The Linearized Bregman Method for Frugal Full-waveform Inversion with Compressive Sensing and Sparsity-promoting

Abstract

Full-waveform inversion (FWI) reconstructs the subsurface properties from acquired seismic data via minimization of the misfit between observed and simulated data. However, FWI suffers from considerable computational costs resulting from the numerical solution of the wave equation for each source at each iteration. To reduce the computational burden, constructing supershots by combining several sources (aka source encoding) allows mitigation of the number of simulations at each iteration, but it gives rise to crosstalk artifacts because of interference between the individual sources of the supershot. A modified Gauss–Newton FWI (MGNFWI) approach showed that as long as the difference between the initial and true models permits a sparse representation, the $$\ell _1$$ -norm constrained model updates suppress subsampling-related artifacts. However, the spectral-projected gradient $$\ell _1$$ (SPG $$\ell _1$$ ) algorithm employed by MGNFWI is rather complicated that makes its implementation difficult. To facilitate realistic applications, we adapt a linearized Bregman (LB) method to sparsity-promoting FWI (SPFWI) because of the efficiency and simplicity of LB in the framework of $$\ell _1$$ -norm constrained optimization problem and compressive sensing. Numerical experiments performed with the BP Salt model, the Marmousi model and the BG Compass model verify the following points. The FWI result with LB solving $$\ell _1$$ -norm sparsity-promoting problem for the model update outperforms that generated by solving $$\ell _2$$ -norm problem in terms of crosstalk elimination and high-fidelity results. The simpler LB method performs comparably and even superiorly to the complicated SPG $$\ell _1$$ method in terms of computational efficiency and model quality, making the LB method a viable alternative for realistic implementations of SPFWI.