Adaptive Seismic Inversion in Piecewise Smooth Media Using Whiteness-based Alternating Directions
Post-stack acoustic impedance inversion is ill-posed because seismic data are band-limited and contaminated by noise. Regularization improves the stability of the inversion, but Tikhonov regularization tends to blur formation interfaces, whereas total variation (TV) regularization may introduce staircase artifacts. To simultaneously characterize abrupt interlayer discontinuities and gradual intralayer variations, we propose an inversion method based on anisotropic Tikhonov-TV regularization and automatic parameter selection. The method decomposes the logarithmic impedance model into piecewise-constant and smooth components. TV and Tikhonov constraints are imposed on these components, respectively, in both the vertical and horizontal directions. The performance of the inversion depends critically, among other factors, on the relative weight of the total regularization term with respect to the data misfit, the relative weight of the two regularization components (the balancing parameter), and the efficiency of computing a candidate solution for a given set of parameters. In this paper, we propose a new adaptive algorithm based on alternating directions, in which (i) a fast candidate-solution computation scheme is developed in the spectral domain by exploiting the Sylvester structure and fast Fourier transforms, thereby reducing the computational cost of parameter searching; (ii) the regularization parameter is selected adaptively using the residual whiteness principle; and (iii) the balancing parameter is adaptively updated according to robust statistical characteristics of the impedance-model gradients. Synthetic and field-data tests demonstrate that, compared with conventional Tikhonov and TV methods, the proposed method better preserves impedance interfaces while reducing staircase artifacts and inter-trace discontinuities, thereby improving the reconstruction of impedance structures.