APPLICATION OF STAGGERED GRID FINITE DIFFERENCE METHOD TO THE COMPUTATION OF 3-D INDUCTION LOGGING RESPONSE
三维感应测井响应计算的交错网格有限差分法

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.