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1.
采用规则六面体单元和并矢Green函数奇异积分等效积分技术,已有的大地电磁积分正演方法具有不能有效模拟地下复杂地质体和计算精度偏低的缺点.本文提出了一种新的三维大地电磁积分方程正演技术,即采用四面体单元、解析的并矢Green函数奇异积分表达式,达到既能模拟地下复杂异常体,又能有效提高已有积分方程法计算精度的目的.首先,采用四面体网格技术离散地下复杂异常体,获得四面体单元上的大地电磁积分方程.然后,利用针对四面体单元开发的新的奇异值积分的解析表达式,准确计算线性方程中的并矢Green函数的奇异积分,从而获得精确的线性方程.借助于PARDISO高性能并行直接求解器,实现了三维大地电磁问题的高精度求解.最后,基于国际标准3D-1模型和六棱柱模型,通过与其他方法结果的对比分析,验证了本文方法的正确性、处理高电导率对比度的能力(1000:1)和处理复杂模型的能力. 相似文献
2.
Three-dimensional em modeling 总被引：1，自引：0，他引：1
Gerald W. Hohmann 《Surveys in Geophysics》1983,6(1-2):27-53
Three-dimensional (3D) interpretation of electromagnetic (EM) dsta is still in its infancy, due to a lack of practical numerical solutions for the forward problem. However, a number of algorithms for simulating the responses of simple 3D models have been developed over the last ten years, and they have provided important new insight. Integral equation methods have been more successful than differential equation methods, because they require calculating the electric field only in small anomalous regions, rather than throughout the earth. Utilizing a vector-scalar potential approach and incorporating symmetry through group theory improves the general 3D integral equation solution. Thin-sheet integral equation formulations have been particularly useful. Much recent research has focused on hybrid methods, which are finite element differential equation solutions within a mesh of limited extent, with boundary values determined by integrating over the interior fields. An elegant eigencurrent technique has been developed for calculating the transient response of a thin 3D sheet in free space, but general 3D time domain responses have only been calculated by Fourier transforming frequency domain results. Direct time domain calculations have been carried out only for 2D bodies. 相似文献
3.
Peter Furness 《Journal of Applied Geophysics》2001,48(4)
The general problem of magnetic modelling involves accounting for the effect of both remanent magnetization and the application of an external magnetic field. However, as far as the disturbing field of a magnetic body in a magnetic environment is concerned, there is an equivalence between the effects of these two causations that allows the remanence to be represented in terms of an equivalent primary magnetic H field. Moreover, due to the linearity of the magnetic field in terms of its causations, the general modelling problem involving an applied magnetic field in the presence of remanence can be simply and more efficiently dealt with in terms of an equivalent primary field acting in the absence of any remanent magnetization. 相似文献
4.
可控源电磁法具有分辨率高及抗干扰能力强等特点,是一种重要的地电磁勘探方法.目前,可控源电磁法的高精度正演计算一直是其核心研究问题之一.传统积分方程法一般采用近似积分公式、简单矩形网格和近似的奇异性体积分计算技术,制约了体积分方程法处理复杂地下异常体的能力,降低了计算精度.针对上述问题,本文基于完全积分公式、四面体非结构化网格和奇异体积分的精确解析解来高精度求解复杂可控源电磁模型的正演响应.首先,从电场积分公式出发,推导了可控源电磁问题满足的积分方程;其次,借助于非结构化四面体网格离散技术,实现了地下复杂异常体的有效模拟.最后,利用散度定理把强奇异值体积分转换为一系列弱奇异性的面积分公式,并通过推导获得了这些弱奇异性的面积分公式的解析解,从而最终实现三维可控源电磁问题的高精度积分求解.以块状低阻体地电模型为测试模型,采用本文提出的积分方程方法获得的数值解与其他公开数值算法解进行对比分析,其对比结果具有高度的吻合性,验证了算法的正确性;同时,设计了球状及复杂地电模型进行算法收敛性测试,进一步验证算法的正确性以及能够处理地下复杂模型的能力. 相似文献
5.
