Exact extrapolation and immersive modelling with finite-difference injection
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Date
2020-06-26
Publication Type
Journal Article
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yes
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Abstract
In numerical modelling of wave propagation, the finite-difference (FD) injection method enables the re-introduction of simulated wavefields in model subdomains with machine precision, enabling the efficient calculation of waveforms after localized model alterations. By rewriting the FD-injection method in terms of sets of equivalent sources, we show how the same principles can be applied to achieve on-the-fly wavefield extrapolation using Kirchhoff–Helmholtz (KH)-like integrals. The resulting extrapolation methods are numerically exact when used in conjunction with FD-computed Green’s functions. Since FD injection only relies on the linearity of the wave equation and compactness of FD stencils in space, the methods can be applied to both staggered and non-staggered discretizations with arbitrary-order spatial operators. Examples for both types of discretizations show how these extrapolators can be used to truncate models with exact absorbing or immersive boundary conditions. Such immersive modelling involves the evaluation of KH-type extrapolation and representation integrals in the same simulation, which include the long-range interactions missing from conventional FD injection.
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published
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Journal / series
Volume
223 (1)
Pages / Article No.
584 - 598
Publisher
Oxford University Press
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Subject
Numerical modelling; Numerical solutions; Wave propagation
Organisational unit
03953 - Robertsson, Johan / Robertsson, Johan
Notes
Funding
694407 - MAchine for Time Reversal and Imersive wave eXperiments (EC)