Frequency-domain Electromagnetic Induction Research Articles

Geostatistical Inversion of Frequency-Domain Electromagnetic Data for Near Surface Modelling

The detailed characterization of near-surface deposits is important for both environmental and economic reasons. These shallow subsurface systems can be very complex and heterogenous due to natural dynamics and anthropogenic interferences. Modeling techniques based exclusively on direct sampling generate limited informed three-dimensional models of the near-surface. Geophysical methods provide valuable and additional information to model the spatial distribution of the near-surface for locations where direct observations are not available. From this set of methods, frequency-domain electromagnetic induction (FDEM) has been successfully applied to image complex near-surface deposits. Yet, predicting the spatial distribution of relevant subsurface properties from geophysical data, and the integration of direct observations, is not straightforward. It requires solving a challenging geophysical inversion problem. Geostatistical modelling tools have been effectively applied to couple direct observations with geophysical data such as seismic reflection. We propose an iterative geostatistical FDEM inversion method able to integrate data from direct measurements of the near-surface with surface loop-loop FDEM measurements to simultaneously predict high-resolution models of electrical conductivity and magnetic susceptibility, and their associated uncertainty. The iterative geostatistical inversion method is based on stochastic sequential simulation and co-simulation as model perturbation and update techniques. The iterative optimization is based on the local data misfit between observed and simulated FDEM data, weighted by the sensitivity of the acquisition equipment. The proposed method is first demonstrated for a synthetic landfill data set created based on real data collected at a mine tailing disposal site in Portugal, and on a real data set collected at a site with archaeological features in Knowlton, UK. The results show the ability of the proposed method to accurately predict and characterize the spatial distribution of electrical conductivity and magnetic susceptibility down to the depth of interest while reproducing the recorded FDEM data.

Comparison of multi-coil and multi-frequency frequency domain electromagnetic induction instruments

IntroductionCharacterization of the shallow subsurface in mountain catchments is important for understanding hydrological processes and soil formation. The depth to the soil/bedrock interface (e.g., the upper ~5 m) is of particular interest. Frequency domain electromagnetic induction (FDEM) methods are well suited for high productivity characterization for this target as they have short acquisition times and do not require direct coupling with the ground. Although traditionally used for revealing lateral electrical conductivity (EC) patterns, e.g., to produce maps of salinity or water content, FDEM inversion is increasingly used to produce depth-specific models of EC. These quantitative models can be used to inform several depth-specific properties relevant to hydrological modeling (e.g. depths to interfaces and soil water content).Material and methodsThere are a number of commercial FDEM instruments available; this work compares a multi-coil device (i.e., a single-frequency device with multiple receiver coils) and a multi-frequency device (i.e., a single receiver device with multiple frequencies) using the open-source software EMagPy. Firstly, the performance of both devices is assessed using synthetic modeling. Secondly, the analysis is applied to field data from an alpine catchment.ResultsBoth instruments retrieved a similar EC model in the synthetic and field cases. However, the multi-frequency instrument displayed shallower sensitivity patterns when operated above electrically conductive grounds (i.e., 150 mS/m) and therefore had a lower depth of investigation. From synthetic modeling, it also appears that the model convergence for the multi-frequency instrument is more sensitive to noise than the multi-coil instrument.ConclusionDespite these limitations, the multi-frequency instrument is smaller and more portable; consequently, it is easier to deploy in mountainous catchments.

Artificial Bee Colony Algorithm with Adaptive Parameter Space Dimension: A Promising Tool for Geophysical Electromagnetic Induction Inversion

Frequency-domain electromagnetic induction (FDEMI) methods are frequently used in non-invasive, area-wise mapping of the subsurface electromagnetic soil properties. A crucial part of data analysis is the geophysical inversion of the data, resulting in either conductivity and/or magnetic susceptibility subsurface distributions. We present a novel 1D stochastic optimization approach that combines dimension-adapting reversible jump Markov chain Monte Carlo (MCMC) with artificial bee colony (ABC) optimization for geophysical inversion, with specific application to frequency-domain electromagnetic induction (FDEMI) data. Several solution models of simplified model geometry and a variable number of model knots, which are found by the inversion method, are used to create re-sampled resulting average models. We present synthetic test inversions using conductivity models based on 14 direct-push (DP) EC logs from Greece, Italy, and Germany, as well as field data applications using multi-coil FDEMI devices from three sites in Azerbaijan and Germany. These examples show that the method can effectively lead to solutions that resemble the known DP input models or image reasonable stratigraphic and archaeological features in the field data. Neighboring 1D solutions on field data examples show high coherence along profiles even though each 1D inversion is independently handled. The computational effort for one 1D inversion is less than 120,000 forward calculations, which is much less than usually needed in MCMC inversions, whereas the resulting models show more plausible solutions due to the dimension-adapting properties of the inversion method.