Calculation of magnetic anomalies caused by 2D bodies of arbitrary shape with consideration of demagnetization 总被引：1，自引：0，他引：1
Nick P. Kostrov 《Geophysical Prospecting》2007,55(1):91-115
Forward calculations of magnetic anomalies caused by two-dimensional bodies of any shape and magnetic properties may be performed either without considering demagnetization as in the equivalent source technique or taking demagnetization into account as in the volume integral equation (VIE) approach, in which, for this purpose, magnetized bodies are divided into a set of rectangular prismatic cells. Ignoring demagnetization may result in distortion of the shape and the amplitude of an anomaly, whereas rectangular cells may not be an optimal representation of the source. Moreover, an inaccurate form approximation in the VIE technique may lead to inconsistent results in the near-body region. In this paper, a method is proposed, based on the VIE approach but differing by applying triangular elementary cells. The method largely overcomes the above-mentioned limitations of the VIE technique. It allows us to delineate large and complex structures exactly and only requires the source to be divided into a few elementary cells to take demagnetization into account satisfactorily. These improvements have been attained through analytical calculation of the Green's function in the complex plane, using the theory of the Cauchy-type integral. Comparing numerical solutions with analytical solutions for homogeneous elliptic cylinders without remanence, the method is found to be consistent with the theory in the range of relative magnetic permeability of 2–20, not only far from but also at subcell distances from the body. The method is appropriate for modelling highly and inhomogeneously magnetized 2D bodies of any shape. It may be of value in interpreting underground measurements or topographic effects, as well as in modelling regional geomagnetic profiles, and it is also a convenient tool for testing questionable geological hypotheses. In the framework of the method, the gravitational anomaly for the same causative bodies can be easily calculated. However, at higher and geologically uncommon values of relative magnetic permeability, the algorithm may become unstable but may be stabilized with SVD regularization. The fact that discrepancies were found with the method employed is a basis for further research. 相似文献
6.
We present a concept of the hybrid finite volume–integral equation technique for solving Maxwell's equation in a quasi-static form. The divergence correction was incorporated to improve the convergence and stability of the governing linear system equations which pose a challenge on the discretization of the curl–curl Helmholtz equation. A staggered finite volume approach is applied for discretizing the system of equations on a structured mesh and solved in a secondary field technique. The bi-conjugate gradient stabilizer was utilized with block incomplete lower-upper factorization preconditioner to solve the system of equation. To obtain the electric and magnetic fields at the receivers, we use the integral Green tensor scheme. We verify the strength of our hybrid technique with benchmark models relative to other numerical algorithms. Importantly, from the tested models, our scheme was in close agreement with the semi-analytical solution. It also revealed that the use of a quasi-analytical boundary condition helps to minimize the runtime for the linear system equation. Furthermore, the integral Green tensor approach to compute at the receivers demonstrates better accuracy compared with the conventional interpolation method. This adopted technique can be applied efficiently to the inversion procedure. 相似文献
7.
Peter Furness 《Geophysical Prospecting》1996,44(1):27-40
Modelling the theoretical response of several important geophysical systems involves the solution of Poisson's equation with homogeneous Neumann boundary conditions (i.e. a zero normal gradient) imposed over either open or closed surfaces. A simple integral equation solution to this problem is derived from first principles. It is applicable to both types of surface and in this respect represents an improvement on existing integral equation techniques. However, the present surface integral equation displays a strong singularity of order 1/R3 which requires an appropriate interpretation for its implementation. A comparison of some numerical results with analytical data taken from the literature demonstrates that the proposed integral equation technique is suitably robust, accurate and efficient for practical application in geophysical interpretation. 相似文献
8.
Mike Jackson 《Pure and Applied Geophysics》1991,136(1):1-28
The magnetic fabric of rocks and sediments is most commonly characterized in terms of the anisotropy of low-field magnetic susceptibility (AMS). However, alternative methods based on remanent magnetization (measured in the absence of a magnetic field) rather than induced magnetization (measured in the applied field) have distinct advantages for certain geological applications. This is particularly true for; (1) adjunct studies in paleomagnetism, in order to assess the fidelity with which a natural remanence records the paleofield orientation; (2) studies of weakly magnetic or weakly deformed rocks, for which susceptibility anisotropy is very difficult to measure precisely; and (3) quantitative applications such as strain estimation. The fundamental differences between susceptibility and remanence (and their respective anisotropies) are due to several factors: (1) susceptibility arises from all of the minerals present in a sample, whereas remanence is carried exclusively by a relatively small number of ferromagnetic minerals; (2) ferromagnetic minerals are generally more anisotropic than para- and diamagnetic minerals; (3) for ferromagnetic minerals, remanence is inevitably more anisotropic than susceptibility; and (4) a number of common minerals, including single-domain magnetites, possess an inverse anisotropy of susceptibility, i.e., they tend to have minimum susceptibility parallel to the long axis of an individual particle; remanence is immune to this phenomenon. As a consequence of all these factors, remanence anisotropy may generally provide a better quantitative estimate of the actual distribution of particle orientations in a rock sample.Contribution number 9102 of the Institute for Rock Magnetism, University of Minnesota. 相似文献
9.
