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.     

Quantitative interpretation of self-potential anomalies due to spherical ore bodies

Summary A quantitative method of interpreting self-potential anomaly caused by a spherical ore body using downward continuation method is presented. Master curves to determine the depth, radius and angle of polarization have been prepared.     

Interpretation of gravity and magnetic anomalies caused due to spherical bodies

Summary The method of continuation has been used to obtain the master curves for gravity and magnetic anomalies caused by spherical bodies. The procedure to calculate the depth of burial and radius of spherical bodies has been outlined.     

Analysis of magnetic anomalies due to some two-dimensional bodies using the Mellin transform

An interpretation technique using the Mellin transform is suggested for the analysis of magnetic anomalies due to some two-dimensional structures namely (i) a vertical sheet of both finite and infinite depth extent, (ii) a thick dyke and (iii) a horizontal circular cylinder. The Mellin transformed magnetic anomalies resemble gamma functions which are amenable to an easy interpretation. This procedure is illustrated with a small number of synthetic examples in each case. The practicality of the method is exemplified with the well-known vertical magnetic anomalies of Kursk (USSR) in the case of an infinite sheet model and Karimnagar magnetic anomaly (India) in the case of a horizontal circular cylinder. The results are compared with the techniques already available and found to be reliable.     

Grandient measurements in the interpretation of magnetic anomalies due to two-dimensional prism-shaped bodies

Summary A direct method of interpreting magnetic anomalies due to two-dimensional prisms is presented here. Measurement of the first vertical derivative supplies additional information concerning the parameters. The normal ground magnetic profile, as well as the gradient profile will have symmetrical points whose distances from the origin are related to the width, depth and height of a two dimensional prism shaped body.     

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.     

Interpretation of spontaneous potential anomalies from some simple geometrically shaped bodies using neural network inversion

A new approach is proposed in order to interpret spontaneous potential (self-potential) anomalies related to simple geometric-shaped models such as sphere, horizontal cylinder, and vertical cylinder. This approach is mainly based on using neural network inversion of SP anomalies, particularly modular algorithm, for estimating the parameters of different simple geometrical bodies. However, Hilbert transforms are involved to determine the origin location in order to reduce the parameters which minimize the ambiguity in the inverted models. The inversion has been tested first on synthetic data from different models, using only one well-trained network. The results of inversion show that the parameter values derived by the inversion are identical to the true values of parameters. Noise analysis has been also examined, where the results of the inversion produce acceptable results up to 10% of white Gaussian noise. The validity of the neural network inversion is demonstrated through published real field SP taken from southern Bavarian Woods, Germany. A comparable and acceptable agreement is shown between the results of inversion derived by the neural network and those from the real field data.     

Computation of magnetic gradients due to three-dimensional bodies

Thc expressions of magnetic gradients due to 3-D homogeneous magnetized polyhedra are systematically derived and presented, fronr which the forward problem of magnetic gradients of an arbitrary shaped geological body is solved. It is shown that in the rotation of coordinate systems there is an essential difference between the transformation of magnetic fields and that of their gradients. In a 2-D coordinate system a unified transformation formula of any order gradients can he derived, hut cannot in the 3-D case. The calculations of synthetic models show the correctness of the expressioils or magnetic gradients. Project supported by the National Natural Science Foundation of China.     

Thermal anomalies and magmatism due to lithospheric doubling and shifting

We present some thermal and magmatic consequences of the processes of lithospheric doubling and lithospheric shifting.Lithospheric doubling concerns the obduction of a cold continental or old oceanic lithospheric plate over a young and hot oceanic lithosphere/upper mantle system, including an oceanic ridge.Lithospheric shifting concerns the translation and rotation of a lithospheric plate relative to the upper mantle.In both cases the resulting thermal state of the upper mantle below the obducting or shifting lithosphere may be perturbed relative to a “normal” continental or oceanic geothermal situation.The perturbed geothermal state gives rise to a density inversion at depth and thus induces a vertical gravitational instability which favours magmatism.We speculate about the magmatic consequences of this situation and infer that in the case of lithospheric doubling our model may account for the petrology and geochemistry of the resulting magma.The original layering and composition of the overridden young oceanic lithosphere may strongly influence magmatic processes.We dwell shortly on the genesis of kimberlites within the framework of our lithospheric doubling model and on magmatism in general. Lithospheric recycling is inherent to the mechanism of lithospheric doubling.     

