A CONTROL OF TWO-DIMENSIONAL MAGNETIC INTERPRETATION BY THREE-DIMENSIONAL MODEL BODY ANOMALIES*

In magnetic routine interpretation the comparison of two-dimensional model curves with measured magnetic anomalies is widely used for an approximate evaluation of the position and depth of magnetic models. Before starting an interpretation of a survey by means of two-dimensional models, it is very useful to have an idea of the shape of anomalies caused by extended but finite bodies, taking into account various strike directions: Three sets of anomalies of thin plates (horizontal length 19, downward length 9, width 1) dipping 30°, 60°, and 90° resp. for various strike directions and an inclination of 20° were computed. Some of these anomalies, e.g. those with nearly N-S strike direction look rather complicated, and at the first glance one would not expect that they are caused by such simple bodies. Several profiles crossing the computed anomalies perpendicularly were interpreted two-dimensionally. For less extended anomalies the depths determined for the top of the plates are 10-20% too small, the magnetization amounts to 50–75 % of the value of the finite bodies. The interpretation of the profiles covering more extended anomalies gave very accurately the same values for the position, depth and magnetization for the two-dimensional body as for the original three-dimensional model. Anomalies of vertical prisms with varying extensions in the y-direction were computed. Their differences in amplitude and in the distance maximum-minimum show that interpretation of short anomalies by two-dimensional methods yields depth errors of up to 20 percent. To see the possibilities of the separation of superimposed anomalies dike anomalies were added to the anomaly of a broad body in great depth and several attempts were made to interpret parts of the composite anomalies. The interpreted bodies lie too deep. In complicated cases the depth values can have large errors, but experienced interpreters should be able to keep the errors in the range of one third of the depth values.     

Detection and identification of north–south trending magnetic structures near the magnetic equator

Long, structurally undeformed north–south trending structures show no magnetic anomaly at the magnetic equator, except at the north and south truncations of the structure. However, folding, faulting, differential erosion or other structural deformation can produce detectable magnetic anomalies in a generally north–south trending equatorial structure. Spatial variation in magnetic susceptibility or remanent magnetization can also produce anomalies in equatorial north–south structures. These anomaly patterns are often more complicated than patterns produced by similar structures at high latitudes, but interpretational insight can be gained through numerical modelling of common structures. Reduction-to-pole and analytic signal filters can aid in interpretation of equatorial anomalies, but these must be applied carefully because of instabilities deriving from filter design and noise amplification.     

THE MAGNETIC ANOMALY OF 3D SOURCES HAVING ARBITRARY GEOMETRY AND MAGNETIZATION

Magnetic anomalies of complicated 3D sources can be calculated by using a combination of analytical and numerical integration. Two surfaces and the magnetization parameters (the amplitudes of the induced and remanent components and the direction cosines) of the source can be defined by arbitrary functions or by discrete data points in a plane. When combined with a polynomial magnetization function in the direction of the third axis, 3D magnetization distribution can also be modelled. The method gives very general equations for anomaly calculation. It can be used for direct modelling of sources interpreted by seismic or other methods and also for interactive interpretation with fast computers. It is possible to calculate anomalies of, for example, intrusives or folded sedimentary beds whose surfaces are functions of horizontal coordinates and which have polynomial magnetization variations in the vertical direction due to gravitational differentiation and arbitrarily varying magnetization in the horizontal direction due to regional metamorphosis. If the distribution of magnetization parameters in the vertical direction cannot be described satisfactorily by polynomials, models can be used whose surfaces are functions of the vertical coordinate and which can then have any arbitrary magnetization distribution in the vertical direction.     

On the interpretation of magnetic anomalies for strong remanent magnetizations

In this paper some aspects concerning the interpretation of magnetic anomalies are treated, particularly when the remanent magnetization intensity is strong. In this case, since total and induced magnetization vectors can have very different directions, a correct anomaly interpretation strictly depends on the knowledge of their declinations and inclinations.Thus, a specific procedure is described to determine such parameters from well-known semi-empirical techniques and vectorial relations.Furthermore, the classical definition of apparent susceptibility is shown to be inadequate to this problem and a more general formulation is suggested, which is not only related to the true susceptibility and to the Koenisberger ratio, but also to the declinations and inclinations of the induced and remanent magnetization vectors.The two apparent susceptibilities are then compared for some synthetic magnetic anomalies and significant differences are found.     