在经典位场理论中,许多简单形体位场异常难以通过积分得到全空间的解析式.圆柱体是一类很重要的理论模型体,常用于模拟圆柱状地质体或非地质体(如管线),但目前还不能用解析公式正演有限长圆柱体在三维空间里的磁异常,而多是采用近似简化为有限长磁偶极子或线模型代替.对于有限长圆柱体,特别是半径相对于上顶埋深较大时,这种近似的误差不可忽略.本文利用共轭复数变量替换法,推导出有限长圆柱体在全空间的引力位一阶、二阶导数,利用Poisson关系得到磁异常正演公式,进而利用有限长圆柱体磁异常正演公式求解管状体的磁异常,得到不同磁化方向、不同大小的管线产生的磁场的特征,并将其推广到截面为椭圆的情况.最后通过模拟计算定量给出了将圆柱体近似为线模型的条件. 相似文献
10.
The forward computation of the gravitational and magnetic fields due to a 3D body with an arbitrary boundary and continually varying density or magnetization is an important problem in gravitational and magnetic prospecting. In order to solve the inverse problem for the arbitrary components of the gravitational and magnetic anomalies due to an arbitrary 3D body under complex conditions, including an uneven observation surface, the existence of background anomalies and very little or no a priori information, we used a spherical coordinate system to systematically investigate forward methods for such anomalies and developed a series of universal spherical harmonic expansions of gravitational and magnetic fields. For the case of a 3D body with an arbitrary boundary and continually varying magnetization, we have also given the surface integral expressions for the common spherical harmonic coefficients in the expansion of the magnetic field due to the body, and a very precise numerical integral algorithm to calculate them. Thus a simple and effective method of solving the forward problem for magnetic fields due to 3D bodies of this kind has been found, and in this way a foundation is laid for solving the inverse problem of these magnetic fields. In addition, by replacing the parameters and unit vectors in the spherical harmonic expansion of a magnetic field by gravitational parameters and a downward unit vector, we have also derived a forward method for the gravitational field (similar to that for the magnetic case) of a 3D body with an arbitrary boundary and continually varying density. 相似文献
11.
In this series of papers we examine magnetic reconnection in a domain where the magnetic field does not vanish and the non-ideal region is localised in space so that the reconnection is fully three dimensional. In a previous paper we presented a technique for obtaining analytical solutions to the full set of stationary resistive MHD equations and examined specific examples of non-ideal reconnective solutions. Here we further develop the model, noting that certain ideal solutions may be superimposed onto the fundamental non-ideal solutions. This provides the first analytical demonstration of a lack of coupling between reconnective and non-reconnective flows. We examine the effect of imposing various such ideal flows. Significant implications are found for the evolution of magnetic flux in the reconnection process so that several reconnection solutions may have the same reconnection rate, as defined by the integral of the parallel electric field along the reconnection line, but each appear quite different in terms of their global effect. It is shown that, in contrast to the two-dimensional case, in three dimensions there is a very wide variety of physically different steady reconnection solutions. 相似文献
12.
Mads Faurschou Knudsen Bo Holm Jacobsen Niels Abrahamsen 《Physics of the Earth and Planetary Interiors》2003,135(1):55-73
A robust finite-element technique is presented for computation of both the internal demagnetization effects and magnetic terrain effects in bodies with arbitrary shape and arbitrary susceptibility distribution. This method facilitates a flexible analysis of the palaeomagnetic deflection problem. Tests on geologically realistic settings of highly magnetic rocks demonstrate that deflections of several degrees may occur even for relatively simple two-dimensional models. Similarly, the magnetic intensity may well be biased by 5-15% by demagnetization effects. The present paper focuses on deflections and intensity variations inside the magnetized body, where we find a systematic shallowing of inclination for bodies with a horizontal elongation. Because the bodies sampled at a typical palaeomagnetic site will have a dominant direction of elongation, the magnetic deflection effect will tend to impose a systematic bias which doesn’t average out. An inversion-based procedure for elimination of the deflection effect is presented. It requires that the magnetic body is quite homogeneous and that its surface geometry is known, as may be the case for historical lava flows. Tests demonstrate that in order to recover both ambient palaeofield direction and the effective susceptibility at blocking temperature it is necessary to sample near strong topographic elements in the magnetic body. Since the surface geometry rarely is known it is proposed as an alternative to inversion that an effective susceptibility is assessed and a horizontal slab correction is applied for samples taken far from topographical features. When shape geometry is unknown and no correction applied, palaeomagnetic conclusions must take into account the possible bias from internal demagnetization and magnetic terrain effects. 相似文献
13.
