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.     

Hartley变换化极

本文采用一种新颖的积分变换Hartley变换,系统推导了其频率域化极方法,提出在实数空间利用Hartley变换进行磁异常化极.结合现有的低纬度化极方法,讨论了低纬度Hartley变换化极特性,实现低纬度化极.理论模型计算表明建立的Hartley变换化极方法准确、可靠,实际资料处理表明该化极方法具有实用性.     

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.     

等效源法三维随机点位场数据处理和转换

为了实现曲面随机点位场数据的曲面延拓和转换,以磁异常位场数据为例,采用一组磁偶极子作为等效源,置于观测面下方的一个曲面上,把观测磁异常作为这组磁偶极子所产生磁异常的边界条件,通过求解线性方程组的方法反演磁偶极子磁矩的大小,再根据反演结果正演所要计算的磁异常数据,实现了曲面随机点磁异常位场数据的向上延拓、向下延拓、求导以及化极处理.在数据量较大时,为了提高反演计算的速度,把磁异常数据和磁偶极子分成若干小块,再利用各块磁异常数据分别反演该块数据下方磁偶极子的磁矩,并通过迭代计算来逐步取得更准确的反演结果.模型试验表明,磁异常位场数据向上延拓的均方根误差小于±2nT,向下延拓和化极也可以取得较高的精度,所提出的分块处理方法提高了延拓和转换的速度,实际资料处理给出了曲面随机点航磁异常数据向下延拓和化极的一个例子.     

重磁场二维希尔伯特变换——直接解析信号解释方法

通过分析解析信号概念,指出目前重磁场解析信号事实上是重磁场梯度解析信号.在借助解析信号分量满足二维希尔伯特变换关系的基础上,提出重磁场直接解析信号的概念,并阐述重力异常及化极磁异常希尔伯特变换——直接解析信号的含义,并给出基于直接解析信号对位场增强的四种处理方法:直接解析信号模、水平分量模、改进Tilt angle和改...     

The antisymmetric factor method for magnetic reduction to the pole at low latitudes

We analyze the characteristics of the wavenumber-domain factor for magnetic reduction to the pole (RTP) at low latitudes, and then propose a new wavenumber-domain method for RTP at low latitudes, herein called the antisymmetric factor method, based on modification of the RTP factor. The method applies the antisymmetric factor in a given scope of directions centered along the magnetic declination to suppress amplification of the RTP factor, stabilizing the RTP. Meanwhile it utilizes the routine RTP factor in other directions to preserve the effective RTP features. The test on the synthetic data demonstrates that the method is robust and effective. Finally, we use the new method, as well as a variable magnetic inclinations algorithm, to perform RTP on the real data of total magnetic intensity anomalies in the South China Sea, and obtain the reliable RTP anomalies.     

Application of Hilbert‐like transforms for enhanced processing of full tensor magnetic gradient data

Commonly, geomagnetic prospection is performed via scalar magnetometers that measure values of the total magnetic intensity. Recent developments of superconducting quantum interference devices have led to their integration in full tensor magnetic gradiometry systems consisting of planar‐type first‐order gradiometers and magnetometers fabricated in thin‐film technology. With these systems measuring directly the magnetic gradient tensor and field vector, a significantly higher magnetic and spatial resolution of the magnetic maps is yield than those produced via conventional magnetometers. In order to preserve the high data quality in this work, we develop a workflow containing all the necessary steps for generating the gradient tensor and field vector quantities from the raw measurement data up to their integration into high­resolution, low­noise, and artefactless two‐dimensional maps of the magnetic field vector. The gradient tensor components are processed by superposition of the balanced gradiometer signals and rotation into an Earth‐centred Earth‐fixed coordinate frame. As the magnetometers have sensitivity lower than that of gradiometers and the total magnetic intensity is not directly recorded, we employ Hilbert‐like transforms, e.g., integration of the gradient tensor components or the conversion of the total magnetic intensity derived by calibrated magnetometer readings to obtain these values. This can lead to a better interpretation of the measured magnetic anomalies of the Earth's magnetic field that is possible from scalar total magnetic intensity measurements. Our conclusions are drawn from the application of these algorithms on a survey acquired in South Africa containing full tensor magnetic gradiometry data.     

