不同高度数据联合欧拉反褶积法研究

基于不同测量高度重力场及其梯度数据可同时对应同一场源并用于反演场源位置的分析原理,拓展不同高度场数据在欧拉反褶积法中的应用范围.首先,立足于对欧拉反褶积方法的理论研究基础,提出不同高度数据融合联合欧拉反演公式.其次,在理论模型上对多种高度数据联合反演做了测试分析计算,验证了不同高度场数据融合联合欧拉反褶积法能够改善位场解释中单一观测面数据计算带来的解的发散问题,收敛过程由此改善.最后,将本文方法应用于龙门山地区实际重力数据的解释,获得了研究区断裂分布特征.     

基于变窗口算法的全张量中心定位研究

重力梯度张量(GGT)矩阵的特征向量与场源体的位置、走向等有关.笔者在前人工作的基础上,对利用GGT定位场源体中心及推断走向的方法进行了研究.文中采用滑动窗口,按不同的异常下限,确定一系列Gzz极值点作为计算点.随后依据距离指标,采用变窗口最小二乘中心定位方法进行了计算.当计算点趋近二维构造时,最小特征值对应的特征向量可以大致推断目标体在该测点处的走向.理论模型数据实验表明,本方法反演结果较为准确,效果明显.     

鄂尔多斯南缘地区重力变化场源特征

以鄂尔多斯南缘地区布格重力异常数据及2014—2017年相对重力观测数据为基础,采用欧拉反褶积方法,对引起重力变化的场源深度进行反演,并对空间分布规律予以解释。通过构建理论模型,反演得到最优模型参数,并对实际数据进行计算和分析。为了减弱和消除欧拉解的发散性,利用水平梯度滤波法优化反演结果。结果表明:①构造指数为1时,适合对相对重力数据进行反演,当滑动窗口选择4—8倍测点间距时,可以获得较为可靠的场源参数;②在主要断裂附近,不同时间尺度的场源呈较好的一致性特征;③引起重力变化的场源深度集中在10—30 km,与鄂尔多斯南缘地区的震源深度基本一致;④不同时间尺度的场源位置相对分散,表明引起重力变化的物质流动具有随机性和波动性。     

欧拉反褶积法在航空重力勘探中的应用

在论述欧拉反褶积基础理论与方法的基础上,以我国某海域航空重力资料为例,对该海域内地质异常体(侵入岩、断鼻构造)及断裂构造等进行了欧拉反褶积反演计算,获得了场源深度等信息,确定了场源位置及边界,并与航空布格重力异常、垂向导数、上延、水平梯度模、剩余异常以及重磁联合反演结果等资料相互验证,取得了很好的应用效果.基于该地区的反演效果,证明欧拉反褶积法可应用于航空重力勘探中,可为其他航空重力勘探区计算场源位置及深度信息提供可靠并且准确的研究方法,从而达到辅助航空重力勘探测量的效果.     

基于时变重力数据的川滇地区场源模型反演和解释

时变重力信号能反映地球内部介质迁移引起的不均衡变化,本文利用三维欧拉反褶积方法,通过建立合适的场源模型获得最佳反演参数,并采用水平梯度滤波法消除部分虚假发散解,优化反演结果.在此基础上,利用川滇地区2015-2019年流动重力重复观测资料,分析了不同时空尺度的区域重力场动态变化特征,开展对川滇地区重力变化场源特征的定性...     

井地有限线源三维电阻率反演研究

有限线源的三维电阻率反演,是地学探测研究的重要课题之一.本文主要讨论了以下几个方面的内容:(1)结合反演方程式改进的共轭梯度算法;(2)基于扰动法的线源Jacobi矩阵的近似计算方法及光滑系数矩阵在各个方向上的光滑因子的计算公式;(3)通过分析阻尼系数与修改量校正量对反演结果的影响,提出了利用校正系数对模型修正量进行校正;(4)较为系统的讨论了阻尼系数λ对反演分辨能力的影响,较好的改善了三维电阻率反演中的电性异常体重心的"上漂"现象.数值实验表明,改进后的共轭梯度法反演对初始模型的依赖程度较小,反演能够稳定收敛,对模型的空间位置分辨率较高.     

变阻尼共轭梯度算法及其性能分析

为了提高反演的分辨率和计算效率,本文在传统阻尼共轭梯度法的基础上,提出了变阻尼共轭梯度算法.由于在最小二乘线性反演过程中,多数情况下都要计算偏导数矩阵,而偏导数矩阵列向量的长度大小决定了解向量在对应分量方向上前进的快慢,变阻尼共轭梯度算法的提出正是利用了偏导数矩阵的这一特点.从理论上讲,它要优于传统的固定阻尼共轭梯度法.最后通过计算实例证明了该算法计算精度高,稳定性好,收敛速度快.因此采用变阻尼共轭梯度算法进行地球物理反演是切实可行的.     

