煤层厚度地震槽波层析成像分辨率分析

透射法地震槽波勘探技术依据不同煤厚槽波频散特征差异,利用敏感频率下槽波走时层析成像算法反演得到煤层槽波速度,进而预测煤层厚度分布.层析反演结果的准确性直接影响煤厚探测的精度,反演得到小异常体常被错误地当作高精细度的体现.槽波层析反演分辨率是衡量反演结果精细程度的重要指标,决定了反演结果的可靠程度,但对于槽波分辨率的估算缺乏有效的技术手段.通过对比分析理论模型、棋盘格模型、射线密度和统计分辨率等方法,探讨这些分辨率分析方法的优缺点.根据义马11061工作面层析成像结果以及后期实际煤厚揭露数据,验证了槽波勘探方法的合理性和准确,认为采用巷帮煤厚作为约束条件,可提高层析成像分辨率,采用统计分辨率方法对反演结果分析较为实用.     

Lg波衰减模型中建模误差的定量评估

对Lg波衰减模型中建模误差的统计特征进行了系统研究,并建立了地壳二维Lg波衰减模型。由于Lg波振幅可能受到几何扩散函数的强烈影响,合理评估反演过程的误差对于能否使用最小二乘意义下的反演非常重要。通过在川滇及其邻近地区收集的建模误差样本,使用K-S数值检验方法、Q-Q图和正态分布图形检验方法对Lg波衰减层析成像反演的输入数据中建模误差的分布特征进行了统计分析。采用奇异值分解(SVD)和反投影方法,分别获得了川滇地区的Q_Lg模型,定量计算模型的协方差矩阵和分辨率矩阵,定量评估了Q_Lg模型中每个格点的分辨率和误差。结果表明：在一阶近似条件下建模误差服从正态分布;通过开发的数据筛选程序,可以产生一个接近完美正态分布的数据集;与反投影方法相比,利用SVD方法获得的地壳Q值的分辨率更高;在射线覆盖较好的区域,Q_Lg模型的分辨率达到100 km,相对误差小于3%。     

有限断层破裂时空过程反演结果误差的随机加权估计

针对非线性方法对有限断层破裂时空过程反演中存在的不唯一性问题,应用随机加权方法对反演结果进行误差估计．通过数值模型计算,定量揭示了滑动量、滑动角、破裂时间及上升时间在断层面上的分辨率值分布．应用随机加权方法对台湾海峡地震及缅中边境地震的误差估计结果表明,对应两次地震破裂中心位置上的参数分辨率值最高,结果最可靠,而在边缘子断层处滑动量与上升时间的分辨率值较低．      

空-地-井重力异常正则化协同密度反演方法

围绕综合利用空-地-井多源重力异常联合反演提升精度的目标,提出正则化协同密度反演方法,从而有效利用多维数据的横向和纵向变化特征提高反演精度,且无需先验信息的约束.此外,还提出利用奇异值谱和深度分辨率工具评价航空数据观测高度和层数对反演分辨率的影响.通过理论模型试验本文方法在空-地、地-井等不同情况下的应用效果,结果表明空-地-井重力异常正则化协同密度反演方法能获得更高分辨率、高精度的反演结果,且证明不同的钻孔位置对反演结果有较大的影响,从而可指导实际的空-地-井联合勘探.最后,利用文顿盐丘实际勘探数据进行空地和空地井重力数据协同反演,反演结果垂向分辨率明显优于地面观测数据反演结果,盐盖的顶面及中心埋深与前人研究和地质资料解释相吻合,验证了方法正确性及实用性,为推进我国空-地-井立体重磁勘探提供了重要的技术手段.     

含衰减地层微地震震源机制反演及其反演分辨率

微地震震源机制的反演对于非常规油气开发具有至关重要的作用.微地震信号主频高、能量小,容易受地层吸收衰减作用的影响使其波形发生畸变,本文提出了一种考虑地层吸收衰减作用的微震源机制反演方法,并利用费雷谢偏导矩阵的SVD分解(特征值分解)方法,分析研究了地层的吸收衰减因子的变化对于微地震震源机制反演分辨率的影响,根据理论计算给出了不同地震数据对各种震源机制反演的适用条件.理论计算证明,采用直达P波和S波数据联合反演震源的T值,单独利用直达P波反演震源的k值,可以有效降低地层吸收衰减作用对反演结果的影响.     

三分量地震资料的偏振分析

将奇异值分解运用于三分量地震资料矩阵中,得到了径向能量这一具有物理内涵的数学表达式.证明了资料矩阵的总能量可用奇异值的平方和来表达,以及P波到达的径向能量最大值在第一奇异向量方向出现.据此得到偏振属性,其中最显著的特点P波出现在径向能量接近于最大的地方,这可以给弱信号提供较准确的到时.为发展同时利用偏振和频散资料的联合反演不同周期面波相速度的横向不均匀分布这一新的反演方法提供偏振分析的基础数据.     

