On the use of the autocorrelation method for estimating the depth to the magnetic basement

The depth to the top of magnetic dykes can be estimated from total field aeromagnetic data using the relation between the depth to magnetic sources and the autocorrelation function of magnetic data. By using synthetic anomalies we show that in the ideal case, depth can be determined to an accuracy of 10% or better, when the anomaly sources are two-dimensional dykes. However, the estimated depths depend on the width of the dykes. The estimated depth is about 0.6 times the actual depth to the top of thin dykes, and around the true depth for thick dykes having width-to-depth ratio around 3. The depth is considerably overestimated for very thick dykes (e.g., contacts, which is a special case of the thick dyke). Thus, the autocorrelation method requires that the width-to-depth ratio of the dyke is estimated independently to correctly estimate the depths. Alternatively, it must be assumed that the width-to-depth ratio for the two-dimensional source body is between 1.5 and 4.     

NUMERICAL MODELLING OF A NEW MULTI-FREQUENCY ELECTROMAGNETIC SYSTEM*

The amplitude of the horizontal magnetic field in the ground between two parallel wires, both carrying an alternating current in the same direction, is likely to have a saddle point if the separation between the wires is small and the frequency is low. The amplitude has a maximum in the vertical direction and a minimum in the horizontal. Rectangular geological structures in the ground which are centered between the wires have a varying effect on the magnetic fields at the surface. In general, the vertical magnetic field “crosses over” at the center of the structure. A shallow and flat lying conductor displays a broad flat type of profile when the horizontal magnetic field between the wires is measured. Changing the structure to a narrower but more conducting one at depth will provide a more pointed but still broad profile. The phase of the horizontal field is also increased. When the structure is a thin vertical dyke, the amplitude of the horizontal magnetic field anomaly due to the dyke rapidly decreases as the depth of the dyke is increased. The phase of the horizontal field is less sensitive to changes in depth of the dyke but is more sensitive to the conductivity ratio of the dyke and the half-space. The amplitude of the vertical magnetic field anomaly due to the dyke is only slightly influenced by conductivity contrast or the depth of the dyke. The phase of the vertical magnetic field, however, is strongly influenced by the conductivity contrast, particularly if the conductivity frequency product is greater than hundred. In essence, the field behaves like that of the conventional vertical loop source, but the fields are uniform over much larger areas. This suggests the possibility of using dip angle measurements for rapid reconnaissance.     

A gradient‐ratio method for the semi‐automatic interpretation of gravity map data sets

The application of semi‐automatic interpretation techniques to potential field data can be of significant assistance to a geophysicist. This paper generalizes the magnetic vertical contact model tilt‐depth method to gravity data using a vertical cylinder and buried sphere models. The method computes the ratio of the vertical to the total horizontal derivative of data and then identifies circular contours within it. Given the radius of the contour and the contour value itself, the depth to the source can be determined. The method is applied both to synthetic and gravity data from South Africa. The Matlab source code can be obtained from the author upon request.     

APPLICATION OF A HILBERT TRANSFORM METHOD TO THE INTERPRETATION OF SURFACE-VEHICLE MAGNETIC DATA*

The development of an alkali vapour vehicle borne magnetometer providing very high resolution and a high sampling rate has called for reconsideration of interpretation procedures. With continuous profiling at ground level, the close proximity to near surface structures requires that the precise interpretation of geological boundaries be of paramount importance. Rapid digital recording also demands efficient data processing. Both these requirements can be met by the method described. Essentially the method reduces to a simple Hilbert transform of the magnetic profile. The calculation provides an extremely well defined position of the contact and accurate specification of the dip, strike, depth of overburden, and magnetic susceptibility parameters. Particular advantages are tolerance to high frequency noise, independence from a predetermined origin and baseline, and freedom from subjective judgements.     

The interpretation of the generalised derivative operator

The Generalised Derivative Operator is an image‐processing tool for the enhancement of potential field data. It produces an amplitude‐balanced image of the derivative of a potential field in any direction in three‐dimensional space. This paper shows how, by using the correct inclination angle ?, the Generalised Derivative Operator can be used to produce images where its maxima/minima lie directly over dipping contacts and thin dykes with arbitrary magnetisation vectors. The dip of contacts and dykes can be found by varying ? until a symmetrical result is obtained (in the absence of unknown remanent magnetisation). Furthermore, the width of the peak of the Generalised Derivative Operator can then be used to determine the depth of the contact or dyke.     

