1098 Subsurface Geologic Methods 



are described by Slotnick,^'^ Soske,^^ and Jakosky.^^ If the velocity in- 

 creases exponentially with depth {V = V o exp (aZ) "■) , the interpreter 

 may use the charts prepared by Slotnick.^^ In certain areas the velocity 

 relationship is best described by the assumption of a linear increase of 

 velocity with time, which becomes a parabolic function {V = FoVl + kZ) 

 when expressed in terms of depth. Houston ^^ has prepared charts that 

 simplify the calculations associated with this velocity function. 



Several mechanical devices have been described in the literature en- 

 abling the seismologist to plot data that are accurately disposed as to dip, 

 depth, and horizontal offset on the cross section.*^^ ^'^ Several slide rules 

 have been proposed for the linear increase of velocity function.^^ ^^ 



To avoid the laborious computation methods involving the curved 

 ray, approximations are often employed in which the actual curved-ray 

 path is replaced by a straight-ray path. The average-velocity-approxima- 

 tion method assumes that the velocity between any reflecting bed and the 

 surface is constant and is equal to the average velocity to the horizon. 

 The paths of the ray are therefore straight, and the depth for the normal 

 ray is simply: 



where V is average velocity 



t is total corrected reflection time 



This method is frequently used in areas of simple geology where correla- 

 tions are possible; however, it is definitely not recommended when dips 

 are to be determined. The modified straight-path approximation is some- 

 times applied when dips are of importance. The method is not applicable 

 in regions where the dip exceeds a few degrees, nor where the depth and 

 horizontal offset of the reflection point are critical factors. 



We have discussed only the variation of velocity with depth; how- 

 ever, one should not overlook the possible effects of lateral variations of 

 velocity. Stulken "^^ shows that in certain areas, such as the San Joaquin 

 Valley of California, the velocity may vary laterally as much as 100 feet 

 per second per mile. (See fig. 579.) Within a distance of some eighteen 

 miles the velocities at a constant reflection-arrival time show a difference 

 of over 2,000 feet per second. A map computed with a single time-depth 



** Slotnick, M. M., On Seismic Computations with Applications, I: Geophysics, vol. 1, no. 1, p. 13, 

 Jan. 1936. On Seismic Computations with Applications, II: Geophysics, vol. 1, no. 3, p. 299, Oct. 1936. 



^ Soske, Joshua, Computing Seismic Reflection Data by a Simple Consistent Method: Mines Mag., 

 vol. 32, no. 10, pp. 489-495, Oct. 1942. 



^ Jakosky, J. J., Exploration Geophysics, pp. 490-498, Los Angeles, Times-Mirror Press, 1940. 



"Slotnick, M. M., op. cit., I. p. 17; II, p. 302. 



^ Houston, C. E., Seismic Paths, Assuming a Parabolic Increase of Velocity with Depth: Geophysics, 

 vol. 4, no. 4, pp. 242-246, Oct. 1939. 



°° Wolf, A., A Mechanical Device for Computing Seismic Paths: Geophysics, vol. 7, no. 1, pp. 61-68, 

 Jan. 1942. 



'" Daly, J. W., An Instrument for Plotting Reflection Data on the Assumption of Linear Increase 

 of Velocity: Geophysics, vol. 13, no. 2, pp. 153-157, Apr. 1948. 



'^ Fillipone, W. R., Depth — Displacement Slide Rule: Geophysics, vol. 11, no. 1, pp. 92-95, Jan. 1946. 



'^Mansfield, R. H., Universal Slide Rule for Linear Velocity vs. Depth Calculations: Geophysics, 

 vol. 12, no. 4, pp. 557-575, Oct. 1947. 



'^ Stulken, E. J., Seismic Velocities in the Southeastern San Joaquin Valley of California: Geo- 

 physics, vol. 6, no. 4, pp. 327-355, Oct. 1941. 



