重力数据三维共轭梯度聚焦反演及应用

基于共轭梯度算法对欠定线性目标函数进行求解。 为改善目标函数的多解性、 消除多余构造信息影响, 引入粗糙度系数矩阵; 为克服“趋肤效应”, 更好地反映地质体的真实形态, 在模型目标函数中引入深度加权函数; 为更好的反映地质体的某些尖锐构造和边界, 本文对目标函数添加了基于最小支撑泛函的聚焦反演约束。 通过对多种模型的计算, 验证了该方法具有较好的有效性和稳定性, 并将该方法应用于实际重力资料地下密度反演中去, 得到了较好的反演结果。     

考虑电流型畸变的大地电磁三维反演

大地电磁测深(MT)的观测数据易受到由近地表小尺度非均匀体或地形起伏引起的电流型畸变干扰,消除或压制这种干扰对获取可靠的深部电性结构至关重要.当区域结构为二维时,电流型畸变可采用张量分解等方法予以消除或压制.当区域结构为三维时,畸变问题更加复杂和严重,传统张量分解方法往往效果不佳或无效,严重地制约了MT三维反演技术的实用性.对此,本文提出一种考虑电流型畸变的MT三维反演算法,将完整的电流型畸变参数引入到目标函数,并采用非线性共轭梯度法与电阻率参数同时反演,从而达到压制畸变的目的.该算法有两个关键点:一是通过分析实测数据所遭受畸变的分布特征,在目标函数中对其进行有效约束;二是在迭代过程中,通过自适应地调整双正则化因子保障算法的稳定和效率.理论模型测试结果显示,常规三维反演算法不能合理解释数据中的畸变成分,而只能通过引入虚假异常体强制地拟合受畸变数据,从而造成电阻率模型严重失真.与之相比,本文算法能够在反演中自动求解各测点所受到的畸变,获得更接近真实的电阻率模型.     

基于数据空间和稀疏约束的三维重力和重力梯度数据联合反演

随着重力和重力梯度测量技术的日趋成熟,基于重力和重力梯度数据的反演技术得到了广泛关注.针对反演多解性严重、计算效率低和内存消耗大等难点问题,本文开展了三维重力和重力梯度数据的联合反演研究,该方法结合重力和重力梯度两种数据,将L0范数正则化项加入到目标函数中,并在数据空间下采用改进的共轭梯度算法求解反演最优化问题.同时,本文摒弃了依赖先验信息的深度加权函数,引入了自适应模型积分灵敏度矩阵,用来克服因重力和重力梯度数据核函数随深度增加而衰减引起的趋肤效应问题.为了提高反演计算效率,本文又推导出基于规则网格化的重力和重力梯度快速正演计算方法.模拟试算表明,改进的共轭梯度法可以降低反演的迭代次数,提高反演的收敛速度;自适应模型积分灵敏度矩阵,可以有效解决趋肤效应,提高反演纵向分辨能力;数据空间和改进的共轭梯度算法结合,可以更好地降低反演求解方程的维度,避免存储灵敏度矩阵,有效地降低反演计算时间和内存消耗量.野外实例表明,该算法可以在普通计算机下快速地获得地下密度分布模型,表现出较强的稳定性和适用性.     

正则参数控制下的波阻抗约束反演

通过势函数方式将波阻抗反演的病态问题转为良态问题，并且给出了边界保护势函数所具备的条件. 在反演过程中，通过改变正则参数数值以及合理地选择正则参数的初值，改善反演结果，提高反演收敛速度. 同时，在具体反演中使用快速模拟退火算法，可以克服目标函数局部极值的限制，从而获得全局最优解. 通过理论模型试算和实际资料处理，说明本文方法具有精度高、实用性强的特点.     

基于Extrapolation Tikhonov正则化算法的重力数据三维约束反演

通过研究重力数据三维反演解的病态性,利用基于拉格朗日插值方法的Extrapolation Tikhonov正则化方法来解决反演中解的不唯一性和不稳定性问题,该方法最大限度的减少了因正则化参数的引入而在反演结果中介入的误差,同时详细讨论了基于三种选择原则的正则化双参数的具体选择方法,模型试算结果表明,与原Tikhonov方法相比,该方法提高了反演的拟合精度.其次,为了消除核函数随深度增加而快速衰减对反演结果的影响,本文改进了前人的重力数据三维反演深度加权函数,改进后的加权函数与原函数相比能更好的识别异常体底部密度分布特征,对于埋深较深的异常体具有较好的识别效果,更好的解决了由近地面趋肤效应作用引起的密度分布不均的问题.同时,利用上下限约束函数限制每一个立方体的密度差范围,并应用于多组人工合成模型.结果表明:该反演方法能准确地获得正演模型的预设参数范围和位置.     

