666 



EXPLORATION GEOPHYSICS 



medium makes an angle ax with the normal. The ray BP which is refracted 

 into the second medium makes an angle ao with the normal such that 

 a2 is related to ai by Snell's law (Equation 10) ; that is, 



• _ Vx . 

 sm ai = 77- sm 02 



In certain cases, namely, when ai exceeds a certain critical value, no 

 refracted ray will be produced. This will be evident from the following 



consideration. For values of ax such that sin ax is greater than 77- , Equation 



K2 



10 cannot be satisfied, and hence no refracted ray such as BS can be pro- 

 duced because sin a^ would have to be greater than 1. (Physically, this 

 means that the incident ray OB is totally reflected for all values of ax 



greater than the critical angle sin 





The particular case of interest in refraction work occurs when ax ap- 



proaches the critical value sin 



-lEi. 



In this case, 02 is almost 90° and the 



refracted ray travels approximately parallel to the boundary. 



Travel-Time Curves for a Subsurface Section Consisting of Two 

 Horizontal Layers. — Figure 411 represents a subsurface section con- 



N J'/WvW.^*^/J«*^4k%!W*W< 



Fig. 411. — Ray paths in a subsurface section consisting of two 

 horizontal strata. 



sisting of two horizontal strata which are homogeneous and isotropic and 

 have longitudinal wave velocities Vx and V2 respectively. Assume that the 

 velocities Vx and V2 increase slightly with depth. Assume also that Vx and 

 V2 differ by a finite amount so that the boundary NN' corresponds to an 

 abrupt discontinuity in velocity. represents the shot-point* and Sh a 

 seismometer station located at a distance x^ from 0. 



* In seismic prospecting the charge usually is imbedded at some depth from the 

 surface. Hence, it generally is necessary to differentiate between the actual location 

 of the charge, i.e., the bottom of the shot-hole, and the shot-point which is a point 

 on the surface vertically above the charge. In the present illustration, however, the 

 charge is assumed to be located at the surface. Hence, the shot-point and the bottom 

 of the shot-hole are identical in this case. 



