基于阈值约束的协克里金法联合反演重力与重力梯度数据

常规协克里金方法反演重力或重力梯度数据具有抗噪性好、加入先验信息容易等优点,其反演的地下密度分布能够识别异常体中心位置,还原异常体基本形态,但反演图像光滑,分辨率低,这是由于常规方法估计的密度协方差矩阵全局发散、平稳.为了通过协克里金方法获得聚焦的密度分布需要改善密度协方差矩阵的性质.首先,本文推导了理论密度协方差公式,其性质表明,当理论模型聚焦分布时,其密度协方差矩阵是非平稳且聚焦分布的.为了打破常规协方差矩阵全局平稳、发散的特征,本文设置密度阈值处理协方差矩阵,通过不断更新协方差矩阵来迭代实现协克里金反演,最终得到相对聚焦的反演结果.用本文方法处理重力与重力梯度数据恢复两种密度模型,均得到了与正演模型匹配的反演结果;再将方法运用于文顿盐丘的实际测量重力与重力梯度数据,反演结果与已知的地质情况匹配较好.

Joint inversion of gravity and gravity gradient data based on Cokriging method with the threshold constraint

The conventional Cokriging inversion of gravity and gravity gradient data has the advantages of good anti-noise performance and being easy to add prior information. And this method can identify the position of the anomaly body and to restore its basic shape. But the inversion image of this approach is smooth and its resolution is low which are due to the density covariance matrix estimated by the conventional method are of global divergence and stationary. So the performance of the density covariance matrix has to be improved for getting focusing density distribution by the Cokriging inversion. Firstly, this paper deduces the theoretical formula of density covariance matrix, which proves that the density covariance matrix is non-stationary and focused when the theoretical model is compact. In order to break the global stationary and divergence of the conventional covariance matrix, we set a density threshold to deal with the covariance matrix and update the covariance matrix to iteratively perform Cokriging inversion until the focused results are obtained. Then we set two kinds of forward models to testify our methods, showing the recovered models match with the forward models. Finally we use our method to process the gravity and gravity gradient data from the Vinton salt dome, and the inversion results are in good agreement with the known geological structures.