基于Lp范数稀疏优化算法的重力三维反演

三维密度反演已经成为重力数据定量解释的常规方法,但由于重力数据本身并没有深度分辨率,为了减少由此引起的重力反演的非唯一性,常用的手段是引入额外的先验信息.本文提出了一种重力三维稀疏反演（以下简称稀疏反演）方法,该方法通过求解物性上下界约束时的L_p范数（0 ≤ p ≤ 1）稀疏优化问题,来获得具有尖锐边界的解.与传统的L₂范数反演方法相比,稀疏反演方法可以更加有效地利用已知的物性信息,获得深度分辨率更高的反演结果.此外,我们也分析了稀疏反演方法与二值、三值反演算法的等价性以及在实际应用中需要注意的问题.最后,通过模型试验以及矿区实测数据反演验证了稀疏反演方法的有效性.     

重力和重力梯度数据联合聚焦反演方法

重力数据包含较多的低频信息,重力梯度数据包含较多的高频信息,将重力数据和重力梯度数据进行联合反演得到的结果更加可信.本文基于聚焦反演方法,实现了这一过程.因为联合反演中分量种类增加,所以计算灵敏度矩阵所需要的时间增加,为此,本文提出了一种快速计算灵敏度矩阵的方法.因为联合反演对内存的要求增大,本文选择有限内存BFGS拟牛顿法求解反演问题.本文通过再加权的方法实现深度加权.文中利用单一分量的反演结果来预测异常体的埋深信息,随后将埋深信息结合到深度加权函数中,将其用于多分量组合反演计算.给出了模型试验,发现预测得到的异常体的埋深信息与其实际埋深存在偏差,但是将这一信息应用到反演计算,能够得到与真实模型一致的结果.之后,本文通过模型试验来探究重力和重力梯度联合反演的优势,发现将重力和重力梯度数据联合,能够识别出额外的噪声,反演得到的模型更加合理.但是,对于不同分量组合得到的反演结果是相近的,反演模型的提高很小.最后,将联合反演方法应用到美国路易斯安那州Vinton岩丘的实际数据中,结果显示,将重力和重力梯度数据联合反演,反演模型得到了提高,反演得到的结果与地质资料吻合.     

改进的约束变密度界面反演策略及其应用

计算密度分界面的起伏变化在区域地质构造研究和石油矿产资源勘探中具有重要意义.已有密度界面反演方法更多侧重约束变密度界面反演算法,而对约束信息的准确性、研究区横向密度变化往往考虑不足,影响了最终反演结果的可信度.本文在变密度界面正反演算法基础之上,结合实际需求,提出已知深度信息约束下的变密度界面反演策略.该策略主要包括变密度约束反演算法、已知深度约束信息校验和分区变密度模型三个方面.其中反演算法提供了带已知深度约束信息的密度界面迭代反演方法;约束信息校验用于评估约束信息精度,通过调差降低约束信息的系统误差;在反演过程中引入水平密度分区以应对不同构造背景密度界面模型,提高反演结果的可信度.最后将本策略应用于南海莫霍面深度反演计算中,结果显示借助已知约束信息,利用分区密度模型能够获得更为可信的深度反演结果,验证了该策略的正确性.     

基于柯西分布约束和快速近端目标函数优化的三维重力反演方法

优化算法的选取在很大程度上影响着三维重力反演的计算效率,从而制约着三维重力反演的实用性.在复杂地质构造背景下,不同岩性单元之间可能会发生物性突变,产生尖锐边界.为此,本文提出了一种新的基于柯西分布约束和快速近端目标函数（Fast Proximal Objective Function,FPOF）优化的三维重力反演方法.FPOF优化方法的一个突出特点是在每一步迭代过程中逐一计算剖分网格内的未知密度参数,因此,有较低的计算复杂度和较高的计算效率.此外,目标函数中柯西范数（Cauchy norm）的引入会对反演结果施加稀疏性,有助于产生块状效果.理论模型测试表明,本文方法不仅能产生更加聚焦的反演效果,而且反演所需的时间也比传统的共轭梯度优化方法少.最后将本文方法应用于我国西部某地区实际重力数据,反演结果与已知的地质信息有较好的一致性.     

