  Frequency-domain electromagnetic instruments allow the collection of data in
different configurations, that is, varying the intercoil spacing, the
frequency, and the height above the ground. Their handy size makes these tools
very practical for near-surface characterization in many fields of
applications, for example, precision agriculture, pollution assessments, and
shallow geological investigations. To this end, the inversion of either the
real (in-phase) or the imaginary (quadrature) component of the signal has
already been studied. Furthermore, in many situations, a regularization scheme
retrieving smooth solutions is blindly applied, without taking into account the
prior available knowledge. The present work discusses an algorithm for the
inversion of the complex signal in its entirety, as well as a regularization
method that promotes the sparsity of the reconstructed electrical conductivity
distribution. This regularization strategy incorporates a minimum gradient
support stabilizer into a truncated generalized singular value decomposition
scheme. The results of the implementation of this sparsity-enhancing
regularization at each step of a damped Gauss-Newton inversion algorithm (based
on a nonlinear forward model) are compared with the solutions obtained via a
standard smooth stabilizer. An approach for estimating the depth of
investigation, that is, the maximum depth that can be investigated by a chosen
instrument configuration in a particular experimental setting is also
discussed. The effectiveness and limitations of the whole inversion algorithm
are demonstrated on synthetic and real data sets.

Numerical Analysis;Numerical Analysis