Inversion Of Controlled-source Electromagnetic Data Research Articles

CSEM Optimization Using the Correspondence Principle

Traditionally, 3D modeling of marine controlled-source electromagnetic (CSEM) data (in the frequency domain) involves high-memory demand, requiring solving a large linear system for each frequency. To address this problem, we propose to solve Maxwell’s equations in a fictitious dielectric medium with time-domain finite-difference methods, with the support of the correspondence principle. As an advantage of this approach, we highlight the possibility of its implementation for execution with GPU accelerators, in addition to multi-frequency data modeling with a single simulation. Furthermore, we explore using the correspondence principle to the inversion of CSEM data by calculating the gradient of the least-squares objective function employing the adjoint-state method to establish the relationship between adjoint fields in a conductive medium and their counterparts in the fictitious dielectric medium, similar to the approach used in forward modeling. We validate this method through 2D inversions of three synthetic CSEM datasets, computed for a simple model consisting of two resistors in a conductive medium, a model adapted from a CSEM modeling and inversion package, and the last one based on a reference model of turbidite reservoirs on the Brazilian continental margin. We also evaluate the differences between the results of inversions using the steepest descent method and our proposed momentum method, comparing them with the limited-memory BFGS (Broyden–Fletcher–Goldfarb–Shanno) algorithm (L-BFGS-B). In all experiments, we use smoothing by model reparameterization as a strategy for regularizing and stabilizing the iterations throughout the inversions. The results indicate that, although it requires more iterations, our modified momentum method produces the best models, which are consistent with results from the L-BFGS-B algorithm and require less storage per iteration.

3-D parallel anisotropic inversion of controlled-source electromagnetic data using nested tetrahedral grids

SUMMARY Geophysicists today face the challenge of quickly and reliably interpreting extensive controlled-source electromagnetic (CSEM) data sets to map subsurface conductivity structures within realistic geological environments. An ideal 3-D CSEM inversion algorithm using tetrahedral grids should be capable of distinguishing different resolution requirements between forward modelling and inversion grids, have an optimal parallel strategy that fully exploits the inherent independence of CSEM data sets while also possessing the capability to handle large-scale geo-electrical models, and incorporate conductivity anisotropy which should be a common characteristic in realistic subsurface environments. However, existing tools in the geo-electromagnetic community often fall short of these three demands. Addressing this gap, our study introduces a scalable and parallel anisotropic inversion technique for CSEM data, capitalizing on the potential of unstructured tetrahedral grids. We first apply the tetrahedral longest-edge bisection method to create a refined dense, heterogeneous forward modelling grid from a coarse inversion grid. This refinement, focused on areas around transmitters and receivers, is seamlessly integrated within the coarser inversion grid’s topology, enabling precise conductivity mapping and preserving electromagnetic response accuracy during model updates. We further innovate with a source-mesh double-level parallel strategy, utilizing the message passing interface technique for parallel handling of independent CSEM data sets and large-scale geo-electrical models. Externally, we dedicate a processor for inversion model updates employing the Limited-memory Broyden–Fletcher–Goldfarb–Shanno optimization algorithm and divide other processors into groups, each associated with specific transmitting sources and frequencies. Internally, in each group, we employ a domain-decomposition-based scalable and robust iterative solvers using the Auxiliary-Space Maxwell pre-conditioner to parallel quickly calculate the electromagnetic responses from its assigned source-frequency set. Additionally, recognizing the potential for electrical conductivity anisotropy in field data, we incorporate the case of vertical transverse isotropy. We validate the effectiveness of our method through examples, including an isotropic land model with undulating topography, an anisotropic marine model and a real-field data case. Results from both synthetic and field data inversions underscore our method’s significant advancements in efficiency and practicality, particularly in addressing large-scale 3-D CSEM data sets inversion challenges in realistic geological environments.

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.

