复杂媒质中聚焦电极系响应的快速算法

利用高效的数值模式匹配方法（NMM）求解二维轴对称介质的位场格林函数，并结合表面积分方程法来匹配球形聚焦电极系上复杂的激励条件，圆满地解决了复杂介质中位场的分析，其数值结果与文献数据相吻合。本文还讨论了无源等位体对球形聚焦电极系测井响应的影响。     

Nonlinear inversion of electrode-type resistivity measurements

Deals with the inversion of low-frequency electrode-type resistivity measurements for the conductivity distribution in a two-dimensional axisymmetric medium. It is well known that the inversion of such transverse magnetic measurements is much more nonlinear than that of transverse electric measurements. The distorted Born iterative method (DBIM) is applied to solve the nonlinear inverse problem. In each iteration of the DBIM, an efficient numerical mode-matching (NMM) method is used as a forward solver. In addition to its efficiency in solving for the predicted data, the NMM method gives a semianalytic expression for the partial derivatives of the Green's function required in the inversion. Several numerical results are presented to demonstrate the applications of the DBIM, and to address several practical issues related to the performance of the nonlinear inversion scheme. Because of the fast forward modeling and semianalytic Green's function available due to the NMM method, the inversion is fast and is practical for the interpretation of measurement data     

一种高分辨率组合侧向电极系及其性能分析

为了解决电阻率测井仪的纵向分辨率和径向探测深度的矛盾。介绍了一种新型的高分辨率组合侧向电极系,并对其测井响应及性能进行了高效数值模拟。数值模式匹配方法是一种解析－数值混合方法,它使非均匀介质中的场的二维数值分析简化为一维数值分析和另一维的解析递推,从而大大了数值计算量。     

3-D numerical mode-matching (NMM) method for resistivitywell-logging tools

A three-dimensional (3-D) numerical mode-matching (NMM) method is presented for Poisson's equation in general inhomogeneons media. It reduces the original 3-D problem into a series of two-dimensional (2-D) eigenvalue problems plus a one-dimensional (1-D) layered medium problem, which can be modeled efficiently by a recursion procedure. The algorithm is tested for several 3-D inhomogeneous media and an excellent agreement between the NMM and analytical solutions is obtained for all test cases. We demonstrate some typical applications of the 3-D NMM algorithm in resistivity well logging, including invasion zones of noncircular shape, vertical and horizontal fractures, and horizontal wells. The solution procedure proposed is directly applicable to wave propagation in 3-D inhomogeneous media     

HIGH EFFICIENCY NUMERICAL SIMULATION OF RESISTIVITY TOOLS WITH DIFFERENT ELECTRODE RADII IN COMPLEX MEDIA

The Numerical Mode-Matching(NMM) method is far more efficient than the integral equation method and the finite element method, but it could not be applied to problems such as low frequency electrode-type resistivity tool with different electrode radii. In this paper, this problem is dealt with using an approximate NMM method, and the simulation of hybrid laterolog-3 tool gives very good results and the computer time is only 1% more than the traditional NMM. It is an extension of the application of NMM method.     

Numerical solution of Green's function of potential field ofeccentric point source in axisymmetric inhomogeneous media

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     

基于积分方程的低数据量的快速反演

本文将变形玻昂迭代法（ＤＢＩＭ）并结合数值模式匹配法（ＮＭＭ）用于实际工程中的深感应测井仪（６ＦＦ４０）的低信息量的反演和剖面成像。在反演迭代过程中,用Ｔｉｋｈｏｎｏｖ正则化求解病态问题,利用ＮＭＭ解的ｚ向解析性质,避免了双重数值积分,同时提高了计算效率和反演质量。文中利用不完备的低信息量工程数据对地层电参数进行了反演,表明该方法实际工程应用的潜力。     

Numerical Mode-Matching Method for Tilted-Coil Antennas in Cylindrically Layered Anisotropic Media With Multiple Horizontal Beds

Tilted-coil antennas (TCAs) have been proposed to increase the directional sensitivity and anisotropy sensitivity of well-logging tools used in oilfield exploration. In this paper, we simulate TCAs in 3-D cylindrically layered and anisotropic earth formations with multiple horizontal beds using an extended numerical mode-matching (NMM) approach. The field components are expanded in terms of longitudinal (vertical) eigenmodes to facilitate the analysis of transverse electric and transverse magnetic fields, which are coupled in this case. The perfectly matched layer is incorporated into the NMM formulation to mimic the Sommerfeld radiation condition in the longitudinal (vertical) direction. NMM results are compared with 3-D simulation results using finite-difference time-domain method and a pseudoanalytical approach based on Sommerfeld integrals (for problems where the latter is applicable), showing very good agreement.     

