The efficient computation of Green's functions for uniaxial anisotropic layered media is investigated. Both field and mixed‐potential layered medium Green's functions (LMGFs) are discussed for different applications. An asymptotic subtraction (singularity extraction) and the weighted average method are combined for the acceleration of LMGF computation. A full collection of Sommerfeld and related identities used in the acceleration is summarized and generalized to uniaxial anisotropic medium for both field and mixed‐potential LMGFs. When lossy media are considered, the effective distance from the source to the observation point becomes a complex number depending on the anisotropic ratio of the horizontal to vertical media parameters. In addition, the evaluation of half‐line source potentials, which are introduced to accelerate the scalar potential correction term for vertical currents, is generalized to the complex domain by analytic continuation. Several numerical examples are used to demonstrate the efficiency and accuracy of the resulting algorithms.

Electromagnetic (EM) telemetry systems are widely used for measurement-while-drilling (MWD), especially in unconventional drilling. In this paper, a numerical method for the simulation of EM telemetry systems in deviated and horizontal drilling is introduced. The underground formation is assumed to be horizontally layered media, and the long, metal drill string acts as an antenna that may be treated as a thin wire excited by a gap voltage source located near the drill bit. The numerical model employs the electric field integral equation (EFIE) and the method of moments (MoM) to obtain a linear system for the axial current distribution on the drill string, which is subdivided into several one-dimensional segments. By using the thin wire kernel, near-field interactions can be evaluated accurately and efficiently, while also reducing problem dimensionality and singularity order of the homogeneous medium contribution to the layered medium Green's function (LMGF). The latter typically takes the form of a dyadic spectral domain integral, the asymptotics of whose integrands may be estimated and combined with Kummer's method to accelerate its evaluation, with the asymptotic correction terms evaluated in closed or easily evaluated forms. Numerical results are presented to verify the fast and accurate performance of the proposed approach. Results for signal voltage receivability by a surface antenna are also presented and discussed.

The objective of this study is to develop a method to model 3D resistivity well logging problems in 2D formation with anisotropy, known as 2.5D modeling. The traditional 1D forward modeling extensively used in practice lacks the capability of modeling 2D formation. A 2.5D finite difference method (FDM) solving all the electric and magnetic field components simultaneously is proposed. Compared to other previous 2.5D FDM schemes, this method is more straightforward in modeling fully anisotropic media and easy to be implemented. Fourier transform is essential to this FDM scheme, and by employing Gauss-Legendre (GL) quadrature rule the computational time of this step can be greatly reduced. In the numerical examples, we first demonstrate the validity of the FDM scheme with GL rule by comparing with 1D forward modeling for layered anisotropic problems, and then we model a complicated 2D formation case and find that the proposed 2.5D FD scheme is much more efficient than 3D numerical methods.

In this letter, a new formulation for calculating an induction logging tool response in a multilayered transversely isotropic (also called uniaxial anisotropic) dipping formation is proposed. Using transmission line theory, only five independent integrals are necessary to form all the components of the dyadic Green’s function in order to calculate the tool response, resulting in a more succinct and efficient formulation. The fast Hankel transform (FHT) is then employed to calculate these spectral integrals efficiently. In special cases, such as horizontal and vertical wells where the direct FHT fails, alternative approaches are proposed. A singularity extraction is implemented to handle the divergent integrals for a horizontal well, whereas the double-exponential integration rule is implemented for a vertical well. In order to speed up the computation, the spectral transmission line currents and voltages are precalculated and then stored in memory, and parallel computing using OpenMP is employed. Numerical examples demonstrate a speedup factor of more than two orders of magnitude compared with other reported results based solely on the FHT.

To simulate the EM telemetry system in deviated and horizontal drilling, the underground formation is assumed to be horizontally layered media, and the long, metal drill string acts as an antenna that may be treated as a thin wire excited by a gap voltage source located near the drill bit. The numerical model employs the electric field integral equation (EFIE) and the method of moments (MoM) to obtain a linear system for the axial current distribution on the drill string, which is subdivided into one-dimensional segments. By using the thin wire kernel, near-field interactions can be evaluated accurately and efficiently, while also reducing problem dimensionality and singularity order of the homogeneous medium contribution to the layered media Green's function (LMGF). Numerical results are presented to verify the fast and accurate performance of the proposed approach.

We have implemented and compared two numerical schemes for 2.5D finite difference (FD) modeling of directional electromagnetic (EM) wave propagation resistivity logging in a 2D fully anisotropic formation. The FD modeling is primarily developed for well placement and for fully anisotropic formation evaluation to interpret the logging responses of deep directional EM tools. Frequency-domain Maxwell's curl equations and current dipole sources are transformed into spectral domain and then discretized by 2D FD method. The first scheme eliminates the longitudinal components of electric and magnetic fields and sources to obtain a compact 2D FD method, while the second scheme keeps all the six components of electric and magnetic fields to develop a concise scheme. The total region is discretized by a combination of uniform grids inside the tool region and nonuniform girds outside the tool region in the x-z plane. Material averaging method is applied to resolve the inhomogenous and fully anisotropic formation. Direct sparse matrix solver is utilized to solve the linear equations in spectral domain at the sampling points of wavenumber. At last, a spectral inverse Fourier transform using Guassian quadrature rule is validated to obtain fast and accurate results. Presentation Date: Tuesday, September 26, 2017 Start Time: 10:35 AM Location: 362A Presentation Type: ORAL

