The multiple scattering effect is commonly present in electromagnetic (EM) scattering and can serve as a priori information to guide the solution of inverse scattering problems (ISPs). As depicted by the Green’s function, the multiple scattering effect exhibits both global and local features, i.e., the interaction between subscatterers is in principle global but the coupling strength is usually large in the neighboring region and decays with distance. For solving ISPs, the convolutional layer (CL) has been proven to be highly effective as a fundamental building block in learning-based solvers. Through supervised learning, CL-based networks can predict the refined result from the pre-solution of EM parameters. However, due to the limitation of local perception capability, CL can only model the local feature of the multiple scattering effect. To remedy this, this article proposes a globally perceptive (GP) module that cascades a global self-attention layer (GSAL) and a CL to capture both global interaction and local emphasis. To show the effectiveness of the GP module, a deep-learning scheme with global perception (DLSGP) is constructed using a U-shape structure, where the pre-solution is provided by the backpropagation (BP) or domain current (DC) method. Validation results using cross-set data, noisy data, and measured data demonstrate the high accuracy, strong generalization ability, and robustness of the proposed module. The study on the global perception ability further confirms that the proposed module contains more information on the multiple scattering effect. Since this effect is common in ISPs, this fundamental module can be applied to other learning-based solvers.

This study proposes a collaborative optimization framework for solving directional electromagnetic logging while drilling (LWD) inverse problems that integrates a physics-constrained sample generation strategy, a hybrid feature compression transformation, and an enhanced UNet++ architecture. First, a Markov chain perturbation strategy is employed to generate formation samples with physical continuity, ensuring that the generated samples closely resemble real geological variations. Second, a hybrid compression transformation method is designed to address the heterogeneous distribution of electromagnetic responses, enhancing feature separability. Finally, the proposed network is improved by dynamically fusing multi-scale and directional features through multi-scale convolutional branches and preserving vertical resolution using an asymmetric downsampling strategy. Experiments demonstrate that R-BInvNet reduces the training loss by 57.5% compared to U-Net and further reduces it by 43.1% compared to UNet++. It also exhibits higher inversion accuracy in complex synthetic formation models and MNIST-derived formation models. The framework offers an efficient solution for real-time geosteering and demonstrates potential in high-dimensional electromagnetic inversion.

This paper presents a modified frequency-hopping deep learning fusion framework (MFHFF) to solve multifrequency electromagnetic (EM) inverse scattering problems (ISPs) in real-time with high accuracy. The proposed MFHFF integrates advantages of the high accuracy of frequency-hopping method and the improved stability of simultaneous inversion strategy. First, the MFHFF cascades multiple monofrequency solvers, each combines a scattered field encoder and a pre-reconstructed result encoder. Additionally, the scattered field encoder utilizes adaptive average pooling to dynamically adjust scattered field data dimensions into standardized input specifications for subsequent convolutional layers. Second, the frequency-hopping connection (FHC) is implemented in the MFHFF by concatenating low-frequency inversion result to high-frequency pre-reconstructed result encoder. The low-frequency results serve as initial estimates for the high-frequency solver according to the FHC, thereby reducing the nonlinearity of high-frequency inversion and improving the accuracy of MFHFF. Third, the simultaneous inversion connection (SIC) is integrated into MFHFF to incorporate low-frequency features into high-frequency solver, facilitating simultaneous processing of multifrequency information and ensuring enhanced stability of MFHFF. The proposed MFHFF exploits an effective framework for solving multifrequency ISPs. The superior stability, accuracy, flexibility and generalization ability of the MFHFF have been demonstrated by the synthetic and the experimental results.

The electromagnetic (EM) inverse scattering problems (ISPs) are characterized by nonlinearity, presenting a challenge in achieving a satisfactory reconstruction of the relative permittivity of strong scatterers. Joint inversion has been demonstrated as an effective approach for improving the quality of EM inversion through the integration of acoustic inversion. However, when solving the ISPs associated with complex structured scatterers and multiple scatterers, the accuracy of the EM parameters reconstructed by previous joint inversion methods is inadequate. Aim to solving this problem, this paper proposes a new inversion method, which is based on framework of the subspace-based optimization method (SOM). The proposed method adopts the joint inversion architecture and incorporates the image segmentation technique. The acoustic data is processed before being employed to construct structural similarity constraints for EM inversion, rather than being directly utilized as in previous methods. And in this new approach, Pyramid Scene Parsing Network (PSPNet) is employed to extracting the boundary information of the targets from high-resolution acoustic images. Subsequently, this information is leveraged to formulate a more effective objective function or a better initial contrast for EM inversion. Compared with previous joint inversion method, this new imaging segmentation-based inversion method (ISIM) of EM and acoustic data offers advantages in inversion accuracy and computational speed by making more efficient use of acoustic information. Additionally, in scenarios involving complex structural scatterers or multiple scatterers, ISIM is capable of achieving more precise results. The effectiveness and advantages of ISIM are validated through several numerical examples.

