起伏地形条件下空间波数混合域重力异常三维数值模拟（英文）

Three-dimensional numerical modeling of gravity anomalies based on Poisson equation in spacewavenumber mixed domain

反在重力勘探中,面向实际应用的空间域和频率域数值模拟计算量和存储量巨大,很难对起伏地形条件下大规模复杂地质模型实现高效、精细化反演成像。针对这一问题,本文提出一种空间波数混合域重力异常三维数值模拟方法。该方法沿水平方向进行二维傅里叶变换,把空间域引力位满足的三维偏微分方程转化为不同波数满足的一维常微分方程,不同波数之间常微分方程相互独立,具有高度并行性;同时保留垂向为空间域,适应复杂地形模拟需求,并兼顾计算精度与计算效率;采用有限单元法求解不同波数满足的常微分方程,充分利用追赶法求解定带宽线性方程组的高效性以进一步提高计算效率。在数值试验中,本文设计了棱柱体模型,通过数值解与解析解的对比验证了本文方法的正确性和可靠性;研究了水平地形和起伏地形条件下基于标准FFT扩边和基于Gauss-FFT的空间波数混合域重力异常三维数值方法计算精度与计算效率。数值试验结果表明:基于Gauss-FFT的空间波数混合域数值模拟精度高。综合考虑计算精度与计算效率,基于标准FFT扩边的空间波数混合域数值模拟更有利于起伏地形条件下反演成像与定量解释。

In gravity-anomaly-based prospecting, the computational and memory requirements for practical numerical modeling are potentially enormous. Achieving an efficient and precise inversion for gravity anomaly imaging over large-scale and complex terrain requires additional methods. To this end, we have proposed a new topography-capable By performing a two-dimensional Fourier transform in the horizontal directions, threedimensional partial differential equations in the spatial domain were transformed into a group of independent, one-dimensional differential equations engaged with different wave numbers. These independent differential equations are highly parallel across different wave numbers. differential equations with different wave numbers, and the efficiency of solving fixedbandwidth linear equations was further improved by a chasing method. In a synthetic test, a prism model was used to verify the accuracy and reliability of the proposed algorithm by comparing the numerical solution with the analytical solution. We studied the computational precision and efficiency with and without topography using different Fourier transform methods. The results showed that the Guass-FFT method has higher numerical precision, while the standard FFT method is superior, in terms of computation time, for inversion and quantitative interpretation under complicated terrain.