Unified matrixvector wave equation, reciprocity and representations
Abstract
The matrixvector wave equation is a compact firstorder differential equation. It was originally used for the analysis of elastodynamic plane waves in laterally invariant media. It has been extended by various authors for laterally varying media. Other authors derived a similar formalism for other wave phenomena. This paper starts with a unified formulation of the matrixvector wave equation for 3D inhomogeneous, dissipative media. The wave vector, source vector and operator matrix are specified in the appendices for acoustic, quantum mechanical, electromagnetic, elastodynamic, poroelastodynamic, piezoelectric and seismoelectric waves. It is shown that the operator matrix obeys unified symmetry relations for all these wave phenomena. Next, unified matrixvector reciprocity theorems of the convolution and correlation type are derived, utilizing the symmetry properties of the operator matrix. These theorems formulate mathematical relations between two wave states in the same spatial domain. A unified wavefield representation is obtained by replacing one of the states in the convolutiontype reciprocity theorem by a Green's state. By replacing both states in the correlationtype reciprocity theorem by Green's states, a unified representation of the homogeneous Green's matrix is obtained. Applications of the unified reciprocity theorems and representations for forward and inverse wave problems are briefly indicated.
 Publication:

Geophysical Journal International
 Pub Date:
 January 2019
 DOI:
 10.1093/gji/ggy451
 arXiv:
 arXiv:1801.07728
 Bibcode:
 2019GeoJI.216..560W
 Keywords:

 Electromagnetic theory;
 Theoretical seismology;
 Wave propagation;
 Physics  Applied Physics
 EPrint:
 52 pages, 1 figure