Inversion of Multiconfiguration Complex EMI Data with Minimum Gradient Support Regularization: A Case Study

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.

Remote Sensing, Archaeological, and Geophysical Data to Study the Terramare Settlements: The Case Study of Fondo Paviani (Northern Italy)

“…Then, the 1D models obtained were stitched together to build a pseudo-3D volume of the investigated area. Inversion was performed using the FDEMtools [83], a free MATLAB software package implementing the numerical algorithms mainly discussed by Deidda et al [84][85][86]. A layered starting model consisting of 30 layers, to a depth of 3.5 m, was used to invert the electromagnetic data.…”

“…where λ is a variable of integration with no particular physical meaning, h is the height of the instrument above the ground, r the coil separation, J0 the Bessel function of order 0, and R0(λ) the response kernel, which is a complex value function of the parameters that describe the layered subsurface (i.e., for the k-th layer: the electrical conductivity σk, the magnetic permeability μk, and the layer thickness dk) besides the frequency and λ. The nonlinear inversion procedure proposed by Deidda et al [84][85][86] is a general procedure that allows the estimation of the electrical properties (electrical conductivity and magnetic permeability) of the subsurface by inverting the complex multi-depth response of different electromagnetic devices designed to record data at multiple coil spacings, using a single frequency, or at multiple frequencies with a fixed coil spacing. Let us suppose that the aim of the survey is estimating the vertical distribution of the electrical conductivity, using a multifrequency electromagnetic dataset (e.g., data recorded with the GEM-2 device).…”

A Comparative Study of Inversion Optimization Algorithms for Underground Metal Target Detection

“…The least-squares inversion is a commonly used inversion algorithm [10] [11]. The least-squares inversion estimates the properties of underground metal targets by minimizing VOLUME 4, 2016 the objective function which measures the misfit between observed values and the fitted values provided by a forward model [12] [13].…”

Laterally constrained inversion (LCI) of multi-configuration EMI data with tunable sharpness

“…One regularization strategy to enforce a sharp or blocky solution is based on the minimum gradient support 40 (MGS) method (Portniaguine & Zhdanov, 1999;Zhdanov, 2002). Within the MGS regularization, a focusing parameter controls the characteristics of the used stabilizer; i.e., a small parameter value promotes sharp solutions while a large value promotes smoother models (Vignoli et al, 2015;Deidda et al, 2020;Vignoli et al, 2021). The MGS regularization has been implemented in sev-45 eral inversion approaches for other geophysical methods.…”