Three direction analytical signal analysis method of magnetic gradient tensor and application in the interpretation

Compared to conventional magnetic data,magnetic gradient tensor data contain more high-frequency signal components,which can better describe the features of geological bodies.The directional analytic signal of the magnetic gradient tensor is not easily interfered from the tilting magnetization,but it can infer the range of the fi eld source more accurately.However,the analytic signal strength decays faster with depth,making it diffi cult to identify deep fi eld sources.Balanced-boundary recognition can eff ectively overcome this disadvantage.We present here a balanced-boundary identifi cation technique based on the normalization of three-directional analytic signals from aeromagnetic gradient tensor data.This method can eff ectively prevent the fast attenuation of analytic signals.We also derive an Euler inversion algorithm of three-directional analytic signal derivative.By combining magnetic-anomaly model testing with the traditional magnetic anomaly interpretation method,we show that the boundary-recognition technology based on a magnetic gradient tensor analytic signal has a greater advantage in identifying the boundaries of the geological body and can better refl ect shallow anomalies.The characteristics of the Euler equation based on the magnetic anomaly direction to resolve the signal derivative have better convergence,and the obtained solution is more concentrated,which can obtain the depth and horizontal range information of the geological body more accurately.Applying the above method to the measured magneticanomaly gradient data from Baoding area,more accurate fi eld source information is obtained,which shows the feasibility of applying this method to geological interpretations.

Fast 3D forward modeling of the magnetic field and gradient tensor on an undulated surface

Magnetic field gradient tensor technique provides abundant data for delicate inversion of subsurface magnetic susceptibility distribution. Large scale magnetic data inversion imaging requires high speed and accuracy for forward modeling. For arbitrarily distributed susceptibility data on an undulated surface, we propose a fast 3D forward modeling method in the wavenumber domain based on(1) the wavenumber-domain expression of the prism combination model and the Gauss–FFT algorithm and(2) cubic spline interpolation. We apply the proposed 3D forward modeling method to synthetic data and use weighting coefficients in the wavenumber domain to improve the modeling for multiple observation surfaces, and also demonstrate the accuracy and efficiency of the proposed method.

Calculation and correction of magnetic object positioning error caused by magnetic field gradient tensor measurement

Magnetic field gradient tensor measurement is an important technique to obtain position information of magnetic objects. When using magnetic field sensors to measure magnetic field gradient as the coefficients of tensor, field differentiation is generally approximated by field difference. As a result, magnetic objects positioning by magnetic field gradient tensor measurement always involves an inherent error caused by sensor sizes, leading to a reduction in detectable distance and detectable angle. In this paper, the inherent positioning error caused by magnetic field gradient tensor measurement is calculated and corrected by iterations based on the systematic position error distribution patterns. The results show that, the detectable distance range and the angle range of an ac magnetic object（2.44 Am^2@1 kHz） can be increased from（0.45 m, 0.75 m）,（0？, 25？） to（0.30 m, 0.80 m）,（0？,80？）, respectively.

Full magnetic gradient tensor from triaxial aeromagnetic gradient measurements:Calculation and application

The full magnetic gradient tensor （MGT） refers to the spatial change rate of the three field components of the geomagnetic field vector along three mutually orthogonal axes. The tensor is of use to geological mapping, resources exploration, magnetic navigation, and others. However, it is very difficult to measure the full magnetic tensor gradient using existing engineering technology. We present a method to use triaxial aeromagnetic gradient measurements for deriving the full MGT. The method uses the triaxial gradient data and makes full use of the variation of the magnetic anomaly modulus in three dimensions to obtain a self-consistent magnetic tensor gradient. Numerical simulations show that the full MGT data obtained with the proposed method are of high precision and satisfy the requirements of data processing. We selected triaxial aeromagnetic gradient data from the Hebei Province for calculating the full MGT. Data processing shows that using triaxial tensor gradient data allows to take advantage of the spatial rate of change of the total field in three dimensions and suppresses part of the independent noise in the aeromagnetic gradient. The calculated tensor components have improved resolution, and the transformed full tensor gradient satisfies the requirement of geological mapping and interpretation.

Forward Modeling of Gravity,Gravity Gradients,and Magnetic Anomalies due to Complex Bodies

On the basis of the results of improved analytical expression of computation of gravity anomalies due to a homogeneous polyhedral body composed of polygonal facets, and applying the forward theory with the coordinate transformation of vectors and tensors, we deduced both the analytical expressions for gravity gradient tensors and for magnetic anomalies of a polygon, and obtained new analytical expressions for computing vertical gradients of gravity anomalies and vertical component of magnetic anomalies caused by a polyhedral body. And also we developed explicitly the complete unified expressions for the calculation of gravity anomalies, gravity gradient, and magnetic anomalies due to the homogeneous polyhedron. Furthermore, we deduced new analytical expressions for computing vertical gradients of gravity anomalies due to a finite rectangular prism by applying the newly obtained expressions for gravity gradient tensors due to a polyhedral target body. Comparison with forward calculation of models shows the correctness of these new expressions. It will reduce forward calculation time of gravity-magnetic anomalies and improve computational efficiency by applying our unified expressions for joint forward modeling of gravity-magnetic anomalies due to homogeneous polyhedral bodies.

