Three-Dimensional Electromagnetic Modelling and Inversion from Theory to Application

Controlled-source electromagnetic (CSEM) method is an important geophysical tool for sensing and studying subsurface conductivity structures. Advanced forward modeling techniques are crucial for the inversion and imaging of CSEM data. In this letter, we develop an accurate and efficient 3-D forward modeling algorithm for CSEM problems, combining spectral element method (SEM) and octree meshes. The SEM based on high-order basis functions can provide accurate CSEM responses, and the octree meshes enable local refinement, allowing for the discretization of models with fewer elements compared to the structured hexahedral meshes used in conventional SEM, while also providing the capability to handle complex models. Two synthetic examples are presented to verify the accuracy and efficiency of the algorithm. The utility of the algorithm is verified by a realistic model with complex geometry.

SUMMARY Most of the existing 3-D electromagnetic (EM) modelling solvers based on the integral equation (IE) method exploit fast Fourier transform (FFT) to accelerate the matrix–vector multiplications. This in turn requires a laterally uniform discretization of the modelling domain. However, there is often a need for multiscale modelling and inversion, for instance, to properly account for the effects of non-uniform distant structures and, at the same time, to accurately model the effects from local anomalies. In such scenarios, the usage of laterally uniform grids leads to excessive computational loads, in terms of both memory and time. To alleviate this problem, we developed an efficient 3-D EM modelling tool based on a multinested IE approach. Within this approach, the IE modelling is first performed at a large domain and on a (laterally uniform) coarse grid, and then the results are refined in the region of interest by performing modelling at a smaller domain and on a (laterally uniform) denser grid. At the latter stage, the modelling results obtained at the previous stage are exploited. The lateral uniformity of the grids at each stage allows us to keep using the FFT for the acceleration of matrix–vector multiplications. An important novelty of the paper is the development of a ‘rim domain’ concept that further improves the performance of the multinested IE approach. We verify the developed tool on both idealized and realistic 3-D conductivity models, and demonstrate its efficiency and accuracy.

In this article, we have presented a three-dimensional transient electromagnetic (EM) force calculation model of the electromagnetic rail launcher (EMRL), which could quickly calculate the transient EM force of the armature and the rail through combining the finite-element method with experiment and proposed the model of structural stiffness nonlinearity of EMRL. To study the interior ballistic characteristics of the EMRL, through the self-programming and the development of commercial finite-element software for the second time, the article presents the first time that an interior ballistic simulation model (IBSM) of the EMRL with EM and structural coupling considering the structural stiffness nonlinearity of EMRL. The correction function is proposed to improve the prediction accuracy of armature dynamic parameters by IBSM and the calculation errors of displacement of IBSM can be guaranteed not to exceed 1% compared with the test results of magnetic probes array. A strain test platform with a demodulation frequency of 8000 Hz was established to verify the IBSM's ability to calculate dynamic characteristics of the armature and the rail. After considering the structural stiffness nonlinearity of EMRL, the simulation accuracy of IBSM has been greatly improved compared with that of linearity. The experimental test results show that the IBSM is ease of application and, meanwhile, performs satisfactorily in terms of high accuracy and low computation.

Resistance spot welding (RSW) has rarely been applied to the fields requiring high welding quality, as it is limited by the instability of welding quality and quality monitoring system. Inversion imaging of nugget is a new developing method of monitoring welding quality at this background. Before the inversion image, this paper does some researches on the electromagnetic forward problem by establishing the forward model and simulating its electromagnetic field. In order to verify the reliability of this model, this paper takes the magnetic field signals as example to carry out the spot welding experiments. By comparison, the data illustrates that this electromagnetic model is reliable within a certain distance range. Besides these, this paper also does some researches on the different patterns of Hall sensor array, in order to find the array pattern with smaller errors to carry out inversion imaging.

