Inversion Of Electromagnetic Data Research Articles

Assessing and Improving the Robustness of Bayesian Evidential Learning in One Dimension for Inverting Time-Domain Electromagnetic Data: Introducing a New Threshold Procedure

Understanding the subsurface is of prime importance for many geological and hydrogeological applications. Geophysical methods offer an economical alternative for investigating the subsurface compared to costly borehole investigations. However, geophysical results are commonly obtained through deterministic inversion of data whose solution is non-unique. Alternatively, stochastic inversions investigate the full uncertainty range of the obtained models, yet are computationally more expensive. In this research, we investigate the robustness of the recently introduced Bayesian evidential learning in one dimension (BEL1D) for the stochastic inversion of time-domain electromagnetic data (TDEM). First, we analyse the impact of the accuracy of the numerical forward solver on the posterior distribution, and derive a compromise between accuracy and computational time. We also introduce a threshold-rejection method based on the data misfit after the first iteration, circumventing the need for further BEL1D iterations. Moreover, we analyse the impact of the prior-model space on the results. We apply the new BEL1D with a threshold approach on field data collected in the Luy River catchment (Vietnam) to delineate saltwater intrusions. Our results show that the proper selection of time and space discretization is essential for limiting the computational cost while maintaining the accuracy of the posterior estimation. The selection of the prior distribution has a direct impact on fitting the observed data and is crucial for a realistic uncertainty quantification. The application of BEL1D for stochastic TDEM inversion is an efficient approach, as it allows us to estimate the uncertainty at a limited cost.

Inversion for 3D Conductivity and Chargeability Models Using EM Data Acquired by the New Airborne TargetEM System in Ontario, Canada

This paper introduces an original approach to the joint inversion of airborne electromagnetic (EM) data for three-dimensional (3D) conductivity and chargeability models using hybrid finite difference (FD) and integral equation (IE) methods. The inversion produces a 3D model of physical parameters, which includes conductivity, chargeability, time constant, and relaxation coefficients. We present the underlying principles of this approach and an example of a high-resolution inversion of the data acquired by a new active time domain airborne EM system, TargetEM, in Ontario, Canada. The new TargetEM system collects high-quality multicomponent data with low noise, high power, and a small transmitter–receiver offset. This airborne system and the developed advanced inversion methodology represent a new effective method for mineral resource exploration.

Quasi-2D inversion of surface large fixed-loop transient electromagnetic sounding data

Abstract In many cases, 1D inversion is still an important step in transient electromagnetic data processing. Potential issues may arise in the calculation of apparent resistivity using induced electromotive force (EMF) due to overshoot and the presence of multi-valued functions. Obtaining reliable and consistent inversion results using a uniform half-space as the initial model is challenging, especially when aiming for efficient inversion. Focusing on these problems, we use the land-based transient electromagnetic (TEM) sounding data, which was acquired by using a large fixed-loop transmitter, and adopt a quasi-2D inversion scheme to generate improved images of the subsurface resistivity structure. First, we have considered directly using magnetic field data or converting induced EMF into magnetic field, and then calculating the apparent resistivity over the whole zone. Next, a resistivity profile that varies with depth is obtained through fast smoke ring imaging. This profile serves as the initial model for the subsequent optimal inversion. The inversion scheme uses a nonlinear least-squares method, incorporating lateral and vertical constraints, to produce a quasi-2D subsurface image. The potentiality of the proposed methodology has been exemplified through the interpretation of synthetic data derived from a 3D intricate resistivity model, as well as field data obtained from a TEM survey conducted in a coalmine field. In both cases, the inversion process yields quasi-2D subsurface images that exhibit a reasonable level of accuracy. These images appear to be less moulded by 3D effects and demonstrate a satisfactory level of agreement with the known target area.

High-Resolution Hybrid-Dimensional Inversion of Transient Electromagnetic Data for Water Hazard Detection in Coal Mines

High-Resolution Hybrid-Dimensional Inversion of Transient Electromagnetic Data for Water Hazard Detection in Coal Mines

A two-dimensional integral model of the first-kind for LIN electromagnetic data inversion

A two-dimensional integral model of the first-kind for LIN electromagnetic data inversion

Deep structural controls on the distribution of carbonate reservoirs and overburden heterogeneity in Central Luconia province, offshore Borneo revealed by 3D anisotropic inversion of regional controlled-source electromagnetic and magnetotelluric profile data