The reliability of aeroplane attitude determination using the main geomagnetic field with application to tensor VLF data analysis

The attitude angles of an aeroplane used for geophysical measurements are necessary in order to calculate field components in a fixed reference frame. In this paper it is shown analytically how the measurement of static magnetic field components can be used to determine the attitude angles. Error analysis shows that when magnetic anomalies are small to moderate (less than 5% of the total field), the attitude angles can be determined to within a few degrees at high latitudes. For a given area the maximum error is linearly related to the magnitude of the anomaly. The technique is illustrated on a tensor VLF data set from an area in Sweden with local magnetic anomalies less than 1% of the regional total magnetic field. Attitude errors propagated into tensor VLF transfer functions are of the same order as their random errors.     

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.     

Use of the Two Dimensional Gabor Filter to Interpret Magnetic Data Over the Marmara Sea, Turkey

Image processing techniques have been frequently used in processing of potential field data. The most important aim in processing potential field data is to figure out the edges of the geological bodies. The Gabor filter was used to determine the discontinuity boundaries of the source bodies causing the magnetic anomalies in this study. The synthetic total magnetic anomaly of three prism bodies with different depths and orientations was used to test the effect of the Gabor filter on the magnetic data. In addition, the Gabor filter was applied on the reduction to the pole aeromagnetic field data of the Marmara Sea and the results were compared with the fault distribution map of the area prepared by various authors.     

Continuous wavelet transform,theoretical aspects and application to aeromagnetic data at the Huanghua Depression,Dagang Oilfield,China

We use the continuous wavelet transform based on complex Morlet wavelets, which has been developed to estimate the source distribution of potential fields. For magnetic anomalies of adjacent sources, they always superimpose upon each other in space and wavenumber, making the identification of magnetic sources problematic. Therefore, a scale normalization factor, a^?n, is introduced on the wavelet coefficients to improve resolution in the scalogram. By theoretical modelling, we set up an approximate linear relationship between the pseudo‐wavenumber and source depth. The influences of background field, random noise and magnetization inclination on the continuous wavelet transform of magnetic anomalies are also discussed and compared with the short‐time Fourier transform results. Synthetic examples indicate that the regional trend has little effect on our method, while the influence of random noise is mainly imposed on shallower sources with higher wavenumbers. The source horizontal position will be affected by the change of magnetization direction, whereas the source depth remains unchanged. After discussing the performance of our method by showing the results of various synthetic tests, we use this method on the aeromagnetic data of the Huanghua depression in central China to define the distribution of volcanic rocks. The spectrum slices in different scales are used to determine horizontal positions of volcanic rocks and their source depths are estimated from the modulus maxima of complex coefficients, which is in good accordance with drilling results.     

Detection of potential fields source boundaries by enhanced horizontal derivative method

A high‐resolution method to image the horizontal boundaries of gravity and magnetic sources is presented (the enhanced horizontal derivative (EHD) method). The EHD is formed by taking the horizontal derivative of a sum of vertical derivatives of increasing order. The location of EHD maxima is used to outline the source boundaries. While for gravity anomalies the method can be applied immediately, magnetic anomalies should be previously reduced to the pole. We found that working on reduced‐to‐the‐pole magnetic anomalies leads to better results than those obtainable by working on magnetic anomalies in dipolar form, even when the magnetization direction parameters are not well estimated. This is confirmed also for other popular methods used to estimate the horizontal location of potential fields source boundaries. The EHD method is highly flexible, and different conditions of signal‐to‐noise ratios and depths‐to‐source can be treated by an appropriate selection of the terms of the summation. A strategy to perform high‐order vertical derivatives is also suggested. This involves both frequency‐ and space‐domain transformations and gives more stable results than the usual Fourier method. The high resolution of the EHD method is demonstrated on a number of synthetic gravity and magnetic fields due to isolated as well as to interfering deep‐seated prismatic sources. The resolving power of this method was tested also by comparing the results with those obtained by another high‐resolution method based on the analytic signal. The success of the EHD method in the definition of the source boundary is due to the fact that it conveys efficiently all the different boundary information contained in any single term of the sum. Application to a magnetic data set of a volcanic area in southern Italy helped to define the probable boundaries of a calderic collapse, marked by a number of magmatic intrusions. Previous interpretations of gravity and magnetic fields suggested a subcircular shape for this caldera, the boundaries of which are imaged with better detail using the EHD method.     

