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

Abstract

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.