Parallel LSQR algorithms used in seismic tomography
地震层析成像LSQR算法的并行化

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.