A FAST FOURIER TRANSFORM METHOD FOR RAPID COMPUTATION OF GRAVITY AND MAGNETIC ANOMALIES DUE TO ARBITRARY BODIES*

The spectrum of a magnetic or a gravity anomaly due to a body of a given shape with either homogeneous magnetization or uniform density distribution can be expressed as a product of the Fourier transforms of the source geometry and the Green's function. The transform of the source geometry for any irregularly-shaped body can be accurately determined by representing the body as closely as possible by a number of prismatic bodies. The Green's function is not dependent upon the source geometry. So the analytical expression for its transform remains the same for all causative bodies. It is, therefore, not difficult to obtain the spectrum of an anomaly by multiplying the transform of the source geometry by that of the Green's function. Then the inverse of this spectrum, which yields the anomaly in the space domain, is calculated by using the Fast Fourier Transform algorithm. Many examples show the reliability and accuracy of the method for calculating potential field anomalies.     

南海磁场特征研究

建立客观的磁力ΔT异常,获得可信的磁力ΔZ_⊥异常、居里面成果, 在此基础上开展综合地质地球物理研究,对于解决南海资源等相关的地质、地球物理问题意义重大.本文汇集我国历年在南海取得的磁力实测资料,重新处理、校正、整合,特别是追溯南海周边的国际地磁台的日变资料进行日变改正,形成的南海磁力ΔT异常,其资料品质得到了极大提高.采用全磁纬变倾角化极技术,获得磁力ΔZ_⊥异常,其与实测证实的磁性海山、海岛有非常好的匹配关系,建立起可以直接用于反演处理解释的南海磁力ΔZ_⊥异常.选择磁力ΔZ_⊥异常的小波多尺度分解四阶逼近,采用单一磁性界面反演技术进行深度反演,获得居里面又称磁性底界面.建立了认识、解释南海的磁场基础体系,证实了南海基性岩浆岩分布区与磁力ΔZ_⊥异常的正磁异常高密切相关,区域性的磁力ΔZ_⊥异常负磁异常区可能与居里面深度相关.     

低纬度磁异常化极的伪倾角方法改进

基于改造化极因子的低磁纬度频率域化极方法具有计算速度快、控制参数少、操作简单、化极稳定等优点.本文分析压制因子法和伪倾角法的化极因子特征及其控制参数的影响,在此基础上改进伪倾角法的化极因子,即在磁偏角垂直方向及附近采用伪倾角法化极因子,而在其他方向采用常规频率域化极因子.改进后的伪倾角法既能有效压制磁偏角垂直方向及附近化极因子的放大作用,使得化极稳定,又能减少其他方向有效信号的化极特征的损失,提高化极精度.理论模型数据试验表明本文改进方法有效.利用本文改进方法对南海海域磁总场异常数据进行了变磁倾角化极,得到南海海域化极磁异常,这为研究南海大地构造特征和岩浆活动提供重要的参考资料.     

Research Note: A proposed procedure for ameliorating edge effects in magnetic data transformations

Reduction to pole and other transformations of total field magnetic intensity data are often challenging to perform at low magnetic latitudes, when remanent magnetization exists, and when large topographic relief exists. Several studies have suggested the use of inversion-based equivalent source methods for performing such transformations under those complicating factors. However, there has been little assessment of the importance of erroneous edge effects that occur when fundamental assumptions underlying the transformation procedures are broken. In this work we propose a transformation procedure that utilizes magnetization vector inversion, inversion-based regional field separation and equivalent source inversion on unstructured meshes. We investigated whether edge effects in transformations could be reduced by performing a regional separation procedure prior to equivalent source inversion. We applied our proposed procedure to the transformation of total field magnetic intensity to all three Cartesian magnetic field components using a complicated synthetic example based on a real geological scenario from mineral exploration. While the procedure performed acceptably on this test example, the results could be improved. We pose many questions regarding the various choices and control parameters used throughout the procedure, but we leave the investigation of those questions to future work.     

