Full waveform inverse problems based on the least-squares principle are generally ill-posed. Their solution is neither unique nor stable and hence they require regularization. The Total Variation (TV) regularization method is used to resolve sharp interfaces obtaining solutions whose edges and discontinuities are preserved and to address the stability problem of full waveform inversion in exploration seismology. TV regularization accomplishes these goals by imposing sparsity on the gradient of the model parameter. The 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 data where the gradient of the cost function is computed using the adjoint-state method (Plessix, 2006). Tests with the Marmousi data set are utilized to highlight our numerical results.


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