Numerical solution of the two-dimensional inverse geomagnetic induction problem

Summary An effective numerical approach to the solution of the two-dimensional inverse geomagnetic induction problem using the linearization method is presented. The numerical realization of the inversion is based on Marquardt's algorithm, for which the solution of the direct problem and the partial derivatives of this solution with respect to the electrical parameters of the medium are computed by the finite difference method. Theoretical models are studied and numerical results are presented.     

基于信噪辨识的矿集区大地电磁噪声压制

为了避免形态滤波方法在大地电磁强干扰分离中的"过处理"、进一步保留大地电磁低频段的有用信息,提出基于信噪辨识的矿集区大地电磁噪声压制方法.首先,从信号处理的角度剖析矿集区典型强干扰与天然大地电磁微弱信号之间的定量辨识关系,利用形态分形维数和形态膨胀谱熵对大地电磁信号与强干扰进行信噪辨识.然后,结合形态滤波技术和阈值法,仅对辨识出明显不是天然大地电磁信号的异常波形进行噪声压制.最后,重构大地电磁有用信号,并对算法进行性能评价.仿真结果表明,形态分形维数和形态膨胀谱熵能较好地定量辨识大地电磁信号与强干扰,大地电磁信号中一些缓变化的低频信息得到了更为精细的保留;与形态滤波整体处理相比,本文所提方法获得的卡尼亚电阻率曲线更为光滑、连续,视电阻率值相对稳定,其结果更为真实地反映了测点本身所固有的大地电磁深部构造信息.     

解释重磁资料中最优化选择法的若干问题

本文中我们将拟牛顿法应用到磁力、重力资料的自动解释中来,通过计算对比说明,在收敛的稳定性上拟牛顿法比常用的阻尼最小二乘法大为优越。文中又讨论了最优化选择法的收敛性、多解性、模型体的选择、参量的选择和约束,以及解释三个矿区磁异常的实例。     

数学形态滤波与大地电磁噪声压制

数学形态滤波是一种新型的非线性滤波方法.介绍了形态学滤波的基本原理,针对大地电磁信号表现出的非线性、非平稳性和非最小相位特性,综合结构元素特征我们提出一种基于数学形态滤波的大地电磁噪声压制方法.为了有效抑制目标信号中的噪声干扰及修正统计偏倚现象,通过选用合理的结构元素及形态开-闭、闭-开组合,将正、负结构元素级联构造组合广义形态滤波器对实测大地电磁信号进行噪声压制.实验结果表明,该方法是切实可行的,有效地剔除了大尺度干扰及基线漂移,较好地还原了大地电磁信号的原始特征,修正了标准形态算子所产生的统计偏倚现象,去噪精度高.该方法计算速度快,具有潜在优势,为矿集区海量大地电磁信号与强干扰的分离提供了一条新的途径,应用前景广阔.     

Magnetotelluric responses of three-dimensional conductive and magnetic anisotropic anomalies

A magnetotelluric finite-element modelling algorithm is developed, which is capable of handling three-dimensional conductive and magnetic anisotropic anomalies. Different from earlier three-dimensional magnetotelluric anisotropic modelling methods, the algorithm we presented has taken the magnetic anisotropy into consideration. The variational equations are produced by the Galerkin method and the governing equations are solved using a hexahedral vector edge finite-element method. The accuracy of this algorithm is firstly validated by comparing its solutions with the results of finite-difference method for a three-dimensional conductive arbitrary anisotropic model, and then validated by comparing with analytical solutions for a one-dimensional magnetic model. The responses of four kinds of models under different conditions are studied, and some conclusions are obtained. It shows that for materials with a high magnetic permeability, its influence on magnetotelluric responses cannot be ignored in some circumstances. Especially, if the magnetic susceptibility is exceptionally high, it may really distort the apparent resistivities of lower resistive anomalies. These conclusions are also beneficial for magnetotelluric survey.     