In this paper, a comb-line array (CLA) antenna with shaped patterns is proposed for millimeter-wave traffic monitoring radars in intelligent transportation systems (ITS). It is demonstrated that radiating elements with a wide tuning range of coupling coefficient, low cross-polarization, and independent control of amplitude and phase are necessary for a CLA to realize a shaped pattern. However, elements with these characteristics have not been reported. It is found that the rectangle patches with recessed microstrip-line feeds possess these characteristics simultaneously when working as radiating elements of a CLA. In addition, it is found for the first time that strong standing waves can persist in the feedline of a CLA even though the impedance matching at its input port is good. By introducing the matching element and reflection cancelling slits, travelling-wave mode can be achieved in the feedline. Consequently, the amplitude and phase of each element of the proposed CLA can be flexibly controlled and a shaped pattern can be then generated. To confirm this design, a microstrip CLA with 16 radiating elements is designed and measured. It has a simple and compact structure and achieves gain of 14.3 dBi at 80 GHz. More importantly, its patterns agree well with the objective cosecant squared curve across the frequency range from 79 GHz to 81 GHz. These features make the proposed antenna suitable for the Internet of Things-based ITS.

The electromagnetic (EM) inverse scattering problems (ISPs) exhibit strong nonlinearity, making it a challenge to reconstruct relative permittivity of strong scatterers with high quality. Joint inversion can leverage the satisfactory solution obtained from acoustic inversion to mitigates the impact of strong nonlinearity on EM inversion. However, how to improve the precision of reconstructing the internal electrical parameter distribution through this kind of joint inversion approach is still a challenge. Aim to improve the quality of reconstruction, a new joint inversion method based on the framework of the subspace-based optimization method (SOM) is proposed in this paper. This new method utilizes the Pearson correlation coefficient (PCC) to construct structural similarity constraints, thereby enhancing the linear correlation between EM and acoustic parameters. In inversion process, all data obtained from acoustic inversion can offer effective constraints. In order to improve convergence speed and stability of the proposed method, a constraint which is consisted of CGF is induced in the object function. And by utilizing the results of the results of acoustic inversion, the inversion domain can be further refined, giving rise to better computational efficiency. With these treatments, the proposed method has better performance in both accuracy and efficiency. The effectiveness and advantages of the proposed method is validated through several numerical examples.

Based on the assumption that the pseudo-random characteristic of VBIM, the retrieved contrast parameter distribution in the discrete cells complies with the Gaussian mixture model (GMM). This article presents a constrained optimization framework that combines GMM and a hierarchical domain constraint (HDC) strategy for solving inverse scattering problems (ISPs). This GMM-HDC framework divides the whole inversion process into several stages, each stage operating within a reduced domain and subject to lower and upper bound constraints. The reduced inversion domain is determined by the GMM’s cluster analysis, thereby eliminating the need for manual threshold selection. And the HDC strategy offers a re-classification mechanism to avoid misclassification of scatterer cells. By narrowing the inversion domain, this approach effectively reduces the solution’s dimensionality, and mitigating the ill-posedness of ISPs. The bound constraint is determined by a hypothesis testing method. When there is prior information of contrast bound, the solution during iteration may not be within the exact bound due to the ill-posedness of ISPs. Therefore, the flexibility-bound constraint can provide more stability. When the prior information is not available, the determined upper bound is also guaranteed to converge probabilistically to the exact upper bound in case of degradation. In each iteration, a quadratic programming (QP) formula is introduced to solve the inverse subproblem in the VBIM, which enables the incorporation of the contrast range determined by the GMM-HDC framework. The formula includes both Tikhonov and total variation regularization terms. Several typical models, including synthetic and experimental measurement data, are presented to verify the performance of the proposed method.

