Wavelet-based double-difference seismic tomography with sparsity regularization

We have developed a wavelet-based double-difference (DD) seismic tomography method. Instead of solving for the velocity model itself, the new method inverts for its wavelet coefficients in the wavelet domain. This method takes advantage of the multiscale property of the wavelet representation and solves the model at different scales. A sparsity constraint is applied to the inversion system to make the set of wavelet coefficients of the velocity model sparse. This considers the fact that the background velocity variation is generally smooth and the inversion proceeds in a multiscale way with larger scale features resolved first and finer scale features resolved later, which naturally leads to the sparsity of the wavelet coefficients of the model. The method is both data- and model-adaptive because wavelet coefficients are non-zero in the regions where the model changes abruptly when they are well sampled by ray paths and the model is resolved from coarser to finer scales. An iteratively reweighted least squares procedure is adopted to solve the inversion system with the sparsity regularization. A synthetic test for an idealized fault zone model shows that the new method can better resolve the discontinuous boundaries of the fault zone and the velocity values are also better recovered compared to the original DD tomography method that uses the first-order Tikhonov regularization.