Poststack seismic inversion using a patch-based Gaussian mixture model

Seismic inversion is a severely ill-posed problem because of noise in the observed record, band-limited seismic wavelets, and the discretization of a continuous medium. Regularization techniques can impose certain characteristics on inversion results based on prior information to obtain a stable and unique solution. However, it is difficult to find an appropriate regularization to describe the actual subsurface geology. We have developed a new acoustic impedance inversion method via a patch-based Gaussian mixture model (GMM), which is designed using available well logs. In this method, first, the nonlocal means method estimates acoustic impedance around wells in terms of the similarity of local seismic records. The extrapolated multichannel impedance is then decomposed into impedance patches. Using patched data rather than a window or single trace for training samples to obtain the GMM parameters, which contain local lateral structural information, can provide more impedance structure details and enhance the stability of the inversion result. Next, the expectation maximization algorithm is used to obtain the GMM parameters from the patched data. Finally, we apply the alternating direction method of multipliers to solve the conventional Bayesian inference illustrating the role of regularization and construct the objective function using the GMM parameters. Therefore, the inversion results are compliant with the local structural features extracted from the borehole data. The synthetic and field data tests validate the performance of our method. Compared with other conventional inversion methods, our method shows promise in providing a more accurate and stable inversion result.