东海陆架盆地雁荡低凸起综合地球物理解释及其成因探讨

通过对东海陆架盆地西部地震和重磁资料的综合地球物理解释,对雁荡低凸起展布形态进行了细致刻画,凸起呈NE方向不连续展布于瓯江凹陷和闽江凹陷之间,长约170 km、宽约15~50 km.地震资料揭示雁荡低凸起上广泛发育了侏罗纪与白垩纪地层,厚度约为500~1500 m,展布面积约5000 km²,局部缺失中生界地层.凸起两侧中生代盆地结构差异明显,西侧瓯江凹陷为典型的断陷盆地,东断西超、断裂发育,半地堑、掀斜断块等中生界构造样式发育;东侧闽江凹陷为坳陷型盆地,断裂、火成岩不发育,挤压背斜、断背斜、反转构造等中生界构造样式发育.自由空间重力异常图与剩余重力异常图上,凸起表现为一系列NE向团块状重力高值区,而磁力异常ΔT图上则表现为深部磁场强度低的特征,火成岩影响部位可见磁力高值异常.综合凸起及邻域重磁震、莫霍面深度等地质地球物理资料,认为雁荡低凸起为一元古界组成的古隆起,区别于东部的台北低凸起.同时,结合区域构造演化及沉积特征,推测侏罗纪时期雁荡低凸起与浙闽隆起区可能连为一体,晚白垩世近东西向伸展作用下浙闽隆起发生裂陷进而形成了雁荡低凸起.     

Magnetic interpretation of pairs of sheets and their equivalence to dykes

Magnetic anomaly profiles over two thin sheets separated by a small distance resemble those of dykes andvice versa. Interpretation of anomalies over a pair of sheets based on the magnetic properties of dykes predicts a dyke whose centre lies midway between the positions of the sheets. The dyke, on the other hand, is magnetically equivalent to a pair of sheets, both lying at the same depth and having the same magnetization.The magnetic anomalies due to a pair of sheets can be interpreted by framing linear equations between the anomalies and their distances measured from an arbitrary reference. Application of this method to anomalies of dipping sheets with a finite depth extent is indicated.     

Separation of magnetic anomalies into induced and remanent magnetization contributions

Inversion of magnetic data is complicated by the presence of remanent magnetization, and it provides limited information about the magnetic source because of the insufficiency of data and constraint information. We propose a Fourier domain transformation allowing the separation of magnetic anomalies into the components caused by induced and remanent magnetizations. The approach is based on the hypothesis that each isolated source is homogeneous with a uniform and specific Koenigsberger ratio. The distributions of susceptibility and remanent magnetization are subsequently recovered from the separated anomalies. Anomaly components, susceptibility distribution and distribution of the remanent and total magnetization vectors (direction and intensity) can be achieved through the processing of the anomaly components. The proposed method therefore provides a procedure to test the hypotheses about target source and magnetic field, by verifying these models based on available information or a priori information from geology. We test our methods using synthetic and real data acquired over the Zhangfushan iron-ore deposit and the Yeshan polymetallic deposit in eastern China. All the tests yield favourable results and the obtained models are helpful for the geological interpretation.     

磁赤道处化极方法

化向地磁极(化极)是最基本的磁测资料处理方法之一,化极能消除或减少斜磁化影响,提高对磁测资料的认识程度和解释水平,对研究地壳产生的磁异常具有重要意义.但低纬度地区特别是磁赤道处,化极处理很不稳定甚至奇异,一直是位场研究的难点.针对地磁纬度较低特别是磁赤道地区磁异常化极的困难,利用从磁北极处垂直磁化向低纬度地区水平磁化方向转换稳定的特点,提出"狭义化赤"概念,并将其与低纬度磁异常"倒相"解释方法结合,提出专门用于磁赤道处化极的方法.该方法扩展了现有的化极理论,实现了磁赤道处的稳定化极.区别于目前任何方法,专门用于(近)水平磁化条件下的化极计算,具有原理简单,实现方便,收敛速度快等特点.对理论模型和实际资料计算表明这种针对磁赤道地区磁异常的化极处理方法是稳定、可靠的.     

