中文摘要：

讨论了地震层析成像的LSQa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．

英文摘要：

We discuss the LSQR algorithms used in earthquake travel time tomography. We keep the epicenter terms in the equation for regional events, and then use the orthogonal projection method to eliminate the epicenter terms. For tele-events, the classic smoothing process is used. The number of non-zero elements in the partial derivative matrix is increased by several times because of the orthogonal projection and smoothing processes. For a large scale inversion problem, the amount of non-zero elements can be dozens of Gigabytes or hundreds of Gigabytes. The huge amount of memory requirement becomes the bottle neck of LSQR algorithms. matrix, designed an efficient data structure for the sparse matrix, used a distributed memory and computation scheme for matrix computation, and implemented it on a multi-processor super-computer. We have derived an estimation formula of parallel efficiency and tested two real tomography models.