810 NAFE AND DRAKE [CHAP. 29 



several different methods. These vahies are not necessarily typical. The table 

 has been constructed to give at least one value of each quantity listed, to illus- 

 trate measurements at high and low porosity, to compare shallow-water and 

 deep-water environments to show changes with frequency and to provide some 

 indication of results that may be expected for different sediment types. Num- 

 bers in brackets are not directly measured but are derived through one or 

 other of the formulae in Table II. Although most of the observations were 

 made on marine sediments a few entries for non-marine sediments have been 

 added at the bottom of the table to illustrate unusual situations, such as 

 inclusions of gas, or to provide estimates of probable values where actual 

 measurements on marine sediments are few or lacking altogether. It is parti- 

 cularly important to assemble information on shear-wave velocities. 



The only values of impedance listed are those of Hamilton et al. (1956). 

 These are not measured but are derived by taking the product pV. It is 

 probably better to find impedance by taking this product than to derive it 

 from a measured reflection coefficient, for measured reflection coefficients 

 are almost invariably complicated by the occurrence of multiple reflections 

 with a consequent increase in the apparent value of the impedance. The 

 error so introduced is much more serious below 1000 c/s than it is above that 

 frequency. 



Velocities derived from critical angle reflections and sub-bottom reflections 

 (Katz and Ewing, 1956) doubtless apply not to sediments close to the water- 

 sediment interface but to those at some distance below. On the same refraction 

 profiles leading to the tabulated numbers there was clear-cut evidence for the 

 existence of a layer close to the interface with a velocity less than water 

 velocity. 



The frequency dependence of the attenuation coefficient y is of particular 

 interest. Shumway (1960a) has reported y to be proportional to /^'^ for 65 

 samples with a standard deviation of 0.98 for the exponent. Measurements were 

 made in the frequency range 20 to 40 kc/s and attenuations apply to compres- 

 sional waves. At much lower frequencies, though not for ocean sediments, 

 McDonal et al. (1958) have observed an approximately linear dependence of 

 attenuation on frequency, the attenuation in dB per thousand feet being 1.05/ 

 for horizontally traveling shear waves from 20 to 152 c/s and 0.12/ for vertically 

 traveling compressional waves from 50 to 450 c/s. Their measurements were 

 made in bores in the Pierre Shale. Since the exponent may depend on the degree 

 of water saturation (Born, 1941) this example is introduced mainly to illustrate 

 the fact that attenuation for shear waves may differ widely from that for 

 compressional waves. 



It will be noted that in not one single instance have measurements been made 

 of all the quantities of interest. In fact, it is frequently the case that in publica- 

 tion of results no clear indication is given of the degree of water saturation, 

 though all evidence points to degree of saturation and water fraction as the 

 most significant variables in determining physical properties. All quantities 

 listed for ocean sediments apply to cases of 100% saturation. 



