Electromagnetic Inversion Research Articles

Review on airborne electromagnetic inverse theory and applications

Airborne electromagnetic (AEM) data processing and inversion has progressed from the early conductivity-depth imaging, to 1D inversion for a layered earth model, and most recently to 2D/3D inversions. The new processes have used methods for searching for solutions, applying constraints, and focusing images, such as Occam’s, laterally constrained, and holistic inversions. For airborne data imaging and 1D inversion, some algorithms are fast, whereas others have control over data misfit and the vertical or lateral smoothness. Beyond 1D algorithms, 2D/3D inversions are based on currently used methods such as isolated conductor models (which are good for highly conductive orebodies in resistive background) and techniques that discretized regions that are used for more complex structures and backgrounds. In the latter case, the computations are slow, so research is focusing on time-efficient computer algorithms for solving the equations such as Gauss-Newton, quasi-Newton, and nonlinear conjugate gradient algorithms. For the electromagnetic (EM) problem, the solution can be obtained in a more practical time frame if material that has minimal impact is ignored. Two approaches can be used to speedup the EM inversion process — the moving footprint and direct solver methods. We hope our work will to some extent help stimulate and focus the research in AEM inversion.

Regularized sparse-grid geometric sampling for uncertainty analysis in non-linear inverse problems

This paper introduces an efficiency improvement to the sparse-grid geometric sampling methodology for assessing uncertainty in non-linear geophysical inverse problems. Traditional sparse-grid geometric sampling works by sampling in a reduced-dimension parameter space bounded by a feasible polytope, e.g., a generalization of a polygon to dimension above two. The feasible polytope is approximated by a hypercube. When the polytope is very irregular, the hypercube can be a poor approximation leading to computational inefficiency in sampling. We show how the polytope can be regularized using a rotation and scaling based on principal component analysis. This simple regularization helps to increase the efficiency of the sampling and by extension the computational complexity of the uncertainty solution. We demonstrate this on two synthetic 1D examples related to controlled-source electromagnetic and amplitude versus offset inversion. The results show an improvement of about 50% in the performance of the proposed methodology when compared with the traditional one. However, as the amplitude versus offset example shows, the differences in the efficiency of the proposed methodology are very likely to be dependent on the shape and complexity of the original polytope. However, it is necessary to pursue further investigations on the regularization of the original polytope in order to fully understand when a simple regularization step based on rotation and scaling is enough.

Modelling soil salinity across a gilgai landscape by inversion of EM38 and EM31 data

SummaryThe soil in arid and semi‐arid areas is often markedly saline, which can severely limit agricultural productivity. Increasingly, geophysical methods are being implemented to map the levels and areal extent of soil salinity. One of the most effective methods is electromagnetic (EM) induction with instruments designed to measure apparent soil electrical conductivity (ECa). This study describes the generation of electromagnetic conductivity images (EMCIs) by inverting ECa data obtained with the EM38 and EM31 devices along two closely‐spaced transects by the EM inversion approach in the EM4Soil package. The EM38 ECa data are shown to be a more effective predictor of soil ECe. Calibration equations based on calculated true electrical conductivity (σ) and measured electrical conductivity of a saturated soil‐paste extract (ECe) provide reliable estimates of ECa. The patterns of σ in a test of the method in soil developed over thick alluvium on a clay plain in central New South Wales, Australia, compare favourably with existing pedological mapping; the mounds and depressions of gilgai were strongly differentiated from the more sandy alluvial sediments that characterize prior stream channels. The overall approach is potentially useful for generating a single calibration equation that can be used to predict ECe at various depths in the soil. Improvements in EMCI modelling can also be sought by joint inversion of EM with other geophysical datasets.

