电阻率法和激发极化法不同装置组合数据三维非线性共轭梯度反演并行算法研究

发布时间：2018-03-14 10:51

本文选题：电阻率法　切入点：激发极化法　出处：《中国地质大学(北京)》2015年博士论文　论文类型：学位论文

【摘要】：直流电阻率法和激发极化法在浅层水文、找矿、工程、环境等领域应用广泛,而浅层的地质目标体一般表现为三维电性结构,一维和二维的数据反演不能完整的恢复三维电性结构,为了避免在反演中三维体不均匀性的影响,需要采用三维数据观测和反演。在找矿方面,基于矿山中钻井的相对位置,我们可以将井中装置与地表装置相结合,即形成地表、地井、井地和井间四种观测方式相结合的复合采集方式。由于三维地球物理问题不仅是欠定的、非线性的,在进行三维反演时还存在耗时长的特点,而且线性反演算法往往使得反演陷入局部极小,所以本文采用非线性共轭梯度反演算法来规避使用线性反演时所带来陷入局部极小的问题,并且在该反演算法中加入MPI和GPU并行算法来提高计算效率。针对直流电阻率法和激发极化法的正演问题,本文采用有限差分法求解点电源三维地电场。针对正演算法中的解方程,采用不完全Cholesky分解的共轭梯度法和不完全LU分解的稳定双共轭梯度法；针对大型系数矩阵,本文采用行压缩存储的格式,不仅减小了内存消耗,还提高了计算的效率。反演算法采用非线性共轭梯度法,非线性共轭梯度法的优势就在于不用求雅克比矩阵,而是直接求取雅克比矩阵或者其转置和一个向量的乘积。该方法不仅避免了存储雅克比矩阵,还大大减少了计算量,每次反演迭代计算一次正演,两次“拟正演”。在并行计算方面,由于MPI含有将多个独立任务分配给多进程同时计算的特性,即可利用MPI进行多个点电源地电场的计算。而在计算正演和“拟正演”过程中,都存在解方程的过程,反演过程的大部分时间都消耗在解方程中,因此,利用GPU快速运算的特性,在解方程时,调用基于GPU开发的CULA Sparse函数库参与解方程运算。CULA Sparse函数库包含多种解方程方法和预处理方法,在本文中,我们采用不完全LU分解的共轭梯度解方程。最后,分别设计单一采集装置和多个将地表、地井、井地和井间相结合的装置,通过模型算例验证实现的非线性共轭梯度并行算法的有效性,并说明了多装置相结合采集的数据参与反演比使用单一装置采集的数据参与反演的结果更好。
[Abstract]:DC resistivity method and induced polarization method are widely used in shallow hydrology, prospecting, engineering, environment and so on. One-dimensional and two-dimensional data inversion can not completely restore the three-dimensional electrical structure, in order to avoid the effect of three-dimensional body inhomogeneity in inversion, it is necessary to use three-dimensional data observation and inversion. In ore prospecting, based on the relative position of drilling in mines, We can combine the in-well device with the surface device, that is, to form a composite acquisition method which combines the surface, ground well, well ground and cross-well observation methods, because the three-dimensional geophysical problem is not only undetermined, but also nonlinear. It also takes a long time to carry out 3D inversion, and linear inversion algorithm often causes inversion to fall into local minima. So this paper uses nonlinear conjugate gradient inversion algorithm to avoid the problem of local minima caused by linear inversion. MPI and GPU parallel algorithms are added to the inversion algorithm to improve the computational efficiency. In this paper, the finite difference method is used to solve the three dimensional geoelectric field of point power supply. The conjugate gradient method of incomplete Cholesky decomposition and the stable double conjugate gradient method of incomplete LU decomposition are used to solve the solution equation of forward algorithm. In this paper, the format of row compression storage is adopted, which not only reduces the memory consumption, but also improves the efficiency of calculation. The inversion algorithm adopts nonlinear conjugate gradient method, and the advantage of nonlinear conjugate gradient method is that it does not need to obtain Jacobian matrix. The method not only avoids storing the Jacobian matrix, but also reduces the computational complexity. In parallel computing, because MPI has the property of assigning multiple independent tasks to multiple processes simultaneously, it can be used to calculate the geoelectric field of multiple point power sources, and in the process of calculating forward and quasi-forward, There is a process of solving the equation, and most of the time of the inversion process is consumed in the solution of the equation. Therefore, by using the characteristics of GPU fast operation, when solving the equation, Calling CULA Sparse function library based on GPU to participate in solving equation. CULA Sparse function library contains many methods of solving equations and preprocessing methods. In this paper, we use the conjugate gradient solution equation of incomplete LU decomposition. A single acquisition device and a number of devices combining ground, ground, well and cross-well are designed, and the effectiveness of the nonlinear conjugate gradient parallel algorithm is verified by a model example. It is shown that the results of multi-device data acquisition are better than that of data collected by a single device.
【学位授予单位】：中国地质大学(北京)
【学位级别】：博士
【学位授予年份】：2015
【分类号】：P631.3

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