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.

     

Analytic signal approach and its applicability in environmental magnetic investigations

We investigate the analytic signal method and its applicability in obtaining source locations of compact environmental magnetic objects. Previous investigations have shown that, for two-dimensional magnetic sources, the shape and location of the maxima of the amplitude of the analytic signal (AAS) are independent of the magnetization direction. In this study, we show that the shape of the AAS over magnetic dipole or sphere source is dependent on the direction of magnetization and, consequently, the maxima of the AAS are not always located directly over the dipolar sources. Maximum shift in the horizontal location is obtained for magnetic inclination of 30°. The shifts of the maxima are a function of the source-to-observation distance and they can be up to 30% of the distance. We also present a method of estimating the depths of compact magnetic objects based on the ratio of the AAS of the magnetic anomaly to the AAS of the vertical gradient of the magnetic anomaly. The estimated depths are independent of the magnetization direction. With the help of magnetic anomalies over environmental targets of buried steel drums, we show that the depths can be reliably estimated in most cases. Therefore, the analytic signal approach can be useful in estimating source locations of compact magnetic objects. However, horizontal locations of the targets derived from the maximum values of the AAS must be verified using other techniques.     

A derivative-based interpretation approach to estimating source parameters of simple 2D magnetic sources from Euler deconvolution, the analytic-signal method and analytical expressions of the anomalies

The major advantage of using either the analytic‐signal or the Euler‐deconvolution technique is that we can determine magnetic‐source locations and depths independently of the ambient earth magnetic parameters. In this study, we propose adopting a joint analysis of the analytic signal and Euler deconvolution to estimate the parameters of 2D magnetic sources. The results can avoid solution bias from an inappropriate magnetic datum level and can determine the horizontal locations, depths, structural types (indices), magnetization contrasts and/or structural dips. We have demonstrated the feasibility of the proposed method on 2D synthetic models, such as magnetic contacts (faults), thin dikes and cylinders. However, the method fails to solve the parameters of magnetic sources if there is severe interference between the anomalies of two adjacent magnetic sources.     

基于差分进化算法的磁梯度张量系统误差校正

针对磁梯度张量系统存在单传感器三轴非正交、三轴灵敏度不一致和零偏以及多传感器测量轴非对准误差等问题,本文提出了一种基于改进差分进化算法的误差校正方法.首先,详细描述上述误差并建立数学模型.然后,基于匀强磁场环境中磁梯度张量系统测得的总磁场为定值、同一方向测量轴输出一致、磁梯度张量分量与张量不变量等于零的特点,提出了基于改进差分进化算法的误差参数估计方法.不同于传统的磁梯度张量系统两步校正方法,该方法只需进行一步反演即可实现单传感器误差参数和多传感器非对准误差参数估计.仿真结果表明：与遗传算法和最小二乘拟合方法相比,本文方法具有较高的求解精度和搜索效率,且抗噪能力较强.实测数据校正结果表明,本文方法可以降低磁梯度张量系统误差引起的测量误差,测量精度得到明显改善.

     

磁总场异常垂直梯度三维相关成像

本文提出了磁总场异常垂直梯度三维相关成像方法,用于成像地下等效磁源分布.它首先将地下待成像空间划分为三维规则网格,然后直接计算每个网格节点磁偶板子在观测面理论磁总场异常垂直梯度与实测磁总场异常垂直梯度的互相关,其相关系数值表征等效磁偶极子分布(即磁偶极子发生的概率).理论长方体组合模型数据和实际某矿区磁测资料试验结果表明本文方法计算得到的相关系数值能基本反映地下的磁源分布,且分辨率明显高于磁总场异常三维相关成像的分辨率,也高于基于熵滤波分离异常的磁总场异常三维相关成像的分辨率.     

Depth Estimation of Simple Causative Sources from Gravity Gradient Tensor Invariants and Vertical Component

The gravity gradient tensor (GGT) is deduced from products of second-order derivatives of the gravitational potential. A new method based on the invariants of the GGT has been proposed in this research to interpret gravity data due to sphere, infinite horizontal cylinder and semi-infinite vertical cylinder. The method estimates the depth of these simple causative sources from the multiplication of the maximum of the gravity vertical component by the maximum value of the invariants I ₁ to I ₂ ratio. To show the reliability and correctness of the estimated depths on 3-D models, the method has been tested using theoretical data with and without random noise. In addition, I have applied the method to a field-data example in Texas, USA and the depth obtained by the present method is compared with those published in the literature.     

