多电极成像测井反演问题的数学模型和数学方法

多电极成像测井是一种新的电阻率测井技术,这一测井技术的电极系中包含有多个测量电极,可提供较多的测量信息,从而有助于用较高的分辨率确定地层电阻率参数。本文对这个问题建立了数学模型,且运用非线性优化等数学方法对多电极成像测井反演问题提出了数值求解方法。并利用一些数值结果证实了这些算法的有效性。     

电阻率测井的数学模型

电阻率测井是石油勘探和开发中一种常用和重要的技术。介绍一种适用于各种电阻率测井的具有等值面边界条件的边值问题数学模型,这类数学模型不同于以往电阻率测井采用的局部边值问题模型,在实际应用中产生了巨大的效果。     

牛顿拉夫逊算法在ERT反演问题中的应用研究

本文研究了电阻率反演成像(ERT)中的牛顿拉夫逊基础算法及改进问题.利用最小二乘法和Tikhonov正则化等方法将反演算法予以优化,获得了与实验样本结构吻合的碳纤维复合层的电阻率分布图像,推广了牛顿拉夫逊算法的数理反演模型.     

n层角域点源电位似镜像性质与电位级数解

本文研究电动 角域点源电位的级数表示式，并导出了任意层介质电阻率与介质分界面夹解与地面实测电位的一个简单关系。     

椭圆问题的非线性边界条件均匀化

在本文我们讨论了在等值面边值问题中的非线性边界条件的均匀化,推广了相应的边界条件均匀化结果,而且可应用到用于处理热敏电阻问题中的一类非线性非局部边值问题的边界条件均匀化问题。     

非均质地层中自然电位测井的数学模型和数值方法

针对非均质地层中电阻率非分块常数,提出一个新的自然电位测井模型.自然电位满足具有交界面跳跃的椭圆边值问题.证明了该椭圆边值问题弱解的存在唯一性;提出一种捕捉交界面电位跳跃的有限差分方法求解此类问题,数值例子验证了该方法的可靠性和有效性.     

判别分析参量的优化选择及其应用

针对复杂地球物理数据集合,应用判别分析技术构建不同集合体识别函数时,需要优选出能敏感反映各类集合体特征的测量参量.声波、电阻率、自然伽马等地球物理测井项目对于岩层中的油、水性质反映能力各不相同,以卫星油田葡萄花油藏的20个油层、10个油水同层、15个水层为研究对象,依据构建集合内参量均匀度参数及集合间距离参数,优选出识别3类岩层的敏感测量项目,并依据这些参量建立贝叶斯判别函数,相对于所有测量参量均参与计算的情况,方法识别精度提高了9.7%.     

Periodic Homogenization for Inner Boundary Conditions with Equi-valued Surfaces: the Unfolding Approach

Making use of the periodic unfolding method, the authors give an elementary proof for the periodic homogenization of the elastic torsion problem of an infinite — dimensional rod with a multiply-connected cross section as well as for the general electroconductivity problem in the presence of many perfect conductors (arising in resistivity well-logging). Both problems fall into the general setting of equi-valued surfaces with corresponding assigned total fluxes. The unfolding method also gives a general corrector result for these problems.     

用电子计算机对微球形聚焦测井极板的考察

(一)引言 随着油田勘探和开发工作的不断发展,对油、气、水层的解释已由过去的定性判断逐步过渡到定量求解。为了可靠地计算含油气饱和度S_0,准确地确定侵入带电阻率R_(XO)是非常关键的。微球形聚焦测井是一种较为理想的侵入带电阻率测井方法。     

三维电阻抗成像的体积元方法的数值模拟和分析

电阻抗成像是一类椭圆方程反问题,本文在三维区域上对其进行数值模拟和分析.对于椭圆方程Neumann边值正问题,本文提出了四面体单元上的一类对称体积元格式,并证明了格式的半正定性及解的存在性;引入单元形状矩阵的概念,简化了系数矩阵的计算;提出了对电阻率进行拼接逼近的方法来降低反问题求解规模,使之与正问题的求解规模相匹配;导出了误差泛函的Jacobi矩阵的计算公式,利用体积元格式的对称性和特殊的电流基向量,将每次迭代中需要求解的正问题的个数降到最低.一系列数值实验的结果验证了数学模型的可靠性和算法的可行性.本文所提出的这些方法,已成功应用于三维电阻抗成像的实际数值模拟.     

The use of the fractal model to complex resistivity in the interpretation of induced polarization data

Several researchers demonstrated that spectral parameters in induced polarization can be applied to discriminate different IP sources. In this paper it was applied an inversion procedure using the Gauss–Newton method to recover the spectral parameters of fractal model to complex resistivity. The finite element method was applied to carry out the forward modeling. The procedure was applied in synthetic data and simulations were carried out in five different frequencies. The inversion of the data were carried out in each frequency, further the inversion was applied also to each cell of the finite element mesh to recover the fractal parameter in order to analyze the possibility of using the fractal model parameters in the interpretation of the induced polarization response to this geological geometry. The results showed that the anomalies are well detected by the image of the fractal model parameters.     

