Search

A new approximation algorithm is developed to compute the electromagnetic (EM) tensor Green's function in the biaxial anisotropic media based on the Fourier series expansion. First, a rectangular region is chosen as the computation region, in which the EM field can be expressed as a 2-D Fourier series. The Fourier coefficients can be regarded as the EM field in discrete wavenumber domain. We further obtain the EM solution in the spatial domain in the form of Fourier series. Then, we use the finite terms of the Fourier series to approximate the EM field for enhancement of computation efficiency. Because the new method avoids the numerical integration in the infinite wavenumber domain, it is more convenient to implement than other methods based on integral transform. Finally, the spatial distribution of the tensor Green's function for a transversely isotropic medium is presented to verify the proposed approach. The agreements between the results obtained by the present method and the analytic solution demonstrate the validity and the robustness of our algorithm.

In this study, the cylindrical finite-volume method (FVM) is advanced for the efficient and high-precision simulation of the logging while drilling (LWD) orthogonal azimuth electromagnetic tool (OAEMT) response in a three-dimensional (3D) anisotropic formation. To overcome the ill-condition and convergence problems arising from the low induction number, Maxwell’s equations are reformulated into a mixed Helmholtz equation for the coupled potentials in a cylindrical coordinate system. The electrical field continuation method is applied to approximate the perfectly electrical conducting (PEC) boundary condition, to improve the discretization accuracy of the Helmholtz equation on the surface of metal mandrels. On the base, the 3D FVM on Lebedev’s staggered grids in the cylindrical coordinates is employed to discretize the mixed equations to ensure good conformity with typical well-logging tool geometries. The equivalent conductivity in a non-uniform element is determined by a standardization technique. The direct solver, PARDISO, is applied to efficiently solve the sparse linear equation systems for the multi-transmitter problem. To reduce the number of calls to PARDISO, the whole computational domain is divided into small windows that contain multiple measuring points. The electromagnetic (EM) solutions produced by all the transmitters per window are simultaneously solved because the discrete matrix, relevant to all the transmitters in the same window, is changed. Finally, the 3D FVM is validated against the numerical mode matching method (NMM), and the characteristics of both the coaxial and coplanar responses of the EM field tool are investigated using the numerical results.

In cylindrical multilayered medium, we develop two tool models for electromagnetic (EM) well logging: a metal mandrel winding with a co-axial (tilted) transmitter coil and a tilted (coaxial) receiver coil. The voltages on receivers in those two models are proven to be the same and only zero-order harmonic of EM field need to be considered for voltage calculation. To calculate the voltage, two pseudo-analytical formulae are presented by using the integral of electrical field in spatial and wavenumber domain, respectively. Those two alternative pseudo-analytical formulae can be used to verify calculation accuracy of each other in some scenarios when other numerical methods do not work well. Furthermore, the reflection coefficients of EM fields, consisting of the ratios of the cylindrical functions, are introduced to avoid overflow problems in the numerical integral. Numerical examples corroborate the correctness and stability of the proposed formulae. These formulae help advance the forward modeling and inversion of logging-while-drilling (LWD) azimuthal resistivity measurements and new extra-deep azimuthal resistivity tools (EDAR).

First, we directly introduce the cosine transform to compute the time-domain electromagnetic (EM) response excited by cause step turnoff. Then, we advance a novel semianalytic algorithm based on integration, summation, and cube spline interpolation (ISCSI) method to efficiently accomplish the cosine transform. The ISCSI method divides the integral into a sum of partial integrals, which can be solved by cube spline interpolation combined with Newton–Leibniz formula. On the basis, we apply a known convolution method to further compute the time-domain response by arbitrarily waveform in airborne transient EM measurement. Finally, numerical tests valid the ISCSI method is easier to implement and more efficient than the traditional digital filter method because the ISCSI method only requires less frequency sampling amount to accomplish the cosine transform.

BackgroundThis study analyzed the imaging data of patients retrospectively to understand the risk of cannulated screw fixation for femoral neck fracture. At the same time, we try to use intraoperative frog lateral view to avoid the risk of screw cutout.MethodThe imaging data of patients with femoral neck fracture treated with cannulated screws between January 2015 and September 2016 was reviewed, and patients with screw cutout or suspicious cutout were found. The postoperative imaging data of 41 patients who attempted to use frog lateral view during the operation was reviewed,and patients with screw cutout or suspicious cutout were found.ResultAmong the 479 patients, only 72 patients underwent CT examination after the operation, and 18 of the 72 patients had obvious screw cutout. Screw cutout cases accounted for 3.8% of the total number of cases and 25% of the patients undergoing CT examination. Of the 41 patients who received intraoperative frog lateral view, only 2 cases were cutout from the neck, and no cases were cutout from the femoral head.ConclusionThe anterior upper part of the femoral head is a high-risk area cutout by cannulated screws. Postoperative CT is very necessary and can accurately detect the screw cutout, for the long-term prognosis of the implications. The application of frog lateral view in the operation of femoral neck fracture can effectively avoid the risk of cannulated screw cutout.

