Chap. 9] 



SEISMIC METHODS 



507 



points 1, 2, and so on, into the upper medium, their spacing for the same 

 time intervals being Vi-t. Since in the schematic of Fig. 9-44 the velocity 

 in the upper medium was assumed to be half that in the lower medium, 

 the spacing of the fronts in the lower medium is twice that in the upper. 



By joining points reached by wave fronts at the same instant, one ob- 

 tains the front BC in the upper medium, which subtends the angle i with 

 the boundary of the lower layer. Schmidt^" has coined the expression 

 "traveling reflection" for this phenomenon. He showed that it is analo- 

 gous to the bow wave which appears when a bullet travels with a velocity 

 greater than that of sound in air (see Fig. 9-45). While the bullet is 

 traveling with the velocity V2 , a compressional wave is produced around 

 the front of the bullet which propagates with the velocity Vi (sound in air). 

 Hence, the angle of the bow wave with the path of the bullet is given by 

 sin I = V1/V2 . This wave does not 

 occur if the bullet (or any other com- 

 pressional impulse) travels mth the 

 velocity of sound in air or with less 

 velocity. In the propagation of re- 

 fraction waves, an analogous phe- 

 nomenon occurs. In the lower me- 

 dium the impulses travel with the 

 velocity of that medium, and a bow 

 wave can not occur. It appears, 

 however, in the upper medium, for its 

 velocity is less than the velocity of 

 the lower medium. 



In Fig. 9-43, let 2<^ ABB' = 2^ 

 C'CD = i, AD = s,B'B = CJC= d^_ 



AB' = CD = d tan i and AB = CD = d/cos i. Then the travel time 

 for the wave traveling the path ABCD is h = 2(AB)/vi + BC/Vi] BC = 

 s — 2d tan i; therefore. 



Fig. 9-45. Bow wave of bullet (adapted 

 from O. V. Schmidt). 



k 



s , 2d . 

 h — cos t. 



V2 Vi 



(9-43) 



Differentiation of this equation gives ds/dti = V2 = cotan fi. Without 

 physical contact with the lower layer it is thus possible to obtain the 

 elastic wave velocity in the layer from the slope of the travel-time curve. 

 Near the shot point the wave traveling directly from A to D arrives ahead 

 of the underlayer wave; beginning with the "critical" distance x, it arrives 

 later than the underlayer wave. A break occurs in the travel-time curve 

 at the distance x, that is, for the simultaneous arrival of both waves. By 



'" O. V. Schmidt, Zeit. Geophys., 12(6/6), 199-205 (1936). 



