Reciprocity and power balance for piecewise continuous media with imperfect interfaces

Abstract

The interaction of elastodynamic waves with imperfect interfaces is usually described by the so‐called linear slip model. In this model it is assumed that the particle displacement of an elastic wave at an interface jumps by a finite amount, linearly proportional to the stress at the interface. In this paper we postulate general boundary conditions at arbitrarily shaped imperfect interfaces for acoustic waves in fluids, elastodynamic waves in solids, electromagnetic waves in matter, poroelastic waves in porous solids, and seismoelectric waves in porous solids in such a way that they cover the linear slip model and other existing models for imperfect interfaces. These boundary conditions are expressed by a single matrix‐vector equation in the space‐frequency domain. Using this equation, we extend two unified reciprocity theorems (one of the convolution type and one of the correlation type) for the various wave phenomena, with an extra integral over the imperfect interfaces. By considering two special cases of these reciprocity theorems, we observe that (1) source‐receiver reciprocity remains valid when the source and receiver are separated by imperfect interfaces and that (2) the extra integral in the correlation‐type reciprocity theorem quantifies the power dissipated by the imperfect interfaces.