Fast inversion of magnetic data using Lanczos bidiagonalization method

This paper describes application of a fast inversion method to recover a 3D susceptibility model from magnetic anomalies. For this purpose, the survey area is divided into a large number of rectangular prisms in a mesh with unknown susceptibilities. Solving the full set of equations is substantially time consuming, and applying an algorithm to solve it approximately can reduce the time significantly. It is shown that the Lanczos bidiagonalization method can be an appropriate algorithm to solve a Tikhonov cost function for this purpose. Running time of the inverse modeling significantly decreases by replacing the forward operator matrix with a matrix of lower dimension. A weighted generalized cross validation method is implemented to choose an optimum value of a regularization parameter. To avoid the natural tendency of magnetic structures to concentrate at shallow depth, a depth weighting is applied. This study assumes that there is no remanent magnetization. The method is applied on a noise-corrupted synthetic data to demonstrate its suitability for 3D inversion. A case study including ground based measurement of magnetic anomalies over a porphyry-Cu deposit located in Kerman providence of Iran, Now Chun deposit, is provided to show the performance of the new algorithm on real data. 3D distribution of Cu concentration is used to evaluate the obtained results. The intermediate susceptibility values in the constructed model coincide with the known location of copper mineralization.     

基于共轭梯度算法的重力梯度数据三维聚焦反演研究

重力梯度数据相对于传统重力数据,能够更细致、准确地描述地球浅部构造和研究矿产资源分布等信息.本文采用共轭梯度算法,在加权密度域求解重力梯度数据三维聚焦反演最优化问题,以恢复地下三维密度分布,目标函数包括数据不拟合函数和最小支撑稳定函数.首先,在推导目标函数对加权密度的一阶导数时,为了得到更合理的计算公式,我们考虑变加权函数中含有密度变量;此外,本文通过密度上下限约束,改善了传统聚焦反演中聚焦因子选取困难的问题.新算法获得的反演结果,对聚焦因子的选择约束较少,相比传统聚焦算法,能够更容易的获得理想结果.将方法应用于理论模型验证其有效性和正确性,并应用本文方法处理文顿盐丘地区的航空全张量重力梯度数据,得到了与已知地质信息匹配的密度分布,表明本文方法具有处理实际数据的能力.     

Inversion of potential field data using the structural index as weighting function rate decay

Nonparametric inverse methods provide a general framework for solving potential‐field problems. The use of weighted norms leads to a general regularization problem of Tikhonov form. We present an alternative procedure to estimate the source susceptibility distribution from potential field measurements exploiting inversion methods by means of a flexible depth‐weighting function in the Tikhonov formulation. Our approach improves the formulation proposed by Li and Oldenburg (1996, 1998) , differing significantly in the definition of the depth‐weighting function. In our formalism the depth weighting function is associated not to the field decay of a single block (which can be representative of just a part of the source) but to the field decay of the whole source, thus implying that the data inversion is independent on the cell shape. So, in our procedure, the depth‐weighting function is not given with a fixed exponent but with the structural index N of the source as the exponent. Differently than previous methods, our choice gives a substantial objectivity to the form of the depth‐weighting function and to the consequent solutions. The allowed values for the exponent of the depth‐weighting function depend on the range of N for sources: 0 ≤N≤ 3 (magnetic case). The analysis regarding the cases of simple sources such as dipoles, dipole lines, dykes or contacts, validate our hypothesis. The study of a complex synthetic case also proves that the depth‐weighting decay cannot be necessarily assumed as equal to 3. Moreover it should not be kept constant for multi‐source models but should instead depend on the structural indices of the different sources. In this way we are able to successfully invert the magnetic data of the Vulture area, Southern Italy. An original aspect of the proposed inversion scheme is that it brings an explicit link between two widely used types of interpretation methods, namely those assuming homogeneous fields, such as Euler deconvolution or depth from extreme points transformation and the inversion under the Tikhonov‐form including a depth‐weighting function. The availability of further constraints, from drillings or known geology, will definitely improve the quality of the solution.     

二维复杂层状介质中地震多波走时联合反演成像

采用新近提出的多次波射线追踪正演算法,结合共轭梯度法求解带约束的阻尼最小二乘最优化反演问题,分析讨论了利用多震相走时资料进行联合反演成像的方法及技术.考虑到不同震相走时的拾取误差不同,反演算法中引入了不同震相种类数据的权系数; 由于同时反演速度模型和反射界面起伏中不同模型参数变化对走时影响程度的不同, Jacobi偏导矩阵元素中引入了不同参数的归一化因子; 另外,为了克服射线密度过大(或过小)区域速度模型的过度(或欠)更新问题,反演算法中引入了等权射线密度的概念.几种数值模拟实例表明(含噪声敏感性试验): 多波走时的联合或同时反演成像技术是一种提高走时成像空间分辨率,进而降低重建模型失真度行之有效的方法.     

