Differential poroelasticity model for wave dissipation in self-similar rocks

Abstract The double-porosity theory of wave propagation in rocks considers a single scale based on soft and stiff pores, and wave attenuation occurs by local fluid flow between these pores. However, rocks exhibit more complicated fabric structures, with heterogeneities presented at multiple scales, having a self-similar fractal nature as reported. We develop a poroelasticity model to describe wave anelasticity in a fluid-saturated medium consisting of infinite components, i.e., an infinituple-porosity medium. Numerical modeling is achieved with infinite iterations, where at each iteration one component is added (a porous inclusion embedded in a porous host), analogous to the differential effective medium (DEM) theory of solid composites. By considering the self-similar structure, the properties of each component (inclusions) are scale-dependent. The example shows that the P-wave velocity dependence on frequency depends on the fractal dimension. Application of the model to sandy sea-bottom sediments shows a good agreement, with fractal dimension of 2.88.