A robust hierarchical domain constraint (HDC) strategy is proposed for the multi-scale contrast objects reconstruction in this letter. The Monte Carlo method and point evaluation are adopted and modified for the classification of background and scatterers cells, the parameters of the background cells are set as the same as the actual background and removed from the inversion. The major work of the HDC strategy is to divide the inversion process into several stages, and the classification of cells is evaluated separately at each stage, making the classification reversible. And the HDC can effectively classify the inversion domain of low-contrast objects without negligence in the multi-scale contrast objects case, as well as the continuously varying inhomogeneous objects’ low-contrast parts. Another advantage of HDC is the threshold determining the classification of cells can be flexibly chosen. This robust constraint of the inversion domain compresses the solution space so that the ill-posedness of the inverse problem is mitigated, and better accuracy thus is achieved. In this letter, the HDC strategy is applied to the Variational Born Iterative Method (VBIM), numerical results validate the accuracy, robustness, and antinoise ability of the proposed VBIM-HDC.

This paper presents a novel early fusion framework (EFF) of deep learning (DL) for solving electromagnetic (EM) inverse scattering problems (ISPs) in real-time with high accuracy. The EFF integrates the scattered field encoder (SFE) and the backpropagation encoder (BPE). On the one hand, the nonlinear relationships constrained by the multiple scattering phenomenon, are introduced in the SFE, which guarantees better external scattering manifestations. On the other hand, the pre-reconstructed backpropagation approximation (BP) distributions provide prior information in ISPs via the BPE, which is in accordance with the internal scattering manifestations. The novel EFF concatenates the features extracted from the scattered field and the BP approximation, achieving more scattering manifestations in the solving process. Furthermore, the multiple scattering information and BP distributions regularize each other’s encoding process effectively, which achieves faster convergence and more stable inversion results. It is expected that the EFF exploits a general framework for solving ISPs, which can be adopted to different scenarios by importing different kinds of prior information according to the fusion approach. The superior veracity, stability and generalization ability of the EFF have been demonstrated by the synthetic and the experimental results.

In this letter, a novel inversion scheme based on the supervised descent method (SDM) for the logging responses interpretation of anisotropic formations is proposed. The inversion scheme combines the characteristics of traditional gradient-based methods and machine learning techniques. In the inversion process, the model parameters can be updated directly according to the descent directions collected from the training phase. Therefore, the inversion can flexibly incorporate the prior information and overcome the dependence of convergence on the initial values. It can also avoid local minima and accelerate global convergence. Moreover, the dynamic regularization scheme is adopted to reduce the ill-posedness of the problem, and the bagging algorithm is incorporated into the training process to reduce the overfitting and enhance the generalization ability. A series of numerical examples are investigated to test the inversion performance in anisotropic formations. Results show that the proposed inversion scheme for anisotropic formations has high accuracy, fast convergence, and strong robustness.

Due to the strong nonlinearity, it is always a challenge to reconstruct strong scatterers with high contrasts and/or large dimensions. This article proposes an iterative domain decomposition technique (IDDT) based on the framework of the subspace-based optimization method (SOM) to solve highly nonlinear inverse scattering problems (ISPs). This method takes advantage of the fact that the reduction of unknowns can reduce the nonlinearity of ISPs and different parts of scatterers have different effects on scattered fields. In the inversion procedure, the domain of scatterers (DoS) is obtained by refining the domain of interests (DoI) first. Then, the DoS is divided into two subdomains according to their contributions to scattered fields: the dominant subdomain and the subordinate subdomain. The induced current of the subordinate subdomain is approximated by its deterministic part. Therefore, only the induced current of the dominant subdomain needs to be reconstructed, greatly reducing the dimensions of the solution domain. Then the properties of the entire DoS are retrieved with the properties of the dominant subdomain as initial guesses. This technique can be used repeatedly to improve the reconstruction quality. Compared with the original SOM, this method can reduce the nonlinearity of ISPs and reconstruct stronger scatterers with better reconstruction qualities and less computation loads. The feasibility and efficiency of IDDT-SOM are discussed from the perspective of the relative distribution of induced current by numerical and experimental examples.

Micro-cylindrically focused logging (MCFL) is a focused micro resistivity logging method which can achieve multiple radial detection depths in shallow formations. The obtained three independent logging responses can be used to invert the formation parameters of different radial layers (e.g., borehole, mud cake, and flushed zone). In this paper, a robust inversion scheme is proposed for logging data interpretation of MCFL based on the Gauss-Newton method. The dynamic regularization scheme is adopted to reduce the ill-posedness of the problem and stabilize the inversion. Besides, the nonlinear transformation and linear search algorithm are incorporated into the program, which impose the parameter constraints based on prior knowledge and enhance the robustness of iteration. Numerical examples of different inhomogeneous formations are also given to prove the feasibility and accuracy of the inversion.