龙门山和相邻地域航磁场特征与汶川大地震

本文应用化极、水平及垂向导数、向上延拓、视磁化强度填图及磁性界面反演等方法处理了龙门山及相邻地域最新的航空磁测数据,分析了龙门山及相邻地域的航磁异常展布特征.研究结果表明:1)龙门山造山带与其东、西两侧可划分为三个磁异常区:松潘—甘孜磁异常区、龙门山负磁异常带、四川盆地磁异常区;三个区、带的地壳介质磁性结构存在明显差异.2)根据该区航空磁异常场的分布特征分别研究了,松潘—甘孜地块、龙门山造山带和四川地块的磁场特征.3)除识别前人识别的断层外,还推断鲜水河ES延伸甘洛—雷波北断裂作为四川盆地与滇西的界带.4)航空磁异常,磁性体上、下界面及磁源体深度的空间分布特征与汶川MS8.0大地震及芦山地震发生相关.     

Interpretation of self-potential anomalies of some simple geometric bodies

Summary An entirely new procedure for interpreting selfpotential anomalies of spheres, rods and dipping sheets is presented. The anomaly of a sphere is divided into two parts — the anomaly of odd symmetry and the anomaly of even symmetry — from which the depth can be obtained by fitting them with the master curves. The self-potential anomalies of a finite rod are transformed to the anomalies of a veritcal sheet, for which standard curves are presented. The case of a sheet was divided into three parts; (a) finite line of poles; (b) infinite double line of poles and (c) finite double line of poles. For the first case logarithmic curves were prepared and presented; by their comparison with the field profile, different parameters can be obtained. In the second case, a geometrical construction is provided to obtain the various values. In the third case, the anomalies of finite sheet (finite double line of poles) are transformed into those due to an infinite double line of poles for interpretation.     

Satellite and surface geophysical expression of anomalous crustal structure in Kentucky and Tennessee

An equivalent layer magnetization model obtained from inversion of long-wavelength satellite magnetic anomaly data indicates a very magnetic source region centered in south central Kentucky. The magnetization maximum nearly coincides with a gravity high elongated north-south and extending into Tennessee. Previous refraction profiles suggest that the source of the gravity anomaly is a large mass of rock occupying much of the crustal thickness. The outline of the source delineated by gravity contours is also discernible in aeromagnetic anomaly patterns. Taken together, the geophysical data suggest a large, localized mass of intracrustal rock which is both dense and very magnetic. A simple magnetization/density model is given which accounts for the gravity and long-wavelength aeromagnetic anomalies due to the body. We interpret it as a mafic plutonic complex, and several lines of evidence are consistent with a rift association. The body is, however, clearly related to the inferred position of the Grenville Front. It is bounded on the north by the fault zones of the 38th Parallel Lineament. The inferred mean magnetization (4 A/m) of the body is large, but not inconsistent with values reported by others for deep crustal bodies associated with long-wavelength magnetic anomalies. Such magnetization levels can be achieved with magnetic mineralogies produced by normal oxidation and metamorphic processes and enhanced by viscous build-up, especially in mafic rocks of alkaline character.     

The possibilities of paleomagnetic and geohistorical analyses of “tiny wiggles” short-period marine magnetic anomalies

Marine magnetic anomalies of the tiny wiggles (TW) type can be used to solve geohistorical and paleomagnetic problems. The model fields corresponding to Paleocene–Eocene anomalies in the northwestern Indian Ocean, which were formed during the fast-spreading stage, were studied. For these fields, widely used interpretation methods were compared with a method proposed previously by the authors. The testing was performed with first the classical block model and then more complex models reflecting actual processes of oceanic accretion and magnetic field variations in the past. It was shown that the proposed method has advantages for this problem; it gives an error close to the minimum possible error and can adequately be used in interpretations. Spectral and statistical methods are used to estimate the magnetic anomaly resolving power and to study some factors that can exert a distorting influence. In addition, model examples have been used to indicate how the TW determination accuracy is affected by diurnal variations in the main magnetic field (MMF) and by ancient magnetization vector determination errors.     

