基于重磁泊松定理的磁化方向估计及应用：以相山铀矿田为例

磁化方向的确定对磁异常处理、反演及解释方面有着重要的参考价值.然而,目前常用的磁化方向估计方法易受计算窗口尺度、化极或叠加异常等影响.为此,本文从重磁泊松定理出发,推导出了磁化强度、磁异常一阶导数及重力位三阶导数的关系式,并在此基础上构建出了可反演磁化强度三分量的线性方程组,进而获得了场源的磁化倾角与偏角.模型试验表明,本文方法能够在多场源的叠加重、磁异常上,有效地反演出各场源的磁化方向,但噪声会在一定程度上降低反演精度,尤其对小规模场源的磁化方向影响较明显.将本方法应用于江西相山铀矿田重磁资料之中,获得了10个测算点的磁化方向,推断了这些测算点位置上重磁同源体的岩石类型,结果表明了研究区内碎斑熔岩具有强剩磁特征,而流纹英安岩则为顺磁性物质,且认为碎斑熔岩之下广泛分布着流纹英安岩,这对该地区组间界面部位铀矿找矿具有重要的指导意义.     

磁化岩石层球面各向同性统计模型

磁化岩石层产生的磁场是利用磁场观测研究地球发电机过程的最主要障碍之一。基于对球面各向同性随机矢量场及其空间两点关联张量的认识,建立了球面各向同性磁化岩石层的统计模型。结果表明,如果岩石层的剩余磁化强度和磁化率均为球面各向同性,那么在地表观测到的岩石层磁场由球面各向同性和准各向同性两个部分组成。因此,即使统计性质最简单的磁化岩石层,其产生的磁场的统计性质也要复杂得多。     

苏格兰当巴（Dunbar）下石炭统的古地磁研究——用烘烤效应解决岩石剩磁年龄问题

苏格兰当巴（Dunbar）下石炭统含钙砂岩组12个采样点的热退磁结果,显示一致的稳定磁化方向:偏角D=196°,倾角 I=-45°,α₉₅=4.3。侵入其中的一条20m厚的石炭系岩脉,其6个采样点的热退磁结果显示不同的磁化方向:D=195°,I=15°,α₉₅=10.7。 本文研究烘烤效应,论证了上述两个磁化方向均为原生。这与现存的对不列颠群岛该时期古地磁方向的看法矛盾。其原因可能是:1.以往的数据解释不可靠,特别是重磁化问题;2.构造原因;3.持续相当时间的异常地磁场。 对比纬度相似的太平洋夏威夷群岛熔岩流的“点记录”,本文针对当巴提出一种磁化模式:各有关古地磁磁化成分可能均产生于同一地质时代. 火成岩的尖晶石相方向,最可能为原生.它在古地磁分析中应给以较大权重.     

关于用有限元法作磁法勘探正演计算的理论问题

本文提出用有限元法解磁法勘探的正问题,不再需要引入均匀磁化假定。 传统的正演计算方法是在均匀磁化的假定下建立的,它不能适应解释复杂磁异常的需要。近几年来,国外学者提出了用迭代方法作非均匀磁化条件下的正演计算,对形状比较简单的磁性体取得了较好的效果。但随着磁性体的形状变得比较复杂,计算所需时间很快增加,精度和稳定性也明显降低。以求能量函数极小的变分原理为依据,用有限元法作非均匀磁化条件下的正演计算,得到的磁位势函数满足磁性体内外的偏微分方程和全部界面条件（文中对此作了证明）。因此,这种方法可以研究各种复杂因素的影响,宜于计算非均匀磁化磁性体的有效磁化强度和磁异常。     

同时考虑退磁和剩磁的有限体积法正演模拟

为分析同时考虑退磁和剩磁对磁测数据解释的影响,探讨了利用有限体积法求静磁场数值解的方法.从静磁场中的麦克斯韦方程出发,导出了有限体积法控制方程的离散表达式,对边界条件近似处理后求解方程组得到磁异常.通过与退磁改正计算结果对比,验证了方法的正确性,并分析得到忽略剩磁的相对误差与科尼斯布格比（Q）相关;利用有限体积法计算长方体模型在无地磁场情况下的磁异常和内部磁化强度,从数值模拟上说明剩磁也需要进行退磁改正,并表明退磁作用对剩磁的影响不仅与磁化率相关,而且与剩磁的方向和磁性体的形态相关;组合模型的计算结果对比表明,退磁作用对剩磁的影响还会因为临近强磁性体的作用发生改变.在青海灶火河西工区的应用说明,开展同时考虑退磁和剩磁的解释方法对准确识别强磁性岩体具有实用价值.     