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.     

Zero-frequency tidal distrotion due to the orbital elements of tide-forming bodies

Summary It has been proved that orbital elements of perturbing bodies should be taken into account when 10^–10 accuracy is required for zero-frequency tidal distortion in the second zonal Stokes parameter of the geopotential. A solution at the 10^–15 level of magnitude has been presented. The zero-frequency tidal distortion in the fourth zonal Stokes parameter has been derived as 1·3×10^–10 if the secular Love number is unity. It should be reflected in the geopotential models respecting the 10^–10 level of magnitude.     

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.     

Gravity anomalies of three-dimensional bodies with a variable density contrast

The exponential decrease in the density contrast of anomalous bodies is equated to a quadratic function. The three-dimensional body is divided into a series of parallel vertical polygonal sections of unit thickness each. The gravity effect of each side of the vertical polygonal cross-section with a quadratic density variation is derived in closed form. Gravity effects of a few equispaced and representative cross-sections are integrated to obtain the gravity anomaly of the entire body. When used in modelling gravity data, the method of considering vertical cross-sections has the unique advantage of easily allowing changes in theZ-coordinates of polygonal sections.     

Use of the Hilbert transform to interpret self-potential anomalies due to two-dimensional inclined sheets

Self-potential anomalies due to two-dimensional inclined sheet of finite depth extent are analysed from their horizontal and vertical derivatives via the Hilbert transform. The depths to the top and bottom of the sheet and the inclination are obtained by means of simple mathematical expressions. The method is applied to a theoretical example and to a field S.P. anomaly over a sulphide deposit in the Kalava fault zone of Cuddapah basin, India. The presence of random noise is analysed for various levels and its effect is discussed. This interpretation process can be automated for all practical purposes by simple programming.     

Distribution of uranium in intrusive bodies due to combined migration and diffusion

Uranium is enriched in the border zones of magmatic bodies and the enrichment is believed to be caused by the migration of hydrous solutions which carry that element along intergranular paths towards the contact zone with the wall rock. We propose that the contact zone is a geochemical barrier at which the uranium, present in the solution, would be deposited if it were not for diffusion away from the increased concentration at the margins.The two particle flows, the one caused by migration and the other caused by diffusion, can be described by a differential equation, whose solution is the concentration of uranium as a function of time, diffusion coefficient and velocity of migration.The distribution of uranium in two intrusive bodies, the Mont Blanc granite (Swiss Alps) and a pluton in the Dshetui-Oguz massif (U.S.S.R.), gives the following parameters: duration of process 0.3–1 m.y., diffusion coefficient 4 × 10^?4 to 5 × 10^?4 cm²/s, and velocity of migration 0.1–0.3 cm/year.The combined process of migration and diffusion is assumed to be an important mechanism for controlling the distribution of uranium throughout the earth's crust and for its change in geological time.     

Tidal potential due to a non-spherical lunar body

Summary The tidal potential is derived at a point on the Earth's surface for the case when the perturbing gravitational field is not spherically symmetrical.     