Recent extensions in the computation of Green's functions for multi-layered media and half-space problems are reported. For anisotropic problems, a two-level asymptotic singularity extraction is combined with extended Sommerfeldrelated identities and the weighted average approach to provide additional acceleration and smoothing of Sommerfeld integrals for efficient simplex interpolation. For lossy anisotropic media, the associated identities must be appropriately continued into the complex plane. For the special case of half-space problems, two novel approaches are examined. The first uses double exponential quadrature to integrate directly between known singularities rather than detouring contours around singularities before reaching the so-called Sommerfeld tail region where the weighted average method can be used. The second technique instead deforms the integration path into a quasi-steepest-descent path, and seems particularly useful for large transverse source and observation point separations.

In this study we present numerical simulations of the Specific Absorption Rate (SAR) for multi-component orthopaedic hip replacement systems. The SAR is used to evaluate the radio frequency (RF)-induced heating of the devices during magnetic resonance imaging (MRI). Because multi-component orthopaedic hip replacement systems have many combinations of components with various designs and sizes, it is computationally intensive, and almost impossible, to evaluate the SAR and the corresponding temperature rise for each possible combination and configuration. In this study, an effective searching strategy and a computational simulation model are developed to evaluate the factors associated with induced SAR in the tissue near an orthopaedic hip replacement system, and to find the “worst case” peak SAR for all possible combinations. The finite-difference time-domain (FDTD) was used to calculate the peak SAR for a typical hip replacement system inside the American Society for Testing and Materials (ASTM) phantom for both 1.5 Tesla (T) and 3T MRI systems. The results indicate that the stem and screw lengths are the most important factors influencing the peak SAR for both field strengths, 1.5T/64 MHz and 3T/128 MHz, respectively. The peak 1 gram averaged SAR reaches 216 W/kg and 103 W/kg for 64 MHz and 128 MHz, respectively. We also found that shortest stems, and the longest screws, typically induce higher peak SAR.

The 2.5D forward method has been widely used in geophysical applications such as single-well, cross-well and controlled source electromagnetic measurements [1]. In this work, we proposed a two-dimensional (2-D) finite-difference frequency domain method for solving geophysical prospecting problems. The method is based on spectral domain and all the field quantities are expanded using Fourier transformation. Starting from the two-curl Maxwell equations, the longitudinal field components are eliminated and four transverse field components are used to represent the unknown fields [2]. The discretization is based on staggered Yee grid. The perfect electric conductor (PEC) boundary condition is employed to truncate the interested domain provided that the source is sufficiently far away to the boundary. The resulted system matrix is being solved using different methods and validated through eigenvalue problems. When finite source excitation is used, our numerical results show that good agreement is achieved compared with analytic solution.

In this paper, a two-level asymptotic subtraction method is developed to remove all unbounded singularities that appear in the curl-type layered-medium Green's function (LMGF) for uniaxial media. This allows for a more robust and more accurate interpolation scheme for the efficient evaluation of the curl-type operators in the LMGF.

In this work, a novel implantable medical stent is designed to reduce the radio frequency (RF)-induced heating from implantable medical stent under magnetic resonance imaging (MRI) procedure. By using segmented structure, the induced specific absorption rate (SAR) for a 100 mm length stent is reduced from 54.4 mW/g to 13.4 mW/g. Numerical simulation demonstrates the effectiveness of the designed structure.

Implantable stents can be used as radiation antennas for wireless communication of cardiovascular health monitoring data. However, such stent can also lead to RF induced heating during MRI procedure. In this paper, we investigate the effect of different stent size on the antenna radiation performance as well as its RF induced heating during MRI procedure. Preliminary investigations show that longer stent typically yields to better radiation efficiency but suffers from higher temperature rises.

In this paper, a quick and efficient approach is proposed to estimate the in-vivo RF induced heating of small medical implants under MRI procedure. The method is based on scaling the in-vivo incident electric fields. Numerical and experimental studies demonstrate the efficiency and accuracy of the proposed method.

Magnetic Resonance Imaging (MRI) has been contraindicated in patients with pacemakers or implantable cardioverter-defibrillators (ICDs) due to safety concerns, such as the heating of adjacent bodily tissue due to radio frequency (RF) induced current. The ISO/IEC 10974 Joint Working Group (JWG) has developed a tiered approach in establishing the worst case RF heating conditions that active implantable devices may experience during MRI utilizing computer simulations. According to the ISO/IEC JWG tier 2 approach, we evaluated the electric fields induced in the implant regions of pacemakers and ICDs in five human body models during 1.5 T MRI scans. The maximum electrical field (Emax) can be used as a conservative estimation to test MRI induced heating. The SEMCAD software package was used to calculate the electric field distribution due to RF fields from high pass and low pass MRI birdcage coils. The variables studied in the simulations also included circularly polarized field rotations, body positions inside RF coils (landmark positions), tissue properties, and RF coil size. The Emax and 95th percentile electric field values were computed from the simulations at each of multiple implant regions.