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Time Domain Full Waveform Inversion with Decomposed Gauss-Newton Hessian
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, 84th EAGE Annual Conference & Exhibition, Jun 2023, Volume 2023, p.1 - 5
Abstract
Summary
Full waveform inversion (FWI) provide high-resolution models of the subsurface. However, the convergence of iterations can be very slow when the steepest-descent direction provided by the gradient is not preconditioned by the inverse of the full Newton Hessian or its linear approximation, namely the Gauss-Newton (GN) Hessian. Various implementations of the Hessian effects have been proposed such as the truncated Newton methods but their implementation in the time domain can be computationally expensive in time and memory. To overcome this bottleneck, we decompose the GN Hessian into a source-side diagonal pseudo-Hessian corresponding to the auto-correlation of the virtual sources and a receiver-side Hessian in the data domain. The pseudo-Hessian doesn’t generate computational overhead while the data-domain Hessian inverse is approximated by a 2D Gabor matching filter to avoid the storage of wavefields. Finally, the computational cost of the decomposed GN direction is two times that of the steepest descent direction. Numerical tests validate that the decomposed GN Hessian can be used either as an approximation of the true Gauss-Newton Hessian or as a preconditioner of quasi-Newton methods such as L-BFGS.
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