Poroelastic finite difference modeling of seismic attenuation and dispersion due to mesoscopic-scale heterogeneity

Seismic attenuation and dispersion are numerically determined for computer-generated porous materials that contain arbitrary amounts of mesoscopic-scale heterogeneity in the porous continuum properties. The local equations used to determine the poroelastic response within such materials are those of Biot (1962). Upon applying a step change in stress to samples containing mesoscopic-scale heterogeneity, the poroelastic response is determined using finite difference modeling, and the average strain throughout the sample computed, along with the effective complex and frequency-dependent elastic moduli of the sample. The ratio of the imaginary and real parts of these moduli determines the attenuation as a function of frequency associated with the modes of applied stress (pure compression and pure shear). By having a wide range of heterogeneity present, there exists a wide range of relaxation frequencies in the response with the result that the curves of attenuation as a function of frequency are broader than in existing analytical theories based on a single relaxation frequency. Analytical explanations are given for the various high-frequency and low-frequency asymptotic behavior observed in the numerical simulations. It is also shown that the overall level of attenuation of a given sample is proportional to the square of the incompressibility contrasts locally present.