Spreading of Localized Information across an Entire 3D Electrical Resistivity Volume via Constrained EMI Inversion Based on a Realistic Prior Distribution

Abstract

Frequency-domain electromagnetic induction (EMI) methods are commonly used to map vast areas quickly and with minimum logistical efforts. Unfortunately, they are often characterized by a very limited number of frequencies and severe ill-posedness. On the other hand, electrical resistivity tomography (ERT) approaches are usually considered more reliable; for example, they do not require specific calibration procedures and can be easily inverted in 2D/3D. However, ERT surveys are, by far, more demanding and time consuming, allowing for the deployment of a few acquisition lines per day. Ideally, the optimal would be to have the advantages of both approaches: ease of acquisition while keeping robustness and reliability. The present work raises from the necessity to cope with this issue and from the importance of enforcing realistic constraints to the data inversion without being limited to (over)simplistic spatial constraints (for example, characterizing the smooth and/or sharp regularization). Accordingly, the present research demonstrates, by means of synthetic and field data, how the EMI inversion—based on realistic prior models—can be further enhanced by incorporating additional pre-existing pieces of information. While the proposed scheme is quite general, in the specific examples discussed here, these additional pieces of information are, respectively, a reference model along a line across the survey area, and an ERT section. The field EMI results were verified against extensive ground penetrating radar (GPR) measurements and boreholes.

Probabilistic Petrophysical Reconstruction of Danta's Alpine Peatland via Electromagnetic Induction Data

“…An extension of the present scheme capable of considering the expected lateral continuity might consist of adding a term taking into account the probability of a 1D model being different from some reference model (possibly, the reference model can result from the previously considered adjacent 1D sounding inversion). Similar attempts are described, for example, in Ardid et al (2021) and Zaru et al (2023).…”

“…The maximum likelihood solution is equivalent to an inversion obtained by minimizing the data misfit in which the well‐posedness of the inversion is enforced by selecting the solution among the prior models (Zaru et al., 2023) rather than via the regularization term. The impact of the prior information is evident as the maximum likelihood reconstruction is characterized by a significant lateral coherence (i.e., the solution turns out to be stable with respect to perturbations in the data—i.e., moving from one sounding to the adjacent one) without an explicit regularization term, and this while the data misfit is comparable with alternative, “more standard,” inversions.…”

“…During the survey, we used a GEM‐2 (Haoping & Won, 2003) in the horizontal co‐planar configuration. This device has a receiver‐transmitter inter‐coil distance of 1.6 m. Performing the standard FDEM processing procedure preliminary to the inversion, we laterally stacked and averaged between adjacent soundings in order to remove the outliers and assess the noise in the data (cf., e.g., Zaru et al., 2023).…”

“…Electrical resistivity tomography has also been found successful (Elijah et al., 2012), especially, when used to reconstruct the variations of chargeability associated with the presence of peat (Comas & Slater, 2004; Slater & Reeve, 2002). However, in general, the above‐mentioned geophysical methodologies can be applied to relatively small areas and are extremely difficult to perform in flooded environments like wetlands/peatlands (Zaru et al., 2023). In this respect, FDEM presents several advantages as it does not require any direct coupling with the surface.…”

“…In this respect, probabilistic approaches have indubitable advantages: prior information can be described and incorporated into the inversion via the prior distribution, which, in turn, can be defined by its samples (Hansen, 2021a; Hansen & Minsley, 2019). This leads to the possibility of creating the samples in accordance with quite arbitrary expectations about the investigated geology (Bai et al., 2021; Zaru et al., 2023), without the limitations connected to the necessity of formalizing that information in terms of a functional to be minimized.…”