A computer program for interpreting vertical magnetic anomalies of spheres and horizontal cylinders

Summary A common computer program for the interpretation of vertical magnetic anomalies of spheres and horizontal cylinders has been developed. The input consists of the observed anomalies noted against their distances measured from an arbitrary point in the profile and a code number for each model. The program is written so that the positions and magnitudes of the maximum and minimum anomalies are located and their ratios and signs are used to define the initial parameters of the model under consideration. The errors resulting from these approximate values are derived and are solved for the increments to be given to the initial values. The process is repeated until the sum of the squares of the errors is less than 0.25% of the sum of the squares of the observed anomalies. The method has been tested on various theoretical examples and the results justify the validity of the programme.     

A different method for interpretation of magnetic anomalies due to 2-D dipping dikes

In this study a new method is presented to determine model parameters from magnetic anomalies caused by dipping dikes. The proposed method is applied by employing only the even component of the anomaly. First, the maximum of the even component is divided to its value at any distance x in order to obtain S1. Then, theoretical even component values are computed for the minimal depth (h) and half-width (b) values. S2 is obtained by dividing their maximum to the value computed for the same distance x. A set of S2 values is calculated by slowly increasing the half-width, and h and b for the S2 closest to S1 are determined. The same procedure is repeated by increasing the depth. The determined b values are plotted against the corresponding values of h. After repeating the process and plotting curves for different distances, it is possible to determine the actual depth and half-width values.     

Magnetic interpretation of long horizontal cylinders using correlation factors between successive least-squares residual anomaly profiles

Procedures are formulated using the correlation factors between successive least-squares residual magnetic anomaly profiles due to long horizontal cylinders for interpreting the three principal anomalies (vertical, horizontal, and total). It is demonstrated that correlation values can be used to determine the depth to the center of the buried structure and the index parameter. Procedures are also formulated to estimate the amplitude coefficient. Two worked examples using theoretical data show the effectiveness of the present method.     

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.     

Fair function minimization for interpretation of magnetic anomalies due to thin dikes, spheres and faults

A new method is proposed to interpret magnetic anomalies due to a thin dike, a sphere, and a fault like structure, where depth, horizontal location, effective magnetization intensity and effective magnetization inclination of a buried structure are simultaneously obtained. The proposed method is based on Fair function minimization and also on stochastic optimization modeling. This new technique was firstly tested on a theoretical synthetic data randomly generated by a chosen statistical distribution from a known model with different random noises components. This mathematical simulation shows a very close agreement between the assumed and the estimated parameters. The applicability and validity of this method are thereafter applied to magnetic anomaly data taken from United States, Australia, India, and Brazil. The agreement between the results obtained by the new method and those obtained by other interpretative methods is good and comparable. Moreover, the depth obtained by such a method is found to be in high accordance with that obtained from drilling information.     

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.     

A simple formula for the second derivative method of interpretation

Summary Second derivative coefficients for various grid systems are derived followingPeters' andElkins' approaches. Two simple formulae, one for three dimensional bodies and the other for two dimensional bodies are also suggested. These utilise the average of the anomalies around a single circle and the anomaly at the central point.All the coefficient sets and the proposed simple formulae are applied to gravity fields of spheres and cylinders. Coefficients ofElkins' type derived with a weightage of 1/r ⁴ to all the circles gave excellent results in both the cases of spheres and cylinders, whereasPeters' coefficients without any weightage to the circles gave reliable results in case of cylinders only. The simple formulae suggested gave more accurate results than any of the above coefficient sets.     

A note on permeability changes in geologic material due to stress

Summary Stress produces framatic changes in fluid permeability of geologic materials. An increase of nearly threefold occurred in granite at high stress, an increase of 20 percent in sandstone, and a hundredfold decrease in compacted sand. Permeability of sand and sandstone did not follow the effective stress law. Flow along joints was very sensitive to effected stress changes, a fourfold change being caused by as little as 1.0 MPa.     