Broadband electromagnetic (EM) modeling increases in importance for virtual prototyping of advanced power electronics systems (PES), enabling a more accurate prediction of fast switching converter operation and its impact on energy conversion efficiency and EM interference. With the aim to predict and reduce an adverse impact of parasitics on the dynamic performance of fast switching power semiconductor devices, the circuit-oriented EM modeling based on the extraction of equivalent lumped R-L-C-G circuits is frequently selected over the Finite Element Method (FEM)-based EM modeling, mainly due to its lower computational complexity. With requirements for more accurate virtual prototyping of fast-switching PES, the modeling accuracy of the equivalent-RLCG-circuit-based EM modeling has to be re-evaluated. In the literature, the equivalent-RLCG-circuit-based EM techniques are frequently misinterpreted as the quasi-static (QS) 3-D Partial Element Equivalent Circuit (PEEC) method, and the observed inaccuracies of modeling HF effects are attributed to the QS field assumption. This paper presents a comprehensive analysis on the differences between the QS 3-D PEEC-based and the equivalent-RLCG-circuit-based EM modeling for simulating the dynamics of fast switching power devices. Using two modeling examples of fast switching power MOSFETs, a 3-D PEEC solver developed in-house and the well-known equivalent-RLCG-circuit-based EM modeling tool, ANSYS Q3D, are compared to the full-wave 3-D FEM-based EM tool, ANSYS HFSS. It is shown that the QS 3-D PEEC method can model the fast switching transients more accurately than Q3D. Accordingly, the accuracy of equivalent-RLCG-circuit-based modeling approaches in the HF range is rather related to the approximations made on modeling electric-field induced effects than to the QS field assumption.

Hydrocarbon saturation in upper Wolfcamp shale formation

Accurate electromagnetic (EM) modeling for packaging structures with lossy interconnects requires to consider the finite conductivity of the conducting interconnects. In the integral equation approach, the conducting loss is usually accounted for through an approximate surface impedance when the skin depth of current is small, but this approximation may not be valid for large skin depth caused by low frequencies or small conductivities. In this paper, we treat the lossy interconnects as dielectric-like media and use the two-region electric field integral equations (EFIEs) to characterize the EM feature of the interconnects. The EFIEs are solved with the method of moments in which the Rao-Wilton-Glisson (RWG) basis function and dual basis function (DBF) are used to represent the electric and magnetic current densities, respectively. The joint use of RWG and DBF can remove the need of wisely formulating integral equations and selecting testing schemes and also alleviate the low-frequency effect in a wideband modeling for multiscale interconnect structures. Numerical examples are presented to demonstrate the approach and its robustness has been verified.

Electromagnetic Environment Associated with Lightning Strikes to Tall Strike Objects

A rigorous three-dimensional (3-D) electromagnetic model is developed to analyze the scattering from anti-personnel (AP) nonmetallic mine-like target when it is buried near a clutter object under two-dimensional (2-D) random rough surfaces. The steepest descent fast multipole method (SDFMM) is implemented to solve for the unknown electric and magnetic surface currents on the ground surface, on the target and on the clutter object. A comprehensive numerical investigation of two clutter sources; the ground roughness and the nearby benign object, is presented based on using more than 800 random rough surface realizations which could not be achieved without using fast algorithms such as the SDFMM. The statistics of the scattered near-electric fields are computed using the Monte Carlo simulations for both polarizations. For the parameters used here, the results show that the average and the standard deviation of the target signature represent 5-7% and 3-3.5% of the total scattered signal, respectively, while they represent 16-20% and 7-12% of the signal for the clutter object, respectively. This study indicates the high possibility of a false alarm during the detection process when the target is located nearby a realistic object such as a piece of a tree root.