Magnetic susceptibility inversion method with full tensor gradient data using low-temperature SQUIDs

Full tensor magnetic gradient measurements are available nowadays. These are essential for determining magnetization parameters in deep layers. Using full or partial tensor magnetic gradient measurements to determine the subsurface properties, e.g., magnetic susceptibility, is an inverse problem. Inversion using total magnetic intensity data is a traditional way.Because of di culty in obtaining the practical full tensor magnetic gradient data, the corresponding inversion results are not so widely reported. With the development of superconducting quantum interference devices(SQUIDs), we can acquire the full tensor magnetic gradient data through field measurements. In this paper, we study the inverse problem of retrieving magnetic susceptibility with the field data using our designed low-temperature SQUIDs. The solving methodology based on sparse regularization and an alternating directions method of multipliers is established. Numerical and field data experiments are performed to show the feasibility of our algorithm.

Understanding the Meaning of the Positive Bouguer Anomaly of Waza (Northernmost Cameroon, Central Africa)

Gravity and magnetic data were analyzed in conjunction with available geological data to determine the origin of observed positive gravity anomaly at Waza and its possible relationship to mafic intrusions. The data analysis includes the construction of a Bouguer gravity anomaly, isostatic residual gravity anomaly, total magnetic gradient and Euler solutions maps, and two and one-half dimensional gravity models. A positive gravity anomaly that occurs in Waza has amplitude of 35 mGal and can be separated into two parts. The top of the disturbing body causing the anomaly cannot be deeper than 4 km. We believe the anomaly is probably caused by a body of basaltic rocks lying at the upper surface of the Precambrian basement and originate from a self-propagating disturbance of magmatic loads on a pre-existing zone of lithospheric weakness. Melt migration might have been aided by tectonic and flexural stresses, such that the intrusion is limited in extent to the melting region of the plume and did not reach the surface. The model calculated to satisfy the observed anomaly consists of a 2.5 Km-thick slab underlain by a 10.5 km deep column. This model is interpreted to represent a sheet or saucer-like mafic intrusion that has a thick deep feeder. Detailed geophysical studies would be necessary to locate any possible economic occurrences.

基于伪磁梯度张量混合方向tilt梯度的磁源定位方法及其应用:以内蒙古塔木素铀矿床为例

斜磁化磁源的准确定位是磁法勘探有效圈定场源分布及划分断裂构造的重要依据.但受磁化方向影响,总磁异常与地质体分布并无明显对应关系.为此,本文从总磁异常垂向积分出发,推导出了伪磁梯度张量,定义了伪磁梯度张量的混合方向tilt梯度及混合方向解析信号振幅,提出了基于伪磁梯度张量混合方向tilt梯度水平导数组合的场源定位方法.模型试验表明,相对于解析信号振幅、tilt梯度的总水平导数及方向tilt梯度的总水平导数模这3种受磁化方向影响较小的方法,本文提出的磁源定位方法能够更有效地反映出不同磁化方向的磁源位置,具有更强的识别能力和定位精度.在内蒙古塔木素铀矿床的航磁资料应用中,新方法较好地展示出了已知断裂带的展布及出露岩浆岩的分布,同时有效地提取了塔木素铀矿床上方的弱磁异常信息,处理结果为研究区圈定隐伏岩体、划分隐伏断裂及扩大铀矿找矿靶区提供了依据.

基于磁梯度张量的滑坡监测方法

滑坡监测是滑坡防治的有效技术手段,针对钻孔测斜仪在滑坡深部发生大位移时失效的问题,提出一种基于磁梯度张量的滑坡监测方法。该方法以磁梯度张量理论为基础,使用了十字形阵列进行监测,通过测得的磁感应强度三分量得到轴心的梯度值,再根据反演计算出目标磁源的空间坐标,通过实验验证了该方法的可行性。在测量前将磁传感器阵列固定并计算偏离角,之后使永磁体按照矩形轨迹缓慢运动,并选取一定的测量点验证了该方法的精度,三轴平均绝对误差在0.1m以内,三轴最大误差在0.2m以内。最后分析了该方法存在误差的原因。