Cross-well seismic and electromagnetic tomography for CO2 detection and monitoring in a saline aquifer

Abstract Geological storage is one of the solutions to avoid the emission of carbon dioxide to the atmosphere. This process requires a careful monitoring of the CO 2 bubble, which can be performed by means of seismic and electromagnetic (EM) methods, on the basis of seismic velocity, attenuation and electrical conductivity contrasts before and after the injection. A successful monitoring depends on many factors, for instance the depth and properties of the reservoir. To test the feasibility of detecting the gas, we have performed cross-well seismic and EM tomographic inversions on a synthetic data set generated from a realistic aquifer partially saturated with CO 2 . We use two different algorithms based on traveltime picks. The method is novel regarding the EM inversion. Besides seismic velocity and conductivity, we have also obtained the seismic quality factor by performing attenuation tomography based on the frequency-shift approach. The RMS differences between the inverted and true initial models show that the methodology (and the adopted acquisition geometry) allows us to obtain reliable results which agree well with the true petrophysical model. Moreover, we have used a forward optimisation method to recover saturation, porosity and clay content from the tomographic seismic velocities, Q values and electric conductivity, with errors less than 15%.

The advantages of logarithmically scaled data for electromagnetic inversion

Non-linear inversion algorithms traverse a data misfit space over multiple iterations of trial models in search of either a global minimum or some target misfit contour. The success of the algorithm in reaching that objective depends upon the smoothness and predictability of the misfit space. For any given observation, there is no absolute form a datum must take, and therefore no absolute definition for the misfit space; in fact, there are many alternatives. However, not all misfit spaces are equal in terms of promoting the success of inversion. In this work, we appraise three common forms that complex data take in electromagnetic geophysical methods: real and imaginary components, a power of amplitude and phase, and logarithmic amplitude and phase. We find that the optimal form is logarithmic amplitude and phase. Single-parameter misfit curves of log-amplitude and phase data for both magnetotelluric and controlled-source electromagnetic methods are the smoothest of the three data forms and do not exhibit flattening at low model resistivities. Synthetic, multiparameter, 2-D inversions illustrate that log-amplitude and phase is the most robust data form, converging to the target misfit contour in the fewest steps regardless of starting model and the amount of noise added to the data; inversions using the other two data forms run slower or fail under various starting models and proportions of noise. It is observed that inversion with log-amplitude and phase data is nearly two times faster in converging to a solution than with other data types. We also assess the statistical consequences of transforming data in the ways discussed in this paper. With the exception of real and imaginary components, which are assumed to be Gaussian, all other data types do not produce an expected mean-squared misfit value of 1.00 at the true model (a common assumption) as the errors in the complex data become large. We recommend that real and imaginary data with errors larger than 10 per cent of the complex amplitude be withheld from a log-amplitude and phase inversion rather than retaining them with large error-bars.

Accuracy and effectiveness of three-dimensional controlled source electromagnetic data inversions

Unconstrained 3D inversion of marine controlled source electromagnetic data (CSEM) data sets produces resistivity volumes that have an uncertain relationship to the true subsurface resistivity at the scale of typical hydrocarbon reservoirs. Furthermore, CSEM-scale resistivity is an ambiguous indicator of hydrocarbon presence; not all resistivity anomalies are caused by hydrocarbon reservoirs, and not all hydrocarbon reservoirs produce a distinct resistivity anomaly. We have developed a method for quantifying the effectiveness of resistivities from CSEM inversion in detecting hydrocarbon reservoirs. Our approach uses probabilistic rock-physics modeling to update information from a preexisting prospect assessment, based on uncertain resistivities from CSEM. The result is an estimate the probability of hydrocarbon presence that accounts for uncertainty in the resistivity and in rock properties. Examples using synthetic and real CSEM data sets demonstrate that the effectiveness of CSEM inversion in identifying hydrocarbon reservoirs depends on the interaction between the uncertainty associated with the inversion-derived resistivity and the range of rock and fluid properties that were expected for the targeted prospect. Resistivity uncertainty that has a small effect on hydrocarbon probability for one set of rock property distributions may have a large effect for a different set of rock properties. Depending on the consequences of this interaction, resistivities from CSEM inversion might reduce the risk associated with predictions of hydrocarbon presence, but they cannot be expected to guarantee a specific well outcome.

