基于高斯牛顿法的二维直流电阻率法的快速反演

Fast inversion for two-dimensional direct current resistivity method based on Gauss-Newton method

从二维线源问题出发,对二维直流电阻率法高效、高精度正反演方法进行研究。在正演数值模拟中,引入直接解法求解器求解线性方程组,既保证了起伏地形条件下有限元法正演数值模拟的计算精度和计算效率,又为反演算法中"拟正演"快速回代求解提供了条件。结合高效、高精度的正演算法,采用高斯牛顿法对电阻率进行反演成像。在弱非均匀介质前提下,基于近似海森矩阵主对角线元素严格占优的特点,采用舍弃海森矩阵非对角线元素的策略,提高整个反演计算的效率。最后,利用合成数据对反演算法的有效性进行检验。结果表明:给出的反演算法稳定、快速,结合偶极-偶极装置和三极装置,能有效地反演出异常体的形状、大小和位置。

Fast and high-precision inversion method for two-dimensional line source problem was studied. In the forward numerical simulation, linear equations solver was applied for direct solution, which not only improved the precision and the speed of numerical simulation of finite element method in the case of rugged topography, but also provided conditions for the ＂quasi forward＂ fast back substitution solution in the inversion algorithm. Combined with high efficient simulation method, Gauss-Newton method was adopted for inversion of resistivity. In the case of low inhomogeneity, the main diagonal elements of the approximated Hessen matrix possessed priority than others. Based on this, non-diagonal elements were deleted when Gauss-Newton iterative equations were solved. The whole process of inversion was made more efficient by this scheme. Finally, synthetic data were used to test the validity of the presented inversion method. The results show that the inversion method is stable and fast. Combine with dipole-dipole and pole-dipole arrays, the shape, size and the location of the anomalous body can be reflected efficiently by the inversion method.