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.