Green's functions and radiation patterns in poroelastic solids revisited

Abstract

A consistent and unified formulation of Green’s functions for wave propagation in poroelastic solids based on Biot’s theory is given. Over the last decades various authors have made the attempt to derive different Green’s tensor representation for poroelastic solids. Due to the various possible combinations of field variables and source terms the different solutions differ significantly. The main solutions are reviewed and compared. It is shown that these previously reported representations of Green’s tensors can be used in a complementary sense such that all possible combinations of field variables and source types are included. As a new element we introduce the concept of moment tensors for poroelasticity. This allows us to describe sources in poroelastic solids in a consistent manner. With the help of the moment tensor concept a pressure source acting on the fluid phase is introduced as well as dipole sources and doublecouple sources. To visualize the results, radiation patterns for all the discussed sources are constructed. The shape of the radiation patterns of the fast compressional and shear wave is the same as in elastodynamics, however, the radiation characteristics of Biot’s slow wave are superimposed. The relative magnitudes of the field variables shown in the radiation patterns can be very different for different source types. In particular, for any source acting in the fluid phase the pressure field is dominated by the Biot slow wave having compressional wave polarization.