A high-order total-variation regularisation method for full-waveform inversion

Full-waveform inversion (FWI) is among the most effective methods of velocity modelling in seismic exploration. However, because of the strong nonlinearity of the FWI, if the velocity in the target geobody is not sharply different from that in its surroundings, the total variation (TV) of the model will not be sufficiently sparse. To alleviate this issue, we propose a novel TV-regularised FWI method that can consider the sparsity of the high-order regularisation operator and consequently improve the stability of the inversion process and produce more focused model boundaries. We use a split-Bregman algorithm to solve the inversion optimisation problem while building the TV-regularised objective function. We show that stable model updates can be obtained by this algorithm, which proved to be effective and reliable in the numerical tests. These tests also show that the proposed method converges faster, can model the velocity domain better than conventional methods and can effectively identify layer boundaries with a weak velocity contrast. We conclude that the novel FWI method based on high-order TV regularisation is robust and accurate.