Assessing soil moisture variability in a vineyard via frequency domain electromagnetic induction data

IntroductionIn agriculture, accurate hydrological information is crucial to infer water requirements for hydrological modeling, as well as for appropriate water management.MethodsTo achieve this purpose, geophysical frequency domain electromagnetic induction (FDEM) measurements are increasingly used for integration with traditional point-scale measurements to provide effective soil moisture estimations over large areas. The conversion of electromagnetic properties to soil moisture requires specific tools that must take into account the spatial variability of the two measurements and the data and model uncertainties. In a vineyard of about 4.5 ha located in Southern Italy, we tested an innovative assessment approach that uses a freeware code licensed from USGS, MoisturEC, to integrate electromagnetic data, collected with a CMD Mini-Explorer electromagnetic sensor, and point-scale soil moisture data.ResultsAbout 30,000 data measurements of apparent electrical conductivity (sa) allowed us to build a 3D inverted electromagnetic model obtained via an inversion process. Soil properties at different depths were inferred from the FDEM model and confirmed through the ground truth sampling.DiscussionThe data analysis tool allowed a more accurate estimation of the moisture distribution of the investigated area by combining the accuracy of the point-scale soil moisture measurements and the spatial coverage of the electrical conductivity (EC) data. The results confirmed the capability of the electromagnetic data to accurately map the moisture content of agricultural soils and, at the same time, the need to employ integrated analysis tools able to update such quantitative estimations in order to optimize soil and water management.

Frequency-domain electromagnetic induction for the prediction of electrical conductivity and magnetic susceptibility using geostatistical inversion and randomized tensor decomposition

High-resolution characterization of near-surface systems is crucial for a variety of subsurface applications. Frequency-domain electromagnetic (FDEM) induction has been widely used in near-surface characterization compared with other geophysical methods due to its flexibility in acquisition and its ability to survey large areas with high resolution but with relatively low costs. FDEM measurements are sensitive to subsurface electrical conductivity (EC) and magnetic susceptibility (MS). However, the prediction of these properties requires solving a geophysical inverse problem. We combine ensemble smoother with multiple data assimilation (ES-MDA) and model reparameterization via randomized tensor decomposition (RTD) to simultaneously predict EC and MS from measured FDEM data. ES-MDA is an iterative data assimilation method that can be applied to nonlinear forward operators and provides multiple posterior realizations conditioned on the geophysical measurements to evaluate the model uncertainty. However, its application is usually computationally prohibitive for large-scale 3D problems. To overcome this limitation, we reduce the model parameters using RTD and then perform the inversion in the low-dimensional model space. The method is applied to synthetic and noisy real data sets. In the synthetic application example, the predicted posterior realizations illustrate the ability of our method to recover the true models of EC and MS accurately. The real case application comprises FDEM data acquired over arable land characterized by quaternary siliciclastic deposits with geoarchaeological features. We assess the performance of the inversion method at a borehole location not used to constrain the inversion. The inverted models do capture the available log data, illustrating the applicability of the inversion method to noisy real data.

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

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.

Structurally constrained inversion by means of a Minimum Gradient Support regularizer: examples of FD-EMI data inversion constrained by GPR reflection data

