EMSchur3D: Airborne EM inversion using decoupled potentials

Abstract:

Airborne electromagnetics (AEM) investigations have established themselves as an invaluable tool for near-surface investigation. They are an economical and efficient means to rapidly obtain a geophysical characterization of electrical properties of the subsurface, which can often be correlated with lithology as well as water content and quality. While many AEM surveys are inherently aimed at obtaining a 3D image of the earth, the most mature means of data interpretation involves stitched 1D inversions. In many AEM surveys the geology is generally layered and changes slowly enough along the survey such that the earth beneath the instrument at any moment is effectively 1D–justifying this approach. However, AEM surveys are being conducted in increasingly challenging locales where these assumptions break down. AEM surveys in areas with large topographic relief, complicated geology, and/or surveys that are concentrated on characterizing compact features do not permit a 1D approximation. The 3D inverse problem is computationally challenging due to large memory requirements as well as the singular nature of Maxwell’s equations in the air.

We propose a deterministic 3D inversion methodology utilizing a vector- and scalar-potential frequency-domain formulation of Maxwell’s equations, which is not degenerate in the air. The potentials are decoupled through Schur decomposition resulting in smaller systems in the forward-problem formulation and no redundant matrix storage. The Schur decomposition also permits the reuse of direct solvers within the forward problem. Time-domain calculations are made tractable by avoiding costly solver refactoring at every frequency and conductivity model. The computational mesh is necessarily finer than the resolving power of the survey and reduced order models are relied upon in order to avoid nearly redundant sensitivity calculations. The proposed inversion approach is able to reproduce 3D features and avoids biases and inaccuracies of 1D interpretation in geologically complicated media.