Controlled-source electromagnetic (CSEM) measurements are complementary data for magnetotelluric (MT) characterization although its methodology on land is not sufficiently developed and tested as in marine environments. Acquiring expertise in CSEM is crucial for surveys in places where MT cannot be performed due to high levels of cultural noise. To acquire that expertise, we perform CSEM experiments in the Vallès fault [Northeast (NE), Spain], where MT results have been satisfactory and allow us to verify the CSEM results. The Vallès basin is relevant for potential heat generation because of the presence of several geothermal anomalies and its nearby location in urban areas. In this article, we present the experimental setup for that region, a 2-D joint MT+CSEM inverse model, several 3-D CSEM simulations in the presence of metallic casing, and its comparison with real data measurements. We employ a parallel and high-order vector finite element algorithm to discretize the governing equations. By using an adapted meshing strategy, different scenarios are simulated to study the influence of the source position/direction and the conductivity model in a metallic casing presence. An excellent agreement between the simulated data and analytical/real field data demonstrates the feasibility of study metallic structures in realistic configurations. Our numerical results confirm that metallic casing strongly influences electromagnetic (EM) responses, making surface measurements more sensitive to resistivity variations near the metallic structure. It could be beneficial getting higher signal-to-noise ratios and sensitivity to deep targets. However, such a casing effect depends on the input model (e.g., conductivity contrasts, frequency, and geometry).

A numerical study was conducted to investigate the governing physics of galvanic source electromagnetic (EM) methods for terrestrial and marine exploration scenarios. The terrestrial exploration scenario involves the grounded electric dipole source EM (GESTEM) method and the examination of how the GESTEM method can resolve a thin resistive layer representing underground gas and/or hydrocarbon storage. Numerical modeling studies demonstrate that the loop transient EM (TEM) and magnetotelluric (MT) methods are insensitive to a thin horizontal resistor at depth because they utilize horizontal currents. In contrast to these standard EM methods, the GESTEM method generates both vertical and horizontal transient currents. The vertical transient current interacts with a thin horizontal resistor and causes charge buildup on its surface. These charges produce a measurable perturbation in the surface electric field at early time. The degree of perturbation depends on source waveform. When the GESTEM method is energized with step-off waveform, the perturbation due to a thin horizontal resistor is small. This is because the step-off waveform mainly consists of low frequency signals. An alternative is taking the time-derivative of the step-off responses to approximate the impulse response which includes higher frequency signals. In order to improve degree of perturbation especially due to a localized small 3-D resistor, the diffusion angle of the vertical transient current, 45 should be considered to make vertical currents coupled to a resistive target efficiently. The major drawback of the GESTEM method lies in the fact that GESTEM sounding can not be interpreted using 1-D inversion schemes if there is near-surface inhomogeneity. The marine exploration scenario investigates the physics of marine frequency-domain controlled source EM (FDCSEM) and time-domain controlled source EM (TDCSEM) methods to explore resistive hydrocarbon reservoirs in marine environments. Unlike the marine MT (MMT) method, these two methods are very sensitive to a thin hydrocarbon reservoir at depth because their sources generate vertical as well as horizontal currents. As for the FDCSEM method, the normalized EM peak response occurs where the airwave starts to dominate the seafloor EM response in the background model. This point is a function of source frequency, seawater depth and seafloor resistivity. The peak magnitude of the normalized EM response depends on whether the high concentration of vertical currents can reach and interact with the reservoir effectively. Noise levels of the EM receivers are important factors for successful FDCSEM and TDCSEM survey design. The major benefit of using magnetic field responses over electric ones is that the noise level of magnetic receiver theoretically allows for greater surface coverage compared to that of the electric receiver. Like the GESTEM method, the TDCSEM method also requires the use of a proper transient EM pulse such that the relatively high frequencies are produced. The impulse response of the TDCSEM method is characterized by two-path diffusion of the EM signal. The initial response is caused by faster signal diffusion through the less conductive seafloor, while the later arrivals result from slower diffusion through the more conductive seawater. Therefore, at larger separations, the effects of the seafloor and seawater are separable. This can be useful in reducing the airwave problem associated with the FDCSEM method in shallow marine environments.

We present a 3D forward modeling algorithm of marine controlled-source electromagnetic (CSEM) fields using finite element method based on unstructured meshes. As the unstructured mesh is incorporated, the algorithm can easily accommodate complex structures, such as dipping interfaces and rough topography. Secondary coupled-potential formulation of Maxwell's equations allows to avoid the singularities introduced by the sources. The primary electromagnetic fields excited by electric dipole source in layered isotropic media are derived from the semi-analytical formulas based on Schelkunoff potentials. To improve the accuracy and efficiency of the algorithm, we propose an effective local mesh refinement strategy, where the elements near the receiver locations and in the abnormal areas are refined using the volume constraints. We validate the finite element code against a 1D and 2D reservoir model and study the performance of the local mesh refinement strategy. The Canonical disc model illustrates the utility of the finite element method for 3D CSEM modeling. The bathymetry model study shows that the seafloor topography gives an important response which needs to be reproduced by numerical modeling to avoid the misinterpretation of measurements.