SUMMARYMany geophysical inverse problems are known to be ill-posed and, thus, requiring some kind of regularization in order to provide a unique and stable solution. A possible approach to overcome the inversion ill-posedness consists in constraining the position of the model interfaces. For a grid-based parameterization, such a structurally constrained inversion can be implemented by adopting the usual smooth regularization scheme in which the local weight of the regularization is reduced where an interface is expected. By doing so, sharp contrasts are promoted at interface locations while standard smoothness constraints keep affecting the other regions of the model. In this work, we present a structurally constrained approach and test it on the inversion of frequency-domain electromagnetic induction (FD-EMI) data using a regularization approach based on the Minimum Gradient Support stabilizer, which is capable to promote sharp transitions everywhere in the model, i.e., also in areas where no structural a prioriinformation is available. Using 1D and 2D synthetic data examples, we compare the proposed approach to a structurally constrained smooth inversion as well as to more standard (i.e., not structurally constrained) smooth and sharp inversions. Our results demonstrate that the proposed approach helps in finding a better and more reliable reconstruction of the subsurface electrical conductivity distribution, including its structural characteristics. Furthermore, we demonstrate that it allows to promote sharp parameter variations in areas where no structural information are available. Lastly, we apply our structurally constrained scheme to FD-EMI field data collected at a field site in Eastern Germany to image the thickness of peat deposits along two selected profiles. In this field example, we use collocated constant offset ground-penetrating radar (GPR) data to derive structural a priori information to constrain the inversion of the FD-EMI data. The results of this case study demonstrate the effectiveness and flexibility of the proposed approach.

Estimating grapevine-relevant physicochemical soil zones using apparent electrical conductivity and in-phase data from EMI methods

This study explores the ability of the frequency domain electromagnetic induction (EMI) method to produce physicochemical soil maps with relevance to grapevine vigor. The study was conducted in the Médoc area of the Bordeaux wine region in France. A flexible clustering approach was used with both the apparent electrical conductivity and the in-phase components of EMI measurements. Soil zones with distinct physicochemical signatures were successfully identified, primarily due to the inclusion of in-phase data in the clustering method. Importantly, this approach does not use prior information to guide zone classification and does not require calibration of EMI measurements. Extensive soil texture and physicochemical measurements were used to compare the different zones identified by the clustering approach. Grapevine vigor was assessed using normalized vegetation index (NDVI) data to help conceptualize the critical physicochemical variables of the soil. It was evident that NDVI and EMI data were correlated to organic matter, nitrogen, CEC, pH, CaO, and copper concentration in one of the investigated sites. Unlike previous work in other Bordeaux soil viticulture areas, soil texture at these sites was relatively homogenous and consequently did not influence plant vigor substantially. This work demonstrates the value of the in-phase component of EMI measurements to estimate soil zonation. More generally, this work demonstrates the ability of coupled EMI and NDVI surveys to inform viticulture at scales relevant to management decisions.

A comparison between Kalman ensemble generator and geostatistical frequency-domain electromagnetic inversion: The impacts on near-surface characterization

The spatial distribution of the physical properties of the first meters beneath the earth’s surface is often complex due to its highly dynamic nature and small-scale heterogeneities resulting from natural and anthropogenic processes. Therefore, obtaining numerical 3D models that accurately describe the spatial distribution of these properties is often challenging yet essential for different fields such as environmental assessment and remediation, geoarchaeological conservation, and precision agriculture. Frequency-domain electromagnetic (FDEM) induction methods have proven their potential to image these properties in high (spatial) detail because FDEM measurements are sensitive to two key soil properties: electrical conductivity and magnetic susceptibility. Predicting subsurface properties from FDEM data requires solving an ill-posed and nonlinear inverse problem with multiple solutions. Recently, there has been a rapid growth of FDEM inversion methods, which may be broadly divided into probabilistic and deterministic methods. We compare two stochastic FDEM inversion approaches: the Kalman ensemble generator (KEG) and another one formulated as an iterative geostatistical FDEM inversion. Both methods are applied to a synthetic data set with spatially heterogeneous physical properties of interest, mimicking a real landfill mining site. The predicted models are compared with the reference models in terms of histogram and variogram models reproduction and in their ability to quantify spatial uncertainty. The results indicate the ability of both methods to predict the reference values. Although the KEG is computationally efficient, it struggles to reproduce the extreme values. In contrast, the geostatistical inversion approach ensures the reproduction of the imposed histograms and variogram models in the predicted models. As the prior information is included in both inversion methods in different ways, the pointwise variance models computed from all of the posterior models have different information. The synthetic data set is available to the community, so it can be used as a benchmark for other FDEM inversion methods.

