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

Walters, SJ ORCID: 0000-0002-4480-767X, Forbes, LK ORCID: 0000-0002-9135-3594 and Reading, AM ORCID: 0000-0002-9316-7605 2020 , '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, vol. 476, no. 2243 , pp. 1-17 , doi: 10.1098/rspa.2020.0636.

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Abstract

This paper presents two approaches to mathematicalmodelling of a synthetic seismic pulse, and acomparison between them. First, a new analyticalmodel is developed in two-dimensional Cartesiancoordinates. Combined with an initial condition ofsufficient symmetry, this provides a valuable checkfor the validity of the numerical method that follows.A particular initial condition is found which allowsfor a new closed-form solution. A numerical schemeis then presented which combines a spectral (Fourier)representation for displacement components andwave-speed parameters, a fourth-order Runge–Kuttaintegration method, and an absorbing boundary layer.The resulting large system of differential equations issolved in parallel on suitable enhanced performancedesktop hardware in a new software implementation.This provides an alternative approach to forwardmodelling of waves within isotropic media whichis efficient, and tailored to rapid and flexibledevelopments in modelling seismic structure, forexample, shallow depth environmental applications.Visual comparisons of the analytic solution and thenumerical scheme are presented.

Item Type: Article
Authors/Creators:Walters, SJ and Forbes, LK and Reading, AM
Keywords: seismology, wave propagation, spectral method
Journal or Publication Title: Proceedings of the Royal Society of London A. Mathematical, Physical and Engineering Sciences
Publisher: Royal Soc London
ISSN: 1364-5021
DOI / ID Number: 10.1098/rspa.2020.0636
Copyright Information:

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

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