Adaptive reconstruction method of impedance model with absolute and relative constraints

Inversion for seismic impedance is an ill-posed and band-limited problem so that inversion results are non-unique and unstable and low and high frequency components of inversion results are missed. Combining regularization with constraints of sonic log data and geological structure information can help to alleviate these problems. To achieve this, we developed an inversion method by constructing a new objective function which includes edge-preserving regularization and soft constraint based on Markov random field (MRF). The method directly introduces absolute constraints with prior impedance and sonic log data in the objective function and indirectly achieves relative constraints with geologic structures of layer interfaces and faults by adjusting the regularization parameter which is the scaling parameter δ. Moreover, we improved the inversion result using anisotropic diffusion smoothing method. Optimization approach utilized in inversion is a fast simulated annealing (FSA). We test the method on both synthetic and field data examples. Tests on 2-D synthetic data indicate that aspects of the discontinuity in the inversion results are significantly improved by adding δ values in faults and layer interfaces. We obtained better results by combining the first-order neighborhood and the third-order neighborhood of MRF. The inversion results of the field data provide more detailed information of the layers. The results of nearby faults were improved by introducing the geological structure constraints.