. Early geophysical papers of the Society of Exploration Geophysicists. Petroleum; Prospecting. i58 MAURICE EWING AND A. P. CRARY where v is the velocity at the depth y, is obtained. Eq. (2) yields dy/dx = ± (b2 esc2 0O - v2)ll2/v, (6) which may be combined with (5) to give the relation: * = + (i/27ra) f v[(v2 - b2)/(b2 esc2 60 - v2)]l'2dv J b = (b2 cot2 do/4Ta) [a — sin a cos a], (7) where sin a= ± tan 6o(v2/b2—iy2. The positive sign should be taken if the wave has not reached its maximum depth. "D 5 .. 10 ft Vertical Distance £0 40 60 ft. Horiiontal Distance Fig. 6.—Tr
. Early geophysical papers of the Society of Exploration Geophysicists. Petroleum; Prospecting. i58 MAURICE EWING AND A. P. CRARY where v is the velocity at the depth y, is obtained. Eq. (2) yields dy/dx = ± (b2 esc2 0O - v2)ll2/v, (6) which may be combined with (5) to give the relation: * = + (i/27ra) f v[(v2 - b2)/(b2 esc2 60 - v2)]l'2dv J b = (b2 cot2 do/4Ta) [a — sin a cos a], (7) where sin a= ± tan 6o(v2/b2—iy2. The positive sign should be taken if the wave has not reached its maximum depth. "D 5 .. 10 ft Vertical Distance £0 40 60 ft. Horiiontal Distance Fig. 6.—Travel-time curve for waves travelling vertically. Fig. 7.—Travel-time curve for waves travelling from surface to depth of 18 feet 6 inches The travel-time t=Jds/v becomes, upon substitution from (5) and (6) t = ± (b/2Ta sin0„) I (i/«0 X [02 - b2)/(b2esc260 - v2)]l'2dv = (b/2wa sin 80) X [a — sin 0O tan-1 (tan a/sin 60)]. (8) For the limiting case, 0o = o, the path is vertical and (7) and (8) become x = o (7O / = (b/2ira)[(v2/b2 - i)1/2 - tan"1 (v2/b2 - i)1'2]. (8') Formulas (7) and (8) make it possible to calculate the time required to traverse any part of any path. Two sets of data were taken to which these formulae may be applied. In the first case records were taken with the geophone buried at a series of depths up to about 20 ft., the shot in each case being at the surface directly above. In the second case the geophone remained at a depth of ft. while shots were fired on the surface at various distances from the mouth of the hole. Figs. 6 and 7 compare the travel-time obtained from these observations with those computed from the above equations using the values of a and b as computed from the time-distance curves. 818. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Society of
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