Marine Electrical Sensing for Detecting Small Inhomogeneities

We consider towed electrical sensing for detecting and localizing small inhomogeneities in the marine environment. Assuming the domain to be homogeneous apart from a few dispersed inclusions, the low-frequency electrical measurements can be modeled using a single-layer potential formulation for a source function defined at the boundaries of the inclusions. A key component of these measurements is the potential induced by the polarization of the inclusions, which at the far field can be shown to be equivalent to the potential of dipole sources centered at the inclusions. Under this approximation, we formulate an inverse problem for localizing the inclusions and then enforce some regularization in the form of an a priori assumption on the shape of the inclusions. In this context, solving the inverse problem requires tracing some coordinates where the polarization potential at the current injecting electrodes becomes zero since these define a set of lines intersecting at the center of the targeted inclusions. This methodology is implemented by a simple algorithm, whose computational complexity mounts to solving a small number of low-dimensional linear systems. Analysis indicates fair robustness of the algorithm to measurement noise and model inaccuracies, and this is also supported by numerical simulation experiments.