# Inversion of multiconfiguration complex EMI data with minimum gradient support regularization: A case study

## TL;DR

This paper presents a novel inversion algorithm for multiconfiguration complex EMI data that incorporates a minimum gradient support regularization to enhance sparsity, improving subsurface electrical conductivity imaging.

## Contribution

It introduces a sparsity-promoting regularization method with a minimum gradient support stabilizer within a Gauss-Newton inversion framework for complex EMI data.

## Key findings

- Enhanced resolution of electrical conductivity distributions.
- Effective depth estimation of the investigation area.
- Validated results on synthetic and real data sets.

## Abstract

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.