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

Three-dimensional inversion of controlled-source electromagnetic data for surveying the Jiutianshan high-speed railway Tunnel, China

Controlled-source electromagnetic surveying was conducted to identify underground faults and potential water hazards that could affect the construction of the Jiutianshan High-speed Railway Tunnel in the Qinling Mountains, western China. The transmitter length was 978 m, and the receivers were positioned along five profiles that were located about 9.5 km from the transmitter. The observation parameter, the electric-field amplitude |Ex|, was inverted using a finite-memory quasi-Newton method in three-dimensional mode. The resultant model is divided into horizontal blocks and vertical layers. The vertical cross-section along the tunnel shows a pattern of alternating high- and low-resistivity layers. The electrical resistivity pattern is divided into two vertical layers, with a clear boundary between the high- and low-resistivity zones. Combined with the results from previous exploration, geological survey, and drilling data, the inversion results identify the strata and faults along the planned route, and four risk areas are delineated. Our results highlight the power of employing geophysical investigations for risk assessments along tunnels.

3-D Inversion of CSEM Data With Hexahedral Mesh in the Multinary Model Space

The controlled-source electromagnetic (CSEM) method is a crucial tool for near-surface investigations and hydrocarbon exploration because of its economic benefits. Limited resolution is one of the inherent defects of the CSEM method, and to obtain high contrast results a multinary transform function was introduced to CSEM 3-D inversion. The multinary transform function was constituted by superposing several error functions, and the transform function transformed the model parameters from continuously distributed space into a semistep distributed multinary space. To deal with complex geometries, the edge-based finite element (FE) method with an irregular hexahedral grid was applied to the modeling and inverse problem. We used the Gauss-Newton optimization method to minimize the Tikhonov parametric function. The complex chessboard model and the marine CSEM model with complex geometry were used to validate the ability of the new method in improving the resolution of the CSEM method. By comparing the results of conventional, focusing, and multinary inversion methods, the effectiveness of the multinary inversion method in depicting sharp boundaries of different physical properties was proved. Additionally, the comparisons proved that multinary inversion method can, to some extent, overcome the insensitivity to low conductors of the CSEM method.

Three-Dimensional Inversion of Controlled-Source Electromagnetic Data in Fanchang Region, Anhui Province

Fanchang area of Anhui Province is an important link in the middle and lower reaches of the Yangtze River. To study the distribution of rock mass near the surface of the area and the contact relationship between the strata, and to determine the possible ore body space, we carry out a 15km controlled-source electromagnetic(CSEM) survey. The observed data is the electric field amplitude data simulating wide-area electromagnetic. For the single-section electric field amplitude data of controlled source, because of the lack of magnetic field data, the impedance data needed for audio geomagnetic inversion cannot be formed. This paper uses the limited memory quasi-Newton(L-BFGS) method to perform a three-dimensional inversion with the source directly. The theoretical model test results show that the inversion method can recover the underground resistivity structure and obtain better anomalous body resolution. The three-dimensional inversion of the CSEM data in Fanchang area shows that we could get the best inversion results when the grid size is about 1/3~1/2 of the dot pitch, the background resistivity is 100 Ω·m, and the error level is 5%. The inversion result of the full-section data, including two sources, shows that the south and north end of the profile is high-resistivity, and the intermediate resistivity is low. However, in the middle of the profile, the resistivity is significantly higher than the two sides. Combined with geological data, this change reflects the distribution of strata/rock masses on the surface of the work area and the contact relationship between them. This consistency verifies the feasibility and necessity of three-dimensional source inversion for the CSEM field amplitude |Ex| data of multi-source and single profile. The underground three-dimensional resistivity structure can be effectively obtained by using the L-BFGS method with the controlled source.

