Magnetic-doublet method of interpretation of arbitrarily large total intensity anomalies

Summary In mining geophysics, analysis of total intensity magnetic anomalies in terms of equivalent magnetic-doublets has been extensively used for approximate determination of depth, offset and the length of the disturbing bodies. Total intensity data collected on the ground over shallow magnetized bodies cannot be interpreted quantitatively by the available methods of interpretation which assume that the resultant field lies in the direction of Earth's normal field as the anomalous field vector is small when compared to the normal field vector. In the present investigation, the above assumption has been eliminated and total intensity magnetic anomalies due to disturbing bodies are analyzed in terms of their magnetic-doublet equivalents. From sets of theoretical total magnetic anomaly curves (some are reproduced) Tables have been prepared using the characteristic points and are shown in Tables 1 to 7. These Tables can be used for the direct determination of depth, offset, etc., by using information from suitably chosen field profiles.Contribution No. NGRI 286.     

Interpretation of gravity and magnetic anomalies when observation plane is inclined

Summary Not infrequently, in mining geophysics, measurements have to be made on the slopes of a hill that contain mineralisation. In this paper, procedures are evolved for interpreting gravity and vertical component magnetic data collected on such slopes and caused by geological bodies that can be approximated by infinite line pole, point pole, infinite line dipole and point dipole. From sets of theoretical magnetic anomaly curves (not reproduced), graphs have been constructed using characteristic points and are reproduced in Figures 5 to 10 and 12 to 17. These can be used for direct determination of depths, offsets, etc., by using information from suitably chosen field profiles. In the case of gravity, the mass can be computed as usual by a surface integration, provided a correction factor (1/cos²) is used, being the angle of the slope.     

论被动源磁电勘探理论

本文从麦氏方程出发,运用电流磁场的等效理论阐明了在磁电勘探中,当矿体的二次极化电流具有垂直对称轴分布时,在地表面及以上空间中任一点的磁异常场（H）均等于零。因而,具有任何垂直对称状电化学矿产模式（石油、天然气、地下水及金属矿床等）的磁电勘探法异常场线积分均不存在。此外,由于对各种形状和任何极化倾角的矿体情况,地表面上均无电流密度垂直分量（i_n）存在,故地表面上异常场线积分均为零（∮_L H·dL=0）。因此,磁电勘探法不具备在地面上寻找此种矿产的物理前提。 本文还对倾斜极化球体和柱体的磁电勘探异常进行了计算,给出了主剖面上理论曲线的异常分布规律,指出了磁电异常的数量级。同时,还对井中磁电异常的分布规律给出了计算资料。为了对比,也对相应条件下的自然电场异常做了计算,指出了电场异常与磁场异常之间的不同特点及其对实际找矿的意义。     

地球非偶极磁场对虚地磁极计算的影响

古地磁学使用的虚地磁极（VGP）是在地心偶极磁场假设下计算的,由于地球非偶极磁场的存在,VGP一般不同于真地磁极（RGP）.为了定量检验非偶极磁场对VGP的影响,本文利用国际参考地磁场模型IGRF 1900～2000,在全球5°×5°的“虚拟测点”网格上计算了VGP和RGP的位置,并求出两种磁极的经纬度偏差和二者的角距离.结果表明,南极地区VGP与GP的角距离最大,可达26°,南大西洋和欧亚大陆北部最大达到24°和18°,其余地区一般小于15°.VGP对RGP的偏差与地磁场分布有关：在非偶极磁场较弱的地区（如太平洋半球）,纬度偏差一般不大（≤10°）,但是在主要地磁异常区（如南大西洋和南极地区）,VGP对RGP的纬度偏差可达25°.VGP对RGP的经度偏差要比纬度偏差大得多,例如在欧亚大陆北部地区,经度偏差分布在-180°到180°的大范围内.     

A new technique of interpreting gravity and vertical magnetic anomalies due to infinite horizontal cylindrical ore bodies

Summary A novel method of interpreting gravity and magnetic anomalies is presented here. Two diagrams of master curves, one for gravity and the other for vertical magnetic interpretation are presented. They are useful in calculating the depth of burial and the radius of infinite horizontal cylindrical bodies irrespective of density contrast or strength and direction of magnetisation. This method also enables us to infer the direction of magnetisation, resultant intensity of magnetisation and from them the susceptibility contrast; and density contrast. ThoughHenderson [8]²) reported the applicability of continuations and derivatives in the interpretation of magnetic anomalies for the first time, the authors have treated them in a more exhaustive manner in the present paper to obtain valuable relationships.     

