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For near surface geophysical surveys, small-fixed offset loop-loop electromagnetic induction (EMI) sensors are usually placed parallel to the ground surface (i.e., both loops are at the same height above ground). In this study, we evaluate the potential of making measurements with a system that is not parallel to the ground; i.e., by positioning the system at different inclinations with respect to ground surface. First, we present the Maxwell theory for inclined magnetic dipoles over a homogeneous half space. By analyzing the sensitivities of such configurations, we,show that varying the angle of the system would result in improved imaging capabilities. For example, we show that acquiring data with a vertical system allows detection of a conductive body with a better lateral resolution compared to data acquired using standard horizontal configurations. The synthetic responses are presented for a heterogeneous medium and compared to field data acquired in the historical Park Sanssouci in Potsdam, Germany. After presenting a detailed sensitivity analysis and synthetic examples of such ground conductivity measurements, we suggest a new strategy of acquisition that allows to better estimate the true distribution of electrical conductivity using instruments with a fixed, small offset between the loops. This strategy is evaluated using field data collected at a well-constrained test-site in Horstwalde (Germany). Here, the target buried utility pipes are best imaged using vertical system configurations demonstrating the potential of our approach for typical applications. (C) 2015 Elsevier B.V. Pill rights reserved.

Given the range of geological conditions under which airborne EM surveys are conducted, there is an expectation that the 2D and 3D methods used to extract models that are geologically meaningful would be favoured over ID inversion and transforms. We do after all deal with an Earth that constantly undergoes, faulting, intrusions, and erosive processes that yield a subsurface morphology, which is, for most parts, dissimilar to a horizontal layered earth.
We analyse data from a survey collected in the Musgrave province, South Australia. It is of particular interest since it has been used for mineral prospecting and for a regional hydro-geological assessment. The survey comprises abrupt lateral variations, more-subtle lateral continuous sedimentary sequences and filled palaeovalleys. As consequence, we deal with several geophysical targets of contrasting conductivities, varying geometries and at different depths. We invert the observations by using several algorithms characterised by the different dimensionality of the forward operator.
Inversion of airborne EM data is known to be an ill-posed problem. We can generate a variety of models that numerically adequately fit the measured data, which makes the solution non-unique. The application of different deterministic inversion codes or transforms to the same dataset can give dissimilar results, as shown in this paper. This ambiguity suggests the choice of processes and algorithms used to interpret AEM data cannot be resolved as a matter of personal choice and preference.
The degree to which models generated by a ID algorithm replicate/or not measured data, can be an indicator of the data's dimensionality, which perse does not imply that data that can be fitted with a 1D model cannot be multidimensional. On the other hand, it is crucial that codes that can generate 2D and 3D models do reproduce the measured data in order for them to be considered as a plausible solution. In the absence of ancillary information, it could be argued that the simplest model with the simplest physics might be preferred.

Most airborne electromagnetic (EM) processing programs assume a flat ground surface. However, in mountainous areas, the system can be at an angle with regard to the ground. As the system is no longer parallel to the ground surface, the measured magnetic field has to be corrected and the ground induced eddy current has to be modelled in a better way when performing a very fine interpretation of the data. We first recall the theoretical background for the modelling of a magnetic dipole source and study it in regard to the case of an arbitrarily oriented magnetic dipole. We show in particular how transient central loop helicopter borne data are influenced by this inclination. The result shows that the effect of topography on airborne EM is more important at early time windows and for systems using a short cut-off source. In this paper, we suggest that an estimate be made off the locally averaged inclination of the system to the ground and then to correct the data for this before inverting it (whether the inversion assumes a flat 1D, 2D or 3D sub-surface). Both 1D and 2D inversions are applied to synthetic and real data sets with such a correction. The consequence on the ground imaging is small for slopes with an angle less than 25 degrees but the correction factor can be useful for improving the estimation of depths in mountainous areas.

Ground loop-loop electromagnetic surveys are often conducted to fulfill the low-induction-number condition. To image the distribution of electric conductivity inside the ground, it is then necessary to collect a multioffset data set. We considered that less time-consuming constant offset measurements can also reach this objective. This can be achieved by performing multifrequency soundings, which are commonly performed for the airborne electromagnetic method. Ground multifrequency soundings have to be interpreted carefully because they contain high-induction-number data. These data are interpreted in two steps. First, the in-phase and out-of-phase data are converted into robust apparent conductivities valid for all the induction numbers. Second, the apparent conductivity data are inverted in 1D and 2D to obtain the true distribution of the ground conductivity. For the inversion, we used a general half-space Jacobian for the apparent conductivity valid for all the induction numbers. This method was applied and validated on synthetic data computed with the full Maxwell theory. The method was then applied on field data acquired in the test site of Provins, in the Parisian basin, France. The result revealed good agreement with borehole and geologic information, demonstrating the applicability of our method.

Electromagnetic induction (EMI) sensors using sufficiently low-frequency harmonic sources and sufficiently small loop separations operate in the low-induction-number (LIN) domain for a relatively wide range of background conductivity. These systems are used in diverse near-surface investigations including applications from soil sciences, hydrology, and archaeology. The special case of portable multiconfiguration EMI sensors operating at frequencies <= 20 kHz offers the possibility of using a fast linear deconvolution method to interpret multichannel data sets in three dimensions. Here, we have developed a fast 3D inversion/deconvolution method regularized with 3D smoothness constraints and formulated in the hybrid spectral-spatial domain. Compared with other linear approaches, the spectral-spatial domain formulation significantly reduces the computational cost of the processing and opens the door for real-time 3D interpretation of large data sets consisting of more than 100,000 data points. First, we test our proposed algorithm on synthetic data sets computed with the full Maxwell theory. Then, we apply our method to a real four-configuration EMI data set acquired to map the thickness of peat layers embedded in a sandy environment. For the synthetic and the field example, we compared our result with the result obtained using a standard point-by-point 1D nonlinear inversion approach. This comparison demonstrates that the proposed methodology provides superior lateral resolution compared with the 1D nonlinear inversion, at the same time significantly reducing the computational cost of the processing.

