基于广义逆的层析成像反演方法研究

为了解决常规反演算法收敛速度慢、无法处理不完全投影和先验信息等问题．提出基于广义逆的层析成像反演方法，将广义逆和求解一般方程组的理论统一起来．阻尼系数的确定是此类反演算法的关键，在分析解估计评价指标与阻尼系数关系的基础上，提出阻尼系数的最优化技术，在多目标优化的框架下，采用理想点法求解，分别对核心异常模型和复合模型进行了数值仿真计算，结果表明该阻尼系数优选方法对初始值不敏感，所得阻尼系数合理，反演结果与原设定模型具有较高的相关性，比常规反演算法有更高的求解效率和精度．     

基于广义逆理论的河网糙率反演研究

引入广义逆和Backus-Gilbert反演理论，构造了牛顿-广义逆方法和自然逆方法计算优化算法的搜索方向，进行 河网糙率反演，并推导了两种算法反演解估计的分辨率矩阵和单位协方差矩阵.理论分析表明,牛顿-广义逆优化算法具有 二阶收敛速度.在反演过程中结合Wiggins方法控制观测数据中的噪声，能够有效调节河道糙率反演结果的分辨率和方差. 数值仿真表明这两种算法与Wiggins方法相结合，选取适当的控制参数，既能达到较高的精度，又能有效地抑制噪声，提 高数值计算的稳定性.     

矩阵的多值广义逆

对于矩阵的ＭＰ逆Ａ＾＋和方阵Ｂ的Ｄｒａｚｉｎ逆Ｂｄ,（Ａ＾＋）＾＋＝Ａ,（（Ｂｄ）ｄ）ｄ＝Ｂｄ,在逻辑上,Ａ＾＋是二值的,Ｂｄ是直觉主义的,本文研究多值逻辑中矩阵的广义逆,建立了ｋ值ＭＰ逆和多值广义逆。     

微重力与微重力梯度异常的广义逆综合反演

将微重力异常与微重力梯度异常同时代入广义逆反演过程中，不需进行人为约束，在微重力异常和微重力梯度异常分别得到拟合的前提下，自动地综合修改模型参数，不仅其反演结果的多解性大大减少，而且其收敛速度比单一异常反演的收敛速度快；此外，综合反演还能使短剖面的异常对复杂地质体的反演成为可能。广义逆综合反演的基本原理可推广应用到其它地球物理方法中去。     

广义分块对角矩阵的广义逆矩阵

本文对广义分块对角矩阵的广义逆矩阵给出了一个运算规则,利用它可以简化求广义分块对角矩阵的广义逆矩阵.     

某些分块矩阵的广义逆

本文首先未加证明地引用[1]中的两个定理作为引理,从而给出了某些分块矩阵的广义逆的简便求法。     

广义逆的两个性质

本文获得了广义逆矩阵的两个性质。     

两种广义逆矩阵A~-的理论证明

给出了秩为ｒ的分块矩阵的两个性质，从而给出了两种广义逆矩阵Ａ－的理论证明     

走时层析成像的迭代Tikhonov正则化反演研究

针对反问题求解常遇到不适定的困难,采用奇异值分析的方法探讨了层析成像反演方程的不适定特征,研究了利用迭代Tikhonov正则化方法求解二维走时层析成像问题.该方法是一种拟线性化的反演算法,采用L曲线法确定最优正则参数,拟定了四个有效的反问题迭代收敛准则,得到在残差范数和解的范数之间取最优折衷的解.核心异常数值化模型的计算结果表明,该方法比传统的联合迭代重建算法(SIRT)收敛快、精度高.     

Near-surface model reconstruction using pseudo well-surface simultaneous travel time tomographic inversion

The static correction of a near-surface model may be improved by using travel time tomographic inversion.We discuss unfavorable factors in the inversion of surface seismic waves that have been analyzed by the first break.These factors show that sources and geophones arranged on the surface,or close to the surface,give a first break that only includes the direct wave and the up going wave from the down going to up going transition.These up going waves have weak directivity when they arrive at a geophone and so the rays passing through the grids have small directional differences and a narrow azimuth.Drawing lessons from the advantages of Vertical Seismic Profiling(VSP)acquisition mode we describe a pseudo well-surface simultaneous travel time tomographic inversion of a near-surface model.The well depth should be increased in the surface seismic study to produce a pure up going wave,to enhance the verticality of the rays and to increase the azimuth and shorten path length of the rays.Simulations of the effect of well depth on a pseudo well-surface simultaneous travel time tomographic inversion model are reported.The results show that the static corrections are improved significantly when the well depth extends below the weathered or sub-weathered layers.The root mean square error of the statics is 1.14 or 0.93 ms for these two situations,respectively.     