基于子空间的二维大地电磁量子遗传反演法研究

量子遗传算法作为一种高效的优化算法,仍存在容易陷入局部极值的缺点.为提高算法的高效性,并探讨将算法应用于大地电磁二维反演的可行性和有效性,本文对算法进行了改进,并通过一维两层D型和四层HK型模型数值试验验证了改进的有效性.然后将改进后的算法引入二维大地电磁反演,在引入滑动子空间思想,同时只考虑最简化反演条件的前提下,对...     

On the determination of marine magnetotelluric receiver orientation using land magnetic observatory data

Marine magnetotelluric measurements using “free‐fall’’ instruments without effective compasses suffer from the problem of unknown orientation of the receivers at the seafloor. While past works indicate that marine magnetotelluric orientation of the instruments can be estimated by reference to land deployments of known orientation using the transfer tensor method, there is limited published information on how this is implemented in practice. We document this method and propose a set of new time‐ and frequency‐domain approaches to solve this orientation problem of the seafloor receivers. We test these methodologies in onshore and offshore magnetotelluric data whose orientations are well known and apply these techniques to marine magnetotelluric data with unknown orientation. For the controlled tests, both time‐ and frequency‐domain approaches produce overall comparable results. To investigate the effects of the subsurface structure distribution on the orientation process, a dimensionality analysis of a controlled dataset is carried out. In subsequent analysis using the available disoriented marine magnetotelluric data from offshore Brazil and from the Vassouras magnetic observatory on the mainland for remote referencing, frequency‐domain methods yield approximate orientation angles among themselves with low standard deviation each. Time‐domain results are consistent for most cases but differ from frequency‐domain results for some situations.     

海底大地电磁数据采集器

进行海底大地电磁数据采集，需借助于专用的水下探测设备 . 虽然大地电磁测深法无论是仪器或是测量手段在陆地上的应用已较为成熟，但把该方法移 植到海洋中，还需解决一些与海洋探测有关的工程技术问题. 主要包括：水下电场信号的提 取，海底环境的监测，仪器在非实时监控运行中的纠错对策以及测量部件的密封承压等等 . 在研制海底大地电磁数据采集器的过程中，采用先进的材料工艺，高精度的电子线路，可 靠的软件编程以及牢固的器件安装结构，有效地解决了上述技术问题. 用所研制的仪器首次 在我国海域进行了探测试验.     

实数编码遗传算法在大地电磁测深二维反演中的应用

作为全局非线性优化的新方法之一的遗传算法,近年来已从生物工程流行到大地电磁测深资料解释中.然而,大地电磁反演问题具有不适定性,解的非唯一性.通过结合求解不适定问题的Tikhonov正则化方法,本文采用实数编码遗传算法求解大地电磁二维反演问题.此算法在构建目标函数时引入正则化的思想,利用遗传算法求解最优化问题.常规的基于局部线性化的最优化反演方法易使解陷入局部极小值,而且严重的依赖初始模型的选择.与传统线性化的迭代反演方法相比,实数编码遗传算法能够克服传统方法的不足且能获得更好的反演结果.通过对大地电磁测深理论模型进行计算,结果表明:该算法具有收敛速度快、解的精度高和避免出现早熟等优点,可用于大地电磁资料解释.     

基于二次场方法的并行三维大地电磁正反演研究

快速且高精度的三维大地电磁法正反演是目前研究的热点.由于大地电磁法场源的平面波特性,以往的正演方法大多采用直接求解总场的方法,在边界强加二维边界条件.本文提出了一种基于二次场方法的三维大地电磁法正演算法,将平面波在层状背景模型中的响应作为场源项,得到二次场满足的偏微分方程,并利用交错网格有限差分法求取二次场.与其他学者的基于总场方法的结果的对比证明了本文采用方法的正确性.在基于二次场的正演算法基础上,实现了基于L-BFGS的三维反演方法,并对公开的数据集进行了反演.另外,针对大地电磁法的多频率观测特性,采用了基于MPI的分频并行策略对程序进行并行化,可达到接近线性的加速比.     

