. 299, pp. 121-125, 1982.
Munk, W. and Wunsch, C., "Ocean Acoustic Tomography: A Scheme
for Large Scale Monitoring," Dtep-Sea Research, v. 26A, pp. 123-161,
1979.
Sound Transmission through a Fluctuating Ocean, ed. Flatte, Stanley,
pp. 3-61, Cambridge University Press, 1979
Spindel, Robert C., "Signal Processing in Ocean Tomography," Adap-
tive Methods in Underwater Acoustics, ed. H.G. Urban, pp. 687-710.
D. Reidel Publishing Company, 1985.
Kinsler, L.E., Frey. A.R.. Coppens. A., and Sanders. J. , Fundamentals
of Acoustics, 3rd ed., pp. 117-120, John Wiley &, Sons, 1982.
Liebelt. P.B.. An Introduction to Optimal Estimation, Addison-Wesley,
Reading, MA, 1907.
Franklin. J.N., "Well-posed stochastic extensions of ill-posed linear
problems," J. Math. Anal. Appi, v. 31, pp. 682-716, 1970.
Jackson, D.D.. "Interpretation of inaccurate, insufficient, and inconsis-
tent data." Geophys. J. R. Astr. Soc, v. 28, pp. 97-109, 1972.
Jordan. T.H. and Franklin. J.N., "Optimal solutions to a linear inverse
problem in geophysics," Proc. Nat. Acad. Sci., vol. 68, pp. 291-293,
1971.
195
[11] Provost, C., A Variational Method for Estimating the General Circu-
lation in the Ocean, PhD Thesis, University of California, San Diego,
1983.
[12] Menke, William, Geophysical Data Analysis: Discrete Inverse Theory,
pp. 35 -160, Academic Press, 1984.
[13] Smethie, Jr., W.M., Some Aspects of the Temperature, Oxygen, and Nu-
trient Distributions m Monterey Bay, California, Moss Landing Marine
Laboratories Technical Publication 73-01, 1973.
[14] Broenkow, W.W. and W. M. Smethie, Jr., "Surface Circulation and
Replacement of Water in Monterey Bay," Estuarine and Coastal Marine
Science, v. 6, pp. 583-603, 1978.
[15] Lasley, S. R., "Hydrographic Changes in Monterey Bay Surface Waters
in Relation to Nearshore Circulation," M.A. Thesis, San Jose State
University, San Jose. CA, May. 1977.
[16] Engineering-Science. Inc., Monterey Peninsula Water Pollution Control
Agency Interim Report No. J,. Draft Oceanographic Predesign Report
Volume 1, pp.II21-II53, October, 1976.
[17] Shepard, F.P. and Emery, K.O., Submarine Topography off the Califor-
nia Coast: Canyons and Tectonic Interpretation. Geological Society of
America, pp. 72-79. 1941.
[18] Scholl, D.W. and others, "The Structure and Origin of the Large Sub-
marine Canyons of the Bering Sea." Marine Geology, v. 8(3/4), pp. 187-
210, 1970.
[19] Shepard, F.P. and Dill. R.F., Submarine Canyons and Other Sea Val-
leys, pp. 81-90. 223-231, 343-345, Rand McNally and Company, 1966.
[20] Normack. W.R.. "Growth Patterns of Deep-Sea Fans," Am. Assoc, of
Petrol. Geol. Bull., v. 54(11), pp. 2187-2192, 1970.
[21] Combellick. R.A., and Osborne, R.H., "Sources and Petrology of Beach
Sand from Southern Monterey Bay, California," J. Sedim. Petrol., v.
47(2), pp. 891-907, 1977.
[22] Welday, E.E.. and Williams, J.W., Offshore Surficial Geologic Map of
California, Map Sheet 26. 1975.
196
[23] Shepard, F.P. and others, Currents in Submarine Canyons and Other
Sea Valleys, pp. 14-51, 78-95, The American Association of Petroleum
Geologists, 1979.
[24] U.S. Army Corps of Engineers and the California Department of Boat-
ing and Waterways, Coastal Data Information Program, Monthly Sum-
mary Report # 143 (December 1981), 6 January 1988.
[25] U.S. Army Corps of Engineers and the California Department of Boat-
ing and Waterways, Coastal Data Information Program, Twelfth An-
nual Report, January 1987 through December 1987, by R.J. Seymour,
D. Castel, and J.O. Thomas, 19 May 1988.
[26] Clay, C.S. and Medwin, H., Acoustical Oceanography: Principles and
Applications, pp. 11 - 16, 78-79 John Wiley & Sons, 1977.
[27] Shea, R.E., and Broenkow, W.W., "The Role of Internal Tides in the
Nutrient Enrichment of Monterey Bay, California,'* Estuarine, Coastal
and Shelf Science, v. 15, pp. 56-66, 1982.
[28] Shepard, F.P., "Progress of Internal Waves Along Submarine Canyons,"
Marine Geology, v. 19, pp. 131-138, 1975.
[29] Bascom, William. Waves and Beaches, pp. 5 - 73, Anchor Books, 1980.