多约束稀布矩形平面阵列天线的方向图综合

针对多约束稀布矩形阵列天线的优化设计问题,该文提出一种新的矩阵映射(NMM)方法。首先,综合考虑阵元的可分布范围与可分布数量,重新定义阵元坐标矩阵的维数以提高阵元分布的自由度。其次,当坐标矩阵定义的阵元数量大于实际阵元数量时,建立选择矩阵以确定各阵元的取舍。再次,针对现有矩阵映射方法无法完全避免不可行解的问题,构建了一种NMM方法,通过两种不同的矩阵映射函数将多约束优化问题转换为无约束优化问题。最后进行仿真对比实验,实验结果证明了算法的有效性。     

基于阵列信息的二维轴对称电导率分布的有效反演方法

本文基于实际工程应用中的阵列感应测井仪（ＡＩＴ）的测量信息,利用变分坡昂迭代法（ＶＢＭ）,在非均匀背景介质中来重构和反演地层的电导率剖面。该方法基于非线性积分方程利用变分方法来建立反演方程,在反演迭代过程中,非均匀剪影介质中的格林函数无须更新,与变形玻昂迭代法（ＤＢＩＭ）相比其计算复杂性大大降低,文中仅利用沿井轴的ＡＩＴ响应对地层电导率进行反演,其胍演结果与起初地层电导率分布吻合的较好。     

基于双感应测井仪低数据量的反演方法研究

将一种迭代方法和双共轭梯度法用于实际工程中常用的双感应测井仪（DIT）的反演和剖面成象。基于目标区内、外电场积分方程,建立DIT的反演积分方程,利用MoM将积分方程高散为矩阵方程。在每次反演迭代过程中,用数值模式匹配法（NMM）求解DIT的感应电动势和格林函数。文中利用沿井轴的DIT不完备的低信息量对地层剖面进行反演,数值模拟结果表明该迭代方法的实际工程应用的潜力。     

An image method application to multilayer spreading resistance analysis

A numerical program to obtain the impurity profile within a semiconductor material from the measured spreading resistance data was developed. In the program, an image method was applied to calculate the spreading resistance of the multilayered structure, which consisted of a stack of layers, each of homogeneous resistivity, with thicknesses equal to the spacing of the spreading resistance data. The solution adopted in the present program is described in this paper. Converting results from the spreading resistance data to the impurity profile of an implanted and diffused sample and buried channel are also shown.     

任意平面分层介质中正演计算的快速方法

在非均匀介质电磁散射、逆散射等领域中，正演计算速度直接影响着反演计算效率。快速高精度的正演计算方法有利于反演效率的改善。对于任意平面分层介质情形，传统高效的数值模式匹配法的正演计算效率并不很高。本文通过首先推得每一从向分层中场量的汉克尔变换表达，再用快速傅里叶变换来完成汉克尔变换计算，从而得到更高效的计算方法。它避免了数值本征模式的求解，特别适用于处理平面分层介质中纵向分层较多的情形。对于其它非均     

A New Inversion Technique for Apparent Resistivity Measurements

A new algorithm for interpreting apparent earth resistivity data obtained from depth sounding measurements is presented. The method is based on fitting the data to an N layer earth model with equal layer heights h where h is equal to the required depth resolution. The spectral reflection coefficient at the earth's surface for the model used is derived as a ratio of two polynomials, the coefficients of which are a function of the resistivity ratios of adjacent layers. This provides the theoretical basis for inferring the model parameters. Measures for improving numerical stability are suggested and applied to a few examples. Results show that the present algorithm is most suited for continuously varying resistivity depth profiles.     