Improved 1D inversions for sea ice thickness and conductivity from electromagnetic induction data: Inclusion of nonlinearities caused by passive bucking

The porosity of sea ice is a fundamental physical parameter that governs the mechanical strength of sea ice and the mobility of gases and nutrients for biological processes and biogeochemical cycles in the sea ice layer. However, little is known about the spatial distribution of the sea ice porosity and its variability between different sea ice types; an efficient and nondestructive method to measure this property is currently missing. Sea ice porosity is linked to the bulk electrical conductivity of sea ice, a parameter routinely used to discriminate between sea ice and seawater by electromagnetic (EM) induction sensors. Here, we have evaluated the prospect of porosity retrieval of sea ice by means of bulk conductivity estimates using 1D multifrequency EM inversion schemes. We have focused on two inversion algorithms, a smoothness-constrained inversion and a Marquardt-Levenberg inversion, which we modified for the nonlinear signal bias caused by a passive bucking coil operated in such a highly conductive environment. Using synthetic modeling studies, 1D inversion algorithms and multiple frequencies, we found that we can resolve the sea ice conductivity within [Formula: see text]. Using standard assumptions for the conductivity-porosity relation of sea ice, we were able to estimate porosity with an uncertainty of [Formula: see text], which enables efficient and nondestructive surveys of the internal state of the sea ice cover.

완전파형역산결과를 구조적 제약 조건으로 이용한 고해상도 전자탐사 복합역산 알고리듬 개발

완전파형역산결과를 구조적 제약 조건으로 이용한 고해상도 전자탐사 복합역산 알고리듬 개발

Contribution of the PSO in the electromagnetic inverse method in terms of convergence and simplicity of implementation

In this paper, we present an electromagnetic inverse particle swarm optimization (PSO)-based method for modeling the electromagnetic radiation of components or systems of power electronics using the near-field technique. The implementation of this method has been applied to the cartography of the magnetic field emitted by different structures. To fully appreciate our approach, the obtained results along with the proposed methods were compared to those obtained by the inverse method, based on the genetic algorithm (GA). Basically, we will compare the results at two levels, theoretical and practical. For the theoretical comparison, both methods are applied to several calculated cartographies of the magnetic field, using the analytical equations of the magnetic and electric dipoles. For the practical comparison, we have used results based on the measurements performed on real systems. The purpose of these comparisons is to show that using the PSO in the electromagnetic inverse method is more interesting than the GA. In fact, the obtained results have shown that the PSO-based method is at least six times faster than the GA-based one.

Three‐dimensional inversion of seafloor magnetotelluric data collected in the Philippine Sea and the western margin of the northwest Pacific Ocean

AbstractWe report a result of three‐dimensional (3‐D) upper mantle electrical conductivity inversion of seafloor magnetotelluric data. We used existing data at 25 sites in the Philippine Sea and the western margin of the Pacific Ocean. In order to obtain a reliable model by 3‐D inversion, we evaluated the large and small‐scale topographic effects. We also conducted a comprehensive search of the one‐dimensional (1‐D) profiles of the study area in order to determine the best initial and prior models. A two‐phase inversion method was applied so that the error floors for the diagonal and off‐diagonal elements of the impedance tensor could be separately controlled. Through this first attempt at inverting real data, we obtained basic knowledge about tuning the inversion parameters and conditions. We also proposed a procedure to evaluate the reliability of the 3‐D conductivity anomalies imaged by the inversion by conducting checkerboard and sensitivity tests. After the iterations converged, 13 distinct anomalies were found in the inverted 3‐D conductivity model; four conductive and two resistive anomalies were confirmed to be resolved enough by the data through the checkerboard test. Then the sensitivity tests were conducted to quantify how each anomaly was required by the observed data, and we confirmed that the intensities of three conductive anomalies and one resistive anomaly were statistically significant. This paper presented an example of possible approach in 3‐D seafloor electromagnetic inversion procedure for imaging reliable electrical conductivity structure of the oceanic mantle, which will be useful in understanding dynamics and evolution of solid Earth.

