Dynamic composite elastic medium theory. Part II. Three-dimensional media

Abstract

Non-self-consistent and self-consistent methods of estimating velocity and attenuation of P waves and S waves at all frequencies for heterogeneous media with three-dimensional inclusions are formulated using the scattering functions of the individual inclusions. The methods are the generalization of methods for one-dimensional media presented in the first paper of this series. The specific case of spherical inclusions is calculated with the exact scattering function and compared with several low frequency approximations. The self-consistent estimates are consistent with Berryman’s low frequency approximation. We present spectra and wave forms of materials with solid and liquid inclusions in a solid matrix. The results show that the exact scattering functions are required to adequately describe wave propagation at all frequencies. The analysis of liquid inclusions demonstrates that viscous damping may become important only if scattering attenuation due to spherical pores is small.

Determination of porosity and saturation using seismic waveform inversion

“…Gassmann, 1951;Biot, 1962;Dvorkin and Nur, 1993) and ones based on scattering theory (e.g. Kuster and Toksöz, 1974;Berryman, 1980;Kaelin and Johnson, 1998). For a porous sand or non fractured rock these relationships are relatively simple at low frequencies (less than 10 kHz): the velocity as a function of porosity and saturation is real valued and non dispersive.…”

“…Elastic wave propagation through a porous medium can be modelled using a multiple scattering approach. The approach is described in detail by Kaelin and Johnson (1998) and it therefore suffices to repeat only the basic ideas here. In a heterogeneous medium The relationship between acoustic, viscoacoustic and poroelastic wave propagation.…”

“…The poroelastic velocities are computed using an effective medium theory (the Dynamic Composity Effective Medium (DYCEM) method; Kaelin and Johnson, 1998). These velocities are complex valued and frequency dependent.…”

Effects of pore fluids in the subsurface on ultrasonic wave propagation

“…The dynamic composite elastic medium theory includes multiple forward scattering from spherical pores and grains as well as intrinsic attenuation of viscous fluids (Kaelin and Johnson, 1998). The elastic P-waves and S-waves experience multiple scattering from grains and pores.…”

Grain-size dependence of shear wave speed dispersion and attenuation in granular marine sediments

“…However, some studies on multiple scattering for the media with solid or liquid inclusions in a solid matrix found that the frequency dependence of speed and attenuation for compressional and shear waves has almost the same trends. [13][14][15] Then, assuming that the same forms as Eq. (22) …”