Chap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 927 



<r, and Young's modulus E follow from a combination of the longitudinal 

 and transverse wave speeds: 



y = v?.S <r = )%, E = 2t,(l+«T). (12-14) 



© 



In homogeneous or nearly homogeneous ground the phase-speed travel- 

 time curves are straight lines of constant slope, that is, they indicate 

 constant velocities which in turn depend solely on the elastic properties 

 and the densities of the formations. In stratified media there occurs 

 a change of velocity with frequency known as dispersion. Where there is 

 an underlayer of higher velocity, the apparent velocity will decrease with 

 frequency, first slowly, and then more rapidly. Generally, therefore, the 

 presence of an underlayer will not be indicated by two true velocities and 

 a break between them, as in the longitudinal wave travel-time curves. 

 Only in such cases where dispersion is not possible, that is, when the fre- 

 quency is less than the overburden velocity divided by four times the 

 depth to the interface, will there be a break in the travel-time curve. 

 Then, velocities will be recorded that are independent of frequency. 



This means that for obtaining travel-time curves with true velocities, 

 one should operate with low frequencies, since in that case no nodal point 

 will develop at the interface and the underlayer will partake in the oscilla- 

 tion. Simple expressions^^ may be written for the apparent velocity, v, 

 measured at the surface, and for the depth, d, to the interface when there 

 is a considerable contrast between the rigidity moduli and, therefore, the 

 velocities Vi and V2 of the two layers. In that case, 



4/vid 



and 



d= 4^=, (12-15&) 



where X is the wave length and / is frequency. 



Owing to the considerable amount of information on surface and sub- 

 surface formations that can be obtained by comparatively simple means 

 from dynamic soil tests, these tests have found increasing application in 

 various engineering fields. Such applications include: determination of 



•1 Ibid. 



