Multichannel impedance inversion in the frequency domain via anisotropic total variation with overlapping group sparsity regularization

Abstract Total variation regularization is widely used in geophysical inverse problems for preserving the edges of geological structures. However, it may lead to staircase artifacts and other inversion errors. To overcome this drawback, we present an impedance inversion method by using anisotropic total variation with overlapping group sparsity regularization. This method can not only preserve edges very well but also makes use of the group sparsity feature of acoustic impedance to reduce inversion error. Moreover, we make full use of the properties of the Toeplitz matrix and speed up the inversion process in the frequency domain. The synthetic data and field data inversion results show that the proposed method has the advantages of stronger anti-noise, faster inversion speed, and less error comparing with the conventional total variation regularization inversion method. In addition, our method can effectively alleviate staircase artifacts and therefore improves resolution.