Understanding the deep structural controls on reservoir distribution and overburden heterogeneity is important for near-field exploration and green-field development of the Miocene to Holocene carbonate buildups in Central Luconia province in offshore northwest Borneo, Malaysia. Data from 59 stations along an approximately 180 km long controlled-source electromagnetic (CSEM) and magnetotelluric (MT) survey line with three segments recorded using different CSEM transmitter-towing directions were available. We applied three-dimensional (3D) anisotropic resistivity inversion with cross-gradient constraint and verified the resulting models using resistivity logs from nearby wells and the acoustic basement interpreted from seismic data. Our anisotropic resistivity models reveal a fragmented carbonate-rich zone atop a segmented basement comprising electrically resistive horsts coinciding with the northerly Mega-platform, Central and Southern Field Highs, separated by steep conductive zones coinciding with the West, East, and Southeast Troughs previously interpreted from seismic data. The structural highs correlate with the spatial distribution of the known carbonate buildups implying a genetic link. The carbonate bodies are overlain and underlain by persistent layers (C2 and C3) of low resistivity and high anisotropy, which we interpret as indicating compressional deformation or detachment zones. Overburden layer C2 (whose base coincides with the top of a key sedimentary package, Cycle V in seismic data) is thinnest over the East Trough and is discontinuous at the eastern margin of the West Trough, which are locations where drilled wells did not find hydrocarbons implying that the seal rocks are inefficient or breached at those localities. We used these observations to refine the existing seismic-based interpretation of carbonate play-types along our transect indicating how 3D joint CSEM-MT imaging can potentially contribute to derisking or optimizing future exploration and/or development work in this province.

Weighted Laterally Constrained Inversion of Airborne Transient Electromagnetic Data with IP Effects

Due to the induced polarization (IP) effects, abnormal fast decay and sign reversals are often observed in the field airborne transient electromagnetic (ATEM) responses, this phenomenon can well be explained by introducing the four-parameter Cole-Cole resistivity model. However, the introduction of multiple parameters makes the non-uniqueness of inversion more serious. To improve this problem, a weighted 1D laterally constrained inversion is proposed to recover the four IP parameters and thickness via adding different weighted factors chosen by lateral constraint conditions, in this paper, a synthetic polarization model is developed and 1D forward modeling with synthetic natural noise is conducted to imitate the field response. The proposed inversion is employed on the synthetic data and the results demonstrate that the method can improve the inversion stability and obtain more reliable result.

3D inversion of multifrequency controlled-source electromagnetic data and its application to geothermal exploration in the Tianzhen region of the northern Datong Basin, China

Owing to its sensitivity to hydrothermal alteration and geothermal fluids, the distribution of subsurface electrical conductivity provides critical information for characterizing geothermal systems. For geothermal exploration, the controlled-source electromagnetic (CSEM) technique provides a crucial tool to image the subsurface resistivity structures, especially in areas with strong cultural noise. Usually, land-based CSEM surveys are carried out with dozens of operating frequencies to enhance spatial resolution. However, the 3D inversion of multifrequency CSEM data using the commonly used direct solver is challenging with limited computational resources. In this study, we implement a practical inversion strategy for interpreting 3D multifrequency CSEM data. By combining a hybrid direct-iterative solver with the inexact Gauss-Newton optimization, 3D inversion of CSEM data involving multiple frequencies can be performed effectively on typical workstations. First, we test the effectiveness of the developed approach using synthetic multifrequency 3D CSEM data generated for a simplified geothermal model. The inversion strategy is then applied to the multifrequency CSEM field data collected for the geothermal exploration at Tianzhen region in Shanxi Province, China. The comparison between the inversion results using the sparse data set (six frequencies) and the dense data set (12 frequencies) highlights the necessity of using data from more frequencies in the inversion to improve the resolution. The resulting 3D resistivity model clearly delineates the clay alteration layers and shallow thermal reservoirs of the potential high-temperature geothermal system within the study area, while its deep heat source is not revealed owing to the limited investigation depth of the survey.

A method to construct statistical prior models of geology for probabilistic inversion of geophysical data

In probabilistic inversion of geophysical data, one must describe the expected noise in the system, and any prior information. In a geoscience context, prior information can provide a quantitative description of the expected spatial variability and correlations of the geology. But in practical inversion cases, driven by difficulty in quantifying geological information and computational complexity, an analytical mathematical smooth prior model is often chosen to describe the spatial variability. This is one of the primary reasons that realistic geological structures are difficult to resolve in geophysical models. Thus, there is currently a need for investigating and proposing practical ways of capturing complex (and often qualitative) geological information in statistical prior models that can be used in probabilistic inversion, which satisfies both the geologist, geophysicist, engineer and the geostatistician. In this research we show how a 1D statistical prior model can be designed that emulates the spatial distribution found in 188 boreholes with Miocene and Quaternary deposits from a study area (approx. 177,5 km2) near Horsens, Denmark. The prior model is built in two major steps 1) a multidimensional distribution describing the sub-division of major geological elements (here represented by lithologies from defined geological periods) and 2) a truncated pluri-Gaussian distribution describing the internal structure of lithologies within each element. The presented prior model can both be used to generate independent realizations, which can be used as part of the extended rejection sampler, as well as allowing the possibility of doing a “random walk” in the model space, as required by the extended Metropolis algorithm. We demonstrate, as an example, how the developed prior model can be used in a probabilistic inversion of airborne transient electromagnetic (AEM) data and discuss the implications the use of such informed prior models can have.

