Unified matrix-vector wave equation, reciprocity and representations

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
93 Downloads (Pure)

Abstract

The matrix-vector wave equation is a compact first-order 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 matrix-vector wave equation for 3-D 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 matrix-vector 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 convolution-type reciprocity theorem by a Green's state. By replacing both states in the correlation-type 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.

Original languageEnglish
Pages (from-to)560-583
Number of pages24
JournalGeophysical Journal International
Volume216
Issue number1
DOIs
Publication statusPublished - 2019

Keywords

  • Electromagnetic theory
  • Theoretical seismology
  • Wave propagation

Fingerprint Dive into the research topics of 'Unified matrix-vector wave equation, reciprocity and representations'. Together they form a unique fingerprint.

Cite this