Diffraction imaging by prestack reverse‐time migration in the dip‐angle domain

Prestack image volumes may be decomposed into specular and non‐specular parts by filters defined in the dip‐angle domain. For space‐shift extended image volumes, the dip‐angle decomposition is derived via local Radon transform in depth and midpoint coordinates, followed by an averaging over space‐shifts. We propose to employ prestack space‐shift extended reverse‐time migration and dip‐angle decomposition for imaging small‐scale structural elements, considered as seismic diffractors, in models with arbitrary complexity. A suitable design of a specularity filter in the dip‐angle domain rejects the dominant reflectors and enhances diffractors and other non‐specular image content. The filter exploits a clear discrimination in dip between specular reflections and diffractions. The former are stationary at the specular dip, whereas the latter are non‐stationary without a preferred dip direction. While the filtered image volume features other than the diffractor images (for example, noise and truncation artefacts are also present), synthetic and field data examples suggest that diffractors tend to dominate and are readily recognisable. Averaging over space‐shifts in the filter construction makes the reflectors? rejection robust against migration velocity errors. Another consequence of the space‐shift extension and its angle‐domain transforms is the possibility of exploring the image in a multiple set of common‐image gathers. The filtered diffractions may be analysed simultaneously in space‐shift, scattering‐angle, and dip‐angle image gathers by means of a single migration job. The deliverables of our method obviously enrich the processed material on the interpreter's desk. We expect them to further supplement our understanding of the Earth's interior.     

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.     

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.     

叠前逆时深度偏移中的激发时间成像条件

与其他偏移方法相比,逆时偏移基于精确的波动方程而不是对其近似,用时间外推来代替深度外推.因此,它具有良好的精度,不受地下构造倾角和介质横向速度变化的限制.激发时间成像条件的求取是叠前逆时偏移的难点之一,本文采用求解程函方程的方法得到地下各点的初至波走时,以此作为叠前逆时偏移的成像条件.基于任意矩形网格和局部平面波前近似的有限差分初至波走时计算方法精度较高并适用于强纵横向变速的复杂介质.试算结果表明,在复杂介质模型中利用叠前逆时深度偏移收到了很好的成像效果.     

Remanence correction in magnetic interpretation with the infinitely deep plate model

Summary Conditions are given under which two thick plates, differing in dip, apparent susceptibility, and remanence, will produce similar magnetic anomalies. From these conditions correction formulae are developed. Using these formulae the dip and susceptibility of a plate with remanent magnetization can be obtained from those of non-remanent plate. An interpretation procedure is suggested where the magnetic anomaly is first interpreted by means of a plate without remanence, dip and apparent susceptibility are then estimated by using the correction formulae developed. Thickness, position and depth of the plate are unaffected by the remanence correction procedure. The procedure is independent of the field component measured.     

瞬变电磁法深度探测正演模拟研究

针对当前瞬变电磁法探测能力有限的问题,利用一次磁场理论公式,分析相同磁矩下、不同发射线圈一次磁场分布及衰减规律,从而确定其信号深度影响范围;对水平层状介质相同磁矩下、不同发射线圈的二次场进行数值模拟,采用Guptasarma和Singh滤波算法及余弦变换法,利用均匀半空间解析公式进行验证,并对不同正演模型结果进行分析,总结发射磁矩决定探测深度大小。对磁矩相同条件下产生的结果数据进行拟合,得出有效探测深度与线圈边长2倍相当的结论,可为野外矿井生产与工程勘探提供施工布置与定量解释的指导依据,从而提高野外工作效率。     

Analysis of magnetic data over part of the Younger Granite Province of Nigeria

The results of a magnetic study of part of the Younger Granite Province of Nigeria are presented here. Spectral analysis of the magnetic anomalies over the area has been carried out in an effort to estimate the depth to magnetic sources. Average magnetic source depth of 286 m has been obtained for the area and this is thought to be related to the depth to the top of the main anomalous structures in the area. Observed magnetic anomaly profiels taken across the area have been interpreted in terms of arbitrarily shaped bodies—whose existence was confirmed by 3-D Hilbert transformation-using nonlinear optimization techniques. The modelled bodies occur at depths of 200–760 m and have magnetizations of 0.29–0.47 A/m. The results from the analysis of the magnetic field are discussed in relation to the results from previous gravity studies over the area and the mode of emplacement of the Younger Granites.     

