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A numerical modeling of wave propagation that is independent of coordinate transformation
LUC T. IKELLE
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CASP Project, Department of Geology and Geophysics, Texas A&M University, College Station, TX 77843-3115, U.S.A.,
JSE 2012, 21(2), 153–176;
Submitted: 9 June 2025 | Revised: 9 June 2025 | Accepted: 9 June 2025 | Published: 9 June 2025
© 2025 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract
It is a remarkable fact that Maxwell’s equations under any coordinate transformation can be written in an identical mathematical form as the ones in Cartesian coordinates. However, in some particular coordinate transformations, like the cylindrical coordinate transformations, the physical properties becomes anisotropic, even if they are isotropic in the Cartesian coordinates. Even the permittivity can be anisotropic. We here review these fundamental results. The remarkable invariance of Maxwell’s equations under coordinate transformation can also extend to elastodynamic wave equations by rewriting them in a new form. We have used this new form of the elastodynamic wave equations to describe a numerical solution of elastic wave propagation which is independent of coordinate transformation.
Keywords
elastodynamic equations
Maxwell’s equations
curvilinear coordinates
natural coordinates
physical coordinates
finite-difference solution
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