Full waveform inversion with steerable variation regularization

We propose a new regularization scheme for Full Waveform Inversion (FWI). The new method makes use of a priori information on the spatial variability of the earth model to overcome the limitations of the inversion in the presence of high velocity contrast geobodies and cycle skipping. It comprises two additional regularization terms to the FWI objective function. The first term evaluates the L1 norm of total variation (TV) of the model, while the second term steers the solution based on local prior information of the model spatial variability. Both regularization terms can be made spatially variant to accommodate different geological features in the model, i.e. sediments (smooth changes), salt bodies (piecewise constant). Our procedure makes use of the split Bregman iterations, an effective algorithm for solving the L1 optimization problems. The result is a computationally efficient and accurate implementation. We show the potential of the method by using the BP 2004 velocity benchmark model. There, our regularization scheme allows the inversion to start from a simple velocity model and delivers a high-quality reconstruction of salt bodies.