The in-phase response collected by portable loop-loop electromagnetic induction (EMI) sensors operating at low and moderate induction numbers (<= 1) is typically used for sensing the magnetic permeability (or susceptibility) of the subsurface. This is due to the fact that the in-phase response contains a small induction fraction and a preponderant induced magnetization fraction. The magnetization fraction follows the magneto-static equations similarly to the magnetic method but with an active magnetic source. The use of an active source offers the possibility to collect data with several loop-loop configurations, which illuminate the subsurface with different sensitivity patterns. Such multiconfiguration soundings thereby allows the imaging of subsurface magnetic permeability/susceptibility variations through an inversion procedure. This method is not affected by the remnant magnetization and theoretically overcomes the classical depth ambiguity generally encountered with passive geomagnetic data. To invert multiconfiguration in-phase data sets, we propose a novel methodology based on a full-grid 3-D multichannel deconvolution (MCD) procedure. This method allows us to invert large data sets (e.g. consisting of more than a hundred thousand of data points) for a dense voxel-based 3-D model of magnetic susceptibility subject to smoothness constraints. In this study, we first present and discuss synthetic examples of our imaging procedure, which aim at simulating realistic conditions. Finally, we demonstrate the applicability of our method to field data collected across an archaeological site in Auvergne (France) to image the foundations of a Gallo-Roman villa built with basalt rock material. Our synthetic and field data examples demonstrate the potential of the proposed inversion procedure offering new and complementary ways to interpret data sets collected with modern EMI instruments.

A comprehensive workflow to analyze ensembles of globally inverted 2D electrical resistivity models
(2022)

Electrical resistivity tomography (ERT) aims at imaging the subsurface resistivity distribution and provides valuable information for different geological, engineering, and hydrological applications. To obtain a subsurface resistivity model from measured apparent resistivities, stochastic or deterministic inversion procedures may be employed. Typically, the inversion of ERT data results in non-unique solutions; i.e., an ensemble of different models explains the measured data equally well. In this study, we perform inference analysis of model ensembles generated using a well-established global inversion approach to assess uncertainties related to the nonuniqueness of the inverse problem. Our interpretation strategy starts by establishing model selection criteria based on different statistical descriptors calculated from the data residuals. Then, we perform cluster analysis considering the inverted resistivity models and the corresponding data residuals. Finally, we evaluate model uncertainties and residual distributions for each cluster. To illustrate the potential of our approach, we use a particle swarm optimization (PSO) algorithm to obtain an ensemble of 2D layer-based resistivity models from a synthetic data example and a field data set collected in Loon-Plage, France. Our strategy performs well for both synthetic and field data and allows us to extract different plausible model scenarios with their associated uncertainties and data residual distributions. Although we demonstrate our workflow using 2D ERT data and a PSObased inversion approach, the proposed strategy is general and can be adapted to analyze model ensembles generated from other kinds of geophysical data and using different global inversion approaches.

Direct current systems employing a kinematic surveying strategy allow to analyze the electrical resistivity of the subsurface for large areas (i.e., several hectares). Typical applications are found in precision agriculture, archaeological prospecting and soil sciences. With the typical survey setting, the collected data sets are often characterized by a rather high level of noise and a rather coarse lateral sampling compared to data acquired with fixed electrodes. We therefore present an efficient one-dimensional inversion approach in which we put special attention on modeling the effects of noise. We apply this method to data recorded with a five-offset equatorial dipole-dipole system employing rolling electrodes. By performing several synthetic tests with realistic noise levels, we found that the considered five-configuration soundings allow for a reliable imaging of two-layer cases in the uppermost two meters of the subsurface, where the subsurface can be assumed to follow a horizontally layered geometry within 3 m around the system. By analyzing the corresponding sensitivity functions, we also show that the equatorial dipole-dipole array is relatively well suited for a 1D inversion approach compared to standard in-line electrode arrays. To illustrate this aspect, we show that our method can provide results similar to those obtained with a 2D Wenner imaging procedure for data recorded across a well-constrained 2D target. We finally apply our method to a large five-offset data set acquired in an agricultural study. The final pseudo-3D model of electrical resistivity is in accordance with borehole data available for the surveyed area. Our results demonstrate the applicability and the versatility of the presented inversion approach for large-scale data sets as they are typically collected with such rolling electrode systems. (C) 2017 Elsevier B.V. All rights reserved.

We present an algorithm that performs sequentially one-dimensional inversion of subsurface magnetic permeability and electrical conductivity by using multi-configuration electromagnetic induction sensor data. The presented method is based on the conversion of the in-phase and out-of-phase data into effective magnetic permeability and electrical conductivity of the equivalent homogeneous half-space. In the case of small-offset systems, such as portable electromagnetic induction sensors, for which in-phase and out-of-phase data are moderately coupled, the effective half-space magnetic permeability and electrical conductivity can be inverted sequentially within an iterative scheme. We test and evaluate the proposed inversion strategy using synthetic and field examples. First, we apply it to synthetic data for some highly magnetic environments. Then, the method is tested on real field data acquired in a basaltic environment to image a formation of archaeological interest. These examples demonstrate that a joint interpretation of in-phase and out-of-phase data leads to a better characterisation of the subsurface in magnetic environments such as volcanic areas.