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, 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.
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References
Blakely, R. J., 1996, Potential theory in gravity and magnetic applications: Cambridge University Press, London, 128–153.
Cai, Y., and Wang, C. Y., 2005, Fast finite–element calculation of gravity anomaly in complex geological regions: Geophysical Journal of the Royal Astronomical Society, 162(3), 696–708.
Cg Farquharson, C. M., 2009, Three–dimensional modelling of gravity data using finite differences: Journal of Applied Geophysics, 68(3), 417–422.
Chakravarthi, V., Raghuram, H. M., and Singh, S. B., 2002, 3–d forward gravity modeling of basement interfaces above which the density contrast varies continuously with depth: Computers & Geosciences, 28(1), 53–57.
Chai, Y., and Hinze, W. J., 1988, Gravity inversion of interface above which the density contrast waries exponentially with depth: Geophysics, 53(6), 837–845.
Chai, Y. P., 1997, Shift sampling theory and its applications: Petroleum Industry Press, Beijing, 15–74.
Feng, R., 1986, The potential field calculation of the three–dimensional physical distribution: Chinese J. Geophys. (in Chinese), 29(4), 399–406.
Forsberg, R., 1985, Gravity field terrain effect computations by fft: Bulletin Géodésique, 59(4), 342–360.
García–Abdeslem, J., 2005, The gravitational attraction of a right rectangular prism with density varying with depth following a cubic polynomial: Geophysics, 70(6), J39–J42.
Granser, H., 1987, Nonlinear inversion of gravity data using the schmidt–lichtenstein approach: Geophysics, 52(1), 88–93.
Holstein, H., 2002, Gravimagnetic similarity in anomaly formulas for uniform polyhedra: Geophysics, 67(4), 1125–1133.
Jahandari, H., and Farquharson, C. G., 2013, Forward modeling of gravity data using finite–volume and finite–element methods on unstructured grids: Geophysics, 78(3), G69–G80.
Jian, Z., Wang, C. Y., Shi, Y., Cai, Y., Chi, W. C., and Douglas, D., 2004, Three–dimensional crustal structure in central taiwan from gravity inversion with a parallel genetic algorithm: Geophysics, 69(4), 917–924.
Nagy, D., 1966, The gravitational attraction of a right rectangular prism: Geophysics, 31(2), 362–371.
Nagy, D., Papp, G., and Benedek, J., 2000, The gravitational potential and its derivatives for the prism: Journal of Geodesy, 74(7–8), 552–560.
Okabe, M., 1979, Analytical expressions for gravity anomalies due to homogeneous polyhedral bodies and translations into magnetic anomalies: Geophysics, 44(4), 730–741.
Paul, M. K., 1974, The gravity effect of a homogeneous polyhedron for three–dimensional interpretation: Pure & Applied Geophysics, 112(3), 553–561.
Pedersen, L. B., 1978a, A statistical analysis of potential fields using a vertical circular cylinder and a dike: Geophysics, 43(5), 943–953.
Pedersen, L. B., 1978b, Wavenumber domain expressions for potential fields from arbitrary 2–, 21/2 and 3–dimensional bodies: Geophysics, 43(3), 626–630.
Pedersen, L. B., 1985, The gravity and magnetic feilds from ellipsoidal bodies in the wavenumber domain: Geophysical Prospecting, 33(2), 263–281.
Plouff, D., 1976, Gravity and magnetic fields of polygonal prisms and application to magnetic terrain corrections: Geophysics, 41(4), 727–741.
Rao, D. B., Prakash, M. J., and Babu, N. R., 1993, Gravity interpretation using fourier–transforms and simple geometrical models with exponential density: Geophysics, 58(8), 1074–1083.
Singh, B., and Guptasarma, D., 2001, New method for fast computation of gravity and magnetic anomalies from arbitrary polyhedra: Geophysics, 66(66), 521–526.
Talwani, M., 1960, Rapid computation of gravitational attraction of three–dimensional bodies of arbitrary shape: Geophysics, 25(1), 203–225.
Tontini F. C., Cocchi, L., and Carmisciano, C., 2009, Rapid 3–D forward model of fields with application to the palinuro seamount gravity anomaly(sourthern tyrrhenian sea, Italy): Journal of Geophysical Research: Solid Earth (1978–2012), 114(B2), 1205–1222.
Wu, X. Z., 1983, The computation of spectrum of potential field due to 3–D arbitrary bodies with physical parameters varying with depth: Chinese J. Geophys. (in Chinese), 26(02), 177–187.
Wu, L. Y., and Tian, G., 2014, High–precision Fourier forward modeling of potential field: Geophysics, 79(5), G59–G68.
Wu, L. Y, 2016, Efficient modelling of gravity effects due to topographic masses using the Gauss–FFT method: Geophysical Journal International, 205(1), 160–178.
Xiong, G. C., 1984, Some problems about 3–D fourier transforms of the gravity and magnetic fields: Chinese J. Geophys (in Chinese), 1(01), 103–109.
Xu, S. Z., 1994, The Finite Element Method in Geophysics: Science Press, Beijing, 6–98.
Zhao, S. K., and Yedlin, M. J., 1991, Chebyshev expansions for the solution of the forward gravity problem: Geophysical Prospecting, 39(6), 783–802.
Zeng, H. L., 2005, Gravity field and gravity exploration: Geological Publishing House, Beijing, 1–35.
Acknowledgements
The authors are very grateful to the three reviewers and editor-in-chief Fan Weicui for their critiques, helpful comments, and valuable suggestions which improved this manuscript significantly. In addition, we would like to thank Prof. Xu Yungui and Associate Prof. Chen Longwei for their guidance and help during the development of this paper.
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This work was supported by the Natural Science Foundation of China (No. 41574127), the China Postdoctoral Science Foundation (No. 2017M622608), and the project for the independent exploration of graduate students at Central South University (No. 2017zzts008).
Dai Shi-Kun, professor, doctoral supervisor. He received his M.S. (1991), Ph.D. (1994) from China University of Geosciences and Ocean University of China, respectively. He completed his postdoctoral fellowship (1997) and worked later at China University of Petroleum (Beijing). He was employed at Central South University (2011), and the main interests are 3D forward modeling, inversion and related software development of gravity, magnetic, electromagnetic and seismic data.
Zhao Dong-Dong received his M.S. (2016) in Earth Exploration and Information Technology from Central South University. He is presently a Ph.D. candidate in Geological Resources and Geological Engineering at Central South University. His main interests is 3D forward modeling of gravity, magnetic and electromagnetic data.
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Dai, SK., Zhao, DD., Zhang, QJ. et al. Three-dimensional numerical modeling of gravity anomalies based on Poisson equation in space-wavenumber mixed domain. Appl. Geophys. 15, 513–523 (2018). https://doi.org/10.1007/s11770-018-0702-9
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DOI: https://doi.org/10.1007/s11770-018-0702-9