Novel Airborne EM Image Appraisal Tool for Imperfect Forward Modelling Wouter Deleersnyder12 David Dudal13 Thomas Hermans2

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Novel Airborne EM Image Appraisal Tool for

Imperfect Forward Modelling

Wouter Deleersnyder1,2, David Dudal1,3, Thomas Hermans2,

1KU Leuven Campus Kortrijk - KULAK, Department of Physics, Etienne Sabbelaan 53,

8500 Kortrijk, Belgium.

E-mail: wouter.deleersnyder@kuleuven.be

2Ghent University, Department of Geology, Krijgslaan 281 - S8, 9000 Gent, Belgium

3Ghent University, Department of Physics and Astronomy, Ghent, Krijgslaan 281 - S9,

9000 Gent, Belgium

ABSTRACT

Full 3D inversion of time-domain Airborne ElectroMagnetic (AEM) data requires specialists’ expertise

and a tremendous amount of computational resources, not readily available to everyone. Consequently,

quasi-2D/3D inversion methods are prevailing, using a much faster but approximate (1D) forward model.

We propose an appraisal tool that indicates zones in the inversion model that are not in agreement with

the multidimensional data and therefore, should not be interpreted quantitatively. The image appraisal

relies on multidimensional forward modelling to compute a so-called normalized gradient. Large values

in that gradient indicate model parameters that do not ﬁt the true multidimensionality of the observed

data well and should not be interpreted quantitatively. An alternative approach is proposed to account for

imperfect forward modelling, such that the appraisal tool is computationally inexpensive. The method is

demonstrated on an AEM survey in a salinization context, revealing possible problematic zones in the

estimated fresh-saltwater interface.

Keywords: Airborne Geophysics; AEM; TEM; Conductivity; Appraisal, Modelling; Electromagnetics

Submitted to Remote Sensing

1 INTRODUCTION

The Airborne ElectroMagnetic induction (AEM) method is a practical tool to map near-surface geological

features over large areas, as electromagnetic induction methods are sensitive to the bulk resistivity. It

is increasingly used for mineral exploration (Macnae and Milkereit, 2007), hydrogeological mapping

(Mikucki et al., 2015; Podgorski et al., 2013), saltwater intrusion (Goebel et al., 2019; Siemon et al.,

2019; Deleersnyder et al., 2022) and contamination (Pfaffhuber et al., 2017). AEM methods will become

more and more important for the challenges in the future, e.g., as an important investigation method

for groundwater management. It is the only viable approach to providing hydrogeological mappings on

a large scale. Among the geophysical EM methods, the advancement of the AEM within the last two

decades method was eminent. While the AEM systems have massively advanced (Auken et al., 2017), the

data interpretation process and the related computational burden remains a main impediment. Full 3D

inversion is an active research area (Engebretsen et al., 2022; Heagy et al., 2017; Cai et al., 2017; Yin

et al., 2016; Ansari et al., 2017; B

orner et al., 2015; Cox et al., 2010). It requires specialists’ expertise

and a tremendous amount of computational resources, not readily available to everyone. Consequently,

quasi-2D and quasi-3D inversion methods are prevailing, using a much faster but approximate (1D)

forward model. While using a 1D forward model is valid for slowly varying lateral variations, the

hypothesis is not always valid. The question remains whether the obtained inversion results are reliable

and can be interpreted quantitatively. In this work, we do not want to dissuade the use of 1D forward

models for AEM interpretation. Rather, we argue that an additional step after each inversion with an

approximate forward model should be added using an image appraisal tool, to verify that no erroneous

interpretation has occurred as a result of the approximate forward model. The tool indicates uncertain

areas in the recovered model, which should be interpreted with extra care or should be reinterpreted using

arXiv:2210.06074v1 [physics.geo-ph] 12 Oct 2022

Submitted to Remote Sensing

a full 3D inversion. In the latter case, this computationally demanding 3D inversion must, fortunately,

only be performed on a subset of the original dataset.

Appraisal tools usually address resolution issues. They are commonly used in electrical resistivity

tomography (Oldenburg and Li, 1999; Binley and Kemna, 2005; Caterina et al., 2013), with e.g. Paepen

et al. (2022) showing an application directly functional in a saltwater intrusion context. Speciﬁcally for

EM, Alumbaugh and Newman (2000) provide an appraisal tool based on the resolution matrix which

provides insight on the resolution and accuracy of the recovered images. Christiansen and Christensen

(2003) provide a quantitative appraisal for AEM by adding a comparison to ground-based data. The

method relies on 1D forward modelling and does not account for multidimensionality effects.