Controlled-source electromagnetics (CSEM) can be used to image subsurface resistivity and add value in petroleum exploration. However, the application of CSEM methods can be particularly challenging in mature oil and gas fields, where the presence of steel casings and complex seabed infrastructure may influence electromagnetic (EM) fields. The effect of this metal infrastructure can be modeled using the method of moments (MoM), which has previously been demonstrated to be effective in simple situations. We have now developed a methodology for modeling the EM response of complex pipeline geometry using MoM, and we validate our approach numerically and experimentally; the difference between finite-element and MoM modeling is less than 3%, whereas the difference between experimental data and MoM results is less than 30%. We further develop a fast and efficient approach to model the EM response of horizontal pipeline infrastructure. First, we create individual pipe sections of custom shape; when assembled, these sections are used to construct the entire pipeline system. We then identify “precise” and “approximate” zones based on how accurately we need to perform the calculations. We find that the electric field values in the approximate zone can be calculated accurately and quickly using previously saved table values, and therefore achieve a considerable reduction in computational requirements. Finally, we apply our methodology to a real situation of a 60 km horizontal seabed pipeline and find that the electric field distortion can be calculated rapidly and efficiently with our custom-built algorithm.

Controlled source electromagnetic (EM) methods represent a unique set of geophysical experiments which can be used to determine the properties and state of the deep continental crust. Unlike natural source EM methods, an artificial EM source technique can be designed to optimize resolution and minimize interactions with local structure. The major drawbacks include restricted depth penetration, insufficient data sets and a limited number of modelling algorithms. Information about the electrical conductivity at lower crustal depths can be obtained but at the expense of requiring large moment sources, sophisticated processing techniques and data redundancy. Moreover, EM data are sufficiently complicated that numerical modelling is often necessary for quantitative interpretation. It is therefore essential to record enough information to justify the choice of interpretation algorithms, particularly since controlled source EM forward modelling routines are generally very restrictive and not widely available. As most interpretations are based on layered earth models, observations of all the EM field components can be useful for testing the “dimensionality” of the data and for justifying interpretations.

Abstract. Titan's interaction with the corotating Saturnian magnetospheric plasma is studied in terms of a three-dimensional electromagnetic hybrid model. This approach treats the electrons as a massless, charge-neutralizing fluid, whereas the ions are represented by macroparticles. The model considers two magnetospheric and three ionospheric ion species. In contrast to any foregoing simulation study, the magnetospheric upstream conditions are not assumed to be stationary, but time variations have been imposed on the electromagnetic fields. The model includes simple periodic distortions of the fields near Titan, the purpose being to illustrate the basic physical mechanisms of ion pick-up in a non-stationary electromagnetic environment. In order to allow a straightforward access to the influence of the electromagnetic field orientation on the pick-up, no variations have been imposed on the density of the impinging magnetospheric plasma. Under stationary upstream conditions, Titan's exospheric tail exhibits a strong asymmetry with respect to the direction of the convective electric field. The simulations show that this characteristic asymmetry cannot develop, if the ambient electromagnetic fields are highly distorted. However, the central tail region directly behind the satellite remains nearly unaffected by the distorted magnetospheric upstream conditions. The central tail where the slow ionospheric species are predominant is able to shield itself against any kind of distortion in the ambient magnetospheric field conditions. The shorter the time period of the distortions, the more efficient is this shielding effect. The dependency of the pick-up on the characteristic time scales of the distortions is discussed in detail for the investigated model cases. Besides, the reaction of Titan's exospheric tail structure on sudden, non-continuous changes of the magnetospheric plasma conditions is analyzed, providing an illustration of some effects that may occur when Titan crosses Saturn's magnetopause.