[30] Miller, J.H., Lynch, J.F., and Chiu, C.S., "Estimation of Sea Surface
Spectra using Acoustic Tomography'" , J. Acoust. Soc. Am., 86(1) pp.
326- 345, July 1989.
[31] Sparton Defense Electronics ASW Technical Center, Operation Manual
for Mobile Inshore Underwater Warfare Moored Sensor Buoy AN/SSQ-
58, (7938-OPMAN-l), Sparton Corporation, Jackson, MI.
[32] Naval Air Systems Command, Sonobuoy Instructional Manual,
(NAVAIR 28-SSQ-500-1), Naval Weapons Support Center, Crane, IN.
[33] Steele, Kenneth E., Lau, JC, and Hsu, Y.L., "Theory and Application
of Calibration Techniques for an NDBC Directional Wave Measure-
ments Buoy," IEEE Journal of Oceanic Engineering, v. OE-10, no. 4.
October 1985.
[34] Collecte Localisation Satellites, ARGOS Location and Data Collection
System, C.L.S., Toulouse, France. July 1987.
19:
[35] Ocean Data Systems, Inc., Multiple Profile Restructuring and Supple-
mental Plot Programs, by G. Jacobs, 30 June 1974.
[36] Van Trees, Harry L., Detection, Estimation and Modulation Theory,
Part I, pp. 273-287, John Wiley k Sons, 1968.
[37] Press, William H. and others, Numerical Recipes, The Art of Scientific
Computing, pp. 86-89, Cambridge University Press, 1986.
[38] Bendat, Julius S. and Piersol, Allan G., Random Data: Analysis and
Measurement Procedures, pp. 314 - 365, John Wiley &: Sons, 1971.
[39] U. S. Naval Oceanographic Office, Integrated Command ASW Predic-
tion Systems (1CAPS), NSTL, Bay St. Louis, MS.
[40] National Oceanic and Atmospheric Administration, Nautical Chart of
Point Sur to San Francisco, 24th ed., DMA Stock No. 18ACO18680.
21 February 1987.
[41] Jones, R.M, Riley, J. P., and Georges, T.M., HARPO: A Versa-
tile Three- Dimensional Hamiltonian Ray-Tracing Program for Acoustic
Waves in an Ocean with Irregular Bottom, NOAA Wave Propagation
Laboratory, Boulder. CO. October, 1986.
[42] Newhall, A.E., Lynch. J.F., Chiu, C.S., and Daugherty. J.R., "Improve-
ments in Three-Dimensional Raytracing Codes for Underwater Acous-
tics/" ms. submitted to IMACS, April, 1989.
[43] Ziemer, Rodger E. and Peterson, Rodger 1., Digital Communications
and Spread Spectrum Systems, pp. 385-404, Macmillan Publishing Com-
pany, 1985.
[44] Birdsall, Ted, letter dated 27 May 1987, "My Introduction to Hadamard
Processes for M-Sequences."
[45] Cohn, Martin and Lempel, Abraham, "On Fast M-Sequence Trans-
forms." IEEE Transactions on Information Theory, pp. 135 - 137, Jan-
uary 1976.
[46] Borish, Jeffrey and Angell, James, "An Efficient Algorithm for Measur-
ing the Impulse Response Using Pseudorandom Noise.'" J. Audio Eng.
Soc, v. 31, No. 7, pp. 478 - 488, July/August 1983.
198
INITIAL DISTRIBUTION LIST
No. Copies
1. Dr. Richard Barber 8
Monterey Bay Aquarium Research Institute
160 Central Avenue
Pacific Grove, CA 93950
2. Defense Technical Information Center 2
Cameron Station
Alexandria, Virginia 22314-6145
3. Library, Code 0142 2
Naval Postgraduate School
Monterey, California 93943-5002
4. Prof. James H. Miller, Code 62Mr 10
Department of Electrical and Computer Engineering
Naval Postgraduate School
Monterey, CA 93943
5. LT Robert C Dees, USN 1
207 Lauber Lane
Derby. KS 67037
6. Prof. Soenke Paulsen, Code 62Pa 1
Department of Electrical and Computer Engineering
Naval Postgraduate School
Monterey. CA 93943
7. Mrs. Theresa Rowan, Code 742 1
Naval Training Systems Center
12350 Research Parkway
Orlando, FL 32826
199
8. Laura L. Ehret, Code 62Eh
Department of Electrical and Computer Engineering
Naval Postgraduate School
Monterey, CA 93943
9. Prof. Timothy Stanton, Code 68St
Department of Oceanography
Naval Postgraduate School
Monterey, CA 93943
10. Prof. Edward Thornton, Code 68Tm
Department of Oceanography
Naval Postgraduate School
Monterey, CA 93943
11. Prof. Lawrence J. Ziomek, Code 62Zm
Department of Electrical and Computer Engineering
Naval Postgraduate School
Monterey, CA 93943
12. Prof. John P. Powers. Code 62
Chairman
Department of Electrical and Computer Engineering
Naval Postgraduate School
Monterey. CA 93943
13. Director of Research, Code 012
Naval Postgraduate School
Monterey. CA 93943
200
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