Direct analytic signal (DAS) method in the interpretation of magnetic data

We presented a new method for interpreting 2D magnetic data, called direct analytic signal (DAS) method, which directly used the analytic signal of magnetic anomaly to compute the depth and the structural index of the source. The DAS method needs only the computation of the first order derivatives of magnetic anomaly, so that the inversion results are more stable than the results obtained by the other existing analytic signal methods. The DAS method is tested on synthetic magnetic data with and without noise, and the DAS method can successfully obtain the depth and the structural index of the source. We also applied the DAS method to interpret a real magnetic data over a shallow geological source whose source parameters are known from closely drilling information, and the inversion results are in accord with the true values.     

Depth and structural index estimation of 2D magnetic source using correlation coefficient of analytic signal

We presented using the correlation coefficient of the analytic signal of real data and the analytic signal of synthetic data generated by the assumed source to estimate the structural index and the depth of the source. First, we assumed that the causative sources are located at different locations in the underground and the structural index of the assumed source is changed from 0 to 3, and then we separately compute the correlation coefficients of the analytic signal of the measured data and the analytic signal of the anomaly generated by each assumed source, the correlation coefficient can get the maximum value when the location and structural index of the assumed source are consistent with the real source. We tested the correlation coefficient method on synthetic noise-free and noise-corrupted magnetic anomalies, and the inversion results indicate that the new method can successfully finish the inversion of magnetic data. We also applied it to measured magnetic data, and we obtain the structural index and the location of the source.     

欧拉反褶积与解析信号相结合的位场反演方法

由于解析信号具有不受(二维)或少受磁化方向影响,能够较好反映磁性体边界的特性,因此受到人们的重视.欧拉反褶积法可以确定场源的位置和深度以及形状因子,具有较强的适应性.因此前人提出将二者相结合的方法.针对前人提出的方法中存在受高频干扰严重的问题,本文提出低阶的欧拉反褶积与解析信号相结合的位场反演方法.本方法在反演中只需计...     

Interpretation of magnetic anomalies by horizontal and vertical derivatives of the analytic signal

Magnetic anomalies are often disturbed by the magnetization direction, so we can’t directly use the original magnetic anomaly to estimate the exact location and geometry of the source. The 2D analytic signal is insensitive to magnetization direction. In this paper, we present an automatic method based on the analytic signal horizontal and vertical derivatives to interpret the magnetic anomaly. We derive a linear equation using the analytic signal properties and we obtain the 2D magnetic body location parameters without giving a priori information. Then we compute the source structural index (expressing the geometry) by the estimated location parameters. The proposed method is demonstrated on synthetic magnetic anomalies with noise. For different models, the proposed technique can both successfully estimate the location parameters and the structural index of the sources and is insensitive to noise. Lastly, we apply it to real magnetic anomalies from China and obtain the distribution of unexploited iron ore. The inversion results are consistent with the parameters of known ore bodies.     

Improved Local Wavenumber Methods in the Interpretation of Potential Field Data

We present two new potential-inversion methods for estimating the depth and the nature (structural index) of the source, which use various combinations of different forms of local wavenumbers and the information about the horizontal location to estimate individually the depth and the nature of a magnetic source. The improved local wavenumber methods only use the horizontal offset and vertical offset of local wavenumbers to estimate the depth and the structural index of the source, so they yield more stable results compared with the results obtained by current methods that require the derivatives of local wavenumbers. Tests conducted with synthetic noise-free and noise-corrupted magnetic data show that the proposed methods can successfully estimate the depth and the nature of the geologic body. However, our methods are sensitive to high-wavenumber noise present in the data, and we reduced the noise effect by upward continuing the noise-corrupted magnetic data. The practical application of the new methods is tested on a real magnetic anomaly over a dike whose source parameters are known and the inversion results are consistent with the true values.     

基于最小反演拟合差的重磁场源深度计算方法

以等效源及位场物性反演为基础,本文提出一种新的求取重磁场源深度的方法.该方法将一层等效源以一定的间隔从浅部向深部移动,并将等效源作为初始模型进行反演,当反演拟合差最小时,停止反演,此时的等效源底深即为所求场源的中心深度.由于仅需要反演一层等效源,比传统的物性反演计算时间大大减少,并且不需要进行深度加权约束.理论模型数据处理结果表明该方法能够获得较准确的场源深度:以长宽比为7.5的薄板模型为例,深度计算误差约为1个点距(25 m);以长宽比为0.5~1.5的厚板模型为例,深度计算误差小于1个点距(25m).将该方法应用于实测航磁梯度数据,计算的磁源中心深度在200~250m之间,钻井资料显示该异常由埋藏深度在200~300m的闪长岩引起,计算结果与钻井资料较吻合.     