基于归一化磁源强度的磁目标实时定位方法

标量三角剖分与测距(STAR)方法利用磁梯度收缩特性实现运动状态下对单个磁偶极子目标的实时定位,且对运动平台的姿态不敏感。然而,磁梯度收缩量(C_(T))引入的非球面误差会限制其定位精度。针对该问题,提出了一种新的磁偶极子目标线性定位方法,利用归一化磁源强度(NSS)代替C_(T),消除了非球面误差的影响。为了分析该方法对不同方位磁目标的定位性能,建立了全向仿真分析模型。仿真结果表明,该方法的实时性与STAR方法相当,在标准差为10 nT的高斯白噪声影响下与STAR方法的最大定位误差分别为0.18 m与1.5 m。现场实验结果表明,当探测距离为1.284 m时,该方法在纬线轨迹上的平均定位误差仅为0.094 m,比传统STAR方法低56.7%;在经线轨迹上的平均定位误差为0.097 m,比传统STAR方法低30.7%。

拖曳式海洋三分量磁力梯度仪的数据处理方法与应用

拖曳式海洋三分量磁力梯度仪能够同时获得地磁三分量和磁力梯度数据,与传统的拖曳式总场磁力仪相比具有降低船磁干扰和抵抗地磁日变影响等优点,也存在灵敏度误差、零点偏移误差、正交性误差和位置误差等校准处理的难点。在实际航次中用拖曳式海洋三分量磁力梯度仪实测得到一条剖面数据,经校准后与G880磁力仪重复线测量的地磁总场数据进行外符合精度评价,表明其具有较高的稳定性和可靠性。根据三分量磁力梯度数据计算得到其张量不变量以及磁边界走向图,并结合欧拉反褶积计算,对测线上的磁源体进行了有效识别和解释。结果显示拖曳式海洋三分量磁力梯度仪能够有效获得地磁总场、分量及梯度等多参量信息,可为海洋地磁场测量提供更有效的技术手段。

基于归一化特征值的重磁数据边界识别方法及其在西藏古堆地热勘探中的应用

基于重磁数据的地质体边界识别是地球物理数据解释的重要内容。随着重磁梯度张量测量技术的不断发展,基于梯度张量数据圈定地质体构造边界位置的方法也在不断发展。本文定义一种基于梯度张量特征值的归一化边界识别滤波器,可同时进行不同深度目标体的边界位置圈定。为验证本文方法的有效性,将建立方法应用于合成的重磁数据中,相比于传统边界识别滤波器,本文滤波器具有更高的水平分辨率和精度,并且在正负叠加异常的试验中,可有效地避免虚假边界的产生。最后,将归一化特征值边界识别滤波器应用于西藏古堆地热田的地质构造解释,结果表明,基于特征值的边界圈定方法能够更准确地显示地质构造的边界位置,发现更多地质体构造细节特征。

基于改进梯度下降算法优化的磁梯度张量组合不变量算法的管道缺陷边缘识别模型

针对油气管道磁记忆检测受方向影响较大且缺陷边缘精确识别困难的问题,提出了一种基于改进梯度下降算法(MGD)优化的磁梯度张量组合不变量算法模型,用于管道缺陷边缘的精确识别。以L245N管线钢为试验材料,预制不同深度、不同直径的圆孔状缺陷,设计磁梯度张量测量系统,结合TSC-5M-32型磁记忆仪进行检测实验,获得管道的磁梯度张量矩阵。为克服检测方向对磁记忆信号的影响,分别提取磁梯度张量第二、第三不变量I_(1)、I_(2),进一步考虑这两种不变量在缺陷边缘处易出现模糊,根据Cardano公式对两种不变量进行改进,并分别设置权值a、b进行叠加获得组合不变量I,利用分数阶求导改进梯度下降算法确定最优权值,建立管道缺陷边缘磁记忆识别模型。研究结果表明:该模型对缺陷边缘识别平均相对误差为3.59%,最大相对误差为6%,为实际工程中管道缺陷边缘精准识别提供了可行办法。

空间—波数域二维强磁场及其梯度张量数值模拟研究

基于磁位泊松方程提出了一种空间—波数混合域二维数值模拟方法。该方法将二维强磁性体磁位满足的偏微分方程通过一维傅里叶变换转化为不同波数之间相互独立的常微分方程,即将二维数值模拟问题转换为一维数值模拟问题,并利用一维有限元法进行求解,可大大降低存储需求和计算量。对求得的强磁场利用紧算子进行迭代以获得高精度近似解。算法中保留垂向为空间域,可根据需求对网格进行灵活剖分,有利于复杂条件下的模拟。另外,不同波数之间常微分方程相互独立,具有较好的并行性。算法充分利用了傅里叶变换的快速性和迭代算法的稳定性,实现了强磁场及其梯度张量的二维数值模拟。设计三个模型(水平地形下的圆柱体模型、棱柱体模型及起伏地形模型)进行计算,对文中方法数值解与解析解、COMSOL软件所得的数值解进行对比,结果表明该算法计算速度快、精度高,适用于起伏地形条件下的数值计算。

