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

• Published in: Applied geophysics 2018-09, Vol.15 (3-4), p.513-523
• Main Authors: Dai, Shi-Kun, Zhao, Dong-Dong, Zhang, Qian-Jiang, Li, Kun, Chen, Qing-Rui, Wang, Xu-Long
• Format: Article
• Language: English
• Subjects: Anomalies; Computation; Computer applications; Computer memory; Computing time; Differential equations; Earth and Environmental Science; Earth Sciences; Exploration; Finite element method; Fourier transforms; Geophysics/Geodesy; Geotechnical Engineering & Applied Earth Sciences; Gravitation; Gravity anomalies; Imaging techniques; Linear equations; Model accuracy; Model testing; Modelling; Partial differential equations; Poisson equation; Spatial discrimination; Terrain; Test procedures; Three dimensional models; Topography; Topography (geology); Wavelengths
• ISSN: 1672-7975; 1993-0658
• DOI: 10.1007/s11770-018-0702-9

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, 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. 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 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.