Triaxial induction tools can be used to evaluate thinly laminated sand-shale sequences and fractured beds. This type of reservoirs exhibit transversely isotropy (TI) or arbitrarily anisotropy (also called as biaxial anisotropy (BA)). There have been several papers to study the responses in the TI model or the simplified BA model whose conductivity principal coordinate is always consistent with the formation coordinate. However, little work covers the most general biaxial anisotropic model whose conductivity tensor’s orientation is arbitrary. We introduce the Euler angles, then the general biaxial anisotropic conductivity tensor can be determined by three principal components and three ordered Euler angles. To derive the electromagnetic (EM) fields in arbitrarily anisotropic medium, we first convert the Maxwell’s equation of frequency-spatial domain into frequency-wavenumber domain by 2D Fourier transform, and obtain an ordinary differential system about horizontal components of EM fields. Using eigenvalue decomposition of the system matrix, this system can be decomposed into two group of equations associated with upward and downward eigen-waves respectively. We derive the solutions of EM fields in frequency-wavenumber domain by introducing transmission matrix, both local and generalized reflection matrix and propagator matrix After that, we use 2D Gauss-Legendre quadrature to calculate inverse Fourier transformation and obtain Green’s function for simulation of the tri-axial induction responses. The numerical results are compared with 3D numerical method in both vertical and deviated wells and the agreement is satisfactory. Finally, we investigate the response characteristics in several formations with different Euler angles The results show that triaxial induction responses are remarkably influenced by Euler angles even if the values of three principal components of conductivity tensor remain unchanged. Compare to the responses of the simplified BA model, those of general BA model are more complex and contain more nonzero components. The results indicate that using TI model or the simplified BA model in complex environment may cause large errors. Our algorithm are more practical than algorithms based on the simplified model because the real depositional environments are usually complicated.

In this paper, we set up an efficient algorithm of the 3D synthetic response and explicit sensitivity matrix of 3D mCSEM inversion in the two different model spaces: block model and pixel model. The Helmholtz equations of coupled electrical scalar-vector potentials with Coulomb gauge is discretized by 3D finite volume method at Yee’s staggered girds to form a large, sparse and complex linear system with multi-transmitters. A direct solver PARDISO is used to stably and accurately solve the system. Furthermore, the scattered EM fields caused by the conductivity perturbation are also solved by the 3D finite volume method based on the scattered scalar-vector potentials at the same Yee’s staggered girds. In order to further enhance the whole computation efficiency, the interpolation operator and projection operator are advanced to realize directly and fast transformation of the terms on right hands side of discrete systems to the EM fields at arbitrary position because the number of receivers is greatly less than that of scattering sources and transmitters. The explicit EM sensitivity matrix in the two different model space will be set up by only addition of a two-matrix multiple. Finally, we investigate the distributing disciplinarian and response characteristics of explicit sensitivity matrix in two different cases for block and pixel inversion.

Human mobility forecasting in a city is of utmost importance to transportation and public safety, but with the process of urbanization and the generation of big data, intensive computing and determination of mobility pattern have become challenging. This study focuses on how to improve the accuracy and efficiency of predicting citywide human mobility via a simpler solution. A spatio-temporal mobility event prediction framework based on a single fully-convolutional residual network (STAR) is proposed. STAR is a highly simple, general and effective method for learning a single tensor representing the mobility event. Residual learning is utilized for training the deep network to derive the detailed result for scenarios of citywide prediction. Extensive benchmark evaluation results on real-world data demonstrate that STAR outperforms state-of-the-art approaches in single- and multi-step prediction while utilizing fewer parameters and achieving higher efficiency., Accepted by MDM 2019