基于欧拉反褶积方法计算川滇交界重力变化场源特征

本文以川滇地区2012-2014年来的多期流动重力观测网络数据为基础,采用欧拉反褶积方法对引起重力变化的场源深度和空间分布规律进行了反演和解释.本文通过构建理论模型。得到了最优的反演参数,并对实际数据进行了计算和分析.结果表明:选择构造指数(SI)为1时适合对流动重力数据进行反演.实际资料的反演结果显示在2012-2014年间的重力变化场源位置更集中于垂直于昭通断裂的北西向分布,场源深度分布在30±10 km范围,形态与鲁甸地震发震构造位置相似.这可能与2014年8月3日鲁甸M_S 6.5地震前的中上地壳的深部应力场变化相关.依据本文研究结果和方法,可以开展由场至源的定量研究,为流动重力变化信号的反演和解释提供一条新思路.     

基于欧拉反褶积方法估算华北地区重力变化的等效源参数

利用华北地区2009—2014年绝对重力与相对重力多期重复观测资料, 得到不同时空尺度的华北区域重力场动态变化图像。 采用欧拉反褶积方法, 通过对理论模型试算, 获得最优反演参数, 对引起华北地区重力场变化的场源深度和空间分布规律进行了反演计算和分析。 结果表明: 当构造指数为1时, 适合对流动重力场变化数据进行反演。 实际资料的反演结果在2009—2014年间的场源位置集中于河套断裂带。 本文研究方法可以用于重力场反演和以场求源的定量研究。 本工作为流动重力变化信号的反演和解释提供一条新思路, 也为构建地震重力预报指标体系提供了定量依据。     

基于欧拉反褶积方法计算辽宁地区重力变化场源特征

以2012—2018年辽宁地区的流动重力观测资料为基础,结合实际地下地质体构造特征构建理论模型,应用欧拉反褶积法对重力变化场源深度及空间分布特征进行反演和解释。结果表明:在辽宁西部辽蒙交界和海城—岫岩断裂带附近场源位置集中,地下介质活动增强;欧拉反褶积方法适用于对流动重力观测资料的重力场反演及以场至源的定量研究应用。     

煤矿井下微震震源高精度定位研究

煤矿井下微震震源准确定位,对于动力灾害监测预警具有重要意义.由于微震震源需要通过井下传感器接收信息反演确定,传感器的安装位置限制于煤矿井下巷道周围,传感器沿巷道近平面的不合理布置将大大降低震源定位精度.针对由传感器信息反演震源位置引起的病态问题,本文提出了基于微震监测测点优化布置的震源高精度定位算法.首先通过计算系数矩阵条件数,判定病态问题;然后利用中心化法和行平衡法联合进行病态矩阵预处理.对预处理后的矩阵A、b利用L曲线法计算正则参数,结合Tikhonov正则化算法计算得到震源坐标正则解.研究结果表明,中心化法有效降低了矩阵数量级,行平衡预处理降低了病态条件数,预处理后Tikhonov正则解的震源坐标误差最小可以达到3.09m,与预处理前的高斯消去解相比误差大大降低.通过上述优化处理,实现了井下受限空间微震监测震源高精度定位.     

对二维磁异常利用广义逆矩阵的选择法

本文利用广义逆矩阵理论反演解释二维磁异常。实现了加阻尼因子法,实现并改进了奇异值人工截除法;讨论了资料分辨矩阵、信息密度矩阵等辅助信息的利用;详细评价了广义逆矩阵算法的优劣。通过与目前重、磁最优化反演中常用的阻尼最小二乘法、变尺度法的对比,指出广义逆矩阵法优于这些算法。最后以河北迁安一个复杂磁异常的反演实例加以证实。     

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.     

2.5D forward modeling and inversion of frequency-domain airborne electromagnetic data

Frequency-domain airborne electromagnetics is a proven geophysical exploration method. Presently, the interpretation is mainly based on resistivity—depth imaging and one-dimensional layered inversion; nevertheless, it is difficult to obtain satisfactory results for two- or three-dimensional complex earth structures using 1D methods. 3D forward modeling and inversion can be used but are hampered by computational limitations because of the large number of data. Thus, we developed a 2.5D frequency-domain airborne electromagnetic forward modeling and inversion algorithm. To eliminate the source singularities in the numerical simulations, we split the fields into primary and secondary fields. The primary fields are calculated using homogeneous or layered models with analytical solutions, and the secondary (scattered) fields are solved by the finite-element method. The linear system of equations is solved by using the large-scale sparse matrix parallel direct solver, which greatly improves the computational efficiency. The inversion algorithm was based on damping least-squares and singular value decomposition and combined the pseudo forward modeling and reciprocity principle to compute the Jacobian matrix. Synthetic and field data were used to test the effectiveness of the proposed method.     

