Fast simulated annealing method of constrained impedance inversion based on nonlinear regularization

Abstract

Inversion for seismic impedance is an ill-posed and nonlinear problem. Hence inversion results are non-unique and unstable, and low and high frequency components of inversion results are missed. Combining regularization with fast simulated annealing (FSA) can help to alleviate these problems. To achieve this, we developed an inversion method by constructing a new objective function including the edge-preserving regularization with absolute and relative constraints. Optimization solution is calculated through a fast simulated annealing method. Moreover, the method uses two kinds of regularization parameters, including "weighting factor" and "scaling parameter" . In the fast simulated annealing procedure, the regularization parameters are adaptively adjusted by the maximum likelihood method in order to improve the inversion result and the convergence speed. We test the method on both synthetic and field data example. Tests on 2-D synthetic data indicate that the inversion results especially the aspects of the discontinuity are significantly sensitive to different regularization functions. The initial values of the regularization parameters are too large or too small to avoid an unstable or over-smoothed result, and affect the convergence speed. The results obtained by constant regularization parameters are smoother than that obtained by adaptively adjusting the regularization parameters, where is reducing and is increasing along with the temperature decreasing. The inversion result of the field data provides more detailed information of both the layers and the faults, and is applicable to field geological cases.