378 ELECTRICAL AND MISCELLANEOUS METHODS
Megger measurements) it is usual, when any theory is applied,
to use the simple direct-current theory. For alternating currents,
the current distribution in the ground will depart from that of
direct current for two reasons: (1) The "skin effect," or mutual
reaction of the current upon itself, will tend to make more of the
current flow at shallower depths than the direct-current dis-
tribution; and (2) a certain amount of current will be induced in
the ground by the surface wire carrying current to the ground
electrodes. These effects will increase with increase in frequency
and also for increase in conductivity.
An exact quantitative statement of the change in current
distribution and the resulting change in apparent resistivity
resulting from the use of alternating currents is not possible, as
the theoretical problem involved does not seem to have been
solved. From consideration of a somewhat similar but not
identical problem which arises in connection with the mutual
impedance and interference between power circuits and telephone
lines, it is probable that, for small-scale work (as in ore pros-
pecting) and for ordinary ground conductivities, there will be
little practical difference between alternating- and direct-current
resistivities for frequencies up to around 100 to 200 cycles but
that there may be very material differences for frequencies
around 1,000 cycles or higher.1
Although an exact theory for calculating the details of the
alternating-current distribution in the ground is not available for
the electrode systems and circuits of ordinary electrical pros-
pecting, we can make some approximate guesses from the theory
for other cases. In general, theory indicates that assuming unit
permeability (which is quite closely true for earth materials)
and neglecting displacement currents (which are quite negligible
for earth conductivities and for frequencies below radiof requency
(see footnote, page 377), the amplitude of current at a depth h
should depend on the factors AVT/P- An exact attenuation
factor cannot be given, as the current distribution is inferred
indirectly from the theory for other effects, such as the mutual
impedance of grounded circuits. However, there are certain
empirical criteria, based on different estimates of the value of
&V77p at which the current is "small" or "negligible," and
calculation of these estimates gives at least a useful approxima-
1 Railroad Commission of the State of California, 1919, p. 158.