796 



NATE AND DRAKE 



[CHAP. 29 



with increasing frequency. Sutton et al. (1957) hfive shown, however, that over 

 the frequency range of from a few tens of cycles per second to one megacycle the 

 velocity change is not likely to exceed 1% for sediments usually encountered. 

 Birch and Bancroft (1938) noted no significant difference between velocities 

 measured on rocks at high frequency and corresponding seismic velocities. In 

 effect, then, particles and fluid may usually be considered to move together. 

 If compressional velocities are observed that are higher than predicted by the 

 Wood equation (Table II, equation 8), the increment will be attributed to an 

 increase of quantity k-\-% [x caused by compaction and cementation. 



Table II 



Equation 



Applicability 



Reference 



. - J'^ 



(4/3)/^ 



1. 1 



2. Vs = Vif^lp) 



/T^\2 ^ 2(l-a) 

 '• \VsJ (l-2a) 



4. E ^ 3k{l-2a) 



5. Q = TT/ycT 



6. p = IfiPi « 



1. c = 2fiCi " 



8. F2 = l/pC " 



9. 1/F = IfilVi 



isotropic elastic solid 

 isotropic elastic solid 

 isotropic elastic solitl 

 isotropic elastic solid 



Bullen (1947) 

 Hiilien (1947) 

 Bullen (1947) 

 Bullen (1947) 



rc = phase velocity „. , ^ 7 /,a..-h 

 plane waves-^ ^ . , Bu-ch e/:a<. (1942) 



[ jf = period 



general 



emulsion or suspension 



emulsion or suspension 

 (Wood's equation) 



transmission perpendicular 

 to a layer sequence 

 (time-average equation) 



Shumway (1960) 

 Shumway (1960) 

 Wood (1941) 



Wyllie el al. (1956) 



"/j = volume fraction of ith constituent (/water = ^)- 

 ^ p and C from equations (6) and (7) respectively. 



Despite the exceedingly complex nature of granular media and the multi- 

 plicity of processes that affect the behavior of the aggregate as a whole, it is 

 clear from Fig. I that some broad general trends may be discerned in the 

 experimental results. The Wood equation (equation 8) is an approximate lower 

 limit to observed compressional velocities for a given porosity. As Wyllie, 

 Gregory and Gardner (1956) have pointed out the time average equation (equa- 

 tion 9) is a fair representation of the main trend of observations for consolidated 

 sediments. The spread of observations is sufficiently limited that rough pre- 

 dictions of porosity and density may be made if velocity is known. Thus, if 

 the compressional velocity is 4 km/sec, it is unlikely that porosity wiU be 

 outside the range 0.15 to 0.25 no matter what other attributes the sediment may 