古地磁多磁成分的分离技术

在古地磁的研究中，如何从复杂多样的退磁数据中获取能够代表岩石形成时期的古地磁场方向的原生剩磁组分，是关系到古地磁数据是否可靠、古地磁结果是否令人信服的根本环节之一，因此，如何充分利用实验室退磁数据所提供的各种信息去获取同源磁化的一组样品的原生剩磁方向是一个很有研究价值的问题。在总结前人的各种定性或定量的多磁成分分离技术的基础上，详细讨论了重磁化大圆的极和线性坳陷区内退磁平面的极的最佳拟合大圆的最小二乘拟合法，提出了综合使用主成分分析法、线性谱分析法、重磁化圆法以及退磁平面及重磁化大圆的二次拟合法，对来自同源磁化的一组样品进行系统分析，以获取一组样品的特征剩磁方向的方法，并应用于实际研究工作中。     

强剩磁强退磁条件下的二维井中磁测反演

强剩磁、强退磁改变了总磁化强度的大小和方向,给磁测资料解释带来困难.为此,本文利用二维井中磁测数据反演磁化强度矢量的二维分布.首先利用井中磁测的磁异常模量反演磁化强度大小的分布.然后,在已知磁化强度大小分布的前提下,拟合磁场分量,反演磁化强度方向的分布.其中,磁化强度大小和方向均用共轭梯度法求解,并通过预优矩阵改善磁化强度大小的反演效果.理论模拟说明,该方法能准确获得磁化强度矢量分布.磁化强度矢量反演结果包括感磁、剩磁及退磁的影响,这为研究强剩磁、高磁化率矿床提供了一种有效方法.     

含菱铁矿砂岩磁性的初步研究

作为煤田盖层产出的中国内蒙古平庄J₃砂岩,其平均磁化率为60×10^-5（SI）;平均剩磁为5×10^-3A/m.经热退磁后,在磁化率、剩余磁化、等温剩磁曲线、粘滞剩磁及磁组构等方面都发生了明显的变化,出现一系列奇异磁特征.岩石透射光与反射光鉴定、物相热红外分析、差热分析、X射线衍射分析表明,该砂岩的胶结物为弱磁性的菱铁矿,它在逐步热退磁过程中逐渐变为磁铁矿,部分变为赤铁矿.并大致确定,该砂岩胶结物含量近50％.此外,对这种砂岩样品仔细地进行了常规方法的退磁试验,得到其特征剩磁方向,确定其J₃古地磁极位置为198.8°E,84.6°N(α₉₅=4.8,k=94.5).     

安徽休宁地区下震旦統休宁羣砂岩的交变場退磁研究

本文使用交变場退磁方法对安徽休宁地区下震旦统休宁羣砂岩定向标本进行了剩磁稳定性检验,结果表明该岩层的天然剩余磁性基本上是稳定的,并得出它们的平均剩余磁化强度方向D_r=311°,I_r=76°,相应时代的古地极位置λ=90°E,φ=45°N,标本产地在当时所处的古纬度是90°-p=63°。最后,文章肯定了交变場退磁方法对古地磁学研究的重要意义;根据实验结果,对研究地区在早震旦世时的古气候提出了看法。     

新石器时代姜寨遗址的考古地磁研究

通过测量姜寨遗址窑灶烧土标本的剩余磁化方向,确定了公元前四千年左右该遗址所在临潼地区的地磁场方向（倾角和偏角）,采用逐步热退磁法,求出了当时、当地的地球磁场总强度值。由此,按照中心偶极模式算得了当时该地区所在的地磁纬度,以及该时期的虚地磁极位置和地球的虚偶极矩。     

Palaeomagnetic distortion modelling and possible recovery by inversion

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.     

