基于PC机群的大地电磁Occam反演并行计算研究

PC cluster basedmagnetotelluric 2-D Occam's inversion parallel calculation.

1. 中国地质大学(武汉), 湖北武汉430074;2. 桂林工学院, 广西桂林541004

China University of Geoscience, Wuhan 430074, China

Occam反演以其稳定收敛和不依赖于初始模型的特性被广泛应用于大地电磁数据的处理,但偏导数矩阵的计算和拉格朗日乘子的求取导致大量的模型正演,使得反演速度较低。为此,研究了用基于PC机群的并行计算来解决这一问题的方法。首先对Occam反演方法进行了阐述;然后,分析了反演方法中各计算耗费的时间,提出对约占计算量90％的偏导数和拉格朗日乘子进行并行计算的思想,即偏导数计算采用频点计算一级的大粒度并行,拉格朗日乘子扫描和一维搜索分别采用μ值计算一级的大粒度并行和频点计算一级的小粒度并行;给出了并行计算的实现方法,即在PC机群上,利用主一从编程模式实现Occam反演的整体并行计算。在计算中,采用任务组合方式,减少了通信量,较好地实现了负载均衡。在4节点PC机群上,对应于拉格朗日乘子的扫描和一维搜索方式,整体加速比分别达到3.36和2.83。

Occam's inversion is widely used inmagnetotelluric data processing for its stability of convergence and independence on initialmodel.But the calculations of Jacobianmatrix and Lagrangemultiplier need some forward calculations, which would result in a low inversion speed.Based on parallel PC cluster computing, this article presents a solution to this problem.Firstly, it gives a general description of the Occam inversion; then it analyzes the calculation time on different part of the inversion, putting forward a thought of parallel computation for derivativematrix and Lagrangemultiplier accounting for about 90% of the total inversion time.The performing procedures is as following: Implementing the parallelism for derivativematrix with frequency based coarse granularity; Lagrangemultiplier scanning with coarse granularity based on μ calculation; La-grangemultiplier one dimensional searching with frequency based fine granularity.The implementationmethod is given:master-Slave programming on a PC cluster completes the whole computation.Task combinationmethods are a-dopted to reduce themessage passing and balance the computation loads.On a 4 nodes PC cluster, the whole speedup of Occam inversion have reached 3.36 and 2.83 corresponding to Lagrangemultiplier scanning and 1-D searchingmode.