Data‐driven time–frequency analysis of seismic data using non‐stationary Prony method

Empirical mode decomposition aims to decompose the input signal into a small number of components named intrinsic mode functions with slowly varying amplitudes and frequencies. In spite of its simplicity and usefulness, however, empirical mode decomposition lacks solid mathematical foundation. In this paper, we describe a method to extract the intrinsic mode functions of the input signal using non‐stationary Prony method. The proposed method captures the philosophy of the empirical mode decomposition but uses a different method to compute the intrinsic mode functions. Having the intrinsic mode functions obtained, we then compute the spectrum of the input signal using Hilbert transform. Synthetic and field data validate that the proposed method can correctly compute the spectrum of the input signal and could be used in seismic data analysis to facilitate interpretation.     

基于离散余弦变换（DCT）的化磁极方法

针对提高磁异常化磁极的质量问题,提出基于离散余弦变换(DCT)的化磁极方法.以位场余弦变换谱分析为基础,从理论上推导了基于DCT的二度和三度体总场磁异常化磁极转换公式.在倾斜板状体模型实验中,化磁极误差小于0.001 nT,具有较高的精度;在单球体及多球体模型实验中,采用基于DCT的化磁极方法在5.倾斜磁化时就可以取得较好的化磁极结果,15°时化磁极的效果更加明显,其等值线的形态、幅值以及所反映的磁性体的水平位置都得到较好的恢复,这说明,采用本文方法进行化磁极时,可以取得较好的效果.     

High‐accuracy practical spline‐based 3D and 2D integral transformations in potential‐field geophysics

Potential, potential field and potential‐field gradient data are supplemental to each other for resolving sources of interest in both exploration and solid Earth studies. We propose flexible high‐accuracy practical techniques to perform 3D and 2D integral transformations from potential field components to potential and from potential‐field gradient components to potential field components in the space domain using cubic B‐splines. The spline techniques are applicable to either uniform or non‐uniform rectangular grids for the 3D case, and applicable to either regular or irregular grids for the 2D case. The spline‐based indefinite integrations can be computed at any point in the computational domain. In our synthetic 3D gravity and magnetic transformation examples, we show that the spline techniques are substantially more accurate than the Fourier transform techniques, and demonstrate that harmonicity is confirmed substantially better for the spline method than the Fourier transform method and that spline‐based integration and differentiation are invertible. The cost of the increase in accuracy is an increase in computing time. Our real data examples of 3D transformations show that the spline‐based results agree substantially better or better with the observed data than do the Fourier‐based results. The spline techniques would therefore be very useful for data quality control through comparisons of the computed and observed components. If certain desired components of the potential field or gradient data are not measured, they can be obtained using the spline‐based transformations as alternatives to the Fourier transform techniques.     

Estimating magnetic dike parameters using a non‐linear constrained inversion technique: an example from the Särna area,west central Sweden

In this paper, we describe a non‐linear constrained inversion technique for 2D interpretation of high resolution magnetic field data along flight lines using a simple dike model. We first estimate the strike direction of a quasi 2D structure based on the eigenvector corresponding to the minimum eigenvalue of the pseudogravity gradient tensor derived from gridded, low‐pass filtered magnetic field anomalies, assuming that the magnetization direction is known. Then the measured magnetic field can be transformed into the strike coordinate system and all magnetic dike parameters – horizontal position, depth to the top, dip angle, width and susceptibility contrast – can be estimated by non‐linear least squares inversion of the high resolution magnetic field data along the flight lines. We use the Levenberg‐Marquardt algorithm together with the trust‐region‐reflective method enabling users to define inequality constraints on model parameters such that the estimated parameters are always in a trust region. Assuming that the maximum of the calculated g_zz (vertical gradient of the pseudogravity field) is approximately located above the causative body, data points enclosed by a window, along the profile, centred at the maximum of g_zz are used in the inversion scheme for estimating the dike parameters. The size of the window is increased until it exceeds a predefined limit. Then the solution corresponding to the minimum data fit error is chosen as the most reliable one. Using synthetic data we study the effect of random noise and interfering sources on the estimated models and we apply our method to a new aeromagnetic data set from the Särna area, west central Sweden including constraints from laboratory measurements on rock samples from the area.     