《Geofísica Internacional》2014,53(3):343-363
Meteorites represent the earliest records of the evolution of the solar system, providing information on the conditions, processes and chronology for formation of first solids, planetesimals and differentiated bodies. Evidence on the nature of magnetic fields in the early solar system has been derived from chondritic meteorites. Chondrules, which are millimeter sized silicate spherules formed by rapid melting and cooling, have been shown to retain remanent magnetization records dating from the time of chondrule formation and accretion of planetesimals. Studies on different meteorite classes, including ordinary and carbonaceous chondrites, have however provided contrasting results with wide ranges for protoplanetary disk magnetic fields. Developments on instrumentation and techniques for rock magnetic and paleointensity analyses are allowing increased precision. Micromagnetic and an array of geochemical, petrographic and electronic microscopy analyses provide unprecedented resolution, characterizing rock magnetic properties at magnetic domain scales. We review studies on chondrules from the Allende meteorite that reveal relationships among hysteresis parameters and physical properties. Coercivity, remanent and saturation remanence parameters correlate with chondrule size and density; in turn related to internal chondrule structure, mineralogy and morphology. Compound, fragmented and rimmed chondrules show distinct hysteresis properties, related to mineral composition and microstructures. The remanent magnetization record and paleointensity estimates derived from the Allende and other chondrites support remanent acquisition under influence of internal magnetic fields within parent planetesimals. Results support that rapid differentiation following formation of calcium-aluminum inclusions and chondrules gave rise to differentiated planetesimals with iron cores, capable of generating and sustaining dynamo action for million year periods. The Allende chondrite may have derived from a partly differentiated planetesimal which sustained an internal magnetic field. 相似文献
14.
I. E. Stepanova I. A. Kerimov D. N. Raevskiy A. V. Shchepetilov 《Izvestiya Physics of the Solid Earth》2018,54(1):91-105
The interrelation between different modifications of the method of linear integral representation is studied. Combined approximations of the topography and geopotential fields enable more refined tuning of the method in solving inverse problems of geophysics and geomorphology and provide a more complete allowance for the a priori information about the surface elevation data and elements of anomalous fields. A technique for finding the numerical solution for the inverse problem for determining the mass distributions equivalent in terms of the external field is presented. The results of the mathematical experiment are discussed. 相似文献
15.
本研究选择川西高原、天山和西伯利亚Kurtak剖面的黄土古土壤样品及亚热带非风成样品进行CBD处理,系统测量并对比处理前后的磁学参数,包括低频磁化率、频率磁化率、非磁滞剩磁、饱和等温剩磁、剩磁矫顽力和热磁曲线(J-T曲线),分析处理前后磁性矿物种类、含量和磁畴的变化.结果表明,CBD方法对于磁性矿物的溶解并无明显的选择性,在温度与反应时间一定的条件下,磁性矿物的溶出量主要受控于其粒径分布.CBD方法可以非常有效地去除具有更大比表面积的细粒(< 1 μm)磁性矿物,同时溶解粗粒(>1 μm)磁性矿物外缘,使其粒径变细.CBD处理后磁化率变化存在多种可能,对于成土作用较强的古土壤,CBD方法可以较为准确地提取成土成因的磁性信息;而干旱和过度湿润条件下的风积黄土,不宜使用CBD方法区分原生与次生磁性矿物. 相似文献
16.
17.
