Dynamic Green's Functions and Integral Equations for a Double-Porosity Dual-Permeability Poroelastic Material

Abstract

Geomaterials such as sedimentary rocks often contain fissures and cracks. Such secondary porosity will result in the so-called mesoscopic flow in wave propagation. Its presence is increasingly believed to be responsible for the significant wave energy loss in the seismic frequency band. In the present research, the double-porosity dual-permeability model is employed to describe such phenomena. Based on the model, we derive both the three-dimensional (3D) and two-dimensional (2D) dynamic Green's functions for the infinite space. The existence of reciprocity relation is demonstrated, which is used to deduce some interesting relations among Green's functions. These relations can serve as a consistency check on the obtained results. The Somigliana-type integral equations, the basis for the boundary element method (BEM), are also established. The complete list of Green's functions appearing in the integral equations is provided, which enables numerical implementation. Furthermore, the asymptotic behavior of the obtained solutions is discussed.