674 



EXPLORATION GEOPHYSICS 



The table is computed for various values of the vertical distance h 

 between the surface of the earth and the point of incidence of the normal 

 ray at the reflecting horizon. It is evident from Figure 415 that h and b 

 are related by the equation h = b cos 6. The velocity values approximate 

 those encountered in certain parts of California and the Gulf Coast 

 region. The table shows the order of magnitude to be expected in observed 

 time differences AT. 



^/^\V//A\Sy/«*^y/«>i!!%N*5i!^»!'«^i!^^ 



^//'<<^y7'^'^Ms^/'\<iW^'vy/Ay///^^ 



Dip Calculation 

 Using the Reflection Method 



In order to investigate the wave propagation in the layered upper 



portion of the earth's crust, generally consisting of sedimentary beds, we 



^ may generalize the situation in the 



following manner. Let the subsurface 

 medium be divided into a number of 

 horizontal layers, each with a constant 

 seismic velocity. This situation is illus- 

 trated by Figure 416 where the upper- 

 most layer is given the index ( 1 ) and 

 the successive layers are numbered 2, 

 3, 4, etc. Let the velocities Vi, V2, Vz, 

 V4, etc. be constant within each layer 

 and different from layer to layer. 



Let a ray start downward from the 

 surface at a vertical angle ai, from 

 the perpendicular. At each boundary it 

 will be refracted according to the law 

 of refraction : 



^^^^^^^^^^^^^^^rT^^'^^T^TP^^P^TT!:^:^^':^^^^ 



'///;^//,^^///iiy///fiy///?^//^v//^^//A\:>y//J^//^ 



Fig. 416. 



-Path of refracted wave through 

 horizontal layers. 



sin 02 _ V2 

 sin ai Vi 



sin 03 _ Vs . sina4 _ V4 



• ~~ TT t • ~~ 17 > etc. 

 sm a2 K 2 sm as V3 



(15) 



By multiplying successive ratios it is found that the vertical angle for 



Vn 



any layer (w) is given by sin an = 77- sin ai 



(16) 



The thickness of the layers may be reduced and their number increased 

 to any desired extent without affecting the law of refraction. In the limiting 

 case, the thickness of the layers may be allowed to approach zero, with an 

 infinitesimal change of velocity between each layer. The limiting case, 

 therefore, is a continuous distribution of velocity with depth. The vertical 



