Three-dimensional numerical modeling of gravity anomalies based on Poisson equation in space-wavenumber mixed domain
Dai Shi-Kun1,2, Zhao Dong-Dong1,2, Zhang Qian-Jiang3, Li Kun1,2, Chen Qing-Rui1,2, and Wang Xu-Long1,2
1. School of Geosciences and Info-physics, Central South University, Changsha 410083, China.
2. Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring, Ministry of Education (Central South University), Changsha 410083, China.
3. School of College of Earth Sciences of Guilin university of technology, Guilin 541004, China.
Abstract：
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 3D numerical modeling method for gravity anomalies in space-wavenumber mixed domain. By performing a two-dimensional Fourier transform in the horizontal directions, three-dimensional 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. This method preserves the vertical component in the space domain, which is beneficial when modeling complex topography. The finite element method was used to solve the transformed differential equations with different wave numbers, and the efficiency of solving fixed-bandwidth 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.
. Three-dimensional numerical modeling of gravity anomalies based on Poisson equation in space-wavenumber mixed domain[J]. APPLIED GEOPHYSICS, 2018, 15(3-4): 513-523.
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2018, Vol. 15 