Gravity and magnetic field interpretation based on transformations of horizontal gradients in the VECTOR system

A method of potential field processing based on the transformation of vectors of the total horizontal gradient in windows of various sizes is considered. The gradients are calculated at the centers of triangles, whose vertices are points of observations, as a rule, of gravity and magnetic fields. Averaging of horizontal gradients of the field rather than initial values of the field is the main distinction of this approach from the known methods. This procedure, referred to in this paper as vector scanning of the field, makes it possible to obtain layer distributions of field sources in a 3-D diagram that is a quasi-density model of the study medium within the framework of certain model concepts. The paper presents a model example demonstrating the possibility of separating the fields produced by two sources located on a vertical line and an example illustrating the application of this method to the interpretation of the gravity field in the zone of the geodynamic influence of the Urals.     

Hilbert transform in the interpretation of magnetic anomalies of various components due to a thin infinite dike

The Hilbert transformH(x) applicable to vertical (Z), horizontal (H), and total (T) magnetic anomalies due to a thin dike of infinite depth extent is derived from the generalised expression of magnetic effectF(x). The depth and dip of the dike is extracted by a simple procedure making use ofF(x) andH(x). A modified version of the amplitude of the analytic signal is given to locate the origin. The abscissa of the point of intersection ofF(x) and the discrete Hilbert transformH(1.x) directly yields the depth to the top. An example for each case is considered theoretically to illustrate the process. Applicability of the method is examined on the vertical component of the well-known magnetic anomaly at Kiirunavaara in northern Sweden, originally described by Von Carlheim Gyllenskjold, as well as on total magnetic anomaly of Bensons Mines, U.S.A.     

A note on magnetic modelling with remanence

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.     

A method for the interpretation of magnetic anomalies of dipping doublets

Summary A simple method for the interpretation of the vertical magnetic anomalies of dipping doublets is presented. In the first step, the line integrals of the anomalies along theX direction, which represent the anomalies of a vertical line double are utilised to obtain the depths to the two poles. In the second step, the profile alongY, through the point of intersection of the doublet with theX axis is used to determine the dip of the dipole.     

A note on secular variation of gravity due to non-tidal geodynamic phenomena

Summary Secular non-tidal variations of geopotential and gravity are estimated due to secular decrease of the second zonal geopotential harmonic, secular polar motion and deceleration of the Earth's rotation.

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重磁异常解释的归一化局部波数法

局部波数法是进行重磁数据解释的常用方法之一.本文提出归一化局部波数法,该方法在不需要任何关于地质体信息的前提下能有效地完成异常的反演工作,且给出了不同归一化方式的应用效果.理论模型试验表明归一化局部波数法能准确地完成异常的反演,且通过对比发现其他归一化方式（中值、几何平均和调和平均）的计算结果相对算术平均归一化结果具有更高的分辨率.将该方法应用于实测磁异常的解释,获得了未知地质体的空间位置.     

A simple borehole dilution technique in measuring horizontal ground water flow

Borehole dilution techniques use repeated fluid column profiling after establishment of an initial uniform condition to monitor the rate at which ambient ground water moves into a borehole. Application of the dilution technique in a monitoring well makes it possible to estimate the horizontal Darcy flow velocity of ground water in the aquifer surrounding the borehole. Previous investigators have demonstrated the technique using either relatively concentrated saline solutions or deionized water to produce a fluid column with properties distinctly different from those of local ground water. We present a new dilution technique using the food color Brilliant Blue FCF (Euro code E-133) to mark the fluid column and using a specially constructed photometric sensor to characterize the dilution of this dye over time. The effective application of this technique is documented by two practical examples.     

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.     

Approximation constructions in interpretation problems of gravity and magnetic surveys: A review

Methods of approximation occupy a significant place at the interpretation stage of gravity and magnetic surveys. Two main directions are the approximation of the initial field by an analytic function and the approximation or parametrization of a geological model.