Three-Dimensional Separate and Joint Inversions of Multi-Component Frequency-Domain Airborne Electromagnetic Data: Synthetic Model Studies.

Airborne electromagnetic (AEM) surveys using airborne mobile platforms enable rapid and efficient exploration of areas where groundwork is difficult. They have been widely used in fields such as shallow resource exploration and environmental engineering. Three-dimensional AEM inversion is the main technique used in fine structural interpretation. However, most current methods focus on separate component data inversions, which limit the kinds of structures that can be recovered in the inversion results. To address this issue, a method for the robust 3D joint inversion of multicomponent frequency-domain AEM data was developed in this study. First, a finite element method based on unstructured tetrahedral grids was used to solve the forward problem of frequency-domain AEM data for both isotropic and anisotropic media. During inversion, a limited-memory quasi-Newton (L-BFGS) method was used to reduce the memory requirements and enable the joint inversion of large-scale multicomponent AEM data. The effectiveness of our algorithm was demonstrated using synthetic models for both isotropic and anisotropic cases, with 5% Gaussian noise added to the modeling data to simulate the measured data for separate and joint inversions. The results of the synthetic models show that joint inversion has advantages over separate inversion in that it enables the recovery of finer underground structures and provides a novel approach for the fine interpretation of frequency-domain AEM data.

Inversion of VLF-R data using a non-linear rank order smoothing constraint and its implementation to image surface rupture of the North Anatolian Fault in Başiskele, Kocaeli, NW Turkey

Inversion of electromagnetic induction data is often realized using smoothing operators for regularizing the process. These operators are applied using derivative matrices, penalizing differences between neighboring mesh cells. The resulting smoothing effect is similar to that of low-pass Gaussian filters and may cause difficulties due to the smoothed boundaries between structures. To prevent such ambiguities, non-linear rank filters are applied widely in image processing applications to filter low frequency variations while keeping boundaries. Correspondingly, we have defined a non-linear rank order smoothing operator for regularization. The effects of the defined parameters are demonstrated on synthetic models and the operator is observed to be able to provide better defined boundaries. The implementation of the operator on field data is realized using single-frequency VLF-R data collected on profiles traversing the surface rupture of the North Anatolian Fault in Kocaeli, Turkey. In the study area, ERT data are also collected on a single profile, and its smooth inversions are realized individually and jointly with VLF-R data for comparisons. Inversions show that the recovered subsurface structure using the rank order smoothing is closer to that indicated by the ERT data and previous studies. According to the recovered models, the clayey fillings in the fault rupture are acting as a barrier affecting the horizontal fluid flow in the near-surface and the resulting water accumulations around the fault rupture may cause susceptibility for earthquake induced damages.

Simultaneous Inversion of Ocean Bottom Pressure and Electromagnetic Tsunami Records for the 2009 Samoa Earthquake

AbstractThis study presents tsunami inversion analyses that simultaneously use ocean‐bottom pressure and ocean‐bottom electromagnetic data along with an accurate tsunami propagation model to estimate the earthquake source model for the 2009 Samoa earthquake. This earthquake was a doublet event that occurred along a pair of normal and thrust faults. To the best of our knowledge, this joint inversion of pressure and electromagnetic data is unprecedented. The incorporation of electromagnetic data in the tsunami inversion analysis was relatively simple, and the inclusion of frequency dispersion, self‐attraction, and loading effects in the tsunami propagation calculations allowed the use of tsunami waveforms recorded at distant locations, which improved the reliability of the solutions obtained. Our best source model indicated that the east‐west extent of the plate‐boundary slip area was approximately 50 km, which is narrower than that of a previous fault model, and explained both electromagnetic and pressure data from the 2009 Samoa tsunami.