3D multinary inversion of controlled-source electromagnetic data based on the finite-element method with unstructured mesh

In controlled-source electromagnetic (CSEM) inversion with conventional regularization, the reconstructed conductivity image is usually blurry and only has limited resolution. To effectively obtain more compact conductivity models, we apply the concept of multinary transformation to CSEM inversion based on the finite-element method with an unstructured tetrahedral mesh. Within the framework of multinary inversion, the model conductivities are allowed to be clustered only within the designed values, which are usually obtained from other a priori information or from conventional inversion. Synthetic studies show that multinary inversion produces conductivity images with clearer model boundaries compared to the maximum smoothness inversion and the focusing inversion for realistic geoelectric models. We further apply the developed method to a land CSEM survey for mineral exploration. The multinary inversion results are closer to the ground truth compared to the conventional maximum smoothness inversion and the focusing inversion. The developed method and the numerical algorithm provide a new approach and workflow for CSEM inversion when the models need to have clear boundaries and clustering model values. Such geoelectric models could be very useful for geologic interpretation in oil and mineral exploration when a priori information (such as the estimated conductivity values) of the exploration targets is known.

Cooperative deep learning inversion of controlled-source electromagnetic data for salt delineation

Various geophysical data types have advantages for exploring the subsurface, and more reliable exploration can be realized through integration of such data. However, the imaging of physical properties based on deep learning (DL) techniques, which has received considerable attention because of its enormous potential, has generally been performed using only a single type of data. We have developed a cooperative inversion method based on supervised DL for salt delineation. Controlled-source electromagnetic (CSEM) data, which can effectively distinguish a salt body with high electrical resistivity from the surrounding medium, are used as data for cooperative inversion, with high-resolution information derived from seismic data used as the constraint. This approach can entrain seismic information into a fully convolutional network designed to invert CSEM data to reconstruct the resistivity distribution. The inversion network is trained using large synthetic data sets, including the seismic information derived from seismic data as well as CSEM data and resistivity models. A cooperative strategy for reasonable entrainment of seismic information into the inversion network is established based on analysis of the network and kernels of the convolutional layers. The performance of the proposed method is demonstrated through experiments on test data generated for resistivity models for complex salt structures. The trained cooperative inversion network shows improved salt delineation results compared to the independent inversion network, irrespective of noise levels added to the test data, due to restriction of the resistivity model to fit seismic information. Moreover, training with noise-added data decreased the effects of noise on prediction results, similar to the case of adversarial training. We develop the possibility of combining geophysical data with a constraint using DL-based techniques.

Location-based parameterization of controlled-source electromagnetic data inversion for the monitoring of hydraulic fracturing with magnetically enhanced proppants

The injection of fluids with electromagnetic (EM) contrast is regarded as a promising tool for EM monitoring. We have developed a novel model-based inversion method, designated as a particle mapping (PM) method, as a fit-for-purpose inversion tool for EM monitoring. The PM method optimizes the location of particles while constraining a priori information on the net physical property-volume products in the inversion domain. In addition, as a regularization method for location-based inversion, a fuzzy clustering method is adopted to integrate the PM method with the geometries of an a priori anomalous distribution. The EM monitoring of hydraulic fracturing is considered as a primary application of the PM method. In particular, numerical experiments focus on the injection of magnetically enhanced proppants and the use of the fracture model as a cluster geometry. Numerical experiments also include situational assumptions of incorrect a priori injected amounts of fluids and the distribution of anomalous regions to fully investigate the practicality of the method. The results indicate not only how clear and intrinsically interpretable the imaging results can be obtained with the PM method but also how known or assumed information on injected fluids and the fracture model can be integrated with the EM inversion.