Depth and structural index from normalized local wavenumber of 2D magnetic anomalies

Recent improvements in the local wavenumber approach have made it possible to estimate both the depth and model type of buried bodies from magnetic data. However, these improvements require calculation of third‐order derivatives of the magnetic field, which greatly enhances noise. As a result, the improvements are restricted to data of high quality. We present an alternative method to estimate both the depth and model type using the first‐order local wavenumber approach without the need for third‐order derivatives of the field. Our method is based on normalization of the first‐order local wavenumber anomalies and provides a generalized equation to estimate the depth of some 2D magnetic sources regardless of the source structure. Information about the nature of the sources is obtained after the source location has been estimated. The method was tested using synthetic magnetic anomaly data with random noise and using three field examples.     

磁张量梯度数据方向解析信号比值的边界识别和空间位置反演方法

磁张量梯度测量具有高分辨率、多参量的优点,能更准确地描述磁源体的分布特征,在矿产资源勘探中具有广阔的用途.磁异常解析信号具有受倾斜磁化干扰小的特点,且为了增强深部地质体的分辨能力,本文提出磁张量梯度数据的解析信号比值的均衡边界识别及空间位置反演技术.磁张量梯度数据的均衡边界识别方法为不同方向解析信号比值的反正切函数,在降低倾斜磁化干扰的同时能有效地均衡不同深度地质体的响应,提高了对较深地质体的分辨率;空间位置反演技术是建立解析信号比值与地质体位置参数的对应方程,利用解析信号比值与地质体的对应关系作为约束条件来反演获得地质体的水平位置和深度信息,具有无需已知任何先验信息的优势.通过磁性体张量异常试验表明解析信号比值的边界识别方法能清晰和准确地获得不同深度地质体的边界,所建立的反演方程能准确地计算出地质体的范围和深度,具有较高的水平分辨率和精度.将本文方法应用于实测磁张量梯度数据的解释,获得了地下铁矿的分布特征,为区域矿产资源潜力评价提供了翔实的基础资料.     

Interpretation of magnetic data using analytic signal derivatives

This paper develops an automatic method for interpretation of magnetic data using derivatives of the analytic signal. A linear equation is derived to provide source location parameters of a 2D magnetic body without a priori information about the nature of the source. Then using the source location parameters, the nature of the source can be ascertained. The method has been tested using theoretical simulations with random noise for two 2D magnetic models placed at different depths with respect to the observation height. In both cases, the method gave a good estimate for the location and shape of the sources. Good results were obtained on two field data sets.     

基于二阶导数的磁源边界与顶部深度快速反演

为实现磁异常反演,首先提出了磁异常非参数快速反演的概念,即无需提供先验信息.在Nabighian提出的磁场通用梯度公式的基础上,推导实现了基于磁异常垂向二阶导数的非参数快速反演(V2D_depth).它不仅可以获取场源的边界信息,同时可以反演场源的埋深.通过与Tilt_depth方法对比,本文方法计算的场源边界更清晰,反演的深度也更接近真实深度,同时较大程度上克服了Tilt_depth方法受叠加异常的影响.理论模型验证了方法的有效性,并通过准噶尔盆地某区块磁异常数据的处理,提取了受强大的区域背景场掩盖的石炭系火成岩产生的弱异常,突出了构造分区、断裂分布等信息,获取了火成岩的位置及埋深参数,为该区的火成岩油气藏勘探提供了有效的处理途径.     

谱矩方法在磁源体深度反演中的应用研究

谱矩方法可以对数据的表面形貌做较为细致的描述.它以随机过程为理论基础,用各阶谱矩及统计不变量等具体的参数表征表面的几何形态,算术平均顶点曲率是一种基于四阶谱矩的统计不变量.通常,埋深不同的场源所引起的磁异常尺度不同,从曲率的角度来理解即为磁异常曲面的弯曲程度不同.因此,本文应用算术平均顶点曲率提取磁异常的几何信息,并将所提取的信息用于场源深度的反演.理论上推导了基于谱矩的球状磁源体和板状磁源体的反演公式,得到了场源深度与磁异常、曲率之间的关系式.结合理论模型计算验证了方法的有效性,并与欧拉反褶积方法进行对比.与传统的方法相比,该方法快速简单,无需调节参数,且有较好的反演精度.最后,将该方法用于塔里木盆地航磁异常的反演和解释中,反演出的磁源体深度可满足区域磁异常数据分析和解释的要求,为克拉通沉积盆地磁异常源的深度划分提供丰富的信息.     