Improvement of MT data processing using stationary and coherence tests

The great majority of data processing methods for magnetotelluric measurements are based on an average Fourier spectral analysis to estimate either the transfer function or the coherence function. This assumes that the time-series data are stationary. The aim of this paper is to present a preprocessing method able to extract the stationary and coherent part of the original signals. The practitioner can then apply the magnetotelluric method of his choice to these new data. This preliminary data sorting is done in four steps: (i) slow drifts are eliminated using a high-pass filter whose cut-off frequency is determined by an iterative procedure. Based on run tests, this procedure is also able to remove segments with non-independent samples in the time series; (ii) non-stationary segments are eliminated after band-pass filtering; (iii) non-coherent segments are eliminated before spectral analysis; (iv) the impedance tensor value is then retained, at a given frequency, only if the signals are coherent. This preprocessing method was tested on the simplest, but still used, magnetotelluric method which uses only two field components, and it was found that the average resistivity standard deviation decreased significantly from 14.6 Ωm without sorting to 8.6 Ωm after sorting.     

Three-dimensional topographic responses in MT using finite difference method

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｒｅａｒｅｍａｎｙｎｕｍｅｒｉｃａｌｍｏｄｅｌｉｎｇｓｔｕｄｉｅｓｏｆｔｏｐｏｇｒａｐｈｙｆｏｒＭＴｆｉｅｌｄｓａｐｐｅａｒｅｄｉｎｔｈｅｐａｓｔｌｉｔｅｒａｔｕｒｅ,ｂｕｔｍｏｓｔｏｆｔｈｅｗｏｒｋｓａｒｅ２－Ｄｒｅｓ...     

Enhancement of Signal-to-noise Ratio in Natural-source Transient Magnetotelluric Data with Wavelet Transform

—For audio-frequency magnetotelluric surveys where the signals are lightning-stroke transients, the conventional Fourier transform method often fails to produce a high quality impedance tensor. An alternative approach is to use the wavelet transform method which is capable of localizing target information simultaneously in both the temporal and frequency domains. Unlike Fourier analysis that yields an average amplitude and phase, the wavelet transform produces an instantaneous estimate of the amplitude and phase of a signal. In this paper a complex well-localized wavelet, the Morlet wavelet, has been used to transform and analyze audio-frequency magnetotelluric data. With the Morlet wavelet, the magnetotelluric impedance tensor can be computed directly in the wavelet transform domain. The lightning-stroke transients are easily identified on the dilation-translation plane. Choosing those wavelet transform values where the signals are located, a higher signal-to-noise ratio estimation of the impedance tensor can be obtained. ? In a test using real data, the wavelet transform showed a significant improvement in the signal-to-noise ratio over the conventional Fourier transform.     

大地电磁资料精细处理和二维反演解释技术研究(一)——阻抗张量分解与构造维性分析

本文对大地电磁观测阻抗实施一种数学变换--"共轭阻抗变换",发现转换后的观测阻抗和区域阻抗之间存在特定的关系,这种特定关系不受电场局部畸变的影响,而且同样不需要关于地下区域结构维性的假设,在区域结构是三维的情况下也是成立的.对转换后的观测阻抗采用已有的Swift旋转方法即可求得区域主轴方位角,然后采用最优化方法求取区域阻抗相位、振幅以及畸变因子.同时根据转换后的观测阻抗重新定义了不受电场局部畸变影响的构造维性参数.采用合成理论数据验证了新算法的正确性,和Swift、Bahr、GB、相位张量、WAL方法进行了对比分析,并将新方法应用于实测资料的解释,发展了一套消除局部畸变和进行构造维性分析的MT精细资料处理技术.进一步的工作是将新算法推广到多点多频,并采用最优化技术分解,发展一种稳定性好、多测点多频点的阻抗张量分解技术.     

