Conclusions

We have introduced a fast and accurate method to estimate the non-stationary triangle smoothing radius for matching seismic datasets using the Gauss-Newton approach. The proposed method was used to show that non-stationary triangle smoothing can be tailored to the properties of the input seismic dataset such that the smoothing is low-cost and edge-preserving. This method was also shown to be effective in field data applications of non-stationary local signal-and-noise orthogonalization, non-stationary local dip estimation, and balancing the spectral content between two seismic datasets acquired over the same area. Compared to the previous first-order line-search method, it is no surprise that the proposed second-order method converges faster and to a more accurate result. An additional factor that made the proposed method faster than the previous method is bypassing the local frequency calculation step. Although matching local frequencies is one way to obtain a reasonable estimate for the smoothing radius, we have shown that it was not necessary. Nonetheless, some potential seismic data matching applications may benefit from matching local frequencies; thus, it is worth expanding the proposed method to match local attributes between seismic datasets. The proposed method can find additional applications in other geophysical data analysis tasks and inverse problems that call for non-stationary regularization.