用改进的光滑约束最小二乘正交分解法实现电阻率三维反演

对三维电阻率反演问题进行了深入研究,提供了一种利用地表观测数据实现三维反演的实用算法.该方法应用有限差分求正演解,并通过对粗糙度矩阵元素进行适当改进,使之适用于各种情况下粗糙度矩阵的求取,进而建立在模型的总粗糙度极小条件下的反演方程.对反演方程采用收敛速度快且稳定的最小二乘正交分解（LSQR）法进行迭代求解,在迭代求解过程中只需利用偏导数矩阵和其转置矩阵乘以一个向量的结果,回避了直接求偏导数矩阵的繁琐计算,节省了内存,加快了反演的计算速度.不同的计算实例表明上述方法是求解大规模三维电阻率反演问题的有效方法.     

贝叶斯同化重力反演方法构建龙门山地壳密度模型

重力异常对地壳横向密度变化敏感,而无约束重力反演得到的密度模型其垂向分辨能力往往不理想.为了改善反演结果的垂向分辨率,本文参考已有先验分层模型,基于贝叶斯原理,提出了一种重震联合反演的新策略,可实现多种参考模型和复杂加权参数条件下的最大后验概率估计.理论模型测试结果表明,对于深度加权、多参考模型约束等多种问题,本文提出的新方法都可以稳健地获得最优化的模型参数.本文同时以中国地震科学台阵在龙门山地区及周边的一维接收函数分层模型和地震层析成像结果为参考,通过此方法对该区的重力异常进行反演,获得了该区的高精度三维密度结构,其水平分辨率优于10 km,垂直分辨率优于5 km.结合四条通过汶川和芦山地震震中的剖面进行分析后发现,反演得到的密度结构模型在过强震震源区位置横向变形显著,其揭示的分层地壳结构和变形模式与地表已知断裂构造具有相关性.本文提出的重震联合反演新策略,可为研究潜在强震风险源区的地壳结构和物性特征提供有效的科技方法支撑.     

Three‐dimensional potential field data inversion with L0 quasinorm sparse constraints

The quantitative explanation of the potential field data of three‐dimensional geological structures remains one of the most challenging issues in modern geophysical inversion. Obtaining a stable solution that can simultaneously resolve complicated geological structures is a critical inverse problem in the geophysics field. I have developed a new method for determining a three‐dimensional petrophysical property distribution, which produces a corresponding potential field anomaly. In contrast with the tradition inverse algorithm, my inversion method proposes a new model norm, which incorporates two important weighting functions. One is the L0 quasi norm (enforcing sparse constraints), and the other is depth‐weighting that counteracts the influence of source depth on the resulting potential field data of the solution. Sparseness constraints are imposed by using the L0 quasinorm on model parameters. To solve the representation problem, an L0 quasinorm minimisation model with different smooth approximations is proposed. Hence, the data space (N) method, which is much smaller than model space (M), combined with the gradient‐projected method, and the model space, combined with the modified Newton method for L0 quasinorm sparse constraints, leads to a computationally efficient method by using an N × N system versus an M × M one because N ? M. Tests on synthetic data and real datasets demonstrate the stability and validity of the L0 quasinorm spare norms inversion method. With the aim of obtaining the blocky results, the inversion method with the L0 quasinorm sparse constraints method performs better than the traditional L2 norm (standard Tikhonov regularisation). It can obtain the focus and sparse results easily. Then, the Bouguer anomaly survey data of the salt dome, offshore Louisiana, is considered as a real case study. The real inversion result shows that the inclusion the L0 quasinorm sparse constraints leads to a simpler and better resolved solution, and the density distribution is obtained in this area to reveal its geological structure. These results confirm the validity of the L0 quasinorm sparse constraints method and indicate its application for other potential field data inversions and the exploration of geological structures.     

