662 EXPLORATION GEOPHYSICS 



adsorption due to the viscous nature of earth materials which results in 

 an exponential decrease in amplitude proportional to the square of the 

 frequency (i.e., the amplitude falls off as ^-'^/'^ where a is an arbitrary 

 constant, / is frequency, and x is distance traveled by the wave) ; (2) solid 

 friction absorptionf in which the amplitude falls off as g-"^*; and (3) 

 scattering which also produces an exponential decrease in amplitude accord- 

 ing to either the first or the second power of frequency or both. Bom| has 

 shown that below 150 cycles per second viscous absorption is probably 

 unimportant. In seismic prospecting solid friction absorption is probably 

 the main cause of attenuation, although the quantitative effect of attenu- 

 ation by scattering has not been evaluated thoroughly. If the scattering is 

 produced by small inhomogeneities,§ much less than a wavelength in size, 

 the scattering is of the familiar Rayleigh type, and the loss in amplitude 

 is of the same nature as for viscous absorption: viz.: ^~^^'*, where b is 

 another arbitrary constant. However, there are larger inhomogeneities 

 existing in the earth that are of the same order of magnitude as the wave- 

 length, and here it is probable that the scattering is of the diffraction type 

 and proportional to the frequency rather than to the square of the frequency. 

 Thus, as far as the decrease in the amplitude of the main wave front is 

 concerned, diffraction scattering is indistinguishable from the attenuation 

 caused by solid friction absorption. Scattering will, of course, add to the 

 difficulty of detecting reflections, since it will diffuse random energy back 

 to the surface, which tends to mask the reflected signals. 



In addition to the above-described phenomena, all of which tend to 

 discriminate against the higher frequencies, it is also probable that a low 

 frequency discrimination exists for reflected waves due to the fact that 

 when the sedimentary strata are thin compared to the wavelength,f f the 

 reflection coefficient becomes considerably smaller than that calculated for 

 thick beds having a given contrast in specific acoustic resistance. This is a 

 result of the interference of the two reflections from the top and bottom 

 of the bed in question. This interference can be either constructive or 

 destructive when the bed is of the order of a quarter wavelength or more 

 in thickness,^! but for smaller thicknesses the interference is believed to 

 be such that the reflection coefficient falls off more or less directly with 

 frequency. This, of course, is a form of' diffraction scattering. 



Thus a stratified earth appears to be homogeneous to the long wave- 

 lengths ; the low frequency energy is not reflected and is returned to the 

 surface only by refraction. As far as reflected seismic energy is concerned, 

 the earth appears as a wide pass "filter." The peak frequency of this 

 "filter" shifts to lower frequencies as the depth of the reflecting bed is 

 increased, because x, the distance traveled by the wave, is in the exponent 

 of the term involving absorption and scattering. This shifts the high 



t W. T. Born, Geophysics, Vol. 6, p. 132 (1941). 



t W. T. Born, loc. cit. 



§ D. H. Clewell and R. F. Simon, Geophysics (to be published), 

 tt D. H. Clewell and R. F. Simon, loc. cii. 

 it Stewart and Lindsay, Acoustics, p. 100 (D. Van Nostrand, 1930). 