基于匹配追踪和遗传算法的大地电磁噪声压制

针对匹配追踪计算量大、大地电磁数据处理效率低的问题,提出基于匹配追踪和遗传算法的大地电磁噪声压制方法.首先,利用Gabor原子构建过完备原子库,并对过完备原子库集合进行划分.然后,借助遗传算法的自适应性,快速搜寻最优匹配原子及所在位置.最后,运用最优匹配原子对待处理信号进行稀疏分解,重构有用信号.通过对计算机模拟的典型强干扰和矿集区实测大地电磁数据进行分析处理,实验结果表明,相对于匹配追踪和正交匹配追踪,文中所提方法能从过完备原子库中快速、自适应地选取最优匹配原子与不同噪声干扰类型高精度的匹配,极大地提升了计算效率;大地电磁时间域序列中的大尺度强干扰被有效剔除,视电阻率曲线更为光滑、连续,低频段的数据质量得到明显改善.     

用边界单元法模拟二维地形对大地电磁场的影响

本文用边界单元法模拟二维地形对大地电磁场的影响.首先用格林公式将二维大地电磁的边值问题转变成积分方程,然后用边界单元法解积分方程,得到地形上的大地电磁场和它的法向导数,由此可计算电阻率.与有限单元法相比,本方法剖分后的地形与实际地形的拟合程度高,向计算机输入原始数据的工作简单,可以在微机上计算地形引起的视电阻率.本方法适合于在野外生产现场进行大地电磁法的地形改正.计算表明,地形对H_x型波的影响比对E_x型波严重得多;随着周期的增长,地形对H_x型波的影响变得稳定.     

基于交叉梯度结构约束的大地电磁主轴各向异性并行三维反演

各向异性介质对大地电磁观测数据的影响往往不可忽略,因此需要提高大地电磁各向异性三维反演的可靠性和有效性.为了满足大地电磁各向异性三维反演的需求,本文研究了一种基于交叉梯度结构约束的大地电磁主轴各向异性并行三维反演算法.根据大地电磁平面波理论假设,正演方程采用背景场与二次场分离的计算方式,二次场利用交错网格有限差分法求解.由于各向异性反演的多解性,本文将各向异性介质简化为主轴各向异性,并在此基础上进一步采用有限内存拟牛顿LBFGS法实现三维各向异性反演.为了提高各向异性反演的分辨率,反演目标函数中引入交叉梯度项,利用先验的结构信息,对三个方向的电阻率参数进行结构约束,最终的反演进一步利用MPI(Message Passing Interface,消息传递接口)技术实现分频并行计算,测试结果显示并行接近线性加速比.     

频率域吊舱式直升机航空电磁资料的马奎特反演

频率域吊舱式航空电磁系统在国内尚处于研究和试生产阶段,由于缺少有效的数据处理手段,限制了该项技术的进一步应用和发展.本文通过对马奎特方法原理介绍,成功地将其运用到频率域航空电磁资料的反演计算中,并对几个关键技术——雅可比矩阵计算、初始模型赋值、形态模型与物性模型反演效果等进行分析,提出了切实可行的算法,并在计算机上加以实现.最后,通过理论模型和实测数据测试验证了算法的有效性和正确性,填补了国内该应用领域的技术空白,取得了较好的应用效果.     

关于大地电磁测深资料反演问题

大地电磁测深资料二维反演问题,由于迭代过程中用数值方法求解修改模型参数后的地表响应函数,因而需要正演的时间相当长。本文引用快速正演的方法,缩短了迭代过程中正演计算的时间。从理论上将一般的二维（双）三次样条公式做了简化,应用到快速正演方法中,提高了效率。并以模拟的数据,实现了两个参数的反演。文中还就确定初始模型参数进行了探讨。     

Robust inversion analysis of local gravity anomalies caused by geological dislocation model of faults

ＲｏｂｕｓｔｉｎｖｅｒｓｉｏｎａｎａｌｙｓｉｓｏｆｌｏｃａｌｇｒａｖｉｔｙａｎｏｍａｌｉｅｓｃａｕｓｅｄｂｙｇｅｏｌｏｇｉｃａｌｄｉｓｌｏｃａｔｉｏｎｍｏｄｅｌｏｆｆａｕｌｔｓＪＩＡＮＬＩＡＮＧＨＵＡＮＧ（黄建梁）ＣＨＯＮＧＹＡＮＧＳＨＥＮ（申...