Depth and shape estimates from simultaneous inversion of magnetic fields and their gradient components using differential similarity transforms

The differential similarity transform of a magnetic anomaly is a linear combination of its intensity and gradient components. This transform is sensitive to the distance between a chosen central point of similarity and the source and depends on the degree of homogeneity of the field. Taking advantage of this property, a new field inversion method resulting in the evaluation of source position and shape type is proposed and implemented. The field gradient components are measured directly in magnetic gradiometry, or they can be calculated from the measured field data. Regional and local linear backgrounds are accounted for by the method. The method can be applied on either regularly or irregularly-spaced data sets, on even or uneven surfaces of observation. The solving of the systems of equations is not necessary. A semi-automated inversion for both location and shape of the sources is implemented. Model and field tests illustrate the effectiveness of the proposed inversion technique for depth and shape estimates.     

An enhanced method for source parameter imaging of magnetic data collected for mineral exploration

We have developed a method for imaging magnetic data collected for mineral exploration to yield the following structural information: depth, model type (structural index) and susceptibility. The active nature of mineral exploration data requires we derive the structural information from a robust quantity: we propose that the first‐ or second‐order analytic‐signal amplitude is suitably stable. The procedure is to normalize the analytic‐signal amplitude by the peak value and then use non‐linear inversion to estimate the depth and the structural index for each anomaly. In our field example, different results are obtained depending on whether we inverted for the first‐ or second‐order analytic‐signal amplitude. This is probably because the two‐dimensional contact, thin sheet or horizontal cylinder models we have assumed are not appropriate. In cases such as these, when our model assumptions are not correct, the results should not be interpreted quantitatively, but they might be useful for giving a qualitative indication of how the structure might vary. With a priori information, it is possible to assume a model type (i.e. set the structural index) and generate estimates of the depth and susceptibility. These data can then be gridded and imaged. If a contact is assumed, the susceptibility contrast is estimated; for the dike model, the susceptibility‐thickness is estimated; for the horizontal cylinder, the susceptibility‐area is estimated. To emphasize that the results are dependent on our assumed model, we advocate prefixing any derived quantity by the term ‘apparent’.     

基于印模法的地面磁电阻率数据三维非线性共轭梯度反演

本文提出了能提高异常体分辨能力,同时得到绝对电导率的地面磁电阻率数据三维反演方法.磁电阻率响应用准直流的低频磁场代替;数值模拟由频率域电场满足的Helmholtz方程出发,采用三维交错网格有限差分法;长直导线源作为发射源,其中源的计算包含在背景场中;结合地面磁电阻率数据各分量的特点,选择y分量进行反演研究;反演采用三维非线性共轭梯度反演技术,为了提高异常体的深度分辨能力,进行迭代重构反演;用印模法对初始模型进行重构,采用的是辅模型在浅部,元模型在深部的组合方式.从合成数据和实际数据的反演结果可以得到以下的认识:(1)由频率域麦克斯韦方程组出发,低频磁场数据反演可以直接得到电导率,而不是相对电导率之比;(2)采用印模法组合初始模型,进行迭代重构反演,可以提高地面磁电阻率数据反演对异常体的分辨能力,确定埋深位置,同时不会丧失对于浅部异常体的分辨能力;(3)在结合印模法的地面磁电阻率数据三维反演中,深部异常体的分辨能力受地表不均匀导电体影响较小;(4)确定印模深度可以采用上一次重构反演结束时的模型变化量,通过相邻两次重构反演结束时的模型变化量之差来确定迭代重构是否终止.因为静磁场与重力场在数学上的相似性,本文的反演方法可以被运用到重力场等位场的地面数据的反演中.     

归一化总水平导数法在位场数据解释中的应用

本文提出归一化总水平导数法,通过对总水平导数进行空间归一化计算实现了异常体水平位置和深度的估计,此外还推导出基于归一化总水平导数的欧拉反褶积法来估算地下地质体的空间位置,两种方法反演结果的相互验证可有效地提高反演结果的可信度.理论模型试验证明空间归一化总水平导数法和归一化总水平导数欧拉反褶积法均能有效地完成异常体的水平位置和深度的估计,所获得的位置参数与理论值相一致.在利用归一化总水平导数法进行磁异常解释时,对数据进行化磁极计算可得到更加准确的结果.将其应用于实际航磁数据的解释,获得了岩脉的大致分布特征.     