时间域航空电磁数据的反演

本文用广义逆矩阵理论讨论了时间域航空电磁数据的反演方法.以水平二层大地和球体模型为例进行了计算,结果表明这种方法对时间域电磁数据的反演是行之有效的.对于理论数据,一般仅需迭代数次即可稳定地收敛到真值.通过奇异值分析,可以确定一个模型中的相对重要参数和无关紧要参数;对于求解某一特定参数,可确定哪些数据起决定性的作用.由奇异值分解而得出的信息密度矩阵、模型分辨矩阵,分别给出了模型响应拟合数据和模型参数分辨率的度量.这些信息对于时间域航空电磁系统的设计、野外测量和资料解释都具有重要的参考价值.最后给出了实例.     

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。     

非均匀介质孔隙流体参数地震散射波反演

弹性波逆散射是非均匀介质参数反演的有效途径．本文从弹性波逆散射理论出发,利用微扰理论和稳相法,将非均匀介质参数视为背景介质与扰动介质参数的叠加,建立了纵波散射系数和非均匀介质中背景介质与扰动介质孔隙流体参数,剪切模量与密度间的直接关系．进而发展了一种非均匀介质孔隙流体参数叠前地震贝叶斯反演方法．该方法假设模型参数（扰动介质与背景介质孔隙流体参数,剪切模量与密度的比值）服从柯西分布,反演目标似然函数服从高斯分布,并采用平滑初始模型约束提高反演稳定性．模型和实际资料处理表明,该反演方法能够稳定合理的直接从叠前地震资料中获取孔隙流体参数,提供了一种高可靠性的非均匀介质流体描述方法．     

基于贝叶斯原理的PP波和PS波AVO联合反演方法研究(英文)

基于Aki-Richards公式和贝叶斯原理,本文发展了利用叠前PP波和PS波资料联合反演P波速度比、S波速度比和密度比的方法。该方法假设参数之间满足正态分布,引入参数协方差矩阵来描述反演参数之间的相关性以提高反演过程的稳定性,并同时使反演的参数序列服从Cauchy分布,引入矩阵Q来描述参数序列的稀疏性以提高反演结果的分辨率。采用本文提出的方法对模型数据和实际多波资料进行反演,结果表明:本文方法正确有效;与传统的单一PP波反演相比,PP波和PS波AVO联合反演具有稳定性更好和反演精度更高等优点。     

Two-dimensional inversion of magnetotelluric data with consecutive use of conjugate gradient and least-squares solution with singular value decomposition algorithms

I investigated the two‐dimensional magnetotelluric data inversion algorithms in studying two significant aspects within a linearized inversion approach. The first one is the method of minimization and second one is the type of stabilizing functional used in parametric functionals. The results of two well‐known inversion algorithms, namely conjugate gradient and the least‐squares solution with singular value decomposition, were compared in terms of accuracy and CPU time. In addition, magnetotelluric data inversion with various stabilizers, such as L2‐norm, smoothing, minimum support, minimum gradient support and first‐order minimum entropy, were examined. A new inversion algorithm named least‐squares solution with singular value decomposition and conjugate gradient is suggested in seeing the outcomes of the comparisons carried out on least‐squares solutions with singular value decomposition and conjugate gradient algorithms subject to a variety of stabilizers. Inversion results of synthetic data showed that the newly suggested algorithm yields better results than those of the individual implementations of conjugate gradient and least‐squares solution with singular value decomposition algorithms. The suggested algorithm and the above‐mentioned algorithms inversion results for the field data collected along a line crossing the North Anatolian Fault zone were also compared each other and results are discussed.     

瞬变电磁波场转换算法的改进

地球物理电磁场数据与虚拟地震波场数据之间存在数学上的等效转换关系,通过这种等效转换,可有效提高地球物理电磁法对地下目标体分界面的辨识度.但是这种转换在数学上属于不适定问题,可采用奇异值分解法处理.由于大奇异值控制计算矩阵的主要信息,小的奇异值控制计算矩阵的次要信息,传统的截断奇异值分解法只保留大奇异值,而忽略小的奇异值,导致数值解不够精确.本文提出一种新的修正方案——改进截断奇异值法,采用岭估计方法计算由小的奇异值引起的虚拟波场.模型计算结果表明：改进截断奇异值法比传统的奇异值分解法得到的波场转换结果更好,对某煤矿采空区探测数据进行了处理,成功分辨出采空区分界面.     

An iterative method for finding small magnetic objects in the subsurface by linear and non-linear inversion1

A method to determine the position and magnetization vector of buried objects producing a magnetic anomaly is described. The data used were collected in boreholes. Since the anomaly is due to a number of objects, a ‘stripping’ procedure is employed for finding them, and therefore the process of inversion for finding all objects causing the anomaly consists of a few inversion steps. In each inversion step, two dipoles are considered as a model which approximates an object. The position and magnetic moments of the dipoles are the unknown parameters. The initial parameters are optimized by minimization of an objective function. The optimization procedure consists of a combination of linear and non-linear inversion. The solution of the linear inversion is obtained by singular value decomposition and that of the non-linear inversion by a six-dimensional simplex method (polytope algorithm). After finding one object, its effect is subtracted (‘stripped’) from the data and a new inversion step is started with new initial models and with a reduced data set. The inversion steps for finding different objects are continued until the absolute norm of the data becomes less than some adjustable value. The data will also be inverted assuming a three-dipole model in order to find the effect of using a more complex model in the inversion. The efficiency of the method is demonstrated using synthetic and real borehole data.     