Rapid computation of magnetic anomalies and demagnetization effects caused by bodies of arbitrary shape

Summary With the aid of formulae derived for the field caused by a finite rectangular prism, a machine method is developed for rapid computation of magnetic anomalies due to a body of any shape. Conversely, the method could be utilised for determination of the magnetization vector from the observed anomalies. An example is given to demonstrate the applicability, accuracy and speed of the method. The method is shown to be suitable also for the evaluation of magnetic terrain effects.In addition, a new method is presented which enables high speed calculation of demagnetization effect caused by a body of arbitrary shape where the magnetization in general may be inhomogeneous. Applicability and accuracy of the method are discussed. The method is applied to study the effect of susceptibility on inhomogeneity of the induced magnetization in a cube specimen.For a body of any shape with low susceptibility, a new concept of average demagnetization factor is introduced. Average demagnetization factors so calculated for a cylindrical specimen are tabulated.

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Zusammenfassung Unter Anwendung der Formeln für das Feld eines Quaders wird eine Methode entwickelt um die durch einen Körper beliebiger Form erzeugten magnetischen Anomalien mit Hilfe eines Rechenautomaten zu berechnen. Umgekehrt kann die Methode verwendet werden, um aus den beobachteten Anomalien den Magnetisierungsvektor zu bestimmen. An einem Beispiel wird die Anwendbarkeit, die Genauigkeit und die Schnelligkeit der Methode erläutert. Die Methode kann auch für die Berechnung von magnetischen Terraineffekten verwendet werden.Zudem wird eine neue Methode dargelegt, welche eine rasche Berechnung des Entmagnetisierungseffektes eines Körpers beliebiger Gestalt und inhomogener Magnetisierung ermöglicht. Anwendbarkeit und Genauigkeit der Methode werden besprochen. Die Methode wurde verwendet, um den Einfluss der Suszeptibilität auf die Inhomogenität der induzierten Magnetisierung in einem Würfel zu untersuchen.Für Körper beliebiger Form mit kleiner Suszeptibilität wls neuer Begriff der mittlere Entmagnetisierungsfaktor eingeführt. Mittlere Entmagnetisierungsfaktoren für eine zylindrische Probe werden tabelliert.

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Part I of the dissertation Theretical study of the magnetic attraction due to rock bodies and experimental investigation of the stability of rock magnetism submitted to the Swiss Federal Institute of Technology (ETH), Zurich, for the degree of Doctor of Natural Sciences.     

A physical approach to computing magnetic fields1

The superposition integral expressing the field due to a magnetic source body is relatively simple to evaluate in the case of a homogeneous magnetization. In practice this generally requires that any remnant component is uniform and the susceptibility of the body is sufficiently low to permit the assumption of a uniform induced magnetization. Under these conditions the anomalous magnetic field due to a polyhedral body can be represented in an intuitive and physically appealing manner. It is demonstrated that the components of the magnetic field H can be expressed as a simple combination of the potentials due to two elementary source distributions. These are, firstly, a uniform double layer (normally directed dipole moment density) located on the planar polygonal faces of the body and, secondly, a uniform line source located along its edges. In practice both of these potentials (and thus the required magnetic field components) are easily computed. The technique is applicable to polyhedra with arbitrarily shaped faces and the relevant expressions for the magnetic field components are suitable for numerical evaluation everywhere except along the edges of the body where they display a logarithmic singularity.     

A FAST FOURIER TRANSFORM METHOD FOR RAPID COMPUTATION OF GRAVITY AND MAGNETIC ANOMALIES DUE TO ARBITRARY BODIES*

The spectrum of a magnetic or a gravity anomaly due to a body of a given shape with either homogeneous magnetization or uniform density distribution can be expressed as a product of the Fourier transforms of the source geometry and the Green's function. The transform of the source geometry for any irregularly-shaped body can be accurately determined by representing the body as closely as possible by a number of prismatic bodies. The Green's function is not dependent upon the source geometry. So the analytical expression for its transform remains the same for all causative bodies. It is, therefore, not difficult to obtain the spectrum of an anomaly by multiplying the transform of the source geometry by that of the Green's function. Then the inverse of this spectrum, which yields the anomaly in the space domain, is calculated by using the Fast Fourier Transform algorithm. Many examples show the reliability and accuracy of the method for calculating potential field anomalies.     