Developing a low-cost frequency-domain electromagnetic induction instrument

Abstract. Recent advancements and the widespread availability of low-cost microcontrollers and electronic components have created new opportunities for developing and using low-cost, open-source instrumentation for near-surface geophysical investigations. Geophysical methods that do not require ground contact, such as frequency-domain electromagnetics, allow one or two users to quickly acquire significant amounts of ground resistivity data in a cost-effective manner. The Colorado School of Mines electromagnetic system (CSM-EM) is a proof-of-concept instrument capable of sensing conductive objects in near-surface environments, and is similar in concept to commercial-grade equipment while costing under USD 400 to build. We tested the functionality of the CSM-EM system in a controlled laboratory setting during the design phase and validated it over a conductive target in an outdoor environment. The transmitter antenna can generate a current of over 2.5 A, and emit signals that are detectable by a receiver antenna at offsets of up to 25 m. The system requires minor refitting to change the functioning frequency, and has been operationally validated at 0.4 and 1.6 kHz. The receiver signal can be measured by off-the-shelf digital multimeters. Future directions will focus on improving the electronic and mechanical stability of the CSM-EM with the goal of using acquired data to make quantitative measurements of subsurface resistivity.

Regularized minimal-norm solution of an overdetermined system of first kind integral equations

Overdetermined systems of first kind integral equations appear in many applications. When the right-hand side is discretized, the resulting finite-data problem is ill-posed and admits infinitely many solutions. We propose a numerical method to compute the minimal-norm solution in the presence of boundary constraints. The algorithm stems from the Riesz representation theorem and operates in a reproducing kernel Hilbert space. Since the resulting linear system is strongly ill-conditioned, we construct a regularization method depending on a discrete parameter. It is based on the expansion of the minimal-norm solution in terms of the singular functions of the integral operator defining the problem. Two estimation techniques are tested for the automatic determination of the regularization parameter, namely, the discrepancy principle and the L-curve method. Numerical results concerning two artificial test problems demonstrate the excellent performance of the proposed method. Finally, a particular model typical of geophysical applications, which reproduces the readings of a frequency domain electromagnetic induction device, is investigated. The results show that the new method is extremely effective when the sought solution is smooth, but produces significant information even for non-smooth solutions.

Frequency domain electromagnetic induction imaging: An effective method to see inside a capped landfill

The frequency-domain electromagnetic (FDEM) methods are a powerful tool for evaluating the impact caused on natural environments by anthropic facilities such as landfills. Noninvasive FDEM rapidly investigates large areas with no impact on the system. This is essential in case of capped landfills, as the impermeable liner represents a strong limitation for the use of all others direct and indirect investigation methods. This technique allows the propagation of the EM fields and collection of subsurface response below the liner thus representing the only effective solution both for static imaging and time-lapse monitoring of the processes that take place into the waste deposits. Traditionally, electromagnetic data are visualized as apparent electrical conductivity (ECa) maps that give practically no information about the variation of the conductivity with depth because ECa is only the equivalent conductivity of a homogeneous soil that would give the same measured response along depth. More recent approaches allow for an inversion of data thus providing clear information on the thickness of the investigated subsurface layers. The need for building a 3D electromagnetic model is crucial in the context of the urban waste landfill characterization, where leachate induces strong anomalies in electrical conductivity, which in turn causes a nonlinear model of the EMI response. A rigorous EMI inversion approach has been tested at a closed landfill in Southern Italy. The inverted model provided detailed information unattainable with other methods, by corroborating the assumption that electromagnetic measurements represent the best technique to characterize closed systems such as capped landfills.

Standoff High-Frequency Electromagnetic Induction Response of Unsaturated Sands: A Tank-Scale Feasibility Study

Standoff electromagnetic induction (EMI) measurements of complex conductivity and complex permittivity for engineering soil properties have the potential to revolutionize the way the US Army handles route planning and infrastructure assessment. An unmanned aerial system (UAS) based EM platform for soil interrogation would have wide reaching impact in a variety of applications including: civil infrastructure inspection, in-theater ingress and egress routing, reduction of false positives in IED detection, and permafrost mapping, among many others. Traditional frequency domain EMI instruments assess conductivity at low-frequencies, generally in the range of 1–20 kHz; however, recent advancements have resulted in instrumentation targeting a broadband range of frequencies, from 10 kHz through 20 MHz. This advancement, known as high-frequency electromagnetic induction (HFEMI) allows the potential to evaluate frequency domain relaxation effects in soils by acquiring both the in phase and quadrature response of the secondary field from the soil. Relaxation phenomena such as induced polarization and dielectric permittivity are related to important soil properties that can potentially be exploited using this HFEMI system. While conductivity measurements using the quadrature component of the EMI response are well established in EMI instrumentation, understanding of the relationship between direct electrical measurements and standoff HFEMI measurements is lacking. In an effort to illuminate this relationship between various electrical and electromagnetic methods at a scale suitable for soil property estimation, we perform side-by-side measurements using galvanic geoelectrical methods (ERT, IP), electromagnetics, time-domain reflectometry (TDR) and ground penetrating radar (GPR). We compare HFEMI obtained quadrature and in-phase responses to ERT, IP, TDR and GPR measurements. A tank-scale test cell was developed for comparison of the above methods and allowed assessment of sand at varying saturation levels. Further, the HFEMI response at varying heights above the sand surface was also assessed. Qualitative observations are reported in an initial attempt to relate the HFEMI response to important soil parameters.

