Feasibility of magnetic susceptibility tomography for shallow targets

Abstract

We present an approach to obtain images of magnetic susceptibility of the subsurface using as data the surface magnetic fields of small dipole sources. The approach relies on measurements taken with the instrument known as EM-38 MK2. This device operates with a pair of coils, one operating as the source and the other as the receiver. Usually four measurements are taken, vertical magnetic dipoles at 0.5 and 1.0 m separations, and horizontal magnetic dipoles at the same two separations. To improve depth discrimination we introduce two new arrays using the same instrument but rotated vertically from its usual horizontal lay out. The different configurations are contrasted by analyzing the subsurface signatures generated by elementary ground contributions, in the way it is currently done for resistivity arrays. We model subsurface objects using continuous variations by assuming that they are a superposition of Hann functions. For the inverse problem the superposition is such that we can model uniform bodies with rounded boundaries. We use quadratic programming for optimizing the fit to the data with only positive magnetic susceptibilities, and standard Tikhonov regularization for stabilizing the models. To deal with the non-uniqueness of the inverse problem we compute the shallowest and deepest models that fit the data. This is accomplished by a simple modification of the standard objective function for regularized optimization. We present simulations with synthetic data to demonstrate the viability of the approach. A case with field data also demonstrates the feasibility of magnetic susceptibility tomography for shallow targets.