改进的各向异性标准化方差探测斜磁化磁异常源边界

针对存在强剩磁作用磁化方向不明的磁异常,本项研究探索直接处理斜磁化磁异常的识别,提出了基于磁力梯度张量模的各向异性边界探测方法.首先利用各向异性尺度改进了各向异性标准差的核函数,突出各向异性高斯函数的作用;结合磁力梯度张量模来消弱斜磁化的影响.数值实验模拟了一组复杂磁异常模型,在斜磁化条件下分析该研究方法的边界探测效果.实验表明：改进方法,即磁力梯度张量模的各向异性标准化方差,它可以探测非垂直磁化磁异常的磁源边界;同时指出,改进方法比基于三维解析信号振幅的各向异性标准化方差对磁化方向的依赖性更小.将该方法应用于中国西部某磁铁矿集区的精细探测,在非垂直磁化条件下对实测磁异常直接进行边界探测,获得了较为理想的处理结果.     

TSVD analysis of Euler deconvolution to improve estimating magnetic source parameters: An example from the Åsele area,Sweden

In this paper, I introduce a new approach based on truncated singular value decomposition (TSVD) analysis for improving implementation of grid-based Euler deconvolution with constraints of quasi 2D magnetic sources. I will show that by using TSVD analysis of the gradient matrix of magnetic field anomaly (reduced to pole) for data points located within a square window centered at the maximum of the analytic signal amplitude, we are able to estimate the strike direction and dip angle of 2D structures from the acquired eigenvectors. It is also shown that implementation of the standard grid-based Euler deconvolution can be considerably improved by solving the Euler's homogeneity equation for source location and structural index, simultaneously, using the TSVD method. The dimensionality of the magnetic anomalies can be indicated from the ratio between the smallest and intermediate eigenvalues acquired from the TSVD analysis of the gradient matrix. For 2D magnetic sources, the uncertainty of the estimated source location and structural index is significantly reduced by truncating the smallest eigenvalue.Application of the method is demonstrated on an aeromagnetic data set from the Åsele area in Sweden. The geology of this area is dominated by several dike swarms. For these dolerite dikes, the introduced method has provided useful information of strike directions and dip angles in addition to the estimated source location and structural index.     

Magnetic mapping for the detection and characterization of UXO: Use of multi-sensor fluxgate 3-axis magnetometers and methods of interpretation

Fluxgate vector magnetometers can be powerful instruments in magnetic mapping and in the detection of unexploded ordnance (UXO). Being lightweight and having low power requirements, they allow the development of multi-sensor use. The main problems in using fluxgate magnetometers arise from calibration errors and drift but these can be overcome using a quick and simple method of calibration in the field. This method also has the advantage of compensating permanent and induced magnetic fields generated by magnetized objects carried with the sensors. Measurement accuracy is similar to that obtained with scalar magnetometers. Multi-magnetometer profiling allows direct inversion of raw magnetic data along profiles in order to locate and characterize dipoles typically generated by UXO. The method used is a non-linear inverse procedure that estimates the three coordinates and magnetization vector of the dipole. Application of the technique to both a synthetic case and a field example illustrates the advantages of the method compared with the use of the analytic signal.     

Analytic Expressions for the Gravity Gradient Tensor of 3D Prisms with Depth-Dependent Density

Variable-density sources have been paid more attention in gravity modeling. We conduct the computation of gravity gradient tensor of given mass sources with variable density in this paper. 3D rectangular prisms, as simple building blocks, can be used to approximate well 3D irregular-shaped sources. A polynomial function of depth can represent flexibly the complicated density variations in each prism. Hence, we derive the analytic expressions in closed form for computing all components of the gravity gradient tensor due to a 3D right rectangular prism with an arbitrary-order polynomial density function of depth. The singularity of the expressions is analyzed. The singular points distribute at the corners of the prism or on some of the lines through the edges of the prism in the lower semi-space containing the prism. The expressions are validated, and their numerical stability is also evaluated through numerical tests. The numerical examples with variable-density prism and basin models show that the expressions within their range of numerical stability are superior in computational accuracy and efficiency to the common solution that sums up the effects of a collection of uniform subprisms, and provide an effective method for computing gravity gradient tensor of 3D irregular-shaped sources with complicated density variation. In addition, the tensor computed with variable density is different in magnitude from that with constant density. It demonstrates the importance of the gravity gradient tensor modeling with variable density.     

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.     