Active magnetic ranging (AMR) is a detection technology in relief well projects for determining the subsurface location of the blowout well by applying active excitations to the formation. In this paper, the detection principle of AMR is introduced and the three-dimensional numerical modeling is realized based on FEM. Several measures are adopted to improve the flexibility and efficiency of the model generation and matrix decomposition. Besides, the detection performance of AMR with different tool configurations and in different formation structures are also investigated. And the influence of tool parameters and formation parameters on the response characteristics is analyzed and summarized, which provides support for the practical application and design optimization of AMR in relief well operations.

Based on composite rough surface and stochastic multiscale models, an improved two-scale model (TSM) is proposed. Different from the classical TSM, the proposed method adopts the integral equation method (IEM) to replace the small perturbation method (SPM) for calculating the contribution from small-scale roughness. Kirchhoff approximation (KA) is still kept in the model to calculate the contribution from large-scale roughness. Because the IEM has wider application range than the SPM, the proposed model exhibits a higher accuracy and has a wider application range in terms of sea surface roughness compared with the classical TSM. Usually, the classical TSM is sensitive to the cutoff wavenumber. The proposed model adopts an adaptive cutoff wavenumber instead of choosing a cutoff wavenumber in the classical TSM. The effectiveness of the proposed model is demonstrated through comparisons with the simulation results of multilevel fast multipole algorithm (MLFMA) and the measured results. Different roughness at different frequencies is analyzed as well.

For target detection in Gaussian noise with unknown covariance matrix, usually sufficient training data are needed to form a nonsingular estimate of the noise covariance matrix. However sufficient training data could not be satisfied in practice. Aiming to design a detector with small training data size, this letter proposes a reduced-dimension detector by incorporating the persymmetric structure of received data. Based on the persymmetric structure, a reduced-dimension approach of subspace transformation-based detector is adopted. Then, the criterion of the generalized likelihood ratio test is used to design the detector. The proposed detector is shown to possess the constant false alarm rate property with respect to noise covariance matrix. Compared with existing detectors, such as conventional polarization-space-time generalized likelihood ratio detector, persymmetric polarization-space-time generalized likelihood ratio detector and subspace transformation-based detector, simulation results demonstrate that the proposed one has better detection performance, especially in the circumstance of limited training data.

Because of strong nonlinearity, it is always a challenge to acquire fine resolution reconstruction results for electric strong scatterers with high contrasts using electromagnetic (EM) data. Many electric strong scatterers have weak nonlinearity in acoustic inversion. To make full use of the advantages of acoustic inversion, two joint inversion methods based on the structural constraints to reconstruct electric strong scatterers using EM and acoustic data are proposed in this article. These two methods utilize the framework of the subspace-based optimization method (SOM). In the inversion process, one of the methods utilizes a cross-gradient function to link the EM and the acoustic inversions, enforcing the structural similarity between the permittivity and the sound velocity. The second method is to utilize the reconstruction result of acoustic data as initial structural information for the EM inversion process. Compared with conventional separate SOM, these two methods achieve finer EM reconstruction for electric strong scatterers. Both structure and contrast values are well reconstructed. The efficiency and the robustness of the methods are validated through numerical experiments.

In this letter, a subspace-based variational Born iterative method (S-VBIM) is proposed to solve the inverse scattering problem. The proposed method retrieves the deterministic subspace of the variational induced current at the beginning of the iterative computation, and thus, the process of the total electric field approximation is more accurate than the Born approximation does in VBIM. Therefore, S-VBIM achieves faster convergence speed and higher solution accuracy than VBIM. In addition, since the singular value decomposition, which is the main process of retrieving the variational induced current for radiation operator matrix, only needs to be performed once, the computational cost is reduced significantly. Finally, the numerical results validate the effectiveness of S-VBIM and comparisons with VBIM are made.

Micro-cylindrically focused logging (MCFL) is a focusing type of resistivity logging method which can measure the resistivity of shallow formations at different depths. In this paper, the measurement principle of MCFL is introduced and three-dimensional electromagnetic modeling is realized by FEM. Simulation results show that the instrument has excellent detection performance and high axial resolution. In addition, the electromagnetic response of MCFL in inhomogeneous media is simulated and variations of the logging response with different formation parameters are investigated and analyzed. The influences of flushed zone, mud cake, and slurry are summarized and explanations of peculiar phenomena are given in detail, which is helpful to guide the production and optimize the instrument.

