Optimized model parametrization using compact full waveform inversion. Issue 1 (13th April 2020) - Xu, Linan; Manukyan, Edgar; Maurer, Hansruedi
SUMMARY: Seismic full waveform inversion (FWI) has the potential to produce high-resolution subsurface images, but the computational resources required for realistically sized problems can be prohibitively large. In terms of computational costs, Gauss–Newton (GN) algorithms are more attractive than the commonly used conjugate gradient methods, because the former have favourable convergence properties. However, efficient implementations of GN algorithms require an excessive amount of computer memory for larger problems. To address this issue, we introduce compact full waveform inversion. Here, a suitable inverse model parametrization is sought that allows representing all subsurface features, potentially resolvable by a particular source–receiver deployment, but using only a minimum number of model parameters. In principle, an inverse model parametrization, based on the Eigenvalue decomposition, would be optimal, but this is computationally not feasible for realistic problems. Instead, we present two alternative parameter transformations, namely the Haar and the Hartley transformations, with which similarly good results can be obtained. By means of a suite of numerical experiments, we demonstrate that these transformations allow the number of model parameters to be reduced to only a few percent of the original parametrization without any significant loss of spatial resolution. This facilitates efficient solutions of large-scale FWI problems with explicit GN algorithms.