基于非结构网格剖分的海洋可控源电磁三维正则化反演研究

为更好地处理与解释复杂海底地形条件下测得的海洋可控源电磁数据,本文提出了一种基于非结构网格剖分的频率域海洋可控源电磁数据三维正则化反演方法.该方法首先对海洋地电模型以非结构四面体单元进行离散,然后基于矢量有限元方法获得海洋可控源电磁响应和灵敏度信息,最后采用共轭梯度法求解高斯-牛顿反演方程计算模型修正量.为提高反演的稳定性,通过在反演过程中采用对数转换方法实现反演模型参数的上下限约束.本文分别测试了单测线水平海底地形反演算例和面积性测量的起伏海底地形反演算例.反演结果表明,本文提出的频率域海洋可控源电磁三维反演能够准确地恢复高阻储油层的位置和电阻率信息,且计算效率较高,可用于实测海洋电磁资料的处理与解释.     

Sharp boundary inversion of 2D magnetotelluric data

We consider 2D earth models consisting of laterally variable layers. Boundaries between layers are described by their depths at a set of nodes and interpolated laterally between nodes. Conductivity within each layer is described by values at a set of nodes fixed within each layer, and is interpolated laterally within each layer. Within the set of possible models of this sort, we iteratively invert magnetotelluric data for models minimizing the lateral roughness of the layer boundaries, and the lateral roughness of conductivities within layers, for a given level of data misfit. This stabilizes the inverse problem and avoids superfluous detail. This approach allows the determination of boundary positions between geological units with sharp discontinuities in properties across boundaries, while sharing the stability features of recent smooth conductivity distribution inversions.
We compare sharp boundary inversion results with smooth conductivity distribution inversion results on a numerical example, and on inversion of field data from the Columbia River flood basalts of Washington State. In the synthetic example, where true positions and resistivities are known, sharp boundary inversion results determine both layer boundary locations and layer resistivities accurately. In inversion of Columbia flood basalt data, sharp boundary inversion recovers a model with substantially less internal variation within units, and less ambiguity in both the depth to base of the basalts and depth to resistive basement.     

Regularized inversion of amplitude-versus-incidence angle (AVA) based on a piecewise-smooth model

Different from the stacked seismic data, pre-stack data includes abundant information about shear wave and density. Through inversing the shear wave and density information from the pre-stack data, we can determine oil-bearing properties from different incident angles. The state-of-the-art inversion methods obtain either low vertical resolution or lateral discontinuities. However, the practical reservoir generally has sharp discontinuities between different layers in vertically direction and is horizontally smooth. Towards obtaining the practical model, we present an inversion method based on the regularized amplitude-versus-incidence angle (AVA) data to estimate the piecewise-smooth model from pre-stack seismic data. This method considers subsurface stratum as a combination of two parts: a piecewise smooth part and a constant part. To fix the ill-posedness in the inversion, we adopt four terms to define the AVA inversion misfit function: the data misfit itself, a total variation regularization term acting as a sparsing operator for the piecewise constant part, a Tikhonov regularization term acting as a smoothing operator for the smooth part, and the last term to smoothly incorporate a priori information for constraining the magnitude of the estimated model. The proposed method not only can incorporate structure information and a priori model constraint, but also is able to derive into a convex objective function that can be easily minimized using iterative approach. Compared with inversion results of TV and Tikhonov regularization methods, the inverted P-wave velocity, S-wave velocity and density of the proposed method can better delineate the piecewise-smooth characteristic of strata.     

三维复杂地壳结构非线性走时反演

中国大陆中西部乃至全球造山带普遍具有复杂地壳结构.随着矿产资源勘探和深部探测研究的深入,探测造山带及盆山耦合区下方地壳精细结构正逐渐成为当前面临的巨大挑战.人工源深地震测深方法正越来越清晰地揭示出不同构造域地壳速度结构的基本特征,然而传统的层状结构模型参数化方法难以准确描述复杂地质模型,通常情况下多忽略速度结构的精细间断面且采用层边界平滑处理,难以满足地壳精细结构成像的发展要求.针对上述困难,本文采用最近发展的块状结构建模方案构建三维复杂地壳模型,基于逐段迭代射线追踪正演走时计算方法,推导了走时对三角形界面深度以及网格速度的偏导数,开展了非线性共轭梯度走时反演方法研究.发展了利用直达波和反射波等多震相走时数据对界面深度和网格速度的多参数联合反演方法,并引人不同种类震相数据的权系数和不同类型参数偏导数归一化的方法.数值算例表明,基于块状结构的非线性共轭梯度走时反演方法适用于复杂地壳结构模型,在利用人工源走时数据反演复杂地壳精细结构领域具有良好的应用前景.