High-resolution resistivity imaging of marine gas hydrate structures by combined inversion of CSEM towed and ocean-bottom receiver data

We present high-resolution resistivity imaging of gas hydrate pipe-like structures, as derived from marine controlled-source electromagnetic (CSEM) inversions that combine towed and ocean-bottom electric field receiver data, acquired from the Nyegga region, offshore Norway. Two-dimensional CSEM inversions applied to the towed receiver data detected four new prominent vertical resistive features that are likely gas hydrate structures, located in proximity to a major gas hydrate pipe-like structure, known as the CNE03 pockmark. The resistivity model resulting from the CSEM data inversion resolved the CNE03 hydrate structure in high resolution, as inferred by comparison to seismically constrained inversions. Our results indicate that shallow gas hydrate vertical features can be delineated effectively by inverting both ocean-bottom and towed receiver CSEM data simultaneously. The approach applied here can be utilised to map and monitor seafloor mineralisation, freshwater reservoirs, CO2 sequestration sites and near-surface geothermal systems.

Variational Bayesian inversion of synthetic 3D controlled-source electromagnetic geophysical data

Inversion of controlled-source electromagnetic data is dealt with for a geophysical application. The goal is to retrieve a map of conductivity of an unknown body embedded in a layered underground from measurements of the scattered electric field that results from its interaction with a known interrogating wave. This constitutes an inverse scattering problem whose associated forward problem is described by means of electric field domain integral equations. The inverse problem is solved in a Bayesian framework in which prior information is introduced via a Gauss-Markov-Potts model. This model describes the body as being composed of a finite number of different materials distributed into compact homogeneous regions. The posterior distribution of the unknowns is approached by means of the variational Bayesian approximation as a separable distribution that minimizes the Kullback-Leibler divergence with respect to the posterior law. Thus, we get a parametric model for the distributions of the induced currents, the conductivity contrast, and the various parameters of the prior model that are obtained following a semisupervised iterative approach. This method is applied to multifrequency synthetic data corresponding to a 3D crosswell configuration in which the sought body is made of two separated anomalies, a conductive heterogeneity and a resistive one, and its results are compared with that given by the classic contrast source inversion (CSI). The method succeeds in retrieving compact homogeneous regions that correspond to the two anomalies whose shape and conductivities are obtained with a good precision compared with that obtained with CSI.

Sparse CSEM inversion driven by seismic coherence

Marine controlled source electromagnetic (CSEM) data inversion for hydrocarbon exploration is often challenging due to high computational cost, physical memory requirement and low resolution of the obtained resistivity map. This paper aims to enhance both the speed and resolution of CSEM inversion by introducing structural geological information in the inversion algorithm. A coarse mesh is generated for Occam's inversion, where the parameters are fewer than in the fine regular mesh. This sparse mesh is defined as a coherence-based irregular (IC) sparse mesh, which is based on vertices extracted from available geological information. Inversion results on synthetic data illustrate that the IC sparse mesh has a smaller inversion computational cost compared to the regular dense (RD) mesh. It also has a higher resolution than with a regular sparse (RS) mesh for the same number of estimated parameters. In order to study how the IC sparse mesh reduces the computational time, four different meshes are generated for Occam's inversion. As a result, an IC sparse mesh can reduce the computational cost while it keeps the resolution as good as a fine regular mesh. The IC sparse mesh reduces the computational cost of the matrix operation for model updates. When the number of estimated parameters reduces to a limited value, the computational cost is independent of the number of parameters. For a testing model with two resistive layers, the inversion result using an IC sparse mesh has higher resolution in both horizontal and vertical directions. Overall, the model representing significant geological information in the IC mesh can improve the resolution of the resistivity models obtained from inversion of CSEM data.

3‐D INVERSION OF FREQUENCY‐DOMAIN CSEM DATA BASED ON GAUSS‐NEWTON OPTIMIZATION

AbstractQuantitative interpretation of large‐scale controlled‐source electromagnetic (CSEM) data in frequency domain requires efficient and stable 3D forward modeling and inversion codes. In this work, we present an efficient approach to 3D inversion of CSEM data, which is based on Gauss‐Newton (GN) optimization in combination with a direct solver for the forward modeling. In order to avoid computing and storing sensitivity matrix explicitly, a preconditioned conjugate gradient solver (PCG) is used to solve the system of the normal equations resulted from linearization at each GN iteration. This scheme only requires matrix‐vector products of Jocabian and its transpose with vectors, which are equivalent to one forward and one adjoint problem. Therefore the matrix factorization obtained when solving forward problem can be used in subsequent PCG process, which dramatically speeds up PCG iterations and reduces overall computational cost. Numerical experiments on synthetic data from land and marine CSEM surveying configurations show that our inversion scheme exhibits excellent convergence rate and only ten‐odd to tens of iterations are needed to reach desired data misfit, demonstrating its efficiency and stability.

