Adaptive laterally constrained inversion of time-domain electromagnetic data using Hierarchical Bayes

Laterally constrained inversion (LCI) of time-domain electromagnetic (TEM) data is effective in recovering quasi-layered models, particularly in sedimentary environments. By incorporating lateral constraints, LCI enhances the stability of the inverse problem and improves the resolution of stratified interfaces. However, a limitation of the LCI is the recovery of laterally smooth transitions, even in regions unsupported by the available datasets. Therefore, we have developed an adaptive LCI scheme within a Bayesian framework. Our approach introduces user-defined constraints through a multivariate Gaussian prior, where the variances serve as hyperparameters in a Hierarchical Bayes algorithm. By simultaneously sampling the model parameters and hyperparameters, our scheme allows for varying constraints throughout the model space, selectively preserving lateral constraints that align with the available datasets. We demonstrated the effectiveness of our adaptive LCI scheme through a synthetic example. The inversion results showcase the self-adaptive nature of the strength of constraints, yielding models with smooth lateral transitions while accurately retaining sharp lateral interfaces. An application to field TEM data collected in Laizhou, China, supports the findings from the synthetic example. The adaptive LCI scheme successfully images quasi-layered environments and formations with well-defined lateral interfaces. Moreover, the Bayesian inversion provides a measure of uncertainty, allowing for a comprehensive illustration of the confidence in the inversion results.