Robust user equilibrium model based on cumulative prospect theory under distribution-free travel time

The assumption widely used in the user equilibrium model for stochastic network was that the probability distributions of the travel time were known explicitly by travelers. However, this distribution may be unavailable in reality. By relaxing the restrictive assumption, a robust user equilibrium model based on cumulative prospect theory under distribution-free travel time was presented. In the absence of the cumulative distribution function of the travel time, the exact cumulative prospect value(CPV) for each route cannot be obtained. However, the upper and lower bounds on the CPV can be calculated by probability inequalities.Travelers were assumed to choose the routes with the best worst-case CPVs. The proposed model was formulated as a variational inequality problem and solved via a heuristic solution algorithm. A numerical example was also provided to illustrate the application of the proposed model and the efficiency of the solution algorithm.     

基于数据采样方法的城市道路自由流行程时间估计

基于交通波模型,提出利用车牌识别数据估计城市道路自由流行程时间. 无需额外架设检测器或现场测算,所提方法具备准确性、科学性、实用性的特点. 基于车辆均匀到达的假设,将行程时间分为自由流行程时间和延误,建立信号影响下的路段行程时间分布函数. 针对现实环境中车流非均匀到达的特点,提出数据重采样方法生成符合均匀流假设的行程时间数据;拟合行程时间分布函数以获得路段自由流行程时间. 在杭州市多个路段的数据验证结果表明,重采样后的行程时间数据较好地拟合了行程时间分布模型,估得的自由流行程时间准确且具备理论支撑.     

由传播时间反演海水中的声速剖面

海水中的声速剖面对声传播有比较重要的影响.利用海上实验的实际数据由声信号的传播时间反演海水中的声速剖面.用经验正交函数表示声速剖面,根据选取的代价函数应用遗传算法搜索最优解.为了提高反演算法的性能,快速反演获得海水中的声速剖面,在射线声学理论下,对传播时间的计算方法进行了改进,有效降低了算法的计算量.利用海上实验的实际数据反演获得的声速剖面与实验时直接测量获得的声速剖面相比较,误差小于2‰.反演结果与实测结果基本相符.     

Nonlinear inversion for electrical resistivity tomography based on chaotic DE-BP algorithm

Nonlinear resistivity inversion requires efficient artificial neural network （ANN） model for better inversion results. An evolutionary BP neural network （BPNN） approach based on differential evolution （DE） algorithm was presented, which was able to improve global search ability for resistivity tomography 2-D nonlinear inversion. In the proposed method, Tent equation was applied to obtain automatic parameter settings in DE and the restricted parameter Fcrit was used to enhance the ability of converging to global optimum. An implementation of proposed DE-BPNN was given, the network had one hidden layer with 52 nodes and it was trained on 36 datasets and tested on another 4 synthetic datasets. Two abnormity models were used to verify the feasibility and effectiveness of the proposed method, the results show that the proposed DE-BP algorithm has better performance than BP, conventional DE-BP and other chaotic DE-BP methods in stability and accuracy, and higher imaging quality than least square inversion.     

芦山余震震源参数及震源区品质因子反演

为了确定2013年4月20日芦山地震部分余震的震源参数及传播路径对地震波的衰减特性,选取30次余震中15个强震台站获取的179组加速度记录,选择其中一次余震作为参考事件,基于广义反演方法计算了芦山余震的位移震源谱及品质因子,采用网格搜索方法确定余震震源参数,进一步确定了震源参数的定标关系.结果表明:芦山地震平均应力降略低于汶川余震平均应力降,震级与应力降没有明显相关性,视应力与应力降正相关;该研究区域0.5~20 Hz频段品质因子为Q(f)=31.867f1.037 5,地震波衰减速度较快.     

广义出行费用下的冰雪条件路网容量可靠性

为体现冰雪条件下出行者路径选择行为,准确评价路网容量可靠性,采用行程时间、行程时间可靠性及安全性的加权和定义广义出行费用,引入坡道行驶安全系数量化安全性出行费用,建立基于广义出行费用的随机用户平衡分配模型.从路段角度定义容量可靠性的概念,建立基于广义出行费用的路网容量可靠性模型,给出Monte Carlo仿真和交通规划...     

一类广义范德蒙矩阵求逆的快速算法

利用线性方程组给出了一类广义范德蒙矩阵可逆的充分条件及逆矩阵的矩阵显式表示式，并给出了求逆的递推公式和快速算法，所需计算量为O(n^2)，一般矩阵求逆的计算量为O(n^3)．