On the interpretation of lunar magnetism

It is proved that if a spherical shell is magnetized in the direction of and proportional to a magnetic field of origin internal to the shell and the magnetizing field later disappears, no magnetic field exists external to the shell. Similarly if a spherical shell is magnetized parallel to and proportional to a magnetic field of external origin and this magnetizing field later disappears, the magnetic field internal to the shell is zero. These theorems are true only if these ideal conditions are met, but are applicable to the interpretation of the natural remanent magnetization of the lunar crust. It is shown that the present absence of a magnetic dipole field of the Moon supports the hypothesis that the magnetizing field was of internal origin but does not distinguish whether this was due to a dynamo in the lunar core or to a primaeval magnetization of its interior. Local magnetic fields around the Moon are interpreted as arising from the departure from sphericity of the shell and large craters.     

地震的感应磁效应（二）

本文是“地震的感应磁效应（一）--三维电磁感应的数值理论”一文的继续。首先从理论和实际计算两个方面证明了三维电磁感应数值方程解的唯一性、收敛性和稳定性,从而充实了作为研究地壳、上地幔电性结构横向不均匀性理论基础的“三维数值方法”。作为这一理论方法的实际应用,文中对不同源场周期和具有不同埋藏深度的三维电导率异常体进行了模拟计算,以研究地震感应磁效应的大小、空间分布特征和频率特性。模拟计算结果表明,对于周期从数秒到数分钟的地磁短周期变化,若电导率异常体的线度与5至7级地震的震源体积大体相当,其电导率较原背景电导率高近一个量级,其感应磁效应主要特征为:在异常体正上方,地面磁场的水平分量变化最大,相对变化量约30％;在异常体于源场方向一致的两侧,垂直分量变化最大,相对变化量约40-50％。因此,观测短周期地磁场的异常变化,有可能是监测地震孕育过程地下电性变化的一种试验途径。但由于上述异常强度在空间上衰减迅速,所以观测必须接近震源区,这对测点的选择是个不利的因素。     

On the calculation of magnetic anomalies of irregular two-dimensional bodies

Summary An easy method of calculating the magnetic anomalies of two-dimensional irregular bodies is presented. The body under consideration is replaced by a set of line doublets with a pole strength equal to the intensity of magnetisation and parallel to its direction. The magnetic effects of some of the equally spaced doublets are obtained, added and multiplied by the distance between them to yield the magnetic anomaly. The expressions involved here are simpler than those existing in geophysical literature.     

Palaeomagnetism of the monzonite porphyry from Milton,New South Wales

Summary Directions of natural remanent magnetization aftermagnetic cleaning of specimens from monzonite porphyry at Milton are given. Thermal and alternating magnetic field stability tests indicate that the resultant direction is that of the earth's magnetic field at the time of cooling. Comprison of the pole position calculated from this result with other pole positions from rocks of known age confirms the probable Permian age of the intrusion and the wide divergence of Australian from European and North American pole positions of this age.     

An analytic signal approach to the interpretation of total field magnetic anomalies1

The analytic signal (AS) is defined as the square root of the sum of the squares of the vertical and the two horizontal derivatives of the total magnetic field ΔT. This paper verifies theoretically that peaks of the AS correlate directly with their magnetic causative bodies and are positioned symmetrically over them, i.e. the main feature of the AS is that it is independent of the inclination of the magnetic field. This avoids the difficulties that are often faced in the conventional process of reduction to pole for ΔT, when the direction of magnetization of the causative bodies is not known. In addition, the AS has characteristics similar to the derivative features of the magnetic field, so that it is very sensitive to edge effects of the causative magnetic bodies. The theoretical derivations are tested by comparison with calculations on models, and, in a field example from Hunan Province, China, the AS is applied successfully to the interpretation of ΔT, whereas the conventional process of reduction to pole fails, due to the reverse magnetization of the causative body.     

Characteristic curves for the inversion of magnetic anomalies of spherical ore bodies

Characteristic curves are presented for interpreting vertical and total components of the anomalous magnetic field caused by spherical ore bodies. The curves use characteristic distances which are easy to measure on an anomaly profile. The method is fast, and does not require prior knowledge of the base level or the origin. Inversion with the characteristic curves is demonstrated on two field examples and the curves computed for the estimated parameters match well the field curves.     

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.     

Analysis and interpretation of anomalous conductivity and magnetic permeability effects in time domain electromagnetic data: Part I: Numerical modeling

Time domain electromagnetic (TDEM) response is usually associated with eddy currents in conductive bodies, since this is the dominant effect. However, other effects, such as displacement currents from dielectric processes and magnetic fields associated with rock magnetization, can contribute to TDEM response. In this paper we analyze the effect of magnetization on TDEM data. We use a 3-D code based on finite-difference method, developed by Wang and Hohmann [Geophysics 58 (1993) 797], to study transient electromagnetic field propagation through a medium containing bodies with both anomalous conductivity and anomalous magnetic permeability. The remarkable result is that the combination of anomalous conductivity and permeability within the same body could increase significantly the anomalous TDEM response in comparison with purely conductive or purely magnetic anomalies. This effect has to be taken into account in interpretation of TDEM data over electrical inhomogeneous structures with potentially anomalous magnetic permeability.     

