Wavefield reconstruction for velocity–stress elastodynamic full-waveform inversion

Abstract

SUMMARY Gradient computations in full-waveform inversion (FWI) require calculating zero-lag cross-correlations of two wavefields propagating in opposite temporal directions. Lossless media permit accurate and efficient reconstruction of the incident field from recordings along a closed boundary, such that both wavefields propagate backwards in time. Reconstruction avoids storing wavefield states of the incident field to secondary storage, which is not feasible for many realistic inversion problems. We give particular attention to velocity–stress modelling schemes and propose a novel modification of a conventional reconstruction method derived from the elastodynamic Kirchhoff–Helmholtz integral. In contrast to the original formulation (in a previous related work), the proposed approach is well-suited for velocity–stress schemes. Numerical examples demonstrate accurate wavefield reconstruction in heterogeneous, elastic media. A practical example using 3-D elastic FWI demonstrates agreement with the reference solution.

Elastodynamic full waveform inversion on GPUs with time-space tiling and wavefield reconstruction

“…In order to perform reconstruction, the recorded wavefield is represented as body force and deformation rate sources. Respectively, these sources read [1]…”

“…This leads, however, to the undesirable property that the inherent memory requirements scale linearly with the half-length of the stencil operator. In contrast, the memory size and interconnection transfers required by wavefield reconstruction methods formulated from conservation of elastodynamic power [25,52,1] are constant across discretization accuracies. For realistic half-lengths of the stencil operator, such as the interval four to sixteen, considering the latter reconstruction method can decrease the memory requirements for wavefield reconstruction by an order of magnitude, compared to stencil based reconstruction methods.…”

“…We consider the combined application of the reconstruction method in [1] in conjuction with time-space tiling for a fast FWI implementation on GPUs, also beyond the device memory size. A key feature is that the memory-efficient reconstruction method significantly reduces the working set, whilst tiling allows efficient computations even when the (reduced) working set oversubscribes GPU memory.…”

“…Within this, we discuss how to accomodate source and receiver functionality, along with wavefield reconstruction methods, within time-space tiling. Furthermore, we give attention to the efficient implementation of the wavefield reconstruction method in [1] within staggered-grid FD methods. This type of wavefield representation method is ubiquitous in the seismic community [42], with uses including separation of wavefield constituents [3] and wavefield redatuming [14,5].…”

Elastic immersive wave experimentation

“…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., Lin et al, 2019;Jaimes-Osorio et al, 2021;Aaker et al, 2020;Pienkowska et al, 2020). Local-domain modeling can also be applied for investigating a target of interest inside a sub-volume of a medium, for example, in nondestructive testing where damage zones are commonly highly localized (e.g., fracture corridors, see Nosjean et al, 2020;Zerbst et al, 2016;Wiggenhauser et al, 2018), in medical acoustics where modeling targets are often local organs such as a beating artery or liver fat (e.g., Kyriakou, 2015;Solovchuk et al, 2015;Robertson et al, 2017), and in modeling of electromagnetic waves such as for ground-penetrating radar (GPR) which are often used to detect a local target in the Earth's subsurface (Lambot et al, 2004;Hartley et al, 2018;Akinsunmade et al, 2019).…”