Performance Analysis for Estimating a Target’s Relaxation Frequencies From Frequency-Domain Electromagnetic Induction Data

We present three analyses that explore the behavior of the Cramer-Rao lower bounds (CRBs) on estimating a target's relaxation frequency response from frequency-domain electromagnetic induction (EMI) data. In the first analysis, we show that the CRB on a given relaxation frequency is independent of the amplitudes of the other relaxations present in the target's relaxation frequency response. In the second, we show that the presence of a second relaxation frequency closer than one decade in frequency greatly increases the CRB on that relaxation frequency. Finally, we illustrate the behavior of the minimum root-mean-square error (RMSE) per relaxation frequency as a function of the number of relaxation frequencies present in the target's relaxation frequency response.

Design of an airborne concentric frequency-domain electromagnetic induction system for shallow subsurface geophysical exploration

For the exploration of shallow and small subsurface targets, rigid-beam helicopter-borne electromagnetic systems are often inconvenient or costly, whereas man-portable or ground-based systems are difficult to operate in complex terrain. An airborne concentric frequency-domain electromagnetic system with an unmanned rotorcraft as a flying platform is proposed to avoid the problems of low security in conventional helicopter-borne electromagnetic method and low efficiency in ground-based electromagnetic method for the exploration of shallow subsurface targets. Compared with the series mode of man-portable system, the currents of transmitting and bucking coils are assumed to be separately and continuously adjustable, which can reduce sensitivity of the small errors of the system. In this paper, the principle of canceling the primary magnetic field is analyzed. The design index of the physical parameters of the sensor is determined. The simulation experiment of layered earth model is carried out to verify the feasibility of the proposed system.

A variational non-linear constrained model for the inversion of FDEM data* *Dedicated to Lothar Reichel on the occasion of his 70th birthday.

Reconstructing the structure of the soil using non-invasive techniques is a very relevant problem in many scientific fields, like geophysics and archaeology. This can be done, for instance, with the aid of frequency domain electromagnetic (FDEM) induction devices. Inverting FDEM data is a very challenging inverse problem, as the problem is extremely ill-posed, i.e. sensible to the presence of noise in the measured data, and non-linear. Regularization methods substitute the original ill-posed problem with a well-posed one whose solution is an accurate approximation of the desired one. In this paper we develop a regularization method to invert FDEM data. We propose to determine the electrical conductivity of the ground by solving a variational problem. The minimized functional is made up by the sum of two term: the data fitting term ensures that the recovered solution fits the measured data, while the regularization term enforces sparsity on the Laplacian of the solution. The trade-off between the two terms is determined by the regularization parameter. This is achieved by minimizing an ℓ 2 − ℓ q functional with 0 < q ⩽ 2. Since the functional we wish to minimize is non-convex, we show that the variational problem admits a solution. Moreover, we prove that, if the regularization parameter is tuned accordingly to the amount of noise present in the data, this model induces a regularization method. Some selected numerical examples on synthetic and real data show the good performances of our proposal.

The Application of Electromagnetic Induction Methods to Reveal the Hydrogeological Structure of a Riparian Wetland