用修正玻昂迭代法重建复杂介质结构

着重阐述了将修正玻昂迭代法结合高效的数值模式匹配法用于感应测井中的反演与剖面成象。首先利用玻昂近拟将非线性问题线性比，然后应用吉洪诺夫正则化与迭代方法求解电磁场的积分方程。     

Modulation and Coding for Noncoherent Communications

Until recently, the theory of noncoherent communications was premised on the use of orthogonal multi-pulse modulation such as frequency shift keying. The main drawback of this modulation scheme has been its poor spectral efficiency (rate/bandwidth). This paper considers instead the more general non-orthogonal multi-pulse modulation (NMM) technique. Optimal and suboptimal noncoherent detection strategies for NMM are reviewed and their asymptotic (high SNR) performances are characterized for the additive Gaussian as well as the Rayleigh fading channels. The resulting non-Euclidean distance measures are then used to design NMM signal sets that yield significantly higher bandwidth efficiencies than their orthogonal counterparts. NMM in conjunction with convolutional coding is also studied as a way to improve energy efficiency. Several optimal convolutional codes are examined together with our signal designs. An introduction to equalization on the noncoherent channel is also presented and illustrated by example. This paper thus contains several new results and attempts at the same time to give a tutorial exposition of the subject of noncoherent communications.     

纳米尺度标准样片光学表征方法的研究

重点研究了纳米尺度标准样片的光学表征方法。采用基于纳米测量机(NMM)的激光聚焦传感器(LFS)和扫描白光干涉传感器(SWLIS)分别对平面尺度的标准样片和台阶标准样片进行了测量、分析与比较。实验结果表明,利用该纳米测量机LFS对标定值为3μm的TGZ1一维栅格样片进行测量,其扩展不确定度为4.2 nm,实现了精确表征。利用SWLIS测量方法对标定值为49.217μm的SHS8-50.0高台阶标准样板进行测量,测量不确定度分析结果为0.065 7μm,实现了采用光学检测技术跨尺度对纳米尺度精密器件和结构进行表征。扩大了基于纳米测量机光学表征方法的应用范围,有利于纳米几何量量值溯源体系的建立。     

基于积分方程的阵列信号的反演方法

本文将收敛速度快的变形玻恩迭代法(DBIM)结合数值模式匹配法(NMM)用于实际工程中的阵列感应成象仪(AIT)的测量信号的反演和剖面成象。在反演迭代过程中,利用NMM解的z向解析性质,避免了双重数值积分,提高了计算效率,同时也提高了反演质量。文中利用不完备的测量数据对AIT进行了反演,表明该方法非常适合实际工程应用。     

Emissivity simulations in passive microwave remote sensing with 3-D numerical solutions of Maxwell equations

In the numerical Maxwell-equation model (NMM3D) of rough-surface scattering, we solve Maxwell equations in three dimensions to calculate emissivities for applications in passive microwave remote sensing of soil and ocean surfaces. The difficult cases for soil surfaces are with exponential correlation functions when the surfaces have fine-scale structures of large slopes. The difficulty for ocean surfaces is that because the emissivities are close to that of a flat surface, the emissivities have to be calculated accurately to correctly assess the rough-surface effects. In this paper, the accuracies of emissivity calculations are improved by using Rao-Wilton-Glisson basis functions. We further use sparse matrix canonical method to solve the matrix equation of Poggio-Miller-Chang-Harrington-Wu integral equations. Energy conservation checks are provided for the simulations. Comparisons are made with results from the pulse basis function. Numerical results are illustrated for soil and ocean surfaces respectively with exponential correlation function and ocean spectrum. The emissivities of soil are illustrated at both L- and C-bands and at multiple incidence angles for the same physical roughness parameters. The brightness temperatures for ocean surfaces are illustrated for cases with various wind speeds. We compare results with those from the sparse matrix methods. Comparisons are also made with experimental emissivity measurements of soil surfaces. Parallel computation is also implemented. Lookup tables of emissivities based on NMM3D are provided.     

Simulation of multifrequency borehole resistivity measurements through metal casing using a goal-oriented hp finite-element method

The authors simulate multifrequency through-casing resistivity tool measurements operating at different frequencies in a borehole environment for the assessment of rock-formation properties. Rock formations are assumed to exhibit axial symmetry around the axis of a vertical borehole. The simulations are performed with a goal-oriented hp-adaptive finite-element method that delivers exponential convergence rates in terms of the quantity of interest (for example, the second vertical difference of the electric potential) against the CPU time. Numerical results confirm the efficiency and accuracy of the method, allowing for high-accuracy and reliable simulations of borehole logging measurements in the presence of highly conductive steel casing. The study of different tool configurations shows the advantages of using calibrated instruments with toroid antennas located on the borehole wall. The agreement between the numerical and analytical results, when the latter is available, is quantified. Errors on the simulations are consistently below 0.1%.