重力梯度张量的预条件共轭梯度法反演

Inversion of gravity gradient tensor based on preconditioned conjugate gradient

针对重力梯度张量反演中的问题,提出基于预条件共轭梯度法的重力梯度张量反演。通过在目标函数中加入粗糙度对模型进行约束以避免反演参数远多于采集点数的欠定问题不稳定,并在目标函数中添加深度加权矩阵对核函数进行补偿,以避免核函数随着深度的增大而快速衰减的问题。分别反演、比较各重力梯度张量分量和联合5个独立分量,并将重力梯度张量5个独立联合反演应用于Y型岩脉。研究结果表明:联合反演效果明显优于单一分量的反演效果,且能较好地与原始模型相吻合,证明了本文算法的有效性。

The 3d inversion based on preconditioned conjugate gradient was proposed for Tensor Gradient gravity data. Roughness matrix was added in the objective function to avoid the unstable defect of inversion problem caused by the number of inverse parameter far than observational point＇s. Depth weighting function was integrated into the objective function to compensate kernel function avoid diminishing rapidly with depth. The inverse tests with every single component and joint five independent measured components of Tensor Gradient gravity data of the synthesized simple model and Y-type dyke show that the joint inversion is better than the others. The inversion result of the last test with joint five independent measured components of Tensor Gradient gravity data of the synthesized Y-type dyke coincides well with the real model. The results demonstrate the effect of the new algorithm.