To overcome the latter shortcomings, we propose a novel appraisal tool that can detect wrongly

ﬁtting multidimensional data i.e., zones in the inversion model that are not in agreement with the

multidimensional (2D/3D) forward model and therefore, should not be interpreted in a quantitative

fashion. To our knowledge, such a tool has never been presented in the scientiﬁc literature. As generating

multidimensional data in a time-domain AEM setting can be challenging, a successful, alternative

approach is presented to function with imperfect forward 2/3D modelling. This allows for more accessible,

computationally tractable computations on coarser discretizations on a single laptop with only a fraction

of the required resources for perfect modelling.

2 METHOD

2.1 Three Types of Forward Modelling

The forward model describes the subsurface’s response to a speciﬁc subsurface realization and a speciﬁc

survey set-up. There are two main common approaches: The ﬁrst is based on (semi-)analytical models

that solve the (continuous) Maxwell equations for a one dimensional subsurface model, meaning that

it assumes horizontal layers without lateral variations. An open-source Python implementation by

Werthm

uller (2017) neatly implements such a forward model by Hunziker et al. (2015) in a fast and

reliable fashion. We refer to this model as the low-ﬁdelity model (LF), as it cannot account for lateral

variations in the subsurface model. The second approach is based on a discretization of the physics on

a mesh. Those simulations mimic the full 3D soil response of the potentially non-1D subsurface and

allow for multidimensional modelling. In this work, the ﬁnite volume method from the open-source

package SimPEG (Heagy et al., 2017) is used. With a suitable discretization of the geometry, an accurate

magnetic ﬁeld response can be obtained. In the case of perfect forward modelling, we refer to these

simulations as the high-ﬁdelity model (HF). However, numerical simulations are not always accurate and

the term high-ﬁdelity should be used with caution. If the accuracy of the simulations is limited due to

the computational burden requiring the use of a coarse mesh, the response contains a modelling error.

That modelling error is different in origin than the one introduced by only considering a one-dimensional

subsurface and depends on the discretization of the user and subsurface model. We refer to this model as

the medium-ﬁdelity model (MF). We visualized the various types of modelling in Figure 1.

2.2 Quasi-2D Inversion

In most geophysical inverse problems, the inversion model

consists of electrical conductivities (EC) and

ﬁts the observed data

dobs

and is simple in Occam’s sense (Constable et al., 1987). This is accomplished

by minimizing an objective function

φ(m) = φd(m) + β φm(m),(1)

where

φd

and

φm

are, respectively, the data and model misﬁt.

is a regularization parameter which

balances the relative importance of the two misﬁts.

In quasi-2D inversion, the data misﬁt

φd(m) = 1

nWddobs −F1D(m)

2(2)

uses a 1D approximation for the forward (LF) model

F1D(m)

, which signiﬁcantly reduces the computa-

tion time of the inversion procedure. The model misﬁt

φm

promotes smooth solutions (Tikhonov, 1943;

2/14

Submitted to Remote Sensing

Input Forward Model Output Fidelity

A. →=F1D(m)∗Low (LF)

B. →=F2.5D(m)High (HF)

C. →=F2.5D(m)Medium (MF)

D. →=F2.5D(m1D)Medium (MF)

∗In the 1D case, notation F1D(m) = F1D(m1D)

Figure 1. Conceptual visualization of the various forward data types used. The input is either a

multidimensional subsurface model (B. and C.) or an 1D subsurface model (in a moving footprint

approach) (A. and D.). The forward model is either a Low-Fidelity (LF) analytical forward model (with

depths and EC as input) (see A.), a High-Fidelity (HF) forward simulation on an accurate mesh (B.) or a

Medium- Fidelity (MF) forward simulation on an inaccurate (coarser) mesh (C. and D.). NOTE: the

presented meshes are illustrative and are not the ones used for multidimensional modelling. Some details

on the MF and HF mesh are described in Appendix A.

3/14

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NovelAirborneEMImageAppraisalToolforImperfectForwardModellingWouterDeleersnyder1;2,DavidDudal1;3,ThomasHermans2,1KULeuvenCampusKortrijk-KULAK,DepartmentofPhysics,EtienneSabbelaan53,8500Kortrijk,Belgium.E-mail:wouter.deleersnyder@kuleuven.be2GhentUniversity,DepartmentofGeology,Krijgslaan281-S8,9000Ge...

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Novel Airborne EM Image Appraisal Tool for Imperfect Forward Modelling Wouter Deleersnyder12 David Dudal13 Thomas Hermans2

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