Improved tilt-depth method for fast estimation of top and bottom depths of magnetic bodies

The tilt-depth method can be used to make fast estimation of the top depth of magnetic bodies. However, it is unable to estimate bottom depths and its every inversion point only has a single solution. In order to resolve such weaknesses, this paper presents an improved tilt-depth method based on the magnetic anomaly expression of vertical contact with a finite depth extent, which can simultaneously estimate top and bottom depths of magnetic bodies. In addition, multiple characteristic points are selected on the tilt angle map for joint computation to improve reliability of inversion solutions. Two- and threedimensional model tests show that this improved tilt-depth method is effective in inverting buried depths of top and bottom bodies, and has a higher inversion precision for top depths than the conventional method. The improved method is then used to process aeromagnetic data over the Changling Fault Depression in the Songliao Basin, and inversion results of top depths are found to be more accurate for actual top depths of volcanic rocks in two nearby drilled wells than those using the conventional tilt-depth method.     

基于交叉梯度约束的重力、磁法和大地电磁三维联合反演

为了降低单一地球物理方法反演的多解性及受噪声的影响程度,本文围绕重力、磁法和大地电磁法开展了三维联合反演的研究.重、磁采用基于对数障碍法的正则化反演算法,大地电磁使用limited-memory BroydenFletcher-Goldfarb-Shanno(L-BFGS)反演算法,引入交叉梯度函数实现了三种物性结构的相互耦合,最终开发出一套重磁电三维联合反演算法,并实现MPI并行加速计算.通过理论模型算例验证了算法的准确性,结果表明:不论是单棱柱体模型还是组合棱柱体模型,联合反演结果相较单独反演对于异常体的空间形态刻画以及物性数值恢复具有较好的提升;单棱柱体模型算例使得异常体的物性参数(密度、磁化率和电阻率)更加接近于真实的物性参数;组合棱柱体模型的联合反演结果不仅仅消除了围岩物性参数的假异常,而且还增强了异常体边界结构的恢复程度.     

Inversion of elongated magnetic anomalies using magnitude transforms

The calculable magnitudes of the anomalous magnetic field from simple 2D sources and their gradients and Laplacians appear as ratios that can be synthesized in functional forms, corresponding to the different source shapes. Field components and first‐order derivatives are involved in the inversion procedures presented. The structural index and source depth are estimated independently of each other. The applied functions allow magnetic profiles and magnetic maps to be shape‐ and depth‐converted with immediate imaging of the inversion results. The contours of these functions outline elongated loops around the 2.5D anomaly axis on magnetic maps. The width of the loops reflects the depth and structural index N of the source in the scale units of the inverted map. Model and field tests illustrate the effectiveness of this approach for fast automatic inversion of large sets of magnetic data for depth, shape, length and location of simple sources.     

iSPITM— the improved source parameter imaging method

Interpretation of an anomalous magnetic response involves determining the parameters that characterize the source of the anomaly. The depth to the top of the structure is a parameter that is commonly sought, and the Source Parameter Imaging^TM (SPI^TM) method is one way of determining this depth estimate. One advantage of the SPI method is that the depths can be displayed on an image. Typically there can be one image for an assumed contact (fault) model and another image for an assumed dipping thin sheet (dike) model. The depth estimate obtained will depend on the model assumed. An improvement to the source parameter imaging method extends the method to horizontal cylinders and at the same time allows the most appropriate model to be determined automatically. This model can be displayed on an image and the correct depth estimate for each anomaly can also be determined. The depth estimates can therefore be summarized on one map independent of an assumed model. The images generated from synthetic and field data show that the improved SPI method makes the task of interpreting magnetic data significantly easier.     

Euler deconvolution of the analytic signal and its application to magnetic interpretation

Euler deconvolution and the analytic signal are both used for semi‐automatic interpretation of magnetic data. They are used mostly to delineate contacts and obtain rapid source depth estimates. For Euler deconvolution, the quality of the depth estimation depends mainly on the choice of the proper structural index, which is a function of the geometry of the causative bodies. Euler deconvolution applies only to functions that are homogeneous. This is the case for the magnetic field due to contacts, thin dikes and poles. Fortunately, many complex geological structures can be approximated by these simple geometries. In practice, the Euler equation is also solved for a background regional field. For the analytic signal, the model used is generally a contact, although other models, such as a thin dike, can be considered. It can be shown that if a function is homogeneous, its analytic signal is also homogeneous. Deconvolution of the analytic signal is then equivalent to Euler deconvolution of the magnetic field with a background field. However, computation of the analytic signal effectively removes the background field from the data. Consequently, it is possible to solve for both the source location and structural index. Once these parameters are determined, the local dip and the susceptibility contrast can be determined from relationships between the analytic signal and the orthogonal gradients of the magnetic field. The major advantage of this technique is that it allows the automatic identification of the type of source. Implementation of this approach is demonstrated for recent high‐resolution survey data from an Archean granite‐greenstone terrane in northern Ontario, Canada.