Footprint-driven stochastic approximation inversion for time-domain airborne electromagnetic data

Abstract

The airborne electromagnetic (AEM) method can be used to effectively explore underground conductivity structures at high resolution. Conventional three-dimensional (3D) AEM inversions are mainly based on gradient-type deterministic methods; however, their results cannot be evaluated without bias because they only provide an updated model from an initial one. Here, we propose a footprint-driven stochastic approximation (FSA) method for 3D time-domain AEM inversion. We first adopt a compressed sensing strategy to speed up the forward modeling process, where random K-set ( K≥1) data are sampled with a preset sampling rate to guarantee a high-precision reconstruction. Then, we establish K-sets of stochastic inversion equations with a preconditioner consisting of the sampling rate and gradient noise and produce K different updates that have different focuses on the underground structure. The final model update in each iteration is obtained using a footprint-driven averaging technique that first considers the contributions of K-set models on the underground structures in terms of AEM footprint, then uses the mean value and standard deviation to determine whether each model is accepted or rejected. Numerical experiments show that the K updates of the FSA inversion gradually reveal similar structures as the inversion proceeds. The small uncertainty and acceptable relative accuracy further demonstrate the efficacy of the proposed parameter selection strategy. As such, the method can provide a reliable conductivity distribution with uncertainty for synthetic data, as well as a practical model from the Lisheen sulfide deposit.