In this paper, we use the 3D cylindrical finite volume (3D FV) method to simulate the Orthogonal Azimuth Electromagnetic Tool (OAEMT) responses Logging While Drilling (LWD) according to the special structure of the OAEMT with multi annular grooves. The algorithm allows the solution of the 3D Maxwell’s equation in inhomogeneous media with arbitrary conductivity and magnetic permeability distributions. For improvement of the computational efficiency and the modeling accuracy of the responses of OAEMT with annular grooves filled with ferrite material on steel mandrel in a completely anisotropic media, several techniques are applied: 1) a 3-D cylindrical irregular grid to avoid stair-casing discretization errors in the transmitter, receiver, and mandrel geometries; 2)the electric field continuation to approximate the perfectly electric conducting (PEC) boundary condition for enhancement of the discrete accuracy of the Helmholtz equations on the surface of steel mandrel; 3)the standardization technique to determine the equivalent conductivity and permeability in a non-uniform element; 4) PARDISO direct solver to solve the discrete equation as far as possible for increase of solution stability. We validate the 3D FV results against the numerical mode matching method. The comparisons show very good agreement. Results from 3-D borehole problems in several complex formation conditions involving eccentric tools and dipping beds are given to demonstrate the robustness of the method.

In this paper, we set up an efficient Frechet derivative algorithm of inversion of multicomponent induction logging (MCIL) data in horizontal layered transversely isotropic (TI) formations based on transmission line method (TLM) in order to simultaneously reconstruct the model vector including both horizontal and vertical conductivities, horizontal interfaces, borehole dipping angle, and tool azimuth in deviated well from the MCIL data. First, MCIL responses in the TI model are efficiently determined by both the spectrum EM fields obtained by TLM and the semianalytical computation of Sommerfeld integrals based on the cubic spline interpolation. Then, the Born approximations are executed to derive the MCIL Frechet derivatives as the sixfold integrals of the products of two spectrum EM fields in infinite domains. By using the integral characters of the 2-D Dirac function, the sixfold integrals of Frechet derivatives are further simplified into twofold integrals: One is the Sommerfeld integral in the radial spectrum domain, and the other is the definite integral in the vertical spatial domain. They are efficiently computed by the semianalytical approach similar to the MCIL simulation. Therefore, we obtain the linear equations between changes in the MCIL responses and small perturbations in the model vector. After that, we iteratively modify all of the model parameters to realize the best fit between the input data and the synthetic data of the inverted model by the normalization of the Frechet derivative and singular value decomposition technique. Finally, we apply numerical results to investigate the characteristics of the Frechet derivatives and to validate the inversion method and its antinoise ability.

An efficient and reliable numerical mode matching (NMM) method is developed to simulate the responses of multicomponent induction logging (MCIL) in the horizontally layered inhomogeneous transversally isotropic (TI) formations with the borehole and the invasion zone. The computation of MCIL responses is entirely transformed into three axially symmetrical problems on the Fourier harmonic components of the electromagnetic (EM) fields. The two extra singular differential operators about the horizontal EM components are introduced to describe the influence of the accumulation charge at the cylindrical interfaces on the EM fields excited by the horizontal magnetic dipoles. The first and second kinds of homogeneous boundary conditions of the different harmonic components of horizontal electrical fields near the borehole axis are derived to ensure that the EM problems become well posed in the cylindrical coordinate system. Then, the NMM is applied to solve the three axisymmetric problems with the extra singular differential operators. The numerical results demonstrate that the proposed method can accurately and efficiently simulate the MCIL responses in the horizontally layered TI formations with the large contrast resistivity.

In this paper, we advance an algorithm of numerical modeling for responses of multicomponent electromagnetic well logging in a deviated and layered anisotropic formation through the 3-D finite difference time domain approach (FDTD). First, we use a Yee's staggered grid and linear interpolation formula to discretize the Maxwell equation in the time domain in an anisotropic medium and determine the non-defined components of electromagnetic (EM) field in the staggered grid in order to obtain the time recursive equation of the EM field on all staggered grids in an arbitrary anisotropic media. At the same time, area weighted average and transformation matrix are utilized to calculate the effective conductive tensors on the grids, and an absorbing boundary condition is executed to reduce the reflection of outer-boundary on the base of uniaxial anisotropic perfectly matched layer (UPML). Then, we apply three mutually orthogonal transmitter coils with a singlefrequency sinusoidal current to excite EM fields in the time domain and extract the amplitude and phase of EM from the EM field through a special two-equation and two-unknown (2E2U) approach to obtain the responses of multicomponent EM propagation logging tool. Finally, by numerical results we validate the algorithm and examine systematically the influence of changes in bed thickness, formation dipping angle and radius of invasion zones on responses of the tool.

In this paper, we advance an efficient algorithm to compute the responses of multicomponent induction logging (MCIL) tool in deviated and layered anisotropic formations through a numerical mode matching method (NMM). First, the three mutually orthogonal magnetic dipoles located at the borehole axis are represented as the sum of three harmonic components about the dipole angle θ so that the electromagnetic (EM) fields produced by the dipoles can be transformed into three axisymmetric problems. And new boundary conditions satisfied by every EM harmonic component at borehole axis are given to assure the EM field near the borehole axis can still be calculated. Then NMM is used to solve the three axisymmetric problems and obtain a semianalytic expression of a dyadic Green function by magnetic current source in the formation. Furthermore, the formula to compute the MCIL response is given. The numerical tests are carried out to validate the algorithm and investigate the characteristics of MCIL response in several different cases.