全张量磁梯度数据的斜导数特征值边界识别方法研究

本文提出了一种全张量磁梯度数据的斜导数边界识别方法,该方法利用全张量磁梯度数据定义了北向斜导数、东向斜导数和垂向斜导数.模型试验表明,北向和东向斜导数无法有效识别磁性异常体边界,异常形态复杂虚假异常较多,而垂向斜导数在高纬度斜磁化或者垂直磁化条件下可以清晰而准确得识别地质体的边界,具有一定的深度识别能力.与现有磁张量梯度的边界识别方法相比,识别效果好,可以有效均衡不同深度地质体的响应.将上述方法应用于大兴安岭地区实测航磁三分量数据转换得到的全张量数据,获得了研究区浅部磁性体的分布,并与三分量数据进行联合解释,取得良好的地质效果.

     

水平层状大地中任意方向偶极源激发的电磁场

目前已存在多种物理模型用于解释地震前兆电磁异常,不同机制下产生电磁波场的源可等效为不同类型偶极源（磁型/电型）的组合.针对不同偶极源激发的电磁响应特征的研究对地震孕育过程中观测的电磁信号的提取与解释具有重要意义.基于此,本文推导了一套正演算法,可用于研究任意方向（方位角和倾角）、大小和位置的一个或多个偶极源在地壳或岩石圈-大气圈-电离层（Lithosphere-Atmosphere-Ionosphere,LAI）模型中产生的电磁波场的传播特征.基于多源组合,该算法可进一步拓展到线电流源和面电流源的电磁响应的计算.本文给出了水平、垂直和倾斜电偶极源响应计算的实例,并针对不同类型的偶极源激发下的地中、地面以及空间电磁场响应特征进行了初步分析.模拟结果显示,相比于单纯水平或垂直的电偶极源,地中倾斜电偶极源激发的电磁响应在地表的各场量辐射花样虽然仍可反映偶极子的方位角和空间位置,但不再具有对称性,其模式更复杂.本文提出的正演算法可用于地中低频电磁辐射源的正演模拟和反演定位.

     

全张量磁梯度数据解释的均衡边界识别及深度成像技术

全张量磁梯度数据具有高精度、高分辨率、多参量的优点,能更加清晰地刻画地质体的分布特征,综合利用磁张量梯度数据准确地获得地质体水平位置和深度信息是解释的主要目的.磁张量数据的方向解析信号具有减小倾斜磁化干扰的优点,常被用来圈定磁源体的水平位置,但解析信号强度随着地质体埋深的增加急剧衰减,难以有效识别较深的地质体.张量数据均衡边界识别技术,利用不同方向解析信号的比值函数,能有效地均衡不同深度地质体的响应,同时显示不同深度地质体的边界,提高了对较深地质体的分辨率.磁张量数据深度成像技术根据实测张量数据与假定模型张量数据的相关系数来给定地质体的深度,综合利用多参量数据联合反演提高了反演结果的准确性,且无需进行复杂的反演运算,是大数据量张量数据解释的有效方法.理论模型试验证明：磁张量数据均衡边界识别技术可清晰和准确地识别地质体的水平范围,受倾斜磁化干扰小;磁张量数据深度成像技术可准确地获得地质体的深度信息,具有较强的抗噪性.将上述方法应用于铁矿区实测航磁张量梯度数据解释,获得了铁矿体水平分布与埋深,深度结果与张量欧拉反褶积法计算结果一致.

     

Multiridge Euler deconvolution

Potential field interpretation can be carried out using multiscale methods. This class of methods analyses a multiscale data set, which is built by upward continuation of the original data to a number of altitudes conveniently chosen. Euler deconvolution can be cast into this multiscale environment by analysing data along ridges of potential fields, e.g., at those points along lines across scales where the field or its horizontal or vertical derivative respectively is zero. Previous work has shown that Euler equations are notably simplified along any of these ridges. Since a given anomaly may generate one or more ridges we describe in this paper how Euler deconvolution may be used to jointly invert data along all of them, so performing a multiridge Euler deconvolution. The method enjoys the stable and high‐resolution properties of multiscale methods, due to the composite upward continuation/vertical differentiation filter used. Such a physically‐based field transformation can have a positive effect on reducing both high‐wavenumber noise and interference or regional field effects. Multiridge Euler deconvolution can also be applied to the modulus of an analytic signal, gravity/magnetic gradient tensor components or Hilbert transform components. The advantages of using multiridge Euler deconvolution compared to single ridge Euler deconvolution include improved solution clustering, increased number of solutions, improvement of accuracy of the results obtainable from some types of ridges and greater ease in the selection of ridges to invert. The multiscale approach is particularly well suited to deal with non‐ideal sources. In these cases, our strategy is to find the optimal combination of upward continuation altitude range and data differentiation order, such that the field could be sensed as approximately homogeneous and then characterized by a structural index close to an integer value. This allows us to estimate depths related to the top or the centre of the structure.     

