地震层析成像LSQR算法的并行化

讨论了地震层析成像的LSQR算法(最小二乘QR分解). 在建立偏导数矩阵方程组时,对区内地震在方程中保留震源项,引入正交投影算子进行参数分离,对区外远震采用传统的平滑处理方式,用LSQR法求解联立的方程组. 由于区内地震的正交分解处理和区外远震的平滑处理,使得偏导数矩阵中的非零元素成倍增加,对于大型反演问题,这些非零元素常常达到几十GB到几百GB的数量级,巨量的内存占用成为LSQR算法的瓶颈. 针对这一问题,本文研究了偏导数矩阵中非零元素的分布规律,设计出合理的存储结构,采用分布式存储进行矩阵计算,提出了LSQR算法的并行化方案,并在联想深腾6800超级计算机上实现. 导出了LSQR算法的并行效率估算公式. 对两个地区的实际地震层析成像数据进行了效率测试.     

层析成像新算法及其在工程检测上的应用

基于走时和振幅的层析成像反演涉及大型稀疏矩阵方程的求解，当矩阵严重病态时，目前流行的正交分解型迭代算法难以取得良好的成像效果．本文介绍一种改进的ＬＳ_ｑＲ算法，即带阻尼的ＬＳ_ｑＲ迭代算法，它应用在北京机场高速公路桥墩施工质量检测中，取得了良好的效果．     

LSQR法在位场反演中的分析与评价

LSQR法具有计算效率高、对计算机内存要求低的优点,适合于大规模问题的求解。为探讨其应用于位场反演的稳定性和可靠性,笔者以加入不同噪声的两个合成模型数据为实验对象,比较分析了Tikhonov正则化与LSQR法求解结果,显示直接利用LSQR法求解位场反问题能够得到满意的正则化解,其解模型相对Tikhonov正则化,最大相对误差仅为0.36%,说明直接利用LSQR法求解位场反问题是可行的。将其应用于四川盆地雅安地区重力三维反演,极大地降低计算成本,获取了区内沉积盆及主要断裂分布情况,为页岩气靶区优选提供了有力支撑。     

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An algorithm for fast 3D inversion of surface electrical resistivity tomography data: application on imaging buried antiquities

In this work a new algorithm for the fast and efficient 3D inversion of conventional 2D surface electrical resistivity tomography lines is presented. The proposed approach lies on the assumption that for every surface measurement there is a large number of 3D parameters with very small absolute Jacobian matrix values, which can be excluded in advance from the Jacobian matrix calculation, as they do not contribute significant information in the inversion procedure. A sensitivity analysis for both homogeneous and inhomogeneous earth models showed that each measurement has a specific region of influence, which can be limited to parameters in a critical rectangular prism volume. Application of the proposed algorithm accelerated almost three times the Jacobian (sensitivity) matrix calculation for the data sets tested in this work. Moreover, application of the least squares regression iterative inversion technique, resulted in a new 3D resistivity inversion algorithm more than 2.7 times faster and with computer memory requirements less than half compared to the original algorithm. The efficiency and accuracy of the algorithm was verified using synthetic models representing typical archaeological structures, as well as field data collected from two archaeological sites in Greece, employing different electrode configurations. The applicability of the presented approach is demonstrated for archaeological investigations and the basic idea of the proposed algorithm can be easily extended for the inversion of other geophysical data.     

地震层析成像中LSQR算法的快速求解

针对传统LSQR反演算法计算时间长、占用内存大的不足,这里提出了一种LSQR的快速算法,通过线性三元组存储稀疏矩阵,实现相应的矩阵运算,使LSQR算法的运算速度及内存占用都有较大地改善。     

Determination of 3-D Velocity Anomalies of the Nanbei Tectonic Zone of China Based on Local Earthquakes

In this paper, 3-D velocity images of the crust and upper mantle beneath the Nanbei tectonic zone of China are constructed using P-wave travel time residuals of earthquakes, with the data supplied by China's seismic networks and the International Seismic Centre.During the model parameterization in the tomographic inversion the interpolation function of grid node velocities is used as the space function of velocity, and the velocity function is allowed to be discontinuous. The difficulties caused by large memory demand and high computing cost in solving the system of equations are avoided by utilizing the least squares QR decomposition algorithm. Thus, the stability of the algorithm is ensured. Though resolution images are not derived in the inversion process based on the resolution theory of Backus and Gilbert, a covariance resolution method is put forward by the authors. The resolution analyses have proved the reliability of the image results. 3-D ray tracing is conducted to obtain the ray paths in a s     

井中声波CT技术系统及其应用

叙述了井中声波CT技术系统的测量方式、数据采集和数据预处理以及CT正反演的基本方法, 列举了在工程勘察和油气田开发中的应用实例,显示出井中声波CT成果为查明目标体的位置和圈定目标体的形态是有效的。同时也显示了井中声波CT技术作为一种精细勘查手段,具有开发潜力和应用前景。     

FMM射线追踪方法在地震学正演和反演中的应用

FMM(Fast Marching Method)射线追踪方法是一种求解非线性程函方程数值解的射线追踪方法.本文在FMM射线追踪算法流程的基础上引入一个数据链表,方便求解射线路径,另外还引入一个与解精度有关的方向参数,可以更好的控制解的精度.然后在一些理论模型中对FMM方法的正演和反演计算做了若干验证,结果表明,FMM方法可以较快而且稳定地得到令人满意的结果.