A strategy for coupled 3D imaging of large-scale seismic and electromagnetic data sets: Application to subsalt imaging

Offshore seismic and electromagnetic (EM) imaging for hydrocarbons can require up to tens of millions of parameters to describe the 3D distribution of complex seabed geology and relevant geophysical attributes. The imaging and data volumes for such problems are enormous. Descent-based methods are the only viable imaging approach, where it is often challenging to manage the convergence of stand-alone seismic and EM inversion experiments. When a joint seismic-EM inversion is implemented, convergence problems with descent-based methods are further aggravated. Moreover, resolution mismatches between seismic and EM pose another challenge for joint inversion. To overcome these problems, we evaluated a coupled seismic-EM inversion workflow and applied it to a set of full-wave-seismic, magnetotelluric (MT) and controlled-source electromagnetic (CSEM) data for subsalt imaging. In our workflow, we address disparate resolution properties between seismic and EM data by implementing the seismic inversion in the Laplace domain, where the wave equation is transformed into a diffusion equation. The resolution of seismic data thus becomes comparable to that of EM data. To mitigate the convergence problems, the full joint seismic-EM inverse problem is split into manageable components: separate seismic and EM inversions and an intermediate step that enforces structural coupling through a cross-gradient-only inversion and resistivity-velocity crossplots. In this workflow, stand-alone seismic and MT inversion are performed first. The cross-gradient-only inversion and the crossplots are used to precondition the resistivity and velocity models for subsequent stand-alone inversions. By repeating the sequence of the stand-alone seismic, MT, and cross-gradient-only inversions along with the crossplots, we introduce the seismic structural information into the resistivity model, and vice versa, significantly improving the salt geometry in both resistivity and velocity images. We conclude that the improved salt geometry can then be used to precondition a starting model for CSEM inversions, yielding significant improvement in the resistivity images of hydrocarbon reservoirs adjacent to the salt.

Spatial prediction of the exchangeable sodium percentage at multiple depths using electromagnetic inversion modelling

AbstractAgriculture in the semi‐arid and arid areas of the world requires irrigation. However, in these areas, soils naturally contain large amounts of sodium (sodic) which can cause amongst other things, surface crusting on the topsoil or structural instability in the subsoil. The exchangeable sodium percentage (ESP) needs to be mapped to guide the application of gypsum. Whilst geostatistical techniques, such as ordinary, co‐ and 3‐D kriging have been used, they have often been criticized because they are unable to take into account soil knowledge concerning distribution, processes and factors of formation. The use of digital soil mapping methods which couple remote or proximally sensed data with soil information is increasingly becoming useful because of the production of high‐resolution ancillary data. In this study, we first invert (using EM4Soil software) the electrical conductivity (σa –mS/m) of DUALEM‐421 data collected along a single transect. In doing this, we generate a 2‐dimensional electromagnetic conductivity image (EMCI). We couple the estimates of electrical conductivity (σ – mS/m) at 0.30 m depth increments down to 1.5 m with measured soil ESP. We compare the results of inversion using various possible coil array configurations of the DUALEM‐421 to determine a suitable set of data. We conclude that the use of the DUALEM‐41 is optimal (r2 = 0.70). We use the calibration to estimate ESP along adjacent transects where we also generate EMCI. We are thus able to estimate ESP at various depths across a clay plain and an associated prior stream channel. We conclude that the collection of additional transects of DUALEM‐421 data as well as the use of a quasi‐3‐D inversion modelling approach would improve prediction.

Three-dimensional inversion of CSEM data: Water leak detection using a small-loop EM method

Abstract Electromagnetic (EM) data sets were acquired using ground-based small-loop electromagnetic (EM) sensors over an artificially constructed sandy ground in Tsukuba, Japan, for three conditions of water saturation. The research aim was to evaluate the imaging capability of the geophysical method for detecting a water leak. Because the sensitivity analysis showed a considerable three-dimensional (3D) distribution of sensitivity around the source–receiver location, 3D inversion was applied to the field data sets. We used an accurate 3D controlled-source electromagnetic (CSEM) inversion algorithm, which adopted an edge-based finite element method as a forward scheme. To obtain the best inversion strategy for our field data and for the selection of the optimal regularization method, 3D inversion was applied to synthetic data sets prior to the inversion of the field data; the synthetic data sets were based on synthetic resistivity models used to simulate the three water-saturation phases of the real test site. Based on the results of sensitivity analysis, different regularization methods were systematically tested and the inversion results were qualitatively analyzed. For our monitoring scenario, the best performance was achieved by combining spatially varying regularization parameters, structural constraints, and the reference model method. The reference model parameters were derived from the less ill-posed model, instead of the main target model, which allowed for more accurate imaging of the main region of interest. This optimal inversion strategy was applied to the test-site field data. The water leak was successfully visualized by small-loop EM data, with systematic application of a priori information as constraints.