Influence of the half-space background on radar signatures of small consumer drones have been investigated in this paper. An integral equation method is presented to calculate the reflections of small drones within a half-space background efficiently and accurately, accelerated by the multilevel fast multiple algorithm. In addition, a two-level discrete complex image method has been applied to speed up the calculations of Sommerfeld integrals existing in the conventional half-space Green's functions. Variations of reflections as a function of variables such as polarization and frequency are explored for free space and half space respectively. Scattering data are also post-processed into two dimensional inverse synthetic aperture radar (ISAR) images to investigate the influence of half-space background further.

Massive multiple-input multiple-output (MIMO) has shown its great capabilities in improving spectral efficiency and energy efficiency, yet the high complexity and cost of hardware are huge challenges. In massive MIMO, antenna selection (AS) is still an effective way to decrease the number of radio frequency chains. In this letter, the AS problem in massive MIMO systems is studied with the consideration of maximizing the channel capacity. To eliminate the limitation of the traditional square maximum-volume (SMV) AS method, the theory of rectangular maximum-volume (RMV) submatrices is introduced. An AS algorithm based on RMV method is also developed for massive MIMO, which can be regarded as a postprocessing of the results of SMV method. Based on the result obtained from SMV method, the proposed algorithm can select a rectangular submatrix with maximum-volume from the channel matrix. Finally, the numerical simulations are presented to show the validity of the proposed RMV method.

Facing the challenges of the transmission attenuation in lossy formations, and the mutual interference of the waves radiated from the different relay coils and the multipath propagations of the different wave components, we proposed an efficient cooperation transmission approach based on the in-phase superposition of the multiple wave components for wireless telemetry of measurement while drilling (MWD) and logging while drilling (LWD) signals. Without any previous knowledge of the inhomogeneous formations, such as the thickness and the electrical parameters of the different layers, we propose this method which is able to achieve in-phase enhancement of the multiple components adaptively, i.e., the cooperation transmission of the MWD and LWD signals, leading to the remarkable enhancement of the field amplitude and the depression of the mutual interference of the multipath components. Therefore, the signal-to-noise ratio in a given cooperation transmission channel can be improved evidently. Some numerical examples have been given in this paper to show the remarkable improvement of the wireless transmission performance quantitatively.

In this letter, a diagonal approximation has been introduced in the framework of subspace-based optimization method (SOM), for reducing computational complexity. Due to this approximation, the operator which relates the electric field and equivalent current becomes a diagonal one, instead of the nonlinear one in full-wave inversion. Consequently, the proposed method is named as diagonal SOM (DSOM). Compared with the original SOM, DSOM has a more simplified objective function with much less computational cost. DSOM can be applied for solving inverse scattering problems involving not only isotropic objects, but also uniaxial anisotropic objects, which is demonstrated by numerical examples. Furthermore, DSOM provides reconstruction results that are comparable in quality to the ones obtained using SOM, but with much less computation load.

Electromagnetic scattering from conducting objects is investigated for the applications of underground detection. The air-soil composite is modeled by a classical half space where the dyadic Green's function can be defined and formulated. The electric field integral equation (EFIE) is employed to guarantee the accuracy and robustness of the analysis for arbitrarily shaped scatterers. The internal resonance of EFIE is first studied under typical working conditions (frequencies, soil water contents, etc.). It is shown that this spurious resonance is much alleviated due to loss of the soil. Next, the unbounded and ill-posed spectrum of the EFIE operator is remedied by a novel localized half-space Calderón preconditioner by further exploring the lossy nature of the background. Such preconditioning is extremely useful for objects containing multiscale features. Finally, the half-space multilevel fast multipole algorithm based on real-image approximation is adopted to accelerate the computation for electrically large scatterers. Several examples in the applications of subsurface sensing are demonstrated to validate the efficiency and accuracy of this method.

An efficient method for the analysis of electromagnetic scattering from 3-D objects straddling the interface of a half-space has been presented in this letter. By truncating the interface, the analysis of scattering from an object within a half-space can be cast into that of a composite (high contrast) dielectric object in the free space. The conventional half-space Green's function involves a Sommerfeld integral that is extremely time-consuming to evaluate, especially when objects get close to or straddle the interface. In this letter, the Green's function of free space has been used to totally avoid the numerical evaluation of Sommerfeld integral. Moreover, fast algorithms, such as the multilevel fast multiple algorithm, can be incorporated easily without any restrictions, effectively compensating the cost due to the introduction of additional unknowns by the truncation. The factors affecting the accuracy and computational cost, such as the truncation radius and the angle of incident wave, have been investigated carefully through an example of a partially buried PEC sphere. A criterion for the truncation radius has been presented based on the coupling mechanism between the scatterer and the interface. Furthermore, the far-field response of the target in a half-space background should be expressed as a differential radar cross section. However, the high contrast problem of air/sea or air/ground requires efficient evaluations, and an integral formulation for modeling high-contrast dielectric objects has been employed to further expedite the computation. Numerical results have been presented to demonstrate the effectiveness and accuracy of the new method.

