双感应测井资料自适应正则化反演

为了准确获得地层真电阻率,确定地层侵入关系,将非线性反演理论与Morozov偏差原理结合,建立双感应测井(Dual-Induction Log)资料的自适应正则化全参数反演算法。首先根据Tikhonov正则化反演理论,将双感应测井资料反演问题变为含稳定泛函非线性目标函数极小化问题;再利用Gauss-Newton算法确定极小化解。在测井资料的最佳拟合迭代过程中,将Morozov偏差原理及Cholesky分解技术结合,建立一套自适应选择正则化因子方法;最后对大庆油田的实际测井资料进行反演处理。反演结论与试油结果表明,该算法在处理薄层、薄互层时能够取得更为满意的效果。     

基于商函数的动态载荷识别最优正则化参数选取方法

为解决载荷识别反问题,研究选取最优正则化参数商函数方法。利用Tikhonov正则化方法的最优化问题的最小二乘解,定义以正则化参数为自变量的商函数;根据不同的正则化参数,使用二次规划理论,求解Tikhonov正则化方法的最优化问题的最优解;基于不同最优解对应商函数的不同特点,将最优正则化参数的商函数方法,与广义交叉检验(Generalized Cross-Validation,GCV)准则所得载荷识别结果进行比较。数值仿真及试验验证结果表明,商函数方法对于共振区及非共振区下载荷识别问题具有较好的合理性和适用性。     

用U曲线法确定地震同震滑动分布反演正则化参数

针对地震滑动分布反演中正则化参数选取问题,提出利用U曲线法确定地震滑动分布反演正则化参数。利用U曲线法、L曲线法设计模拟实验,并将两种方法应用到芦山实际震例反演中。模拟实验以及芦山实际震例反演结果表明,利用U曲线法确定正则化参数反演地震滑动分布结果与L曲线法相比具有反演精度高、无需依赖数据拟合精度等优势。     

基于QSSP的震源破裂过程反演方法

在Qt平台上,基于QSSP软件,利用C⁺⁺进行地震破裂过程反演方法研究。采用按阶段反演的方法,第1阶段反演采用热浴算法进行全局搜索,先按断层区域的构造背景等初始条件对参数范围进行划取,在该范围内随机给定一组初始值开始迭代,使波形初步拟合避开局部最优解;第2阶段反演使用拟牛顿法进行快速收敛,提高波形拟合程度,迭代至目标函数小于误差条件时停止,输出满足误差条件的待解模型参数。为避免模型参数出现病态问题,使用拉普拉斯方程建立平滑矩阵并引入平滑因子对断层模型进行平滑约束。使用棋盘模型验证该方法的稳定性和可靠性。最后,将全国13个台站的重力数据积分后对2013-04-20芦山7.0级地震的破裂过程进行反演,并与其他研究结论进行对比分析。     

信息扩散函数在半参数地壳形变分析中的应用

提出一种利用信息扩散函数构建正则矩阵的新方法。首先,仅保留半参数模型的参数化模型部分,利用最小二乘估计获取参数模型的最小二乘残差;然后,将此残差向量作为信号,计算信号的信息扩散函数估值;最后,将信息扩散估计值作为正则矩阵的主对角元素构建正则矩阵。与时间序列法相比,新方法淡化了对信号连续性和光滑性的要求,且信息扩散函数估值本质上是残差的概率分布,相当于事先合理地确定了信号权阵,使得参数估计具有良好的稳健性。中国大陆华北块体的半参数地壳形变分析结果表明,新方法具有明显优势。     

预优共轭梯度法及井资料约束的磁化强度成像

磁化强度成像反演方法可以得到地下介质的磁化强度分布,可以反演任意形状磁性体,比模型参数反演占优势。但因
为该方法计算量和存储量较大,分辨率低,“趋肤效应”严重,导致其应用受到限制。共轭梯度法迭代计算的基本单位是列向量,减
少了计算时间和存储空间。再将核矩阵作用于与单元体深度有关的预优矩阵,可以提高反演分辨率并减弱“趋肤效应”,并且对于
有钻孔的区域,进行井资料约束,克服了反演问题的多解性。该理论模型模拟及青海省尕林格矿区地面高精度磁测磁化强度成像
反演说明该方法具有良好的应用效果。      

剩磁条件下磁性体磁化方向相关估计方法

针对强剩磁条件下磁化方向估计中存在的问题,提出在剩磁影响下磁性体磁化方向相关估计方法。首先,对磁倾角和磁偏角选取确定的参数范围,并以等间隔的步长进行递变,获得一系列的磁化方向数值;然后,根据不同的磁化方向对铁磁物质的实测磁总场异常数值进行化极处理;最后,求解磁总场化极数据与实测归一化磁源强度数据的互相关系数,取互相关最大值对应的磁化方向作为最终结果。仿真和实验结果表明,本方法能有效估计出近等轴状磁性体的总磁化方向。     