《Advances in water resources》2005,28(10):1048-1056
For steady two-dimensional free surface flow over a horizontal impervious base, the Dupuit–Forchheimer theory assumes that the vertical component of velocity is zero, even for non-zero accretion rate at the free surface. This is improved by assuming that the vertical velocity component is zero at the base, and is proportional to height above the base. This requires the piezometric head to depend linearly on the square of the height, and the two parameters in this relation can be fitted to the two boundary conditions at the free surface, to give an expression for the free surface slope in terms of accretion, free surface height, and the pressure integral. For problems in which the pressure integral is known explicitly, this first order of ordinary differential equation for the free surface height can be solved numerically. The solutions are more accurate than the Dupuit–Forchheimer expressions for the free surface, and much easier to calculate than numerical solutions to the full two-dimensional problem. Four examples are given, leading to some simple analytical approximations for quantities of interest. 相似文献
18.
To further evaluate the potential of magnetic anisotropy techniques for determining the origin of the natural remanent magnetization (NRM) in sedimentary rocks, several new remanence anisotropy measurement techniques were explored. An accurate separation of the remanence anisotropy of magnetite and hematite in the same sedimentary rock sample was the goal.In one technique, Tertiary red and grey sedimentary rock samples from the Orera section (Spain) were exposed to 13 T fields in 9 different orientations. In each orientation, alternating field (af) demagnetization was used to separate the magnetite and hematite contributions of the high field isothermal remanent magnetization (IRM). Tensor subtraction was used to calculate the magnetite and hematite anisotropy tensors. Geologically interpretable fabrics did not result, probably because of the presence of goethite which contributes to the IRM. In the second technique, also applied to samples from Orera, an anisotropy of anhysteretic remanence (AAR) was applied in af fields up to 240 mT to directly measure the fabric of the magnetite in the sample. IRMs applied in 2 T fields followed by 240 mT af demagnetization, and thermal demagnetization at 90°C to remove the goethite contribution, were used to independently measure the hematite fabric in the same samples. This approach gave geologically interpretable results with minimum principal axes perpendicular to bedding, suggesting that the hematite and magnetite grains in the Orera samples both carry a depositional remanent magnetization (DRM). In a third experiment, IRMs applied in 13 T fields were used to measure the magnetic fabric of samples from the Dome de Barrot area (France). These samples had been demonstrated to have hematite as their only magnetic mineral. The fabrics that resulted were geologically interpretable, showing a strong NW-SE horizontal lineation consistent with AMS fabrics measured in the same samples. These fabrics suggest that the rock's remanence may have been affected by strain and could have originated as a DRM or a CRM.Our work shows that it is important to account for the presence of goethite when using high field IRMs to measure the remanence anisotropy of hematite-bearing sedimentary rocks. It also shows that very high magnetic fields (>10 T) may be used to measure the magnetic fabric of sedimentary rocks with highly coercive magnetic minerals without complete demagnetization between each position, provided that the field magnetically saturates the rock. 相似文献
19.
Summary The potential of the electric field of a stationary current in a two-layered Earth is calculated by applying Green's formula in the case where a three-dimensional inhomogeneity of different conductivity is located in the basement of the layer. It is proved that the potential outside and inside the perturbing body can be calculated from the potential of an electric double-layer distributed on the surface of this body. An integral equation of the Fredholm type is derived for the surface density of the double-layer, together with some of its integral properties. A similar procedure can be applied to computing the magnetic anomalies of three-dimensional magnetized bodies, geothermal anomalies due to three-dimensional inhomogeneities of different heat conductivity, as well as to potential problems of theoretical electrical engineering. 相似文献
20.
Spherical harmonic coefficients (SHCs) for the daily magnetic variation fields (solar and lunar) and the main field of the earth are usually estimated by the method of least squares applied to a truncated spherical harmonic series. In this paper, an integral method for computing the SHCs for the solar quiet daily magnetic variation fieldSq is described and applied toSq data for May and June 1965. TheSq SHCs thus derived are then compared with the results obtained using both unweighted and weighted versions of the least squares method. The weighting used tends to orthogonalize the least squares terms. The integral and weighted least squares results agree closely for terms up to order 4 and degree 30, but both disagree considerably for the higher degree terms with the results of the unweighted least squares. Errors introduced by the numerical integration can be shown to be small, hence the disagreement between integral and unweighted least squares coefficient sets arises from improper weighting. Also, it is concluded that discrepancies between the geomagnetic northward and eastward component-derived coefficient sets arise from either time-dependent external sources that produce non-local-time, based fields or nonpotential sources and not from truncation of the spherical harmonic series as has previously been suggested.Deceased. 相似文献