(中南大學(xué) 地球科學(xué)與信息物理學(xué)院，三維電磁反演與成像實(shí)驗(yàn)室，長沙 410083)
摘 要: 從二維線源問題出發(fā)，對二維直流電阻率法高效、高精度正反演方法進(jìn)行研究。在正演數(shù)值模擬中，引入直接解法求解器求解線性方程組，既保證了起伏地形條件下有限元法正演數(shù)值模擬的計(jì)算精度和計(jì)算效率，又為反演算法中“擬正演”快速回代求解提供了條件。結(jié)合高效、高精度的正演算法，采用高斯牛頓法對電阻率進(jìn)行反演成像。在弱非均勻介質(zhì)前提下，基于近似海森矩陣主對角線元素嚴(yán)格占優(yōu)的特點(diǎn)，采用舍棄海森矩陣非對角線元素的策略，提高整個反演計(jì)算的效率。最后，利用合成數(shù)據(jù)對反演算法的有效性進(jìn)行檢驗(yàn)。結(jié)果表明：給出的反演算法穩(wěn)定、快速，結(jié)合偶極-偶極裝置和三極裝置，能有效地反演出異常體的形狀、大小和位置。
關(guān)鍵字: 直流電阻率法；高斯牛頓法；起伏地形；反演
（The Laboratory of Three-dimensional Electromagnetic Imaging, School of Geosciences and Info-Physics,
Central South University, Changsha 410083, China）
Abstract: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.
Key words: direct current resistivity method; Gauss-Newton method; topography; inversion