Interpretation of magnetic anomalies by horizontal and vertical derivatives of the analytic signal

Magnetic anomalies are often disturbed by the magnetization direction, so we can’t directly use the original magnetic anomaly to estimate the exact location and geometry of the source. The 2D analytic signal is insensitive to magnetization direction. In this paper, we present an automatic method based on the analytic signal horizontal and vertical derivatives to interpret the magnetic anomaly. We derive a linear equation using the analytic signal properties and we obtain the 2D magnetic body location parameters without giving a priori information. Then we compute the source structural index (expressing the geometry) by the estimated location parameters. The proposed method is demonstrated on synthetic magnetic anomalies with noise. For different models, the proposed technique can both successfully estimate the location parameters and the structural index of the sources and is insensitive to noise. Lastly, we apply it to real magnetic anomalies from China and obtain the distribution of unexploited iron ore. The inversion results are consistent with the parameters of known ore bodies.     

磁异常揭示的峨眉山大火成岩省的深部结构

峨眉山大火成岩省位于中国西南部,在晚二叠纪约260 Ma喷发出巨量的大陆溢流型玄武岩.对于大火成岩省的岩浆喷发,在地下必定有一个相应的大规模岩浆聚集和运移系统.地球物理方法是探测岩石圈内部的有效方式.峨眉山大火成岩省为镁铁质岩浆喷发,由于镁铁质-超镁铁质岩石一般具有强磁性,因此,在喷发结束之后,地下岩浆系统如果被镁铁质岩浆填充,冷却固化成为岩石圈的一部分,很有可能会引起磁异常.本文使用区域磁异常数据来对峨眉山大火成岩省的深部构造进行研究.该区域的磁异常由一系列离散的异常组成,通过3D磁化率反演可以得到磁性体的空间分布.由于磁异常中具有明显的剩磁,直接使用经典的反演方法会有较大误差,我们首先将磁异常转换为弱敏感于磁化方向的磁异常模量,再使用模量数据进行3D反演,得到地下空间内磁异常源的分布.经过分析认为这些离散分布的磁异常源反映了岩石圈内部的镁铁质-超镁铁质侵入体.侵入体的位置可能反映了底侵和内侵的镁铁质岩浆固化形成的侵入体,代表镁铁质岩浆房位置或者岩浆运移的主要通道.     

AN ITERATIVE METHOD FOR THE SOLUTION OF ANON-LINEAR INVERSE PROBLEM IN MAGNETIC INTERPRETATION*

A method is presented for determining the lower surface of a two-dimensional body producing a magnetic anomaly when its upper surface and the intensity of magnetization are given. The magnetization vector is assumed to lie along a specified direction but the sense of magnetization may be different in different vertical sections of the body and may be regarded as unknown. The method is illustrated using the computed anomalies of some theoretical models.     

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.     

Age of the source of the Jarrafa gravity and magnetic anomalies offshore Libya and its geodynamic implications

The interpretation of the Jarrafa magnetic and gravity highs, NW Libyan offshore, suggests that it may be caused by a body of high-density and high magnetization. Analysis of their power spectra indicates two groups of sources at: (1) 2.7 km depth, probably related to the igneous rocks, some of which were penetrated in the JA-1 borehole, (2) 5 km depth, corresponding to the top of the causative body and (3) 10 km depth, probably referring to the local basement depth. The boundary analysis derived from applied horizontal gradient to both gravity and magnetic data reveals lineaments many of which can be related to geological structures (grabens, horsts and faults).The poor correlation between pseudogravity fields for induced magnetization and observed gravity fields strongly suggests that the causative structure has a remanent magnetization (D = −16°, I = 23°) of Early Cretaceous age, fitting with the opening of the Neo Tethys 3 Ocean.Three-dimensional interpretation techniques indicate that the magnetic source of the Jarrafa magnetic anomaly has a magnetization intensity of 0.46 A/m, which is required to simulate the amplitude of the observed magnetic anomaly. The magnetic model shows that it has a base level at 15 km.The history of the area combined with the analysis and interpretation of the gravity and magnetic data suggests that: (1) the source of the Jarrafa anomaly is a mafic igneous rock and it may have formed during an Early Cretaceous extensional phase and (2) the Jarrafa basin was left-laterally sheared along the WNW Hercynian North Graben Fault Zone, during its reactivation in the Early Cretaceous.     