A novel approach for a wireless transmission of MWD and LWD signals in lossy formations has been proposed in this paper. First, the quasi-TEM mode of the extremely low frequency (ELF) near field is excited by a voltage gap on the pipe, guided by and propagated along the metal pipe string in LWD or MWD (logging/measurement while drilling) environment. Once the signal received on the ground is weaker than a certain threshold as the drilling depth increases, a relay segment (transceiver) is installed into the pipe string to receive, amplify, and retransmit the signals to extend the transmission distance and ensure the required propagation range of the ELF wave. In this paper, the details of the transceiver antennas and the relay segment suitable for efficient coupling to quasi-TEM mode have been given first, and then, the numerical simulations of the ELF wave propagation in LWD or MWD environment and the coupling between the guided wave and the relay segment have been made to show the coupling performance of the relay segment to quasi-TEM mode quantitatively. It has been shown that the propagation attenuation of the ELF near field with the guidance of the metal pipe string is much less than that of the space wave in the same lossy media without the guidance of the pipe string, and the scheme of the wireless relay provides an efficient way to extend the propagation range of the EM telemetry evidently and open a new freedom of frequency optimization for wireless transmission systems.

Due to the nonlinear property of large uniaxial anisotropic scatterers, many iterative optimization methods have a high risk of being trapped in local minima. In this paper, a frequency-hopping subspace-based optimization method (SOM) is proposed to reconstruct the relative permittivity distribution of 2-D large uniaxial anisotropic scatterers with transverse electrical (TE) illumination. This hybrid method utilizes the results obtained at lower frequency to provide good initial guesses for higher frequency reconstruction, which reduces the occurrence of local minima for the inversion at the higher frequency. For lower frequency, it can only obtain coarse resolution image although it is unable to show the details of the scatterers. However, this coarse image provides a priori information for the reconstruction at higher frequencies to get finer resolution. Numerical examples demonstrate that the proposed hybrid method can effectively rebuild large uniaxial anisotropic scatterers (six wavelengths) with higher stability compared with conventional SOM that uses only single-frequency data.

Positioning 3-D targets buried in layered medium with electromagnetic waves has widespread applications, such as the detection of land mines. Most of the current electromagnetic inverse methods need to know the preknowledge of the dielectric properties for layered background medium, in order to accurately reconstruct concealed targets. However, this condition is hardly satisfied in real problems. In this letter, an electromagnetic inverse scattering series method (EISSM) is developed and derived for positioning 3-D targets buried in two-layered medium. The prominent advantage of the proposed method is that it does not need any prior information about the dielectric properties of the layered medium. The position error predicted by the EISSM is analyzed and discussed. Compared with the commonly used time-reversal-mirror technique, numerical simulations show that the EISSM is capable of positioning the target buried in two-layer medium with less error.

The electromagnetic scattering from 3-D perfectly electrically conducting (PEC) objects straddling the interface of a half-space is analyzed in this letter. The adaptive cross approximation (ACA) algorithm is adopted to enhance the computational efficiency. As the object is naturally separated into two parts by the interface of the half-space, two different mesh densities are required due to the contrast of the two background materials. Therefore, two multilevel tree structures are set up individually in the two regions. When the source and field points are in the same region, which corresponds to the primary terms and reflection terms, the implementation is similar to the free-space case. However, when considering the mutual coupling of the two regions, which corresponds to the transmitted terms, difficulties arise since the two trees are independent and the numbers of levels are, in general, different. In this case, a z-dependent grouping strategy is proposed to redefine the well-separated interactions and match the abrupt changes at the interface. Three clustering strategies are proposed and discussed carefully to account for the mutual coupling in the two different regions of the half-space. The combined field integral equation (CFIE) formulation is further applied to improve the convergence of the system. Several numerical examples are demonstrated to validate the proposed schemes.

