ADMM-based full-waveform inversion with unknown source signatures

Abstract

Full waveform inversion (FWI) requires an accurate estimation of source signatures. Indeed, the coupling between the source signatures and the subsurface model can make small errors in the former to translate into significant errors in the latter. When direct methods are used to solve the forward problem, classical frequency-domain FWI efficiently processes multiple sources for source signature and wavefield estimations once a single Lower-Upper (LU) decomposition of the impedance matrix has been performed. Classical FWI relies on the exact solution of the wave equation and hence is highly sensitive to the inaccuracy of the velocity model due to cycle skipping. Recently, FWI with search-space extension tackles this sensitivity issue by solving the wave equation with a data assimilation. When the wavefields and the source signatures are jointly estimated with this approach, the extended wave equation operator becomes source dependent, hence making direct methods and, to a lesser extent, block iterative methods ineffective. We propose a simple method to bypass this issue and estimate source signatures efficiently during extended FWI. The method computes each wavefield with a blended source to make the optimization problem source independent. Besides computational efficiency, the additional degrees of freedom introduced by spatially distributing the sources allow for more accurate signature estimation at the physical location of the sources when the velocity model is rough. Numerical tests on the 2004 BP salt synthetic model confirm the efficiency and the robustness against velocity model errors of the new method compared to the case where source signatures are known.