Three-dimensional forward modelling of gravity field vector and its gradient tensor using the compact difference schemes
Three-dimensional forward modelling of gravity field vector and its gradient tensor using the compact difference schemes
复制标题
利用紧致差分格式对重力场矢量及其梯度张量进行三维正演建模
DOI：
10.1093/gji/ggaa511
复制
发表时间：
2021-02-01
影响因子：
2.8
通讯作者：
Tang, Jingtian
中科院分区：
文献类型：
--
作者：
Pan, Kejia;Zhang, Zhihao;Tang, Jingtian
传统的重力正演偏微分方程（PDE）方法只能获得二阶精度。在由重力位计算重力场矢量和梯度张量时，这些数值微分方法不可避免地会失去精度。为了缓解这个问题，我们提出了一个高效和准确的三维正演模拟算法的基础上四阶紧致差分格式。首先，采用19点四阶紧致差分格式，在x，y和z方向上具有一般的网格尺寸来离散三维泊松方程。得到的对称正定线性方程组用预条件共轭梯度法求解。为了获得具有四阶精度的一阶导数（即重力场矢量）和二阶导数（即重力梯度张量），我们试图通过使用快速托马斯算法来求解由上述有限差分离散化得到的一系列三对角线性方程组。最后，两个合成模型和一个真实的地形起伏来验证我们的方法的准确性。数值结果表明，该方法不仅对引力位，而且对引力场矢量及其梯度张量都能得到近四阶精度的近似，明显优于传统的偏微分方程方法.
The traditional gravity forward modelling methods for solving partial differential equations (PDEs) only can yield second-order accuracy. When computing the gravity field vector and gradient tensor from the obtained potential, those numerical differentiation approaches will inevitably lose accuracy. To mitigate this issue, we propose an efficient and accurate 3-D forward modelling algorithm based on a fourth-order compact difference scheme. First, a 19-point fourth-order compact difference scheme with general meshsizes in x-, y- and z-directions is adopted to discretize the governing 3-D Poisson’s equation. The resulting symmetric positive-definite linear systems are solved by the pre-conditioned conjugate gradient algorithm. To obtain the first-order (i.e. the gravity field vector) and second-order derivatives (i.e. the gravity gradient tensor) with fourth-order accuracy, we seek to solve a sequence of tridiagonal linear systems resulting from the above mentioned finite difference discretization by using fast Thomas algorithm. Finally, two synthetic models and a real topography relief are used to verify the accuracy of our method. Numerical results show that our method can yield a nearly fourth-order accurate approximation not only to the gravitational potential, but also to the gravity field vector and its gradient tensor, which clearly demonstrates its superiority over the traditional PDE-based methods.