互相关系数自约束的重力三维反演与高效求解

A Self-Constrained 3D Inversion and Efficient Solution of Gravity Data Based on Cross-Correlation Coefficient

本文将拟合残差计算所得的互相关系数作为先验信息,与深度加权函数同时引入到重力正则化反演的模型约束中,以提升反演结果的可靠性。针对三维反演中的大型线性方程组问题,引入阻尼LSQR(最小二乘QR分解)算法,结合等效几何格架技术,将大矩阵按照模型单元划分为若干个子矩阵进行存储与运算。理论模型计算结果表明:同时利用互相关系数和深度加权的模型自约束反演,能较清晰地反映真实异常体;基于分块矩阵的阻尼LSQR算法求解线性方程组较直接法节省了几千甚至上万倍的存储量,且计算速率提高了数倍,可在普通计算机上实现较大规模的反演计算。将其应用于云南芦子园铁铅锌铜多金属矿床隐伏花岗岩体定位,取得了良好的效果。

In this study,we applied both cross-correlation coefficient from fitting residual and depth weight to the constrained model of regularization gravity inversion to improve the reliability.In our approach,for the solutions in the system linear equations of gravity 3D inversion,damping LSQR algorithm method was introduced.Combined with the equivalent geometric trellis technology,the large matrix was divided into several sub-matrixes for storage and computation according to the model unit.The results of the theoretical model indicate that through the application of the cross-correlation coefficient with the depth weight into the constraint inversion model at the same time,the true anomaly can be clearly reflected.The damping LSQR algorithm method is sufficient for improving thousands or even tens of thousands of times of storage,and for increasing several times of computation rate.Thus,a large scale inversion calculation can be realized on a normal computer.The developed model is applied to the buried granite positioning in Luziyuan area,and the result is consistent with the true situation.