AbstractUnderstanding ecologically sensitive wetlands often requires non‐invasive methods to characterize their complex structure (e.g., deposit heterogeneity) and hydrogeological parameters (e.g., porosity and hydraulic conductivity). Here, electrical conductivities of a riparian wetland were obtained using frequency domain electromagnetic induction (EMI) methods. The wetland was previously characterized by extensive intrusive measurements and 3D electrical resistivity tomography (ERT) surveys and hence offers an ideal opportunity to objectively assess EMI methods. Firstly, approaches to obtain structural information (e.g., elevation and thickness of alluvium) from EMI data and inverted models were assessed. Regularized and sharp inversion algorithms were investigated for ERT calibrated EMI data. Moreover, the importance of EMI errors in inversion was investigated. The hydrological information content was assessed using correlations with piezometric data and petrophysical models. It was found that EMI data were dominated by the thickness of peaty alluvial soils and relatively insensitive to topography and total alluvial thickness. Furthermore, although error weighting in the inversion improved the accuracy of alluvial soil thickness predictions, the multi‐linear regression method performed the best. For instance, an iso‐conductivity method to estimate the alluvial soil thickness in the regularized models had a normalized mean absolute difference (NMAD) of 21.4%, and although this performed better than the sharp inversion algorithm (NMAD = 65.3%), the multi‐linear regression approach (using 100 intrusive observations) achieved a NMAD = 18.0%. In terms of hydrological information content, correlations between EMI results and piezometric data were poor, however robust relationships between petrophysically derived porosity and hydraulic conductivity were observed for the alluvial soils and gravels.

Airborne mapping of the sub-ice platelet layer under fast ice in McMurdo Sound, Antarctica

Abstract. Basal melting of ice shelves can result in the outflow of supercooled ice shelf water, which can lead to the formation of a sub-ice platelet layer (SIPL) below adjacent sea ice. McMurdo Sound, located in the southern Ross Sea, Antarctica, is well known for the occurrence of a SIPL linked to ice shelf water outflow from under the McMurdo Ice Shelf. Airborne, single-frequency, frequency-domain electromagnetic induction (AEM) surveys were performed in November of 2009, 2011, 2013, 2016, and 2017 to map the thickness and spatial distribution of the landfast sea ice and underlying porous SIPL. We developed a simple method to retrieve the thickness of the consolidated ice and SIPL from the EM in-phase and quadrature components, supported by EM forward modelling and calibrated and validated by drill-hole measurements. Linear regression of EM in-phase measurements of apparent SIPL thickness and drill-hole measurements of “true” SIPL thickness yields a scaling factor of 0.3 to 0.4 and rms error of 0.47 m. EM forward modelling suggests that this corresponds to SIPL conductivities between 900 and 1800 mS m−1, with associated SIPL solid fractions between 0.09 and 0.47. The AEM surveys showed the spatial distribution and thickness of the SIPL well, with SIPL thicknesses of up to 8 m near the ice shelf front. They indicate interannual SIPL thickness variability of up to 2 m. In addition, they reveal high-resolution spatial information about the small-scale SIPL thickness variability and indicate the presence of persistent peaks in SIPL thickness that may be linked to the geometry of the outflow from under the ice shelf.

Performance Bounds for Target Parameter Estimation From Frequency-Domain Electromagnetic Induction Data

We derive the Cramer–Rao lower bounds (CRBs) for all target parameters associated with noisy measurements of a specific class of targets using a frequency-domain electromagnetic induction (EMI) system. The target parameters include the target tensors, the relaxation frequencies and their corresponding amplitudes, as well as the target location. We validate the derivation through Monte Carlo simulation. We then derive approximate CRB (ACRB) expressions based on a new low-rank model perspective for EMI data. These approximate expressions are significant simplifications over the full CRB expressions. They also facilitate the analysis and improve the understanding of the factors impacting the lower bounds on the target parameters. We demonstrate the utility and accuracy of the ACRB expressions for two example targets.

Frequency domain electromagnetic induction: an efficient method for investigating Fort Ancient village dynamics

AbstractElectromagnetic induction (EMI) has been used in archaeology for decades, but still lags in use and development when compared to magnetometry and ground‐penetrating radar. While it has become more popular than electrical resistivity area survey, it is now less commonly used than electrical resistivity tomography. The EMI method is likely underutilized due to drift problems and a lack of multi‐sensor, vehicle‐towed systems capable of rapid, high‐density data collection. In this article we demonstrate not only the effectiveness of EMI survey, but a case where entire villages would have remained undetected without it. At the Singer‐Hieronymus Site in central Kentucky, USA, a vehicle‐towed frequency domain EMI survey detected the location of plazas, residential areas, and trash disposal areas across multiple Fort Ancient villages that contained both intact and heavily disturbed deposits. Additionally, three new villages were revealed. Through this process, we discovered how Fort Ancient village dynamics may be studied through a geophysical investigation of village shape, size, and spatial organization.