反射地震走时层析成像中的大型稀疏矩阵压缩存储和求解

Compression storage and solution of large sparse matrix in traveltime tomography of reflection seismic data

反射地震走时层析成像是一种精度较高的速度求取方法,最终可归结为线性方程组的求解.方程组具有很大的维数,常规解法需要很大的存储量和计算量.本文考虑到当投影函数取为走时残差,图象函数取为慢度残差时,灵敏度矩阵中的元素表示射线经过网格的长度的特殊物理意义,采用行索引的压缩存储方式,在射线追踪正演模拟过程中直接压缩存储灵敏度矩阵,在层析反演过程中利用压缩后的矩阵进行求解,大大降低了存储量和计算量.

Traveltime tomography of reflection seismic data is one of those methods which have higher accuracy to obtain velocity and finally comes down to the solution of the large sparse equation system. But very large storage amount and calculation amount are demanded when solving the equation matrix in regular way, due to the high dimension and the iterative solution style, which strongly restricts the practical application of tomography method. Thus the research on the methods reducing calculation amount and storage amount is very important and significative. In this paper, the methods of compression storage and solution of large sparse matrix are used in tomography inversion. The line-indexed compression storege is chosen, due to that the element of sensitivity matrix has special physical meaning that the value of the element represents the length of ray in each velocity cell, when considering traveltime residual as projection function and slowness residual as image function in Radon transformtion. Thus each line in the sensitivity matrix can be directly stored in a compression style in ray-tracing modeling, and the large amout of storage can be retrenched since a ray only passes very a few cells. Furthermore the tomography inversion can be easily implemented with compression-stored sensitivity matrix because only the multiplication operation between matrix（or matrix trans- pose） and vector is demanded in solution of tomography equation system, and the operation can be easily achieved. And research shows that more stroage amount and calculation amount can be retrenched if the sensitivity matrix, has larger sparseness.