In this paper, we advance a fast iterative inversion algorithm of multicomponent induction well-logging (MCIL) datum to simultaneously reconstruct a total model vector in a deviated well in the horizontally stratified transversally isotropic (TI) formation (TI medium) with the case-neglecting borehole. The model vector consists of the horizontal and vertical conductivities, the interface depth of each bed, and a borehole dipping angle. Because an electromagnetic field emitted by a horizontal magnetic dipole is no longer axially symmetrical, we first decompose the horizontal magnetic dipole located at borehole axis as the sum of two harmonics only so that the computation of MCIL responses can be entirely transformed into three axially symmetrical problems. Therefore, we solve them through the numerical mode matching method and obtain the semianalytic (SA) solution of an EM field in an arbitrary bed. Then, based on the perturbation principle and spatial distribution of formation conductivity related to the model vector, we set up an efficient SA algorithm of Frechet derivatives of the MCIL response with respect to the model vector. Then we extract an initial model from synthetic logs for the inversion through a special blocking technique. Finally, we give an iterative process to simultaneously reconstruct all model parameters from the logs through a combination of a normalization and singular value decomposition technique. Numerical tests validate the algorithms.

In this paper, we present an efficient algorithm to simulate the response of a multicomponent induction well-logging (MCIL) tool in a cylindrically layered anisotropic formation (transversely isotropic media). The tool consists of three pairs of orthogonally arranged transmitter-receiver coils for measuring the magnetic field around a borehole for oil and gas exploration. First, we will derive the EM field components to present the coupled transverse magnetic and transverse electric modes in the spectral domain for an arbitrary observation layer from the Maxwell equation and obtain the spectral-domain Green's function. The new local transmission and both the local and generalized reflections for the media are given. After that, we use a cubic spline interpolation to realize the inverse Fourier transformation and obtain the spatial-domain Green's function for the investigation of the response characteristics of the MCIL tool. Finally, we give some numerical results to explore the response characteristics of the tool in several different environments.

In this paper, we advance a fast approximative iterative inversion technique (FAIIT) of dual induction tool (DIT) logs. First, we establish the fast algorithm of Frechet derivatives of DIT logs with respect to bed interfaces and formation resistivities simultaneously, and give the process of the iterative inversion by use of normalization and singular value decomposition (SVD). The initial model parameters including interface and resistivities per bed must be extracted by comprehensively blocking of DIT logs for realization of the inversion of both synthetic and field logs. After the initial model is obtained, the bed resistivity and interface per bed are iteratively revised through the inversion of the medium induction log (IM) only. Then, deep induction log (ID) is only used to reconstruct other bed resistivities. Due to the difference of ID and IM at exploring depth, the former can obviously give shallower resistivities at exploring depth than the later. The inversion results of both synthetic and field logs clearly prove that the inversion results from ID and IM respectively can demonstrate the exact characteristics of formation invasion. Besides, because of ID with deeper exploring depth, inversion results of ID are largely closer to formation virgin resistivities than apparent resistivity of ID in beds of either deep or shallow invasion, so the better estimation of formation virgin resistivity is also obtained.

The expression and algorithm of the Born approximation of dual-laterolog (DLL) are different from nonfocusing resistivity tools because the currents and potentials on the surfaces of the electrodes must be satisfied with the special focusing conditions. The Born approximation is described by a linear integral equation about the changes in current density, bucking currents, and potentials on the surfaces of all the electrodes, caused by small perturbations in the formation conductivity. Using the complex forward modeling of DLL, and the semi-analytic solution of the Green's function, we advance the fast algorithm of the Frechet derivative matrix containing the partial derivatives of both the apparent resistivities and bucking currents with respect to all components of the model vector. A normalization approach is used to transform the matrix into a dimensionless matrix. We then develop a multiparameter iterative inversion technique to simultaneously reconstruct all model parameters. Furthermore, we analyze the influence of both noises in data and errors of some model parameters on the inversion solution and give a method to choose the regularization factors. Finally, numerical result tests show the characteristics of the normalized Frechet matrix, the influence of errors of both bed thickness and flushed zone resistivity, etc, on the inversion solution when they are fixed, and the great improvement of the inversion quality when all model parameters are simultaneously reconstructed from both the apparent resistivities and bucking currents.