3D Inversion of Large-scale Time Domain Electromagnetic Data

Airborne time-domain electromagnetic (EM) surveys are effective tools for mineral exploration, geologic mapping and environmental applications. These surveys can be an economical way to explore large prospective regions. Traditionally, the data from such surveys have been interpreted using time constant analysis, conductivity to depth imaging (CDI) or possibly 1D inversions. These methods assist in a simple interpretation of the data, however because they do not fully model the physics in 3D, they can fail to accurately represent environments such as real world structures and geological targets. Airborne EM datasets are characterized by large volumes of data, as each EM sounding implies a new transmitter location. As a result, inverting this data in 3D is a computationally difficult problem that until recently has not been possible for the exploration community. In this abstract we demonstrate a methodology for inverting large airborne EM surveys in 3D using multiple meshes, each spanning the full model domain. By using an adaptive meshing procedure during the forward modeling, each mesh is optimally designed for computational efficiency on the local domains defined by a subset of transmitters. This procedure allows the computational cost of each mesh to be dependent on the number of subset transmitters considered, rather than the total survey size. Since the forward modeling operation is the bottleneck for any inversion, this results in a highly parallel algorithm that can handle arbitrarily large datasets. In this abstract we outline our airborne electromagnetic inversion methodology and demonstrate it using synthetic and field data examples.

A New Algorithm of Full‐Time‐Domain of Inverse Transformation from the Transient Electromagnetic Diffuse Field into the Fictitious Seismic Wave Field

AbstractTo realize 3D transient electromagnetic (TEM) inversion, we can transform the diffuse equations of TEM into wave equations, and then make pseudo wave imaging of TEM using seismic imaging methods. For such a transformation, we adopt the preconditioned regularization conjugate gradient method to solve inverse transformation of the wave field. First, we compare several ways of discretization, and use the one with least condition number to make discretization of the equations. Then, we choose the optimal regularization parameters to make the wave field from inverse transform stable and reliable, and use the super‐relaxation pre‐conditioned method to process the coefficient matrix to reduce its condition number. Finally, we employ the conjugate gradient method (RCG) to conduct iterative solving with a fast convergence. The comparison of inverse transformation results with known fictitious wave field functions shows that the algorithm is stable and convincing. Comparison with previous studies and application to real data indicate that the method suggested in this paper is correct and effective. Combined with the algorithm of inverse transformation, we also analyze the models with varied parameters and summarize the propagation rules of the fictitious seismic wave field in dispersion media.

Three-dimensional magnetotelluric inversion using a heterogeneous smoothness-constrained least-squares method

This paper presents a fast algorithm for electromagnetic data inversion to three-dimensional (3D) resistivity models. The algorithm is distinctive for the level of accuracy it attains while bypassing the sensitivity matrix update. A common sensitivity matrix for homogeneous half-space is used in all iterations. Instead of updating the sensitivity matrix, the smoothness filter coefficients at each model element are updated, based on the spatial variations in resistivity in the model derived from the latest iteration. This substitution is expected not only to reduce the computation time required for large-scale inversions, such as those for 3D surveys, but also to allow the resolution of sharp boundaries in resistivity structures. Our algorithm was applied to 3D magnetotelluric inversion in order to confirm its effectiveness. Using synthetic examples under several conditions, we demonstrated that the method can reduce the number of forward calculations required to reduce data misfits to noise level, and that the method is robust for constructing target models even with sharp boundaries without generating fatally false resistivity structures or boundaries under noisy conditions.

