Print Email Facebook Twitter Unified matrix-vector wave equation, reciprocity and representations Title Unified matrix-vector wave equation, reciprocity and representations Author Wapenaar, C.P.A. (TU Delft Applied Geophysics and Petrophysics) Date 2019 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. Subject Electromagnetic theoryTheoretical seismologyWave propagation To reference this document use: http://resolver.tudelft.nl/uuid:eb49b58e-7917-4bd2-a89d-8e86a61009a9 DOI https://doi.org/10.1093/gji/ggy451 ISSN 0956-540X Source Geophysical Journal International, 216 (1), 560-583 Part of collection Institutional Repository Document type journal article Rights © 2019 C.P.A. Wapenaar Files PDF ggy451.pdf 573.09 KB Close viewer /islandora/object/uuid:eb49b58e-7917-4bd2-a89d-8e86a61009a9/datastream/OBJ/view