926 MISCELLANEOUS GEOPHYSICAL METHODS [Chap. 12 



Therefore, a maximum in amplitude occurs when 



LVi \V2 Vi/. 



2i7r, (12-13a) 



and a minimum occurs when 



icoT— + sf i - -\\ = (21 ± IV, (12-L36) 



Lvi \V2 Vi/J 



where w is the angular frequency and i = 0, 1, 2, 3, 4 • • • . It is noted that 

 the amplitude has to be considered as a function not only of distance bu^ 

 of frequency as well. Taking, first, the variation of amplitude with 

 frequency at a given distance s, we see that the ratio of two frequencies 

 at which successive minima occur is equal to the ratio of two successive 

 uneven numerals (or = [21 — 1]/[21 + 1]), whereas the frequency ratio 

 corresponding to two successive maxima is equal to the ratio of two suc- 

 cessive numbers, or 1/(1 + 1.) On the other hand, if the frequency / is 

 held constant, the distance As between two adjacent minima is given by 



±1 

 As = —r, 7\ . (12-13c) 



\Vi Va/ 



Similar relations may be written for the interference of the reflected with 

 the directly transmitted waves. 



Measurement of vibrations at various distances from the source has 

 the advantage that the speed of propagation of the waves may be measured. 

 This is done by observing the time of occurrence of equiphase amplitudes, 

 usually the troughs, and by plotting these times as functions of distance 

 (see Fig. 12-21). The speed of vibrator waves is much less than that of 

 first impulse (longitudinal) waves generated by explosion. The nature of 

 vibrator waves is still a matter of speculation; it is fairly certain, however, 

 that they are transverse waves. Ramspeck^" assumes that they are Love 

 waves. In any event, it is permissible to state their velocity of propaga- 

 tion by an expression of the form v? = y/5, where y is the modulus of rigid- 

 ity and 6 the density. Therefore, when vibrator measurements are made 

 in conjunction with seismic refraction observations, all important elastic 

 properties of the surface layers may be calculated, provided density deter- 

 minations are available. Thus, the modulus of rigidity y, Poisson's ratio 



90 A. Ramspeck, and G. A. Schulze, Degebo Veroff., 6, 1-27 (1938). 