In this letter, a novel broadband electromagnetic (EM) propagation logging method with linear frequency modulation (LFM) continuous waves (LFMCWs) as well-logging signals has been proposed for logging while drilling (LWD). The logging response of the layered media to the LFMCWs under the noise environment has been numerically modeled using numerical mode matching (NMM) and inverse fast Fourier transform (IFFT). Based on the frequency spectrum of LFM signals, the NMM method is used first to calculate both the amplitude and the phase of the signals in receiving coils for every frequency point, and then, IFFT is applied to convert them to the logging response in the time domain. After that, the matched filter method has been imposed to realize pulse compression of the received signals and to improve the peak SNR (PSNR) significantly. As the logging responses of the EM propagation logging tool, the amplitude ratio and the phase difference between the compressed signals from the two separated coils at the peak point are obtained, respectively. Then, the apparent conductivity based on the amplitude ratio and the phase difference is obtained to have the logging curves. It has been shown from the simulation results that using LFMCWs as wideband logging signals can improve the SNR and the logging resolution remarkably, particularly under the condition with correlated noise that restrained the SNR and logging resolution strongly in traditional logging with a single-frequency continuous wave.

The wireless transmission of the logging signal by using metal drill pipe as a dipole antenna with an extremely asymmetric feeding is one of the potential techniques for logging (or measurement) while drilling (LWD, or MWD) and has drawn a lot of attention in recent decades. In this paper, a precise numerical model based on numerical mode matching (NMM) theory has been built for solving the very low-frequency radiation of the asymmetrical feeding dipole antenna in the layered background medium. First of all, the feeding gap of the antenna has been equalized as a magnetic current loop, and NMM numerical solutions have been applied to expand the field excited by the equivalent source, and then, the characteristics of input impedance and the near field radiated by the dipole have been calculated based on the field solutions. Furthermore, the results have been compared with the corresponding results of the “method of moments” and the “equivalent transmission line model,” respectively. The inference of the relevant parameters, such as the asymmetry of the feeding, the working frequency, the conductivity of the formation, the size of the insulating gap, the size of the casing, etc., on the transmission performance of the signal of electromagnetic MWD (EM-MWD) system has been discussed. In addition, the method for receiving the LWD signal transmitted to the ground is also evaluated, and an adaptive impedance matching scheme in transmitting terminal is proposed based on the numerical analysis in this paper.

Numerical modeling of electromagnetic subsurface detection is always challenging because the computational domain is large and the frequency is very low. This paper describes a nonconformal finite-element-method-based domain decomposition method (NC-FEM-DDM) for an efficient and accurate modeling of subsurface detecting problems in any frequency band. It first compares several transmission conditions (TCs) employed in DDM and identifies the most appropriate TC for subsurface applications. A tree-cotree splitting (TCS) strategy is then applied to hexahedral-based hierarchical basis functions to eliminate the low-frequency breakdown of NC-FEM-DDM at very low frequencies. Numerical results of a few testing problems show excellent convergence and accuracy obtained with an improved second-order TC in conjunction with the TCS at any frequencies even close to dc. Numerical results of a real-life application further demonstrate the efficiency and capability of this method for subsurface detection applications.

The numerical modeling of the advanced electromagnetic well-logging problems is very challenging because it requires tremendous workload of grid meshing and computation. For example, global meshing and simulation have to be done repeatedly for every logging position, because the model includes complex sensor arrays moving continuously along the borehole. In this paper, an efficient nonconformal finite element domain decomposition method is developed to solve these problems efficiently. First, the well-logging model is divided into two nonconformal subdomains so that the sensing arrays inside the borehole are separated from the beds outside. Since the mesh size between different subdomains can be inconsistent, well-logging modeling can significantly reduce the unknowns and computational cost. Second, a second-order transmission condition is implemented successfully in a quasi-symmetrical form via a novel treatment of Gaussian integration on the nonconformal interface. Finally, a hierarchical hexahedral basis function is introduced to further reduce the unknowns and extend the applicability of the method to multiscale problems. Numerical examples show that this method greatly reduces the memory cost and speeds up the computation compared with the traditional finite element method, especially when the response needs to be simulated repeatedly while the logging tools keep moving along the borehole.

In this paper, phase-extracted (MPE) basis functions with both the traveling wave terms and the standing wave terms have been proposed to analyze the scattering from the electrically large targets. This kind of basis functions, called modified phase-extracted (MPE) basis function, can be defined on the relatively large patches and constructed with the higher order hierarchical vector basis functions. The constructing idea of the MPE basis function is first introduced. Then, their characteristics were compared with the relevant basis functions. It has been demonstrated that the MPE basis function is suitable for the scattering analysis of the perfect electric conductors (PECs) with smooth convex surfaces as well as the concave structures, such as the electrically large cavities. The numerical solutions to the electromagnetic scattering from both the convex targets and the cavity-like targets with strong mutual couplings have been given to show the capability of the MPE basis functions in the description of the complex distribution of the induced current on the PEC surfaces. Some numerical examples have been given to demonstrate the validation of this kind of basis functions.