空间自适应方向全变分地震数据去噪模型

随着我国油气勘探工作的不断推进,地震勘探面临着重大挑战。受到复杂的勘探环境、采集方式、检波器灵敏度等因素的影响,野外采集的地震数据中往往混杂着大量随机噪声,导致后续地震数据处理的保真度、信噪比和分辨率降低,并且最终影响地质解释的精确性、可靠性。为了突破传统地震数据处理问题的局限性,提出了一种用于地震数据随机噪声压制的空间自适应方向全变分正则化模型。首先,针对地震反射同相轴具有空间变化的方向性和倾角计算抗噪性差的问题,提出了基于梯度结构张量的空变倾角逐点估计公式来获取同相轴的方向信息;然后,建立空间自适应方向全变分地震数据去噪模型,并采用优化最小化算法求解模型;最后,讨论了该模型的参数选取方法,将合成地震数据和实际地震数据的去噪结果与同类方法进行比较。实验结果表明,所提出的模型不但能较好地提高地震剖面的垂直分辨率和同相轴的横向连续性,而且在提高信噪比的同时能够保留更多的地质特征信息。

均匀磁化直立长方体磁力三阶梯度张量无解析奇点正演计算公式研究

均匀磁化直立长方体是磁力异常正演模拟与三维反演的最基本、最常用的一种场源模型,推导其正演计算解析公式具有重要的理论意义和实用价值。磁力三阶梯度张量是最近提出的一个新概念,可能是未来卫星与航空等磁测研究的一个重要发展方向。此外,多种磁力异常转换参量也涉及磁力三阶梯度张量的部分元素。因此,在前人研究基础上推导了均匀磁化直立长方体的磁力三阶梯度张量无解析奇点正演计算公式。首先验证了该公式的正确性,然后将其应用于总磁场强度异常一阶垂向导数的解析信号、磁力二阶梯度张量不变量的一阶导数、正则化磁源强度的一阶导数的计算。这些高精度、高效率的正演计算解析公式可为将来磁力三阶梯度张量勘探方法研究及基于磁力异常转换参量的解释方法研究奠定重要基础。

磁梯度张量不变量约束条件下的两点定位方法

文中针对单点磁梯度张量定位方法受地磁场估计误差影响较大,同时多点磁梯度张量定位方法容易陷入局部最优解等问题,提出一种两点磁梯度张量定位方法。该方法在单点磁梯度张量定位算法的基础上,采用两点磁梯度张量测量数据,叠加张量几何不变量的约束条件,构建关于目标位置坐标的非线性目标函数,采用基于自然选择的粒子群算法对目标位置坐标进行求解。仿真实验表明,文中提出的方法受地磁场估计误差影响较小,且能实现对全局最优解的搜索,定位精度较高。仿真分析不同系统基线长度和磁力仪灵敏度条件下文中方法对磁性目标的定位效果可知,当系统的基线长度越大,磁力仪的灵敏度越高,磁性目标定位误差越小。

基于交变信号源的磁定位技术研究

针对磁偶极子定位系统中静态磁信号源产生的静态磁场容易受到背景磁场和环境噪声的干扰的问题,提出了以交变磁场作为磁信号源进行梯度张量定位,研究了其稳定性。以正弦交变磁场信号为发射源,并利用锁相放大器实现对交流信号的解调,通过单点定位算法完成定位。实验结果表明:当噪声的信噪比逐渐减小时,静态磁源的绝对定位误差明显增大,而交变磁源定位系统受环境噪声的影响较小,具有较强的稳定性。

基于两点磁梯度张量不变量的目标定位法

针对传统基于单点磁梯度张量的目标定位方法无法消除背景地磁场及其他干扰磁场影响的问题,通过分析磁梯度张量矩阵特征值和特征向量之间的关系,构造出与磁偶极子位置矢量与磁矩矢量夹角无关的不变量,给出位置矢量和磁矩矢量关于特征值及特征向量的数学关系表达式。建立线性方程组,解算线性方程组实现磁目标定位。实验表明,与传统Nara法相比可以有效避免干扰磁场的影响,定位精度更高,相对定位误差在10%以内,磁传感器精度和系统基线距离是影响定位误差的重要因素。

超导航磁全张量梯度测量系统的发展趋势

航磁矢量探测方法中,矢量梯度测量直是国内外的研究热点,磁法理论方法和量子精密测量技术的不断发展,为深部复杂地质体的高分辨率和多参数探测奠定了基础,作为最新代的航空磁测技术,基于超导量子干涉器(Superconducting Quantum Interference Device,简称SQUID)的磁张量梯度测量系统具有高灵敏度、低噪声及宽频带的优点,可以测量磁矢量场的梯度值,对共模磁场有很强的抑制能力.