A rotation total variation regularization for full waveform inversion

Mathematically, full waveform inversion is a nonlinear and ill-posed inverse problem, requiring a regularization method to obtain a reasonable result. Total variation regularization is an effective regularization method which can preserve the sharp edges of the solution. It is well-known that the standard total variation regularization usually leads to stair-casing artifacts in slanted structures. Thus, the standard total variation regularization may not be effective in solving the full waveform inverse problem, due to the slanted properties of the subsurface structures. In this paper, we propose a rotational total variation regularization method based on the weighting rotational transform operator and the standard total variation regularization for the full waveform inverse problem. To further improve the resolution of the inverted results for different directional structures, a hybrid regularization method combining the rotational and standard total variation regularization is proposed. An efficient version of the conjugate gradient method, i.e., CGOPT, is used to efficiently solve the proposed methods. Numerical experiments based on Sigsbee and Marmousi2 models are carried out to demonstrate the effectiveness of our methods.