Full Waveform Inversion with Total Variation Regularization

Waveform inverse problems are mathematically ill-posed and, therefore, regularization methods are required to obtain stable and unique solutions. The Total Variation (TV) regularization method is used to resolve sharp interfaces obtaining solutions where edges and discontinuities are preserved. TV regularization accomplishes these goals by imposing sparsity on the gradient of the model parameters. Full waveform inversion is carried out using the L-BFGS method in the frequency domain by selecting a limited number of frequencies from low to higher frequency. Tests with the Marmousi data set are utilized to highlight our numerical results.