A new approach to seismic wave propagation in unconsolidated and consolidated porous media

Abstract

Compressional and shear waves in porous media, including saturated marine sediments and dry sedimentary rocks, exhibit an attenuation that scales as the first power of frequency. Biot developed a theory of wave propagation in such materials in which the dissipation was taken to be viscosity of the pore fluid. This, however, yields an attenuation that scales as the square of frequency below some threshold frequency, above which it converts to the square root of frequency. Recently, Buckingham developed an alternative wave theory of porous media in which the dissipation arises from stress relaxation at grain boundaries. Such a mechanism is consistent with the fact that stress and strain in porous media do not follow one another instantaneously. With an appropriate choice for the internal material response function, representing a time-dependent stick-slip process between grains, it turns out that the attenuation scales as the first power of frequency, in accord with observations. Moreover, the dissipation also introduces stiffness into the material, allowing it to support shear, even though the elastic modulus of the medium may be identically zero. These new ideas will be explored in the presentation, and the theoretical predictions will be shown to be consistent with experimental data.