Frequency-domain electromagnetic induction for the prediction of electrical conductivity and magnetic susceptibility using geostatistical inversion and randomized tensor decomposition

Abstract

High-resolution characterization of near-surface systems is crucial for a variety of subsurface applications. Frequency-domain electromagnetic (FDEM) induction has been widely used in near-surface characterization compared with other geophysical methods due to its flexibility in acquisition and its ability to survey large areas with high resolution but with relatively low costs. FDEM measurements are sensitive to subsurface electrical conductivity (EC) and magnetic susceptibility (MS). However, the prediction of these properties requires solving a geophysical inverse problem. We combine ensemble smoother with multiple data assimilation (ES-MDA) and model reparameterization via randomized tensor decomposition (RTD) to simultaneously predict EC and MS from measured FDEM data. ES-MDA is an iterative data assimilation method that can be applied to nonlinear forward operators and provides multiple posterior realizations conditioned on the geophysical measurements to evaluate the model uncertainty. However, its application is usually computationally prohibitive for large-scale 3D problems. To overcome this limitation, we reduce the model parameters using RTD and then perform the inversion in the low-dimensional model space. The method is applied to synthetic and noisy real data sets. In the synthetic application example, the predicted posterior realizations illustrate the ability of our method to recover the true models of EC and MS accurately. The real case application comprises FDEM data acquired over arable land characterized by quaternary siliciclastic deposits with geoarchaeological features. We assess the performance of the inversion method at a borehole location not used to constrain the inversion. The inverted models do capture the available log data, illustrating the applicability of the inversion method to noisy real data.