GPU parallelization of a three dimensional marine CSEM code

One of the main problem of 3D time domain controlled source electromagnetic (CSEM) inversion is the high runtimes of forward modeling codes. We reduced the runtime of the 3D time domain finite difference CSEM code TEMDDD by the GPU-parallelization of expensive algorithms. The code solves the electromagnetic diffusion equation by discretization of spatial operators and subsequent calculation of eigenpairs. These eigenpairs are found by approximation of the eigenspace in a Krylov subspace using the spectral Lanczos decomposition Method. This algorithm was in its original form not parallelizable due to implementation of the upper boundary condition at the air–water interface. We show for the marine case that replacing the original boundary condition at the air–water surface by a discretized air layer allows GPU parallelization of every time consuming algorithm of the code in the marine case. Speedups between 20 and 60 have been achieved compared to the original code for a larger 3-D model. In this model the bathymetry from a survey area offshore Egypt is used as an example demonstrating that the parallelized version of the code is applicable to real survey scenarios.

Technique for inversion of an inhomogeneous bianisotropic slab through an optimisation approach

An electromagnetic inversion method is presented to reconstruct the constitutive parameters of an inhomogeneous bianisotropic slab. The measured co- and cross-reflection and transmission coefficients are used to extract the electromagnetic parameters profiles of the inhomogeneous bianisotropic media from the proposed method, using truncated Fourier series expansion and Gravitational Search Algorithm (GSA). GSA is used to improve the speed and accuracy of the optimisation process because of the complexity of inhomogeneous bianisotropic media, highly non-linearity of optimisation problem, and extremely large search space. Finally, the accuracy and robustness of the proposed reconstruction method are validated using some typical examples.

Pitfalls of 1D inversion of small-loop electromagnetic data for detecting man-made objects

In order to interpret field data from small-loop electromagnetic (EM) instruments with fixed source–receiver separation, 1D inversion method is commonly used due to its efficiency with regard to computation costs. This application of 1D inversion is based on the assumption that small-offset broadband EM signals are insensitive to lateral resistivity variation. However, this assumption can be false when isolated conductive bodies such as man-made objects are embedded in the earth. Thus, we need to clarify the applicability of the 1D inversion method for small-loop EM data. In order to systematically analyze this conventional inversion approach, we developed a 2D EM inversion algorithm and verified this algorithm with a synthetic EM data set. 1D and 2D inversions were applied to synthetic and field EM data sets. The comparison of these inversion results shows that the resistivity distribution of the subsurface constructed by the 1D inversion approach can be distorted when the earth contains man-made objects, because they induce drastic variation of the resistivity distribution. By analyzing the integrated sensitivity of the small-loop EM method , we found that this pitfall of 1D inversion may be caused by the considerable sensitivity of the small-loop EM responses to lateral resistivity variation. However, the application of our 2D inversion algorithm to synthetic and field EM data sets demonstrate that the pitfall of 1D inversion due to man-made objects can be successfully alleviated. Thus, 2D EM inversion is strongly recommended for detecting conductive isolated bodies, such as man-made objects, whereas this approach may not always be essential for interpreting the EM field data. ► The resistivity of the subsurface constructed by the 1D inversion can be distorted. ► Small-loop EM response has considerable sensitivity to lateral resistivity variation. ► The application of 2D EM inversion can alleviate the pitfall of 1D EM inversion. ► 2D EM inversion is strongly recommended for detecting man-made objects.

3D modeling and inversion of VLF and VLF-R electromagnetic data

Three-dimensional linearized nonlinear electromagnetic inversion is developed for revealing the subsurface conductivity structure using isolated very low frequency (VLF) and VLF-resistivity anomalies due to conductors that may be arbitrarily directed towards the measuring profiles and the VLF transmitter. We described the 3D model using a set of variables in terms of geometric and physical parameters. These model parameters were then optimized (parametric inversion) to obtain their best estimates to fit the observations. Two VLF transmitters, i.e., the [Formula: see text], [Formula: see text] (“E”) and the [Formula: see text], [Formula: see text] (“H”) polarizations, respectively, can be considered jointly in inversion. After inverting several noise-free and noisy synthetic data, the results revealed that the estimated model parameters and the functionality of the approach were very good and reliable. The inversion procedure also worked well for the field data. The reliability and validity of the results after the field data inversion have been checked using data from a shear zone associated with uranium mineralization.