CSC频率—空间域波动方程数值模拟  

Numerical modeling of wave equation in frequencyspace domain with CSC.

作　　者：吕晓春[1,2] 顾汉明[1,2] 成景旺[1,2] 周丽[1] 

机构地区：[1]中国地质大学(武汉)地球物理与空间信息学院 [2]中国地质大学(武汉)构造与油气资源教育部重点实验室,湖北武汉430074

出　　处：《石油地球物理勘探》2014年第2期288-294,219,共7页Oil Geophysical Prospecting

基　　金：国家重大科技专项"南海深水区油气勘探地球物理关键技术"(2011ZX05025-001)资助

摘　　要：针对频率—空间域波动方程数值模拟需要巨大内存空间的现状,提出了利用列索引压缩存储(CSC)技术存储大型稀疏非对称复数型的矩阵系数。CSC技术将系数矩阵转化为三个一维数组来存储,分别存储系数非零元素、非零元素对应所在的行以及每列起始非零元素所在位置。经CSC技术压缩存储后显著减少了内存空间及计算量,在计算时只有少许的非零元素参加计算,且根据三个一维数组可以简便地找到对应的非零元素,进而采用LU分解快速而精确地求解。本文基于Jo等提出的最优化9点差分方法,首次应用CSC技术在频率—空间域进行二维声波方程数值模拟。通过对Corner-edge模型和二维Marmousi模型进行试算,可以显著节省内存需求,明显提高计算速度,进而得到精度较高的正演结果。Numerical modeling of wave equation in frequency-space domain faces difficulty when storing enormous coefficient matrix.In order to solve the problem and store large sparse non-symmetric complex coefficient matrix,compressed sparse column(CSC)method is proposed in this paper.CSC method converts the coefficient matrix into three one-dimension arrays which respectively store nonzero coefficient,the row of each non-zero element and indices of the first non-zero element in each column.This method reduces greatly the memory space and the amount of calculation,and it is convenient for the LU decomposition to solve the wave equation.In this paper,the authors adopt the optimal 9-point finite difference for the acoustic modeling,and introduce the perfect matched layer(PML)in order to eliminate boundary reflection. Through numerical tests on Corner-edge and Marmousi model,validity and reliability of the method are proved.

关 键 词：频率-空间域 CSC 系数矩阵 一维数组 LU分解 数值模拟 

分 类 号：P631[天文地球—地质矿产勘探]