空间—波数混合域二度体重力异常正演

Forward modeling for 2D-body gravity anomaly in the space-wavenumber mixed domain

针对任意密度分布的二度体重力异常的计算,提出了一种空间-波数混合域二度体重力异常正演方法。该方法将二度体引力位满足的偏微分方程通过一维傅里叶变换,转化为不同波数相互独立的常微分方程,并采用基于二次插值的一维有限单元法求解该常微分方程。该方法充分利用了傅里叶变换的高效性和垂向网格剖分的灵活性,实现了二度体重力异常的高效、高精度数值模拟。采用截面为矩形的常密度和变密度的二度体模型,对所提算法的计算精度和速度进行检验,结果表明,与传统的二度体正演方法相比,算法在保证计算精度的同时,提高了计算效率。

An efficient and high-precision forward modeling of 2D-body gravity anomaly in a space-wavenumber mixed domain is proposed to calculate the gravity anomaly in the case of arbitrary density distribution.By performing 1D Fourier transform,2D partial differential equation governing gravity potential in the spatial domain is transformed into a group of independent 1D differential equations engaged with different wavenumbers.The method preserves the vertical direction in the spatial domain,thus shallow and deep meshes for modeling can be fine and coarse respectively.By this way,both the accuracy and the efficiency of calculation are taken into account.1D finite element method is used to solve the transformed differential equations with different wave numbers.Moreover,the efficiency of solving linear equations with a fixed bandwidth assembled by the finite element analysis is further improved by a chasing method.To test the proposed algorithm,a constant-density 2D model and a variable-density 2D model are designed.Numerical test results show that the proposed algorithm not only guarantees the calculation accuracy,but also improves the calculation efficiency compared with the conventional methods.