基于FFT-MA谱模拟的快速随机反演方法研究

虽然基于地质统计学的随机反演方法能够有效融合测井资料中的高频信息,但计算效率低,占用内存大,限制了它在实际资料中的应用.本文在保留传统随机反演方法优点的基础上,创造性地引入傅里叶滑动平均(Fast Fourier Transform-Moving Average,FFT-MA)谱模拟进行频率域的地质统计模拟,并利用逐步变形算法(Gradual Deformation Method,GDM)确保模拟结果与实际地震数据的匹配,构建了基于FFT-MA谱模拟的新的快速随机反演方法.与常规随机反演相比,新方法不仅分辨率高,而且能够使反演解得到快速收敛,有效提高计算效率,减少内存占用.模型试算获得了与理论模型吻合度较好的高分辨率反演结果.实际资料分析也表明新方法所得到的高分辨率反演结果能够对薄互储层进行良好的展示,为薄储层的识别提供高效可靠的技术支持.     

Mogi模型在长白山天池火山区的应用

文中首先介绍了Mogi模型的阻尼最小二乘反演,得出应用形变资料联合反演压力源参数的公式,再指出用等效源半径反演时不同初始值对反演结果的影响,说明选择合适的初始值可以方便地得到可靠的反演结果。然后用此方法反演长白山天池火山区压力源的大小和位置参数。采用垂直和水平位移的联合反演,数据为2002—2005年共4期的水准和GPS观测资料,最后结合其它观测资料,分析近年来岩浆可能的活动特征。结果显示岩浆的位置在发生变化,体积增量逐年减小,表明火山岩浆在2002—2005年的活动逐年减弱     

1D inversion of DC resistivity data using a quality-based truncated SVD

Many DC resistivity inversion schemes use a combination of standard iterative least-squares and truncated singular value decomposition (SVD) to optimize the solution to the inverse problem. However, until quite recently, the truncation was done arbitrarily or by a trial-and-error procedure, due to the lack of workable guidance criteria for discarding small singular values. In this paper we present an inversion scheme which adopts a truncation criterion based on the optimization of the total model variance. This consists of two terms: (i) the term associated with the variance of statistically significant principal components, i.e. the standard model estimate variance, and (ii) the term associated with statistically insignificant principal components of the solution, i.e. the variance of the bias term. As an initial model for the start of iterations, we use a multilayered homogeneous half-space whose layer thicknesses increase logarithmically with depth to take into account the decrease of the resolution of the DC resistivity technique with depth. The present inversion scheme has been tested on synthetic and field data. The results of the tests show that the procedure works well and the convergence process is stable even in the most complicated cases. The fact that the truncation level in the SVD is determined intrinsically in the course of inversion proves to be a major advantage over other inversion schemes where it is set by the user.     

Inversion for elliptically anisotropic velocity using VSP reflection traveltimes

This paper presents a traveltime inversion approach, using the reflection traveltimes from offset VSP data, to reconstruct the horizontal and vertical velocities for stratified anisotropic media. The inverse problem is reduced to a set of linear equations, and solved by the singular value decomposition (SVD) technique. The validity of this inversion scheme is verified using two sets of synthetic data simulated using a finite‐difference method, one for an isotropic model and the other for an elliptically anisotropic model. The inversion result demonstrates that our anisotropic velocity inversion scheme may be applied to both isotropic and anisotropic media. The method is finally applied to a real offset VSP data set, acquired in an oilfield in northwestern China.     

SOME REMARKS ON NOISE STABILITY IN DYNAMIC INVERSION OF REFLECTION SEISMIC DATA1

The dynamic inversion of reflection seismic data is investigated with reference to the influence of noise on pseudo-impedance logs. Model traces are calculated with 0, 5, 15 and 50% noise, respectively. In solving the inversion problem, the algorithm of Marquardt and Levenberg is used in connection with singular value decomposition (SVD). The results are within a 1% error range so that there was no visible change in the logs. Further signal analysis show that there is no dependence on the phase content of the wavelet used if all other parameters of the model are known.     

基于逆算子估计的AVO反演方法研究

传统反演算法以优化算法为主,而基于逆算子估计的AVO反演算法则利用了直接求逆的思路.算法的关键在于寻找存在逆函数的子域,进而可以在子域内直接求逆,这种解决反问题的思路不同于一般的优化类算法所采用的直接搜索解的方式,具有更高的效率.AVO反演利用了振幅随着偏移距的变化特征,反演的精度受到地震资料质量的影响,通过加入L1范数约束以及合理的初始模型有助于提高反演的稳定性以及准确度.模型测算和实际应用表明,基于逆算子估计的AVO反演方法具有较高的精确程度和可靠性.