Volume integral equations of the scattering problem of poroelasticity and their properties

Scattering of monochromatic waves on an isolated inhomogeneity (inclusion) in an infinite poroelastic medium is considered. Wave propagation in the medium and the inclusion are described by Biot's equations of poroelasticity. The problem is reduced to 3D‐integro‐differential equations for displacement and pressure fields in the region occupied by the inclusion. Properties of the integral operators in these equations are studied. Discontinuities of the fields on the inclusion boundary are indicated. The case of a thin inclusion with low permeability is considered. The corresponding scattering problem is reduced to a 2D integral equation on the middle surface of the inclusion. The unknown function in this equation is the pressure jump in the transverse direction to the inclusion middle surface. An inclusion with a thin layer of low permeability on its interface is considered. The appropriate boundary conditions on the inclusion interface are pointed out. Methods of numerical solution of the volume integral equations of the scattering problems of poroelasticity are discussed.