Magnetic properties of oceanic basalts — effects of pressure and consequences for the interpretation of anomalies

The stability of natural remanent magnetization of three samples of oceanic basalts (DSDP Leg 25) is tested by alternating fields, thermal and pressure demagnetization. The possibility of low-temperature oxidation is examined by means of thermomagnetic curves.The effects of uniaxial compressions on initial susceptibility and induced magnetization are studied for the three samples. These experiments, performed in a field comparable to the geomagnetic field have shown large variations of magnetization. The results of paleomagnetism, as well as the interpretation of anomalies when the effects of the pressure of water and of possible sediments far from the ridge itself are taken into account, are discussed. The results could partly account for the decrease of magnetic anomaly amplitudes with distance from the mid-ocean ridge.     

JOINT INTERPRETATION OF GRAVITY AND MAGNETIC DATA OVER AXIAL SYMMETRIC BODIES WITH APPLICATION TO THE DARNLEY BAY ANOMALY,NWT CANADA*

A method is presented for determining bounds of the properties of axial symmetric bodies from a finite number of gravity and magnetic observations based on Parker's theory of ideal bodies. Bounds on the density contrast and the intensity of magnetization are calculated as a function of depth to the top of the anomalous source, restricting the range of smallest possible solutions to fit the data. The model studied is approximated by an array of vertical annuli cylinders, each of uniform density and magnetization. Linear programming algorithms based on the ideal body theory were used to calculate the distribution of these parameters within the body. Simultaneous inversion of gravity and magnetic data is performed assuming a constant ratio between the density contrast and the intensity of magnetization and that a common body is responsible for both observed fields. The parameter k(|J|/δp) provides information about the rock type of the structure. Interpretation of gravity and aeromagnetic data from Darnley Bay, NWT, Canada, indicated the presence of a shallow ultrabasic intrusion.     

三维导电导磁体电磁响应的数值解

本文提出一种关于自由空间三维导电导磁体在谐变磁偶极场中电磁响应的数值计算方法。从麦克斯韦方程组导出以体内涡流密度和磁化强度为未知函数的一个联立微分积分方程组。采用迭代方法计算涡流和极化磁矩之间的相互作用,使联立的微分积分方程转化为两个独立的积分方程,再用积分方程法和有限差分法来求解。这种混合方法的优点在于它的计算速度较快。     

Magnetic properties of a freshly fallen LL ordinary chondrite: the Bensour meteorite

A comprehensive rock magnetic, magnetic anisotropy and paleomagnetic study has been undertaken in the brecciated LL6 Bensour ordinary chondrite, a few months only after its fall on Earth. Microscopic observations and electronic microprobe analyses indicate the presence of Ni-rich taenite, tetrataenite and rare Co-rich kamacite. Tetrataenite is the main carrier of remanence. Magnetization and anisotropy measurements were performed on mutually oriented 125 mm³ sub-samples. A very strong coherent susceptibility and remanence anisotropy is evidenced and interpreted as due to the large impact responsible for the post-metamorphic compaction of this brecciated material and disruption of the parent body. We show that the acquisition of remanent magnetization postdates metamorphism on the parent body and predates the entering of the meteorite in Earth’s atmosphere. Three components of magnetization could be isolated. A soft coherent component is closely related to the anisotropy of the meteorite and is interpreted as a shock remanent magnetization acquired during the same large impact on the parent body. Two harder components show random directions at a few mm scale. This randomness is attributed either to the formation mechanism of tetrataenite or to post-metamorphic brecciation. All components are likely acquired in very low (≈μT) to null ambient magnetic field, as demonstrated by comparison with demagnetization behavior of isothermal remanent magnetization. Two other LL6 meteorites, Kilabo and St-Mesmin, have also been studied for comparison with Bensour.