Inversion of multi-configuration complex EMI data with minimum gradient support regularization. A case study

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Abstract
Frequency-domain electromagnetic instruments allow the collection of data in different configurations, that is, varying the inter-coil spacing, the frequency, and the height above the ground. This makes these tools very practical, also because of their handy size, for the characterization of the near surface in many fields of applications, for example, precision agriculture, pollution assessments, 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 promoting 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 against the associated solutions obtained via a standard smooth stabilizer. An approach to estimate the depth of investigation (DOI), 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 datasets.

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