English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

International audienceS U M M A R Y We derive a fast discrete solution to the scattering problem. This solution allows us to compute accurate synthetic seismograms or waveforms for arbitrary locations of sources and receivers within a medium containing localized perturbations. The key to efficiency is that wave propagation modelling does not need to be carried out in the entire volume that encompasses the sources and the receivers but only within the subvolume containing the perturbations or scatter-ers. The proposed solution has important applications, for example, it permits the imaging of remote targets located in regions where no sources or receivers are present. Our solution relies on domain decomposition: within a small volume that contains the scatterers, wave propagation is modelled numerically, while in the surrounding volume, where the medium isn't perturbed, the response is obtained through wavefield extrapolation. The originality of this work is the derivation of discrete formulas for representation theorems and Kirchhof–Helmholtz integrals that naturally adapt to the numerical scheme employed for modelling wave propagation. Our solution applies, for example, to finite difference methods or finite/spectral elements methods. The synthetic seismograms obtained with our solution can be considered 'exact' as the total numerical error is comparable to that of the method employed for modelling wave propagation. We detail a basic implementation of our solution in the acoustic case using the finite difference method and present numerical examples that demonstrate the accuracy of the method. We show that ignoring some terms accounting for higher order scattering effects in our solution has a limited effect on the computed seismograms and significantly reduces the computational effort. Finally, we show that our solution can be used to compute localized sensitivity kernels and we discuss applications to target oriented imaging. Extension to the elastic case is straightforward and summarized in a dedicated section. The main objective of this paper is to develop an efficient method for computing synthetic seismograms in an arbitrary complex reference medium that has been perturbed locally. To do so, we need to solve the so called scattering problem, that is, to determine the wavefield generated by the interaction of waves travelling through the medium with the scatterers, that is, the perturbations with respect to the reference medium. For the sake of efficiency, we search for a solution where the numerical modelling of wave propagation is confined to the smallest computational volume possible, that is, the limited subvolume that encompasses the scatterers. Furthermore, for the sake of completeness, the desired solution should accommodate arbitrary data sets, that is, provide us with synthetic seismograms for arbitrary sources/receivers configurations. For a source/receiver pair, since the source and the receiver can either lie inside or outside the computational volume, there are only four canonical setups that need to be addressed as illustrated in Fig. 1. More complicated setups involving multiple sources and receivers can be treated as combinations of these four simple geometries. Throughout this paper , we derive general formulae that allow us to calculate the seismic wavefield recorded with arbitrary acquisition setup, for propagation through a medium with localized buried scatterers. 1.2 Motivation Fast and accurate calculation of elastic wavefields within heterogeneous media is key for developing and improving accurate imaging 674

Fast computation of synthetic seismograms within a medium containing remote localized perturbations: a numerical solution to the scattering problem