THEORY OF REFRACTION SHOOTING 267

Fig, 114. The depth from this mean elevation to the high-speed
bed will be Z + (2J/2). Thus, the depth can be determined just
as in the case where shot point and detector are level except
that the depth must be figured from the mean elevation of the
two ends of the path considered.

Sloping Beds. Shooting Down Dip.—Consider next the case
in which the velocity discontinuity is assumed to be dipping at
an angle 8 with the horizontal. Consider first the case in which
the slope is downward from the shot point toward the detector.
This case is like that just considered for shot point and recorder
at different elevations except that x is now measured along the

DETECTOR

FIG. 115.—Inclined bed. Shooting down dip.
surface of the ground and the distance parallel to the sloping
surface is x cos 6. Also, Z is measured perpendicular to the
sloping bed (Fig. 115). The distance corresponding to the
difference in elevation becomes x sin 6. With these substitutions,
Eq. (227) becomes
™ re cos 8 (2Z + x sin 6) cos i /OOQs
Ti = -y^- +----------TQ--------- (228)
Substituting l/Vi = sin i/V^
m _2Z cos i , a; cos 6 sin i x sin 6 cos i
' Tl ~ ~TT~ + To + Fo
2Z cos i . x f * • ' , • ,, ^
— —T?------1" 17" (cos 0 sin $ + sin 0 cos t)
Y 0 r 0
2Z cos i , x . f. ^ ,OOAv
= —?r----+ TT sin (z + 0) (229)
Y o P 0
The slope of the Ti segment of the time-distance curve is now
Sm(i + e) = sm(i + e}
J