强磁性三度体内部磁化强度的分布

本文讨论稳定磁化场中强磁性三度体内部磁化强度的数值解法。展示了由于退磁作用而造成的不均匀性,并以长方体内一些典型截面为例,较详细地讨论了磁化强度的特征,作了分布图;推导了较均匀磁化体磁化强度分布的近似公式,并计算了一组长方体的视退磁系数。     

磁激发极化法中水平圆柱体的一些研究结果

本文简要介绍导电柱体在全空间和半空间的均匀电流场中形成的异常电流磁场理论,给出了正、反演理论公式;计算出了磁电阻率法和磁激发极化法理论剖面曲线;得到了相应的模型实验结果以及在浸染型铜矿上的野外试验结果。这些资料证明了所建立的理论。     

A dipole approximating to the highest possible degree the earth's magnetic field

Summary The coordinates and the components of the dipole approximating to the highest possible degree the earth's magnetic field are determined minimizing a sum of squares of differences between the dipole field and the earth's magnetic field. Numerical results by the aid of a digital computer have been obtained for epoch 1932, 1937, 1942, 1945, 1950, 1955 and 1960 on the basis of magnetic data from 61 observatories.     

Quantitative interpretation of self potential anomalies of some specific geometric bodies

Summary Some direct and quantitative methods of SP anomalies caused by some specific geometric bodies have been developed in this paper. The models of current sources which have been considered are i) single pole, ii) a doublet, iii) a pair of single point poles separated by a horizontal distance, iv) single finite line pole, v) single infinite line pole and vi) two similar double infinite vertical line poles separated by a horizontal distance.     

A magnetic method for determining the geometry of hydraulic fractures

Summary We propose a method that may be used to determine the spatial orientation of the fracture plane developed during hydraulic fracture. In the method, magnetic particles are injected into the crack with the fracturing fluid so as to generate a sheet of magnetized material. Since the magnetization of a body with extreme dimension ratios, such as a crack, exceeds that of an equidimensional body and since this magnetization is sensitive both to orientation and geometry, this could be used to obtain information about the crack. By measuring the vertical and horizontal components of the magnetic field and field gradients at the earth's surface surrounding the injection well with superconducting magnetometers having 10^–4 gamma sensitivity and also by measuring field direction within the well itself, it should be possible to calculate the orientation and perhaps infer the approximate geometry of the fracture surface. Experiments on electric field potential operated in conjunction with this experiment could further constrain estimates of shape and orientation.     

Magnetic field transforms with low sensitivity to the direction of source magnetization and high centricity

Magnetic data interpretation faces difficulties due to the various shapes of magnetic anomalies and the positions of their extrema with respect to the causative bodies for different directions of the source magnetization. The well‐known transforms — reduction to the pole, pseudogravity field, and analytic signal (total gradient) — help in reducing the problem. Another way to achieve the required effect is the transformation of magnetic data, ΔT or Z, into values of the anomalous magnetic intensity T. In this respect, we have found some transforms based on differential operators such as the gradient of T and its modulus R = |?T|, the Laplacian L = ?²T, the product T ?²T and its square root Q, and the Laplacian ?²(T²) and its square root E, to be useful. They are slightly sensitive to the magnetization orientation and their extrema occur above the sources. For a 2D anomaly of a homogeneous causative body, the proposed transforms do not depend on the inclination of magnetization. In the 3D case, such independence does not exist even for the elementary field of a point dipole. The influence of the magnetization direction is estimated by an integral coefficient of sensitivity. This coefficient takes values of up to 2.0 for ΔT or Z anomalies, while their transforms T, R, E, Q and L have values of less than 0.28, 0.29, 0.24, 0.16 and 0.07, respectively, i.e. on average, 10 times less. The estimation of the centricity is carried out using the relative deviation of the principal extremum of the anomaly or its transforms from the epicentre of the model body at a depth equal to 100 units. For a ΔT anomaly this deviation is up to 67%; for the L transform it is less than 8%; for Q, E, R and T it is less than 10%, 15%, 20% and 25%, respectively. The proposed transforms take only non‐negative values. With respect to their shape, the peripheral magnetic extrema are removed, the anomalous configuration is simplified and the resolution of complicated interference patterns is improved. Their calculation does not require additional data for the direction of magnetization, which is an essential advantage over the reduction‐to‐the‐pole and pseudogravity‐field transforms. A joint analysis of the measured field and its transforms T, E and L offers possibilities for more confident separation of the anomalous effects and direct correlation to their sources. The model tests performed and the 3D field applications to real magnetic data confirm the useful properties of the transforms suggested here.