重力全张量数据联合欧拉反褶积法研究及应用

全张量测量技术是在空中或海上用加载了多个加速度计的移动平台技术测量位场的五个独立分量.各张量分量包含不同方向的地下地质体信息,水平张量分量T_(xx)、T_(yy)、T_(xy)、T_(xz)、T_(yz)通常用于识别和映射与地质构造或地层变化有关的测量区域中的目标,垂直张量分量Tzz用于估计深度.然而,这些分量传统上是彼此分开解释,经常遇到错失关键信息的风险.本文所用全张量欧拉反褶积是在单独z方向的欧拉反演基础上发展而来的,它融合了重力异常垂直分量以及其三个方向导数、水平分量以及其三个方向导数.全张量数据信息得以有效应用的同时,欧拉反褶积结果也比常规欧拉反褶积结果更加收敛.最后,结合美国墨西哥湾地区实测航空FTG数据,用重力梯度张量数据进行联合欧拉三维反演研究,有效的识别岩盖的边界信息,划分岩盖范围,为进一步研究盖层底下深部复杂地质情况提供可靠的解释结果.     

Modeling viscous damping in nonlinear response history analysis of buildings for earthquake excitation

The Rayleigh damping model, which is pervasive in nonlinear response history analysis (RHA) of buildings, is shown to develop ‘spurious’ damping forces and lead to inaccurate response results. We prove that a viscous damping matrix constructed by superposition of modal damping matrices—irrespective of the number of modes included or values assigned to modal damping ratios—completely eliminates the ‘spurious’ damping forces. This is the damping model recommended for nonlinear RHA. Replacing the stiffness‐proportional part of Rayleigh damping by the tangent stiffness matrix is shown to improve response results. However, this model is not recommended because it lacks a physical basis and has conceptual implications that are troubling: hysteresis in damping force–velocity relationship and negative damping at large displacements. Furthermore, the model conflicts with the constant‐damping model that has been the basis for fundamental concepts and accumulated experience about the inelastic response of structures. With a distributed plasticity model, the structural response is not sensitive to the damping model; even the Rayleigh damping model leads to acceptable results. This perspective on damping provides yet another reason to employ the superior distributed plasticity models in nonlinear RHA. OpenSees software has been extended to include a damping matrix defined as the superposition of modal damping matrices. Although this model leads to a full populated damping matrix, the additional computational demands are demonstrated to be minimal. Copyright © 2015 John Wiley & Sons, Ltd.     

位场向下延拓的最小曲率方法

针对位场向下延拓的不适定性,我们将位场向下延拓视为向上延拓的反问题,提出以位场最小曲率作为约束条件来求解稳定的下延位场.我们将剖面位场向上延拓表达式用傅里叶矩阵的形式表示,以矩阵乘法形式给出延拓的表达式,同时向待反演的下延位场引入最小曲率约束,得到向下延拓的最小曲率解,并利用正交变换给出了更为简洁的频率域解.随后,利用Kronecker积将上述全部结果拓展至三维位场,给出了三维位场向下延拓的最小曲率解.此外,我们将位场数据的填充、扩充问题与向下延拓问题统筹考虑,提出一种新的向下延拓迭代格式,该算法面向实际资料处理需求、无须预扩充或填补数据.下延迭代时,对原始数据直接向下延拓,而空白部分利用上一次下延位场估计的上延值替代其空白值并对其向下延拓,直至获得最小曲率约束下稳定的向下延拓结果.同时,我们也讨论了利用改进L曲线和广义交叉验证(GCV)计算正则参数最优估计的问题.对理论模型和实际航空重力资料进行了向下延拓检验,处理结果表明位场向下延拓的最小曲率方法解能满足实际位场资料对向下延拓处理的需求,具有较高的下延精度.     

Response of non-classically damped structures in the modal subspace

The evaluation of the dynamic response of non-classically damped linear structures requires the solution of an eigenproblem with complex eigenvalues and modal shapes. Since in practice only a small number of complex modes are needed, the complex eigenvalue problem is solved in the modal subspace in which the generalized damping matrix is not uncoupled by classical real modes. It follows that the evaluation of the structural response requires in both cases the determination of complex modes by numerical techniques, which are not as robust as techniques currently used for the solution of the real eigenvalue problem, and the use of complex algebra. In the present paper an unconditionally stable step-by-step procedure is presented for the response of non-classically damped structures in the modal subspace without using complex quantities. The method is based on the evaluation of the fundamental operator in approximated form of the numerical procedure. In addition, the method can be easily modified to incorporate the modal superposition pseudo-static correction terms.     

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.     

TUTORIAL LINEAR INVERSE FILTERS IN ORTHOGONAL COORDINATES*

The linear filter is used extensively in exploration geophysics, and is usually computed using the least squares normal equations. In the general field of time series, the inverse problem is often solved through eigenvalue expansion solutions to integral equations. The normal equations can be solved in terms of the eigenvalues and eigenvectors of the autocorrelation matrix. It has been suggested that a spectral expansion technique should be used which computes the inverse directly without explicit use of the normal equations. If all possible spiking positions are calculated using the normal equations, the spiking operator matrix is obtained. The matrix operator obtained from the spectral expansion is closely related to the spiking operator matrix. Thus, it is possible to compute the spectral expansion filter using the normal equations. Therefore, it is possible to use the best features of both methods, i.e. obtaining the optimum filter with the normal equations, and discarding the poorly determined parts of the solution based on spectral expansion.