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对直流电阻率法勘探而言,对其反演结果的精度和速度的要求越来越高,这就需要提出一套优化有限元数值正演速度和精度的计算方案。设计了系数矩阵的一维非零元素压缩存储模式,设置了索引数组以便按照行号和列号对元素进行索引,与变带宽存储模式相比,其内存占用量明显减小。为提高正演计算速度,利用预条件共轭梯度法(PCG)求解有限元中的大型稀疏线性方程组。在PCG法中,将雅可比迭代中的对角阵作为预处理矩阵,与其它预处理矩阵相比,其具有求逆方便、无需存储空间的特点,使得大型线性方程组的求解速度大大提高。另外,在直流电阻率三维正演中,采用了异常电位法,提高了电源点附近的解的精度。以二层地层的电阻率勘探为例,初步验证了计算方案的实用性。利用上述方案,重点对隧道含水断层的电阻率法超前探测进行了有限元数值正演,并进行了相应的物理模型试验。对比显示,数值正演结果与试验数据基本一致,且数值正演的速度和精度均显著提高。
For the DC resistivity exploration, the accuracy and speed of the inversion results are getting higher and higher, which requires a set of calculation scheme to optimize the speed and accuracy of numerical forward modeling. A one-dimensional, non-zero-element, compressed storage mode of a coefficient matrix is designed. An indexed array is set to index elements by row number and column number. Memory usage is significantly reduced compared to variable-bandwidth storage mode. In order to improve the forward calculation speed, a large-scale sparse linear system in finite element method is solved by the preconditioned conjugate gradient method (PCG). In the PCG method, the diagonal matrix in the Jacobian iteration is used as the preprocessing matrix. Compared with other preprocessing matrices, the PCG method has the advantages of convenient inversion and no need of storage space, which greatly improves the speed of solving large linear equations. In addition, DC resistivity in the three-dimensional forward, the use of the abnormal potential method to improve the power point near the solution accuracy. Taking the resistivity exploration in the second strata as an example, the practicability of the calculation scheme is verified. Using the above scheme, the finite element numerical forward modeling of the resistivity method of water cut in the tunnel is emphatically carried out, and the corresponding physical model tests are carried out. The comparison shows that the numerical forward results are basically consistent with the experimental data, and the speed and accuracy of numerical forward are significantly improved.