LAUSR

Abstract Full Waveform Inversion (FWI) is a promising method for reconstructing subsurface parameters from the full information content in the seismogram. However, FWI is facing many difficulties in practice. The lack of the source wavelet information, the nonlinearity of the forward problems, and ill-posedness of the formulation all contribute to a pressing need for novel regularization techniques and fast algorithms to speed up and improve inversion results. In this paper, by making use of the variable projection method for nonlinear least squares problems, we develop a source-independent frequency-domain FWI strategy. Specifically, the source wavelet for each frequency is removed automatically using a minimum norm solution between the measured and simulated data. Therefore, the inversion process becomes source independent. In order to overcome the defects of overly smoothed edges caused by the classical Tikhonov regularization, sparsity constrained regularization is applied to FWI based on the ability of curvelets to efficiently represent geophysical images. However, non-differentiability of the objective function make it challenging to find an efficient numerical solution. By using the proximal mapping and the Barzilai-Borwein step size rule, we derive a new accelerated proximal gradient algorithm to handle such non-smooth objective functions. The numerical examples show that very good reconstruction results can be obtained by the proposed algorithm without knowledge of the source. Compared to the gradient descent method with a constant step size, the accelerated algorithm gaves a superior result with much higher resolution.