Electromagnetic Induction Tomography (EMIT) is an interesting
and promising new imaging tool which can be used for a variety of
geophysical and environmental monitoring problems, for example
for the monitoring of pollutant plumes in or above the ground water table.
It uses very low-frequency electromagnetic
waves (about 1 kHz or less). The advantage of these low frequency waves
is that they can penetrate sufficiently deep into the earth to reach
the interesting regions. However, the resulting mathematical
inverse problem is inherently three-dimensional, large-scale,
highly nonlinear and extremely ill-posed. We present a novel inversion
algorithm for 3D EMIT which tries to overcome these difficulties by
formulating the inverse problem as a shape reconstruction problem.
Since the number and topologies of the shapes are a priori
unknown, a powerful tool needs to be used for modelling and
propagating these shapes during the inversion process. We have
chosen to use a level set representation for this purpose.
We will present in the talk numerical results of this new
3D inversion algorithm from synthetically created data for
realistic model problems, and will discuss the advantages
and limitations of this method.
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