Abstract
Many modelling studies of wave scattering require repeated numerical simulations through models with properties that differ only in a small sub-domain. Hence, it is of interest to recompute the wavefields that account for wave propagation through the whole domain, using simulations that are performed only in the sub-domain. Immersive boundary conditions (IBCs) can be used to establish such a local wavefield modelling scheme which enables accurate wavefield recomputation, including all interactions between the locally-perturbed medium and the full domain. We develop IBC theory for elastic wave propagation, in which the boundary conditions are updated dynamically at each time step of a simulation in the local domain. These updates are calculated by wavefield extrapolation based on the Kirchhoff-Helmholtz integrals using Green's functions in the background medium. Wavefield recording and injection in IBCs can be implemented either using finite-difference (FD) injection methods, or using the method of multiple point sources (MPS). The latter method is significantly less computationally demanding in terms of both memory and number of calculations. We therefore both extend acoustic FD injection methods to elastic media, and propose a new second-order accurate MPS method to implement elastic IBCs, which is numerically exact. In higher-order FD modelling, the MPS method is not numerically exact but still produces highly accurate IBC wavefields when compared to global-domain simulations.
Highlights
Many numerical studies such as full waveform inversion (FWI) [e.g., 12,55,67] and the design of wave-based imaging and monitoring surveys [e.g., 36,49,52] require wave simulations for a suite of closely related models
The general algorithm of using FD injection for immersive wavefield modelling can be found in van Manen et al [30], and in this paper, we extend the algorithm to elastic wave equations and implement elastic immersive boundary conditions (IBCs)
We introduced immersive boundary condition (IBC) theory for elastic local wavefieldcomputation that includes all higher-order long-range interactions between the simulated local domain and global domain
Summary
Many numerical studies such as full waveform inversion (FWI) [e.g., 12,55,67] and the design of wave-based imaging and monitoring surveys [e.g., 36,49,52] require wave simulations for a suite of closely related models. In these applications, model changes may be restricted to small sub-domains within the global model, in which case it is not computationally attractive to perform the simulations on the full model to recompute seismic responses after those changes. Recomputing the full wavefield while performing only local wavefield simulations on a sub-domain that encloses the model alterations would significantly reduce the required computational resources, so this has been an active area of research in exploration geophysics and seismology [e.g., 1,22,28,42].
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