SEISMIC WAVE TRAVEL The elastic wavelets which propagate through 



the various isotropic regions of the inhomo- 

 geneous crustal material are of three types: (1) longitudinal or compressional, 

 (2) transverse or shear, and (3) surface. In general, only the first is useful in 

 subsurface exploration, the transverse and surface waves (when recorded) being 

 relegated to the category of noise. There are exceptions; e.g., depth determin- 

 ations by composited reflections (Ricker and Lynn, 1950), dynamic soil studies 

 (Heiland, 1939), and the phase velocity method of exploration (Press, 1957). 

 Both longitudinal and transverse waves are body waves, i.e., propagating 

 within a material body as opposed to traveling along its surface. The longitudinal 

 wave is characterized by particle motion to-and-fro along the direction of propa- 

 gation. It travels with a velocity, V L , which depends on Young's modulus, 

 E, density, 8, and Poisson's ratio, a, for the material, given by the expression 



Vi 



- JK 1 -a 



X 8 (/ -2a) (1 + a 



In terms of bulk modulus, K, and modulus of rigidity, /", the velocity can be 

 written as 



y = J 3K + 4u . 



In the transverse plane wave, particles oscillate at right angles to the 

 direction of propagation. The propagation velocity, V T , of the transverse wave 

 is not dependent upon the compressibility of the material but only on its 

 rigidity and density and 



v - Je _j _ > 



Vt - ^r 2(1+ a) - ^8 



Brief comparison of these two velocity expressions leads to the conclusions that 

 the longitudinal velocity of a medium is always greater than its transverse and 

 that fluids, having very low values of rigidity can be considered as failing to 

 support transverse waves. [It has been estimated (Gutenberg, 1951) that the /j. of 

 fluids is in the order of 10" 6 that of steel.] 



Among the several factors that control the seismic wave velocity of 

 formations are lithology, depth of burial, structural position, and geologic age. 

 The typical values given in Table 26-1 illustrate the effect of some of these factors. 

 We note that in general, the greater the depth of burial or the greater the geologic 

 age, the higher the velocity. In light of the velocity equations, one would think 

 that the increase in density which accompanies greater compaction should 

 decrease rather than increase velocity. Since it is velocity that we observe, we 

 can only conclude that the elastic constants increase to a greater degree than 



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