Inversion of TEM measurement data via a quantum particle swarm optimization algorithm with the elite opposition-based learning strategy

The fine interpretation and inversion of transient electromagnetic method measurement data have the problems of nonlinearity, multi-solution, and ill condition. However, the conventional particle swarm optimization (PSO) nonlinear inversion methods suffer from prematurity, slow convergence, and low calculation accuracy. To solve these problems, a quantum PSO (QPSO) algorithm based on the elite opposition-based learning (EOL) strategy is proposed. Firstly, three performances tests of the EOL-QPSO algorithm are carried out with Peaks, Schaffer and Rastrigin functions. The results show that the EOL-QPSO algorithm has excellent solution accuracy, efficient calculation speed and balanced exploitation and exploration capability. Secondly, the conventional PSO algorithm and the EOL-QPSO algorithm are used to compare the inversion of the theoretical model and the synthetic data with noise, and combined with Bayesian method, the posterior model probability statistics of the synthetic data are carried out. The research shows that the EOL-QPSO inversion algorithm is improved in terms of calculation accuracy, calculation efficiency, anti-noise performance and exploitation and exploration capability, and it can accurately obtain the posterior estimates of the real model. Finally, the inversion of field-measured data demonstrates that the EOL-PSO inversion method accurately reflects the position of the water-accumulated goaf.

Geometric 2.5D inversion of marine time domain electromagnetic data with application to hydrocarbon deposits prospecting

To solve the problem of detection and delineation of marine hydrocarbon deposits located at different depths in an inhomogeneous medium, we propose an approach to 2.5D inversion of electromagnetic (EM) data measured in the time domain (TD) using a differentially normalized method of electrical prospecting. The approach is based on geometric inversion, in which block structures are used to parameterize the geological medium. The sizes of blocks in the initial model are set depending on the depth. Bathymetry is taken into account as a 3D surface. As a result of inversion, the coordinates of block boundaries and conductivity inside blocks and layers are determined. The minimized functional is represented as a sum of weighted residuals between computed and practical data and regularizing terms. Adaptive regularization is used to satisfy parameter constraints. To solve a 3D forward problem and calculate derivatives with respect to parameters, the finite element method (FEM) is used. We propose to use a priori data on the depth of the target layers and use various options of block structures with an analysis of possible uncertainties in detecting target bodies and determining their boundaries. We present the results of a 2.5D inversion of field data obtained in one of the areas in the North Sea. Target bodies discovered as a result of inversion are confirmed by well data. Coincidences were obtained both for productive wells and for dry ones. Using synthetic data for various geoelectric models and options of block structures, we justify the proposed approach to the inversion of marine TD EM data and make recommendations for its use.

Crosshole radio electromagnetic tomography using apparent source intensity and logarithmic barrier

Crosshole radio-frequency (typically from 1 to 36 MHz) electromagnetic methods are powerful tools for locating conductive ores and distribution of electric properties of rocks between boreholes. In the range of these frequencies, electromagnetic field can be approximated by the wave field. Usually, crosshole radio-frequency electromagnetic inversion requires exact source intensity but it is difficult to determine that.We present a ray-based inversion method of crosshole radio electromagnetic data which does not require exact source intensity. We introduce a concept of apparent source intensity, establish the method of determining that and realize absorption coefficient and conductivity imaging of crosshole radio electromagnetic data using that. And then we improve accuracy and reliability of tomographic inversion of crosshole radio electromagnetic data using positive constraints for absorption and conductivities. Inversion is based on simultaneous iterative reconstruction technique or adaptive control gradient method.Tests of synthetic and field data show that the method we propose has high reliability.

Constrained 2D inversion of radio-magnetotelluric and controlled-source audio-magnetotelluric data using high-resolution reflection seismic data: An example in groundwater surveying from Heby, Sweden

We advance a previously established method for 2D inversion of electromagnetic data, in which the smoothness constraints are locally reweighted according to the seismic envelope fractional gradients (SEFGs). As the first step of our modifications, seismic envelope values are edited and normalized. This results in the rejection of noise-contaminated parts, clipping the envelope outliers and increasing the reflectivity power of weak seismic signals. Second, we introduce a weighting matrix in the normalization process to incorporate prior information in the constrained inversion regarding the relative contrasts of electrical resistivity in the given parts of the model. Third, due to normalizing the SEFG, there is no need to search for an optimum stabilization factor to modify local smoothing weights, and hence, we set it to a constant value. Finally, an Occam inversion with additional Levenberg-Marquardt damping is used to mitigate possible artifacts in the resistivity model generated by reflection seismic constraints. In applying the proposed scheme to a synthetic example, interfaces of various geologic units are restored as sharp boundaries. In addition, artifacts generated in the original approach are effectively mitigated thanks to the applied normalization process. For the first time, we apply the method to radio-magnetotelluric (RMT) and controlled-source audio-magnetotelluric (CSAMT) field data acquired along a profile across a known aquifer in Heby, Sweden. Our inversion models compare favorably to previously presented results from seismic and geoelectric data. By modifying the smoothness weights based on SEFG, the depth to the bedrock is recovered well, being constrained by the corresponding interfaces in the seismic image. The resistivity models from seismically constrained inversions of RMT and CSAMT data reveal steeply dipping and possibly fractured bedrock underneath the valley-shaped aquifer in the area. This interpretation is verified by borehole logs.

