频率域最小二乘反演

本研究目的在于利用频率域的全波场有限元最小二乘反演求取地下更多的岩性信息如各向异性弹性参数、粘性参数等物性参数,对石油勘探中油气藏的直接检测和油藏描述等岩性解释很有帮助。由于直接求取所有的各向异性及粘性参数是高度非线性的、非常困难的,所以先选择了比较简单一些的弹性波速度信息：纵波速度与横波速度进行求取,这比常规声波方程资料处理能够多得到横波的信息,对岩性解释很有帮助。在频率域弹性波有限元正演方程的基础上,依据使目标函数(也就是观测数据和正演数据残差的二次范数)最小的准则,导出了频率域弹性波有限元最小二乘反演算法。其中用矩阵压缩存储与LU分解技术存储与求解正演方程中的大型稀疏复系数矩阵,用Green函数更快速的求取Jacobian矩阵,用共轭梯度算法求解大型稀疏矩阵的最小二乘解。

THE LEAST-SQUARES WAVEFORM INVERSION IN FREQUENCY DO-MAIN

The objective of this research is to obtain more subsurface lithologic information such as anisotropic,in-elastic parameters than onventional processing,by using the finite-element least-squares inversion in frequency domain,which is very helpful to direct detection or depiction of oil or gas reservoir, etc. Since to invert all the 1ithologic coefficients including anisotropic,inelastic directly is very nonlinear and difficult,we first select some sim-ple parameters to invert,such as P-wave and S-wave velocities,which can obtain more lithologic information:S-wave velocity than conventional acoustic-wave inversion.We deduce the formula of the finite-element least-squares inversion on the basis of forward modeling equations according to minimum of square roots of data residuals between field and calculation. We apply several advanta-genus methods,such as applying the compressional matrix-storage and LU-decomposition techniques to save and solve the large sparse complex-valued coefficient matrix,applying Green functions to solve the Jacobi coefficients in inversion fast,using the conjugate-gradient method to solve unknowns.