ACCURATE DETERMINATION OF THE DIP ANGLE OF A GEOLOGICAL CONTACT USING THE GRAVITY METHOD*

From a gravity profile over a truncated horizontal plate, the horizontal derivative and, by means of the Hilbert Transform, the vertical derivative are obtained. When the horizontal derivative is plotted against the vertical derivative, the axis of symmetry of the resulting curve is inclined at the angle of dip of the face of the truncated plate. The depths to the upper and lower surfaces of the plate can be obtained uniquely from the symmetrical figure. Because of the derivatives being used, the method avoids the difficulties which arise from other methods of interpretation which depend upon a knowledge of the position of the origin of the gravity field data. The entire procedure for interpretation can be accommodated on a programmable calculator. An illustrative example is given.     

Magnetic basement: gravity‐guided magnetic source depth analysis and interpretation

We present a new integrated approach to the interpretation of magnetic basement that is based on recognition of characteristic patterns in distributions and alignments of magnetic source depth solutions above and below the surface of magnetic basement. This approach integrates a quantitative analysis of depth solutions, obtained by 2D Werner deconvolution of the magnetic data, with a qualitative evaluation of the Bouguer gravity anomalies. The crystalline/metamorphic basement and sedimentary cover have different origins, tectonic histories, lithologies and magnetic properties. These differences result in different geometries of magnetic sources associated with faults, fracture zones, igneous intrusions, erosional truncations, subcrop edges and other structural discontinuities. Properly tuned, 2D Werner deconvolution is able to resolve the intra‐sedimentary and intra‐basement magnetic source geometries into distinctly different distributions and alignments of calculated depth solutions. An empirical set of criteria, basement indicators, was developed for identification and correlation of the basement surface. The ambiguity of basement correlation with limited or non‐existent well control, which is common for onshore frontier and offshore explorations, can be reduced by incorporating the Bouguer gravity data into the process of correlation.     

海底电性源频率域CSEM勘探建模及水深影响分析

为了探索我国海域油气和水合物等高阻目标体CSEM勘探的可行性和方法技术,本文研究了在海水中水平电性源激励下有限水深海洋地电模型的频率域电磁响应,为进一步的1D和3D仿真计算奠定了理论基础.在推导电磁响应公式时,首先给出了各层介质的Lorentz势,然后根据Coulomb势与Lorentz势的关系,得到了各层介质的Coulomb势.各层介质中的电磁场均可以由Lorentz势或者Coulomb势计算得到,但在有限元计算时Coulomb势具有优势.长导线源的电磁场和势函数可以由电偶源的电磁场和势函数沿导线长度积分得到.文中具体给出了海水中水平电偶源和长导线源在海水层的电磁场公式,并根据该公式计算了不同水深环境下海底表面的电磁场分布,分析了海水深度对海底油气储层电磁异常的影响.结果表明,随着水深减小,异常幅度和形态特征发生明显变化.当水深很浅时(如50 m),只有同线方向的E_x和E_z两个电场分量存在明显异常.最后,以两个已知海底油田为例,计算了不同水深环境下可观测到的电场异常,展示了电性源频率域CSEM在海底勘探中(包括浅海环境)的良好应用前景.对于该方法实用化过程中还需进一步解决的问题,文中结尾部分也进行了初步探讨.     

Magnetic study of the dolerite dyke near Amarpur,Dhanbad (Bihar)

Summary The dolerite dyke of post-lower Gondwana age reported earlier by the authors [5]²) has been taken for detailed magnetic study. Seven magnetic traverses have been taken across the dyke using Schmidt vertical force variometer. Negative anomalies varying from 1400 to 2200 gammas have been observed. Magnetic susceptibility of samples from the dyke has been determined on both cores and crushed material, using the Model MS-3 susceptibility bridge. The average susceptibility of 20 samples has been found to be 1930x10^–6 C.G.S. units. Direction and intensity of remanence on 10 oriented samples have been determined by an Astatic magnetometer. The average intensity of remanence has been found to be 3.13x10^–3 C.G.S. units and the average direction has a declination of 323° and inclination-68° (up dip). The Koenigsberger ratio varies from 1.6 to 5.6. The high negative magnetic anomalies have been explained in terms of remance-that more than 80% of the anomaly is due to remance and that negative anomalies are due to negative inclination of remanent direction of the rocks. The magnetic direction for the dyke gave the position for Dhanbad as 51° south latitude in Jurassic period. This is in conformity with the deductions made by other workers from the palaeomagnetic studies of the Deccan and Rajmahal traps. The virtual geomagnetic pole in Jurassic period as deduced from the palaeomagnetism of the dyke has a position of latitude 8 1/2°N and longitude 71°W, in the southern Carribean. On palaeomagnetic evidence this dyke has been correlated with Rajmahal traps of eastern Bihar.