一种构造正则化矩阵的新方法

在系数矩阵病态时进行参数求解,合理地选择正则化参数和正则化矩阵可以提高参数估计的可靠性。针对正则化矩阵如何构造的问题,提出一种新的正则化矩阵构造方法。通过法矩阵较小奇异值对应的特征向量构造出一个对称矩阵,用该矩阵的主对角线元素构造出对角矩阵,然后与单位矩阵组合得出一种新的正则化矩阵。实验表明,当正则化参数小于1时,新算法的参数估值优于岭估计。     

高程异常拟合病态EIV模型的广义岭估计算法

应用法方程矩阵的特征向量构造正则化矩阵,改进通过单一参数既要实现降正则化、又要实现正则化的高程异常拟合病态模型算法。以二次多项式拟合模型为例,应用实测数据对算法进行验证,并与现有病态模型的正则化算法进行比较。     

基于卫星重力梯度数据的密度反演研究

为解决卫星重力梯度大尺度密度反演存在的平面模型误差、病态矩阵正则化、大型矩阵求逆、先验数据融合等问题,依托Tesseroid单元体模型,分别采用广义岭估计、代数重建(ART)、遗传算法完成了附加高斯白噪声的模拟异常体密度反演实验,并将反演结果与原始设定模型进行比较分析。     

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利用上行波进行VSP数据旅行时反演

利用双层剥层法同时对层速度和界面形态参数进行反演,并采用最小二乘法迭代求解。为了消除局部极值的影响,减少病态方程的产生,利用了 Ｍｏｎｔｅ Ｃａｒｌｏ 方法调整参数初始值。通过改变参数单位以均衡微分系数矩阵元素等措施,使这种反演方法具有较快的速度和较好的稳定性。对井底以上地层和井底以下地层均适用。     

Undersea Buried Pipeline Reconstruction Based on the Level Set and Inverse Multiquadric Regularization Method

The electric inversion technique reconstructs the subsurface medium distribution from acquired data. On the basis of electric inversion, objects buried under the earth or seabed, such as pipelines and unexploded ordnance, are detected and located in a contactless manner. However, the process of accurately reconstructing the shape of the target object is challenging because electric inversion is a nonlinear and ill-posed problem. In this work, we present an inverse multiquadric (IMQ) regularization method based on the level set function for reconstructing buried pipelines. In the case of locating underwater objects, the unknown inversion area is split into two parts, the background and the pipeline with known conductivity. The geometry of the pipeline is represented based on the level set function for achieving a noiseless inversion image. To obtain a binary image, the IMQ is used as the regularization term, which 'pushes' the level set function away from 0. We also provide an appropriate method to select the bandwidth and regularization pa-rameters for the IMQ regularization term, resulting in reconstructed images with sharp edges. The simulation results and analysis show that the proposed method performs better than classical inversion methods.     

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等式约束病态总体最小二乘模型的正则化解及其精度评定

利用平差参数间合理的先验信息能够显著提高解的精度。在病态总体最小二乘模型的基础上,引入等式约束条件,建立等式约束病态总体最小二乘模型,构建该模型的约束正则化准则,并根据拉格朗日极值法导出参数的迭代解及方差-协方差阵,最后以数值算例和病态测边网算例验证公式的正确性。结果表明,新方法通过正则化准则能改善法矩阵的病态性,且遵从EIV准则顾及系数阵的误差,同时还考虑参数间合理的先验信息,其解的精度得到显著提升。     

Application of gravity inversion focused in Changbai Mountain

Focusing inversion is accomplished by the iterative of abnormal source to make the image gradually focused. It can better reflect the underground geological geometry and physical parameters. The model experiments in the study show that gravity focusing inversion allows inversion image stabilization and polymerization, which solves the multiple solutions and instability of inversion and so on. The method is applied to measured gravity data processing of certain region of Changbai Mountain, compared to Euler deconvolution, the results show that the method for determining the horizontal position and depth of underground anomalies has good efforts.     

Combined analysis of gravity and magnetic anomalies using normalized source strength

The traditional combined gravity and magnetic analysis uses the linear regression of the first order vertical derivative of the gravity anomaly and the reduction to the pole ( RTP) magnetic anomaly, and provides the quantitative or semi-quantitative interpretation by calculating the correlation coefficient, slope, and inter-cept.In the calculation process, due to the remanent magnetization, the RTP anomaly still contains the effect of oblique magnetization, as a result, the homologous gravity and magnetic anomalies may display irrelevant results in the linear regression calculation.To solve this problem, we present a new combined analysis using normal-ized source strength ( NSS ) .Based on the Poisson's relation, the gravity field can be transformed into the pseudomagnetic field of the direction of geomagnetic field magnetization under the homologous condition.The NSS of the pseudomagnetic field and that of the original magnetic field are calculated, which are insensitive to the remanence, and then the linear regression analysis is carried out.The approach is tested using synthetic model under complex magnetization, the results show that it can still identify the gravity and magnetic anomalies from same source under strong remanence, and can establish the Poisson's ratio.Finally, this approach is ap-plied in Wudalianchi in China.The results demonstrated that this approach is feasible and can provide the ref-erence for further data processing and interpretation.