Study Of DC And IP 3-D Nonlinear Conjugate Gradients Parallel Inversion Algorithm For The Different Record Layouts Combined Data

The direct current (DC) and induced polarization (IP) method is widely used in shallow hydrology, exploration, engineering and environment fields. Because most of shallow geological targets are the three-dimensional (3D) electrical structures and the 1D and 2D inversion cannot recovery the 3D electrical structures. In order to avoid the 3D inhomogeneity effect, the 3D record layout and inversion should be adopted. Based on the location of borehole in mine, we will combine surface observation with borehole observation, in other word, the record layout combined surface, surface-borehole, borehole-surface and borehole-borehole. The 3D geophysical problem is not only nonlinear and underdetermined, but also spends more time during inversion. If the linear inversion method is adopted, it is will obtain local minima for the inversion results. Thus, this paper will use nonlinear conjugate gradients inversion method to solve the local minima problem and add MPI and GPU parallel algorithms to speed up the efficiency of computation.In the paper, finite difference method is used to calculate 3D geoelectric field of point sources for forward problem of DC and IP. During forward modeling, the incomplete Cholesky decomposition conjugate gradients (ICCG) and incomplete LU decomposition (ILUO) biconjugate gradient stabilized (BICGSTAB) method are employed for computation of linear equation.And for the coefficient matrix storage, the CSR (compress sparse row) matrix format will be used, that is not only save memory consumes, but also speed up the efficiency of computation. The nonlinear conjugate gradients algorithm is adopted for inversion. The advantages of nonlinear conjugate gradients (NLCG) inversion is that jacobian matrix needn’t to be calculate any more, but compute jacobian matrix or transpose of it multiply with a vector, and the computation for linear equation during the process of multiplication is called "pseudo-forward". This method avoid store jacobian matrix and decrease computation. Nonlinear conjugate gradients iteration is used to calculate one forward and two "pseudo-forward" problems.Because massage passing interface (MPI) can assign independent multi-task to multi-process, so MPI can be used for computation geoelectric field when multi-point sources exist. Because of it will involves solving linear equation in forward and "pseudo-forward" modeling, high efficiency of GPU and most of time is spend in it during the inversion, so CULA Sparse (a set of GPU-accelerated numerical linear algebra libraries) is called for solving linear equation. CULA Sparse library contains many kinds of solving equation methods and preconditioners.We will adopt ILUO preconditioner and CG method in this paper.Finally, some single record layouts and combination record layouts are designed. synthetic data examples illustrate that this parallel inversion algorithm is effective, and it is also demonstrate that inversion results from the data collected by record layout that combine two or more record layout are better than the results from the data acquired by single record layout.