3D CSEM data inversion using Newton and Halley class methods

For the first time in 3D controlled source electromagnetic data inversion, we explore the use of the Newton and the Halley optimization methods, which may show their potential when the cost function has a complex topology. The inversion is formulated as a constrained nonlinear least-squares problem which is solved by iterative optimization. These methods require the derivatives up to second order of the residuals with respect to model parameters. We show how Green's functions determine the high-order derivatives, and develop a diagrammatical representation of the residual derivatives. The Green's functions are efficiently calculated on-the-fly, making use of a finite-difference frequency-domain forward modelling code based on a multi-frontal sparse direct solver. This allow us to build the second-order derivatives of the residuals keeping the memory cost in the same order as in a Gauss–Newton (GN) scheme. Model updates are computed with a trust-region based conjugate-gradient solver which does not require the computation of a stabilizer. We present inversion results for a synthetic survey and compare the GN, Newton, and super-Halley optimization schemes, and consider two different approaches to set the initial trust-region radius. Our analysis shows that the Newton and super-Halley schemes, using the same regularization configuration, add significant information to the inversion so that the convergence is reached by different paths. In our simple resistivity model examples, the convergence speed of the Newton and the super-Halley schemes are either similar or slightly superior with respect to the convergence speed of the GN scheme, close to the minimum of the cost function. Due to the current noise levels and other measurement inaccuracies in geophysical investigations, this advantageous behaviour is at present of low consequence, but may, with the further improvement of geophysical data acquisition, be an argument for more accurate higher-order methods like those applied in this paper.

A modeling study of augmenting coarse-grid 3D controlled-source electromagnetics with data from a towed receiver array

We have considered the simultaneous 3D inversion of controlled-source electromagnetic data from a towed receiver array and a coarse grid of stationary seabed receivers. Our 3D synthetic model demonstrated the sensitivity and effect on imaging of towed and seabed receiver data. The short-offset data from the towed receivers at 1–3 km offset are effective at resolving a shallow resistor at a 400-m burial depth. On the other hand, the data from the stationary seabed receivers have less noise and will resolve the 3D geometry of resistive structures buried at the 1–2 km depths typical of a hydrocarbon reservoir. We have determined how the complementary sensitivity of data from the two receiver types can be used in simultaneous inversion to recover the shallow and deep resistors.

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.

Joint MT and CSEM data inversion using a multiplicative cost function approach

We have developed an inversion algorithm for jointly inverting controlled-source electromagnetic (CSEM) data and magnetotelluric (MT) data. It is well known that CSEM and MT data provide complementary information about the subsurface resistivity distribution; hence, it is useful to derive earth resistivity models that simultaneously and consistently fit both data sets. Because we are dealing with a large-scale computational problem, one usually uses an iterative technique in which a predefined cost function is optimized. One of the issues of this simultaneous joint inversion approach is how to assign the relative weights on the CSEM and MT data in constructing the cost function. We propose a multiplicative cost function instead of the traditional additive one. This function does not require an a priori choice of the relative weights between these two data sets. It will adaptively put CSEM and MT data on equal footing in the inversion process. The inversion is accomplished with a regularized Gauss-Newton minimization scheme where the model parameters are forced to lie within their upper and lower bounds by a nonlinear transformation procedure. We use a line search scheme to enforce a reduction of the cost function at each iteration. We tested our joint inversion approach on synthetic and field data.