三维感应测井响应计算的交错网格有限差分法  

APPLICATION OF STAGGERED GRID FINITE DIFFERENCE METHOD TO THE COMPUTATION OF 3-D INDUCTION LOGGING RESPONSE

作　　者：汪功礼[1] 张庚骥[1] 崔锋修 高峰[2] 

机构地区：[1]石油大学(华东)地球资源与信息学院,东营257061 [2]新疆石油管理局测井公司,克拉玛依834000

出　　处：《地球物理学报》2003年第4期561-567,共7页Chinese Journal of Geophysics

基　　金：中国石油天然气集团公司"九五"重点科技项目 ( 970 3 0 2 ) .

摘　　要：应用交错网格有限差分法计算三维复杂环境中的感应测井响应 .其中 ,利用Krylov子空间不变性求解离散得到的大型稀疏复对称线性方程组 .在构造Krylov子空间时使用其系数矩阵的伪逆以改善迭代的收敛性 .迭代中 ,使用不完全Cholesky分解共轭梯度法求解 4个三维Poisson方程以得到新的Lanczos向量 .通常迭代不超过 2 0次可得到理想结果 .另外 ,提出一种新的物质平均公式以计算电导率平均值 ,可保证电流守恒 .The finite difference method using staggered grid is applied to simulate the induction logging response in 3D media. The invariance property of the Krylov subspace is used to solve the large sparse complex symmetric linear system. To improve iteration convergence the pseudo inverse of the coefficient matrix is employed when constructing the Krylov subspace instead of the coefficient matrix itself. In each iteration four 3D Poisson equations are computed to get a new Lanczos vector with incomplete Cholesky decomposition conjugate method. Generally, the desirable solution is achieved with no more than 20 times of iteration. Also, a new material averaging formula is presented to get a reasonable average of the conductivity, which guarantees the conservation of the electric current.

关 键 词：三维感应测井响应 交错网格有限差分法 计算 KRYLOV子空间 电导率平均值 地球物理勘探 

分 类 号：P631.81[天文地球—地质矿产勘探]