In this paper, the tangential equivalence principle algorithm (T-EPA) combined with characteristic basis functions (CBFs) is presented to analyze the electromagnetic scattering of large-scale antenna arrays. The T-EPA is a kind of domain decomposition scheme for the electromagnetic scattering and radiation problems based on integral equation (IE). CBFs are macrobasis functions which are constructed by conventional local basis functions. By utilizing CBFs together with the T-EPA, the scattering analysis of large-scale arrays will be much more efficient with decreased unknowns compared with the original T-EPA. Further, the multilevel fast multipole algorithm (MLFMA) is applied to accelerate the matrix-vector multiplication in the T-EPA. Numerical results are shown to demonstrate the accuracy and efficiency of the proposed technique.

At low grazing angles (LGA), sophisticated electromagnetic scattering of sea surfaces may give rise to complicated surface-current distribution. Therefore, for the multilevel fast multipole algorithm (MLFMA) with the Rao-Wilton-Glisson basis function, the sea scatterer must be meshed fine enough to ensure the precision of the scattering at LGA, which brings huge computational costs. The higher order hierarchical Legendre vector basis functions can bring a great reduction of the unknowns and sparsification of the impedance matrix. The MLFMA with higher order hierarchical Legendre basis functions is applied in the electromagnetic-scattering approach of 3-D breaking water wave crests at LGA for the first time. In addition, an adaptive-order technique is also introduced for the first time in describing the currents which can achieve accurate results and maximally reduce the computational costs from some case analysis. It has been investigated in analyzing the vertically (VV) and horizontally (HH) polarized scattering of profiles of the LONGTANK breaking waves. "Sea-spike" phenomenon has been demonstrated at LGA.

The higher order vector basis functions defined in large patches have been utilized in the numerical solution of integral equations in this paper to sparsify the impedance matrix and relieve the memory pressure. The physical explanation for the sparsification of the impedance matrix is also elucidated. Furthermore, the maximally orthogonalized bases have been applied to improve the condition number of the impedance matrix. The scaling factor was reformed to speed up the iteration convergence in the numerical solution. Finally, the iterative method for sparse matrix equations is applied to improve the solution efficiency. Some numerical results are provided to illustrate the excellent performance both in the sparsification of the impedance matrix and solution efficiency for numerical analysis of the scattering problem.

A new iteration method for electromagnetic inverse scattering is presented. This method, called the variational Born iteration method (VBIM), shows its efficiency much better than the distorted Born iteration method. VBIM has also been used for hybrid iteration inversion. Moreover, the analytic characteristics of the numerical mode match (NMM) solution were used in the inversion integral equation to speed up the calculation. Some procedures to gain the stability of the inverse solution are also discussed.

With its fast convergence, the distorted Born iterative method (DBIM) has been widely used in low-frequencg inverse scattering analysis, however its inherent drawback, sensitive-to-noise disturbance, may greatly limit its practical applications. In this paper, the numerical analysis is made to compare the DBIM and the Born iterative method (BIM). Then a hybrid BIM is presented. In this method, the DBIM is employed to speed the solution convergence in the initial several iterations and the BIM is used to improve the solution stability in the later iterations. The switch condition is also given. The simulation results show that the method is valid for the inverse scattering solution.

An analysis has been performed for a borehole direct-current resistivity boundary value problem in axisymmetric inhomogeneous media. In order to solve the problem of eccentric excitative sources in actual electrical logging, the authors apply an efficient numerical mode matching (NMM) theory to present Green's function of the potential field of an eccentric point source. The basic and higher order modes are described by applying numerical eigenmode expansion, and the local reflection and transmission matrices are used to match the boundary condition of potential field on every planar layer. Some typical examples are calculated and analyzed. The first example is concerned with a 16-in normal tool, which results are in excellent agreement with the data published previously in references. The second example about the micro laterolog-3 point electrodes is calculated to display a range of different eccentric effects. Some interesting and useful results are obtained.

A symmetrical form of the solution for an electrical source in a multibed well-logging environment is derived. The method uses local reflection and transmission operators of a single-bed boundary and a general recursive algorithm to derive generalized reflection and transmission operators. Using this method, the computation time scales linearly as N, where N is the number of beds in the environment. A computer program was developed to implement the solution. The program is robust and generates accurate results from 20 kHz to 25 MHz.>