SOME NEW MAGNETIC TRANSFORMATIONS*

All magnetic transformations are governed by one simple differential relation between the observed and the transformed quantities. A magnetic map for any component, at any location, and for any given direction of magnetization can be converted into one for which any one, two, or all three parameters differ. Three new magnetic transformations are introduced: (i) reduction to equator, (ii) orthogonal reduction, and (iii) elimination of remanence. The first eliminates (or minimizes) the asymmetry and the lateral shift of the measured total field anomalies, exactly as in Baranov's reduction to pole. The second produces perfect asymmetry so that a symmetrical target lies vertically below the zero anomaly point, midway between the maximum and minimum. When remanence is a contributing factor, the direction of resultant magnetization must be known a priori in all cases, except for transformation of one component into another in the same area. Explicit working formulae are presented for reduction to equator and pole, and orthogonal reduction.     

Research on RTP aeromagnetic gradient data and its applicability in different latitudes

Aeromagnetic gradient data needs to be reduced to the pole so that it can be better applied to geological interpretation through theoretical derivation. In this paper, we conduct research on the morphological characteristics of the total and horizontal gradient modules before and after reduction to the pole and design models at different latitudes, with consistent and inconsistent magnetic field direction and geological body magnetization direction. We discuss how to use the total gradient module and horizontal gradient module in geological interpretation. The reduced-to-the-pole (RTP) method is required for the horizontal gradient module method but not for the total gradient module. Finally, the conclusions derived from the theoretical models are verified through analysis of real data. The position determination of a geological body using the total gradient method, gradient data, or total-field data works better without RTP, ensuring data primitive authenticity. However, the horizontal gradient module should be reduced to the pole to determine the boundary of the geological body. Finally, the theoretical model is verified by actual data analysis. Both the total and horizontal gradient methods can be applied to geological interpretation.     

Gravity and magnetic investigation on the distribution of volcanic rocks in the Qinggelidi area,north‐eastern Junggar Basin (north‐west China)

A detailed investigation on the location of magmatic intrusions in the Carboniferous strata of the Qinggelidi area, north‐eastern Junggar Basin, is presented based on the interpretation of gravity and magnetic data constrained by petrophysical data, seismics and surface geology. The wavelet multi‐resolution analysis based on the discrete wavelet transform is adopted to the regional‐residual separation of gravity and magnetic anomalies. A power spectrum analysis is applied to estimate the source depths corresponding to different scales. A comparative analysis on the characteristics of local gravity and magnetic anomalies improved our understanding of volcanic rock distribution in the Carboniferous strata. Generally speaking, in total 75 anomalies are recognized, among which 23 are inferred to be the responses of basalts, diabases and andesites with high density and strong magnetization. Twelve anomalies are assumed to be caused by andesites, rhyolites and volcanic breccias with medium‐low density and high magnetization. There are still five anomalies that are believed to be generated by volcanic tuffs with low density and weak magnetization. Lastly, four cross‐sections in 3D gravity and magnetic modelling are displayed to provide a more thorough image of volcanic rocks in our study area.     

Spherical earth gravity and magnetic anomaly analysis by equivalent point source inversion

To facilitate geologic interpretation of satellite elevation potential field data, analysis techniques are developed and verified in the spherical domain that are commensurate with conventional flat earth methods of potential field interpretation. A powerful approach to the spherical earth problem relates potential field anomalies to a distribution of equivalent point sources by least squares matrix inversion. Linear transformations of the equivalent source field lead to corresponding geoidal anomalies, pseudo-anomalies, vector anomaly components, spatial derivatives, continuations, and differential magnetic pole reductions. A number of examples using 1°-averaged surface free-air gravity anomalies and POGO satellite magnetometer data for the United States, Mexico and Central America illustrate the capabilities of the method.