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Analytic and numerical solutions to the seismic wave equation in continuous media


Walters, SJ and Forbes, LK and Reading, AM, Analytic and numerical solutions to the seismic wave equation in continuous media, Proceedings of the Royal Society of London A. Mathematical, Physical and Engineering Sciences, 476, (2243) Article 20200636. ISSN 1364-5021 (2020) [Refereed Article]

Copyright Statement

Copyright 2020 The Author(s) Published by the Royal Society. All rights reserved

DOI: doi:10.1098/rspa.2020.0636


This paper presents two approaches to mathematical modelling of a synthetic seismic pulse, and a comparison between them. First, a new analytical model is developed in two-dimensional Cartesian coordinates. Combined with an initial condition of sufficient symmetry, this provides a valuable check for the validity of the numerical method that follows. A particular initial condition is found which allows for a new closed-form solution. A numerical scheme is then presented which combines a spectral (Fourier) representation for displacement components and wave-speed parameters, a fourth-order Runge–Kutta integration method, and an absorbing boundary layer. The resulting large system of differential equations is solved in parallel on suitable enhanced performance desktop hardware in a new software implementation. This provides an alternative approach to forward modelling of waves within isotropic media which is efficient, and tailored to rapid and flexible developments in modelling seismic structure, for example, shallow depth environmental applications. Visual comparisons of the analytic solution and the numerical scheme are presented.

Item Details

Item Type:Refereed Article
Keywords:seismology, wave propagation, spectral method
Research Division:Earth Sciences
Research Group:Geophysics
Research Field:Seismology and seismic exploration
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the earth sciences
UTAS Author:Walters, SJ (Mr Stephen Walters)
UTAS Author:Forbes, LK (Professor Larry Forbes)
UTAS Author:Reading, AM (Professor Anya Reading)
ID Code:147925
Year Published:2020
Funding Support:Australian Research Council (DP190100418)
Web of Science® Times Cited:2
Deposited By:Physics
Deposited On:2021-11-24
Last Modified:2022-08-24

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