Imaging of 3D electromagnetic data at low-induction numbers

Abstract

We expressed electromagnetic measurements at low induction numbers as spatial averages of the subsurface electrical conductivity distribution and developed an algorithm for the recovery of the latter in terms of the former. The basis of our approach is an integral equation whose averaging kernel is independent of the conductivity distribution. That is, the recovery of conductivity from the measurements leads to a linear inverse problem. Previous work in one and two dimensions demonstrated that using a kernel independent of conductivity leads to reasonably good results in quantitative interpretations. This study extended the approach to 3D models and to data taken along several profiles over a given area. The algorithm handles vertical and horizontal magnetic dipoles with multiple separations for appropriate depth discrimination. The approximation also handles issues like negative conductivity measurements, which commonly appear when crossing near-surface conductors. This happens particularly when using vertical magnetic dipoles; whose averaging kernel has significant negative weights in the space between the dipoles, something that does not happen for the horizontal dipoles. In general, the more complex the kernel, the more complicated the signature of any given anomaly. This makes qualitative interpretations of pseudosections somewhat difficult when dealing with more than one conductive or resistive body. The algorithm was validated using synthetic data for imaging data from horizontal or vertical coils or from a combination of them. Imaging of field data from a mine tailings site recovered a shallow 3D conductive anomaly associated with the tailings.