Full waveform inversion by model extension

Abstract:

Full-waveform inversion (FWI) has the potential of being able to retrieve high-resolution subsurface parameters. However, due to its inherently nonlinear behavior, the objective function is non-convex and presents multiple local minima. The main challenge of FWI is its inability to correctly recover the Earth’s subsurface parameters from an inaccurate starting model; especially, when long-period waves (or low wavenumbers) are missing. To overcome this problem, we propose a new objective function in which we modify the nonlinear modeling operator of the FWI problem by adding a correcting term that ensures phase matching between predicted and observed data. This additional term is computed by demigrating an extended model variable, and its contribution is gradually removed during the optimization process while ensuring convergence to the true solution. Since the proposed objective function is quadratic with respect to the extended model variable, we make use of the variable projection method. We refer to this technique as full-waveform inversion by model extension (FWIME). We provide a theoretical description of our method and illustrate its potential on synthetic examples for which FWI fails to retrieve the correct solution. We show that FWIME can recover a very accurate and high-resolution subsurface model by starting with a naive initial guess and without the use of low-frequency energy.