MULTIPLE PARAMETERS IDENTIFICATION PROBLEMS IN RESISTIVITY WELL-LOGGING

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Reconstruction of electron-phonon interaction function from temperature dependence of electrical resistivity for metals

The determination of the electron-phonon interaction function (EPIF) from the temperature dependence of the electrical resistivity (TDER) for metals within a selected moderate temperature range is numerically demonstrated based on the general theory of the amplitude-phase-retrieval problem and an iterative algorithm. From the model calculation, the convergent solution can be obtained; however, the profile of the recovered EPIF depends on the initial frequency distribution used in the algorithm since this inversion problem is inherently ill-posed. In order to get reasonable result, it is necessary to introduce additional information about the feature of the EPIF for guiding the choice of the initial distribution. The algorithm can also furnish a robust reconstruction of EPIF from TDER contaminated with random noise. It means that this algorithm is relatively stable and insensitive to external perturbation; therefore in a sense, the presented algorithm overcomes the ill-posedness of the inversion problem.     

Global strong solution to the three dimensional nonhomogeneous incompressible magnetohydrodynamic equations with density‐dependent viscosity and resistivity

In this paper, we consider an initial boundary value problem for the 3‐dimensional nonhomogeneous incompressible magnetohydrodynamic equations with density‐dependent viscosity and resistivity coefficients over a bounded smooth domain. Global in time unique strong solution is proved to exist when the L² norms of initial vorticity and current density are both suitably small with arbitrary large initial density, and the vacuum of initial density is also allowed. Finally, we revisit the Navier‐Stokes model without electromagnetic effect. We find that this initial boundary problem also admits a unique global strong solution under other conditions. In particular, we prove small kinetic‐energy strong solution exists globally in time, which extends the recent result of Huang and Wang.     

Nonexistence of self-similar singularities in the viscous magnetohydrodynamics with zero resistivity

We are concerned on the possibility of finite time singularity in a partially viscous magnetohydrodynamic equations in Rn, n=2,3, namely the MHD with positive viscosity and zero resistivity. In the special case of zero magnetic field the system reduces to the Navier-Stokes equations in Rn. In this paper we exclude the scenario of finite time singularity in the form of self-similarity, under suitable integrability conditions on the velocity and the magnetic field. We also prove the nonexistence of asymptotically self-similar singularity. This provides us information on the behavior of solutions near possible singularity of general type as described in Corollary 1.1.     

Environmental degradation of carbon nanotube-modified composite laminates: a study of electrical resistivity

The environmental durability of carbon nanotube (CNT)-modified carbon-fibre-reinforced polymers (CFRPs) is investigated. The key problem of these new-generation composites is the modification of their polymer matrix with nanoscaled fillers. It was recently demonstrated that the damage tolerance of these materials, as manifested by their fracture toughness, impact properties, and fatigue life, can be improved by adding CNTs at weight fractions as low as 0.5%. This improvement is mainly attributed to the incorporation of an additional interfacial area between the CNTs and the matrix, which is active at the nanoscale. However, this additional interface could have a negative effect on the environmental durability of the aforementioned systems, since it is well known that the moisture absorption ability of a matrix is enhanced by the presence of multiple interfaces, which serve as an ingress route to water. To examine this problem, CNT-modified CFRPs were exposed to hydrothermal loadings. At specified intervals, the composites were weighted, and the water uptake vs. time was recorded for both the modified and a reference systems. The electrical conductivity of the composites was registered at the same time intervals. After the environmental exposure, the interlaminar shear properties of the conditioned composite systems were measured and compared with those of unmodified composites, as well as with the shear properties of unexposed laminates. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 1, pp. 31–48, January–February, 2009.     

Induced polarization forward modelling using finite element method and the fractal model

The modeling of induced polarization data from 2D and 3D geological medium was developed. We applied the finite element method and the fractal model to complex resistivity of rocks as an intrinsic electrical property of geological medium. The LU factorization and pre-conditioned complex bi-conjugated gradient method were applied to solve the complex linear equation system. The modeling implemented in this work was efficient and prompt. In addition, the induced polarization survey using the fractal model as intrinsic property of the medium is a promising method for environmental investigation.     

Rayleigh-Taylor instability of compressible finitely conducting rotating fluid in the presence of a magnetic field

The character of the equilibrium of a non-viscous, compressible finitely conducting rotating fluid in the presence of a vertical magnetic field along the direction of gravitational field has been investigated. It is shown that the solution is characterised by a variational principle. Based on the existence of variational principle, an approximate solution has been derived for the case of a fluid having exponentially varying density in the vertical direction. Due to finite resistivity of the medium it is found that potentially stable or unstable configuration retains its character. Further the growth rate of disturbance has been obtained corresponding to short and long wavelengths and it is found that electrical resistivity suppresses the growth rate for large wavelengths but it increases the same for small wavelengths. It is further shown that magnetic field has a destabilizing influence for large wavelengths and a stabilizing influence for small wavelengths.     

L∞ continuation principle to the non‐baratropic non‐resistive magnetohydrodynamic equations without heat conductivity

The aim of this paper is to establish a continuation principle for strong solutions to the full compressible magnetohydrodynamic system without resistivity and heat conductivity. We prove that if the solution loses its regularity in finite time, the dominated part is due to the hyperbolic effect. More precisely, it is essentially shown that the strong solution exists globally if the density, temperature, and magnetic field are bounded from above, where vacuum is allowed to exist. This verifies a problem proposed by D.Serre. Copyright © 2016 John Wiley & Sons, Ltd.