Three-dimensional inversion of airborne time-domain electromagnetic data for ground sources

While most airborne time-domain electromagnetic (ATEM) surveys are carried out using moving-source systems, semi-airborne systems that use a ground-based source, such as GREATEM, have gained popularity in recent years because they allow for more in-depth exploration than moving-source systems. We presented a three-dimensional inversion method for interpreting transient data collected in semi-airborne surveys. Our method is based on a Gauss–Newton minimization approach. The forward problem is solved in the frequency domain using a secondary-field finite-difference technique, and the resulting solution and sensitivity are Fourier-transformed to the time domain using a digital filter. The sensitivities are evaluated by the adjoint-equation method, except for those of a surface region immediately below the source, which are derived by forward modeling the response of a perturbed model based on finite differences. We tested our inversion method on synthetic and real data. The synthetic tests show that the resolution capability of the semi-airborne surveys is dependent on the location of the ground source, which suggests that it is desirable to employ multiple source locations and perform joint inversion of all data sets to ensure the reliability of semi-airborne surveys. Finally, the real data example demonstrates that the recovered conductive zone is consistent with the known distribution of the mineralized zone.

Three-dimensional inversion of semi-airborne electromagnetic data with a second-order finite-element forward solver

SUMMARYThe analysis of controlled-source electromagnetic (EM) data recorded with semi-airborne exploration systems requires advanced simulation and inversion tools that are capable of handling realistic survey geometries. Semi-airborne EM setups with elongated transmitters deployed in mountainous terrain prohibit the exploitation of secondary-field formulations in numerical approximations without producing hardly quantifiable errors. Building upon the open-source software custEM for forward modeling and pyGIMLi for geophysical inversion, we present an inverse modeling procedure based on highly accurate second-order finite-element forward solutions on irregular grids and fast-converging Gauss–Newton minimization. Using the total-field formulation of the electric field approach in combination with a direct solver enables calculating explicit sensitivities with comparatively cheap back-substitutions for thousands of ground and airborne receiver stations in multiple flight areas. Second-order basis functions show general superiority over first-order basis-functions regarding the accuracy and performance of the forward problem. Beyond that, synthetic and real data inversion studies related to semi-airborne geometries indicate that second-order basis functions help particularly to avoid high modeling errors for the weakest field components and artifacts in the vicinity of transmitters or at the surface. This leads generally to a better convergence and final inversion results of higher robustness and quality. The presented tools are freely available such as the underlying software.

Parallelized 3-D Inversion of Controlled-Source Electromagnetic Data Based on Spectral Element Method With Infinite Element Boundary

Parallelized 3-D Inversion of Controlled-Source Electromagnetic Data Based on Spectral Element Method With Infinite Element Boundary

Fast Bayesian Inversion of Airborne Electromagnetic Data Based on the Invertible Neural Network

The inversion of airborne electromagnetic (AEM) data suffers from severe non-uniqueness of the solution. Bayesian inference provides the means to estimate structural uncertainty with a rich suite of statistical information. However, conventional Bayesian methods are computationally demanding in nonlinear inversions, especially considering the huge volumes of observational data, and thus are not feasible in practice. In this study, we develop a fast Bayesian inversion operator based on the invertible neural network (INN) to fully explore the posterior distribution and quantitatively evaluate the model uncertainty. The INN uses a latent variable to capture the information loss during measurement and constructs bijective mappings between AEM data and the resistivity model. We also introduce another noise variable into the INN to account for data uncertainties. Synthetic tests demonstrate that the INN can effectively recover the posterior distribution by a relatively small ensemble of predicted resistivity models whose AEM responses show a significant agreement with the true signal. We also apply the INN inversion operator to a field data set and obtain results consistent with previous studies. The INN shows considerable adaptability to field observations and strong noise robustness. Meanwhile, the INN delivers the inversion result with posterior model distribution for 23366 AEM time series in 20 seconds on a common PC. The inversion efficiency can be further improved for large data set due to its natural parallelizability. The proposed INN method can support fast Bayesian inversion of AEM data and offer tremendous potential for near real-time uncertainty evaluation of underground structures.