A New Best-Estimate Methodology for Determining Magnetic Parameters Related to Field Anomalies Produced by Buried Thin Dikes and Horizontal Cylinder-like Structures

A new best estimate methodology is proposed and oriented towards the determination of parameters related to a magnetic field anomaly produced by a simple geometric-shaped model or body such as a thin dike and horizontal cylinder. This approach is mainly based on solving a system of algebraic linear equations for estimating the three model parameters, e.g., the depth to the top (center) of the body (z), the index parameter or the effective magnetization angle (θ) and the amplitude coefficient or the effective magnetization intensity (k). The utility and validity of this method is demonstrated by analyzing two synthetic magnetic anomalies, using simulated data generated from a known model with different random errors components and a known statistical distribution. This approach was also examined and applied to two real field magnetic anomalies from the United States and Brazil. The agreement between the results obtained by the proposed method and those obtained by other interpretation methods is good and comparable. Moreover, the depth obtained by such an approach is found to be in high accordance with that obtained from drilling information. The advantages of such a proposed method over other existing interpretative techniques are clarified, where it can be generalized to be automatically applicable for interpreting other geological structures described by mathematical formulations.     

CURRENT CHANNELLING IN SQUARE PLATES WITH APPLICATIONS TO MAGNETOMETRIC RESISTIVITY1

The magnetometric resistivity (MMR) method uses a sensitive magnetometer to measure the low-level, low-frequency magnetic fields associated with the galvanic current flow between a pair of electrodes. While the MMR anomalies of simple structures such as dikes and vertical contacts have been determined analytically, there is a lack of systematic information on the expected responses from simple three-dimensional bodies. We determine the characteristic anomalies associated with square, plate-like conductors, which are excellent models of many base metal mineral deposits. The anomalies of plates of finite size are determined numerically using an integral equation method. A plate is subdivided into many sections and the current flow within each section is solved by equating the electrical field within each section to the tangential electrical field just outside it. When the plate size is small in relation to either the depth or the transmitter spacing, the shape and amplitude of the anomaly produced is closely approximated by a current dipole model of the same length and depth. At the other extreme, a large plate is represented by a half-plane. The dipole and half-plane models are used to bracket the behaviour of plates of finite size. The form of a plate anomaly is principally dependent on the shape, depth and orientation of the plate. A large, dipping plate near the surface produces a skewed anomaly highly indicative of its dip, but the amount of skew rapidly diminishes with increased depth or decreased size. Changes in plate conductivity affect the amplitude of the anomaly, but have little effect on anomaly shape. A current channelling parameter, determined from the conductivity contrast, can thus be used to scale the amplitude of an anomaly whose basic shape has been determined from geometrical considerations. The separation into geometrical and electrical factors greatly simplifies both the interpretation and modelling of MMR anomalies, particularly in situations with multiple plates. An empirical formula, using this separation, predicts the anomaly of two or more parallel plates with different conductances. In addition, the relation between the resolution of two vertical, parallel plates of equal conductance and their separation is determined. The ability of the integral equation method to model plate-like structures is demonstrated with the interpretation of an MMR anomaly in a survey conducted at Cork Tree Well in Western Australia. The buried conductor, a mineralized graphitic zone, is modelled with a vertical, bent plate. The depth to the top of the plate, and the plate conductance, is adjusted to fit the anomaly amplitude as closely as possible. From the modelling it would appear that this zone is not solely responsible for the observed anomaly.     

A NOTE ON MAGNETIZED SPHERES*

The interpretation of total field anomalies becomes somewhat complicated, especially when an arbitrarily magnetized spherical ore mass happens to be the causative body. Even though some attempts have been made to analyze total field anomaly maps, they are often too complicated and their underlying assumptions in respect of permanent and induced components of magnetism are far from realistic. In this note, an attempt has been made to show that vertical magnetic anomalies are capable of yielding interpretation with ease and precision as far as magnetized spheres are concerned. An empirical method has been outlined for computing the magnetization inclination in the plane of the profile using the measured distances between principal maximum, principal minimum, and zero anomaly positions on a magnetic anomaly profile.