Flexible quasi-2D inversion of time-domain AEM data, using a wavelet-based complexity measure

Abstract

Summary Regularization methods improve the stability of ill-posed inverse problems by introducing some a priori characteristics for the solution such as smoothness or sharpness. In this contribution, we propose a multidimensional, scale-dependent wavelet-based ℓ1-regularization term to cure the ill-posedness of the airborne (time-domain) electromagnetic induction inverse problem. The regularization term is flexible, as it can recover blocky, smooth and tunable in-between inversion models, based on a suitable wavelet basis function. For each orientation, a different wavelet basis function can be used, introducing an additional relative regularization parameter. We propose a calibration method to determine (an educated initial guess for) this relative regularization parameter, which reduces the need to optimize for this parameter, and, consequently, the overall computation time is under control. We apply our novel scheme to a time-domain airborne electromagnetic data set in Belgian saltwater intrusion context, but the scheme could equally apply to any other 2D or 3D geophysical inverse problem.

Machine Learning for Bayesian Experimental Design in the Subsurface

“…Occam's razor is frequently invoked to justify the use of a gradient or roughness operator, which results in smoothness constraint inversion. It can also be incorporated into advanced operators seeking compactness or minimal structure (e.g., Deleersnyder et al 2022, 2021. Such approaches will produce either smooth or "simple" solutions (Loke et al, 2013), which are rarely geologically plausible (Linde et al, 2015;Zhdanov and Tolstaya, 2004); see also Appendix B.…”