Grain size dependent potential for self generation of magnetic anomalies on Mars via thermoremanent magnetic acquisition and magnetic interaction of hematite and magnetite

Early in the history of planetary evolution portions of Martian crust became magnetized by dynamo-generated magnetic field. A lateral distribution of the secondary magnetic field generated by crustal remanent sources containing magnetic carriers of certain grain size and mineralogy is able to produce an ambient magnetic field of larger intensity than preexisting dynamo. This ambient field is capable of magnetizing portions of deeper crust that cools through its blocking temperatures in an absence of dynamo. We consider both magnetite (Fe₃O₄) and hematite (α-Fe₂O₃) as minerals contributing to the overall magnetization. Analysis of magnetization of magnetic minerals of various grain size and concentration reveals that magnetite grains less than 0.01 mm in size, and hematite grains larger than 0.01 mm in size can become effective magnetic source capable of magnetizing magnetic minerals contained in surrounding volume. Preexisting crustal remanence (for example ∼250 A/m relates to 25% of multi-domain hematite) can trigger a self-magnetizing process that can continue in the absence of magnetic dynamo and continue strengthening and/or weakening magnetic anomalies on Mars. Thickness of the primary magnetic layer and concentration of magnetic carriers allow specification of the temperature gradient required to trigger a self-magnetization process.     

Nomograms for rapid evaluation of magnetic anomalies over long tabular bodies

The magnetic anomaly due to a long tabular body usually consists of a maximum and a minimum. The distances and the amplitudes of the maximum and the minimum, when defined in dimensionless quantities, may be used as characteristics of the source. In this paper, a method based on the positions of the maximum and the minimum on the magnetic anomaly due to a long tabular body has been presented. Characteristic ratios,D andA involving the distances and amplitudes of the maximum and the minimum points on the anomaly curve are defined. Nomograms showing the variations ofD andA with the parameters of (1) the dike and (2) the vertical fault models are presented. The parameters of the causative source are evaluated from the two ratiosD andA and the nomograms, using some simple analytical relations presented here. From the nomograms, it is observed that (a) for a thick dike,A is always greater thanD, (b)A=D for a thin sheet and (c) for a vertical fault,A is always less thanD. Thus from the characteristic ratiosD andA it is possible to evaluate the source parameters and also to distinguish whether the source is a dike, sheet or a vertical fault. The method is fast and is applicable for the magnetic anomalies either in total, vertical or horizontal component. The method has been applied on two field examples and the results are found to be in close agreement with those obtained by using other methods. A simple method of locating the origin on the anomaly curve is included. The limitations of the method are also discussed.     

强磁性体ΔT异常计算的误差分析研究

本文主要针对当前磁法勘探中高精度处理解释的需求,对强磁性体ΔT异常计算存在的误差进行分析研究.我们首先通过理论模型计算试验,证明常规计算采用的投影关系的ΔT与实际测量的模量差ΔT之间的误差E在磁异常幅值大时是明显存在的,其影响不容忽视.其次,当磁性强且剩磁存在时,投影ΔT曲线及其误差曲线在磁化方向与地磁场方向改变时具有一定的对称性;地磁场T0、磁性体形态(如二度水平圆柱体模型的半径r、柱体埋深R)和磁性参数(如磁化率κ)等参数确定的情况下,最大误差值出现在磁性体正上方,且其大小与磁性参数(κ)和模型体规模(如r/R)之间皆是指数关系;另外,研究还发现ΔT的计算误差曲线的一些其他规律特点,如在各纬度带上,ΔT计算误差的最大值Emax曲线的极值主要分布在中纬度地区;磁异常矢量 T a与地磁场 T 0的夹角θ逐渐变化时,随θ变化Emax曲线的极值分布在θ=90°~120°范围内;当磁异常幅值小于10000 nT时,最大误差近似为磁异常矢量垂直于地磁场方向的测点附近的误差值;另外,磁性体(圆柱体为例)的半径(即尺度)与埋深的比值r/R超过0.5,且磁化率超过0.1SI时误差已达到3.9 nT,磁化率增大与对应的Emax的值呈指数增长特点.因此,我们的研究表明,在强磁性体、磁异常幅值大的数据处理、反演及解释时,现有方法会产生较大的误差,应该基于严格的模量差ΔT,完善相应的处理以及反演方法.     

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.