21世纪重力与磁法勘探的展望

对21世纪重力与磁法勘探的仪器，数据处理技术，解释理论与方法，应用领域等方面的发展方向进行了分析与展望，发展航空标量，矢量，梯度重力测量和航空全梯度磁力测量，三分量磁力测量，提高综合信息采集能力；开展卫星重磁测量，综合卫星，航空，地面重磁测量资料研究地球结构与构造；发展高精度数据处理技术；重磁异常弱信号的提取，不同深度重磁异常的划分，低纬底变倾角化磁极以及位场面延拓；发展复杂条件下三维重磁场多参数综合反演可视化技术以及快速自动反演技术；探索磁性多参数的应用新领域，充分发挥磁法在环境污染调查中的作用并开拓应用新领域。     

大地电磁全信息资料三维共轭梯度反演研究(英文)

在对张量阻抗数据、倾子数据和共轭梯度算法深入分析的基础上,我们实现了大地电磁全信息资料三维共轭梯度反演算法。基于全信息资料的三维共轭梯度反演研究,探讨了同时利用五个电磁场分量整理得到的大地电磁资料进行三维反演定量解释的方法以及全信息数据在三维反演中的作用。理论模型合成数据的反演结果表明,在三维反演中使用张量阻抗和倾子数据结合的全信息数据的反演结果优于只使用张量阻抗数据(或只使用倾子数据)的反演结果,提高了反演结果的分辨率和可信度。合成数据的反演算例也验证了所实现的大地电磁全信息资料三维共轭梯度反演算法的正确性和稳定性。     

Inversion of geo-magnetic full-tensor gradiometer data

The fast and sensitive SQUID (Superconducting Quantum Interference Device) system, which was developed at IPHT Jena, allows the geo-magnetic prospection of large land areas. The system's simultaneous high-resolution recording of all components of the Earth's magnetic field gradient tensor represents a high-quality data base for precise inversion calculations. Thus, we developed a software tool for the fast and direct inversion of full-tensor data from especially dipole-like sources. Our motivation is to localize buried magnetic objects and inhomogeneities in the underground only by measuring the gradient components at the surface. The application of the algorithm will be shown by two examples, first on a synthetic data set and second on a real data set measured at the IPHT test site with well-defined buried targets.     

Determination of depths to centroids of three-dimensional sources of potential-field anomalies with examples from environmental and geologic applications

A method is developed for determining the depth to the centroid (the geometric center) of ‘semi-compact' sources. The method, called the anomaly attenuation rate (AAR) method, involves computing radial averages of AARs with increasing distances from a range of assumed source centers. For well-isolated magnetic anomalies from ‘semi-compact' sources, the theoretical AARs range from 2 (close to the sources) to 3 (in the far-field region); the corresponding theoretical range of AARs for gravity anomalies is 1 to 2. When the estimated source centroid is incorrect, the AARs either exceed or fall short of the theoretical values. The levelling-off of the far-field AARs near their theoretical maximum values indicates the upper (deeper) bound of the centroid location. Similarly, near-field AARs lower than the theoretical minimum indicate the lower (shallower) bound of the centroid location. It is not always possible to determine usable upper and lower bounds of the centroids because the method depends on characteristics of sources/anomalies and the noise level of the data. For the environmental magnetic examples considered in this study, the determined deeper bounds were within 4% of the true centroid-to-observation distance. For the case of the gravity anomaly from the Bloomfield Pluton, Missouri, USA, determination of only the shallower bound of the centroid location (7 km) was possible. This estimate agrees closely with the centroid of a previously determined three-dimensional model of the Bloomfield Pluton. For satellite magnetic anomalies, the method is appropriate only for high-amplitude, near-circular anomalies due to the inherent low signal-to-noise ratio of satellite magnetic anomalies. Model studies indicate that the AAR method is able to place depths within ±20–30 km of actual center locations from a 400-km observation altitude. Thus, the method may be able to discriminate between upper crustal, lower crustal, and mantle magnetic sources. The results from the prominent Kentucky anomaly are relatively well-resolved (centroid depth 30 km below the Earth's surface). For the Kiruna Magsat anomaly, the deleterious effects from neighboring anomalies make a determination difficult (possible depth could be between 20 and 30 km). The centroid depths are deeper for the Kursk anomaly (40–50 km). These depths may indicate that magnetic anomalies from the near-surface Kursk iron formations (a known contributor) and deep crustal magnetic sources could combine to form the Kursk Magsat anomaly.     

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.