3D density inversion of gravity gradient data using the extrapolated Tikhonov regularization
Liu Jin-Zhao1,2, Liu Lin-Tao2, Liang Xing-Hui2, and Ye Zhou-Run2
1. First Crust Monitoring and Application Center, China Earthquake Administration, Tianjin 300180, China.
2. State Key Laboratory of Geodesy and Earth's Dynamics, Institute of Geodesy and Geophysics, CAS, Wuhan, 430077, China.
Abstract We use the extrapolated Tikhonov regularization to deal with the ill-posed problem of 3D density inversion of gravity gradient data. The use of regularization parameters in the proposed method reduces the deviations between calculated and observed data. We also use the depth weighting function based on the eigenvector of gravity gradient tensor to eliminate undesired effects owing to the fast attenuation of the position function. Model data suggest that the extrapolated Tikhonov regularization in conjunction with the depth weighting function can effectively recover the 3D distribution of density anomalies. We conduct density inversion of gravity gradient data from the Australia Kauring test site and compare the inversion results with the published research results. The proposed inversion method can be used to obtain the 3D density distribution of underground anomalies.
This work is supported by National major special equipment development (No. 2011YQ120045) and The National Natural Science Fund (No. 41074050 and 41304023).
Cite this article:
Liu Jin-Zhao,Liu Lin-Tao,Liang Xing-Hui et al. 3D density inversion of gravity gradient data using the extrapolated Tikhonov regularization[J]. APPLIED GEOPHYSICS, 2015, 12(2): 137-146.
[1]
Bear, G. W., Al-Shukri, H. J., and Rudman, A. J., 1995, Linear inversion of gravity data for 3-D density distributions: Geophysics, 60(5), 1354−1364.
[2]
Beiki, M., and Pedersen, L. B., 2010, Eigenvector analysis of gravity gradient tensor to locate geologic bodies: Geophysics, 75(6), 137−149.
[3]
Chen, S. H., Zhu, Z. Q., Lu, G. Y., et al., 2013, Inversion of gravity gradient tensor based on preconditioned conjugate gradient: Journal of Central South University(Science and Technology), 44(2), 619−625.
[4]
Commer, M., 2011, Three-dimensional gravity modelling and focusing inversion using rectangular meshes: Geophysical Prospecting, 59(5), 966−979.
[5]
Dransfield, M., 2007, Airborne gravity gradiometry in the search for mineral deposits: Proceedings on Mineral Exploration edited by B. Milkereit, Fifth Decennial International Conference, 341−354
[6]
Feng, J., Meng, X. H., Chen, Z. X., et al., 2014, The investigation and application of three-dimensional density interface: Chinese J. Geophys.(in Chinese), 57(1), 287−294.
[7]
Guo, W. B., Zhu, Z. Q., and Lu, G. Y., 2011, Quasi-BP neural network inversion of gravity gradient tensor: Journal of Central South University (Science and Technology), 42(12), 3797−3803.
[8]
Guo, L. H., Meng, X. H., Shi, L., et al., 2009, 3-D correlation imaging for gravity and gravity gradiometry data: Chinese J. Geophys. (in Chinese), 52(4), 1092−1106.
[9]
Hämarik, U., Palm, R., and Raus, T., 2007, Use of extrapolation in regularization methods: Journal of Inverse and Ill-Posed Problems, 15(3), 277−294.
[10]
Hämarik, U., Palm, R., and Raus, T., 2008, Extrapolation of Tikhonov and Lavrentiev regularization methods: 6th International Conference on Inverse Problems in Engineering: Theory and Practice; Journal of Physics: Conference Series, 135(1), 1−8.
[11]
Ke, X. P., Wang, Y., Xu, H. Z., et al., 2009, The three-dimensional crustal structure of the Tibetan plateau from gravity inversion:Progress in Geophysics (in Chinese), 24(2), 448−455.
Li, Y. G., and Oldenburg, D. W., 1996, 3-D inversion of magnetic data: Geophysics, 61(2), 394−408.
[14]
Li, Y. G., and Oldenburg, D. W., 1998, 3-D inversion of gravity data: Geophysics, 63(1), 109−119.
[15]
Li, Y. G., 2001, 3-D inversion of gravity gradiometer data: 71st Ann. Soc. Expl. Geophys. Mtg., Expanded Abstracts,, Expanded Abstracts, 1470−1473.
[16]
Liu, Y. P., Wang, Z. W., Du, X. J., et al., 2013, 3D constrained inversion of gravity data based on Extrapolation Tikhonov regularization algorithm: Chinese J.Geophys.(in Chinese), 56(5), 1650−1659.
[17]
Martinez, C., and Li, Y. G., 2012, Understanding gravity gradiometry processing and interpretation through the Kauring test site data: 22nd ASEG International Geophysical Conference and Exhibition, 1−4.
[18]
Palm, R., 2010, Numerical comparison of regularization algorithms for solving ill-posed problems: PhD Thesis, University of Tartu.
[19]
Rama, P., Rao, K. V., Swamy, I. V., and Radhakrishna Murthy, 1999, Inversion of gravity anomalies of three-dimensional density interfaces: Computers & Geoscience, 25(8), 887−896.
[20]
Pawlowski, B., 1998, Gravity gradiometry in resource exploration: The Leading Edge, 17, 51−52.
[21]
Rama, P., Rao, K. V., Swamy, I. V., and Radhakrishna, M., 1999, Inversion of gravity anomalies of three-dimensional density interfaces: Computers & Geoscience, 25(8), 887−896.
[22]
Hämarik, U., PalmR., and Raus, T., 2010, Extrapolation of Tikhonov regularization method, Mathematical Modelling and Analysis, 15(1), 55−68.
[23]
Vasilevsky, A., Droujinine, A., and Evans, R., 2005, Regularized inversion of 3D full tensor gradient (FTG) data for dynamic reservoir monitoring: 75th Ann. Soc. Expl. Geophys. Mtg., Expanded Abstracts, 24, 700−703.
[24]
Wang, Z. W., Xu, S., Liu, Y. P., et al., 2014, Extrapolated Tikhonov method and inversion of 3D density images of gravity data: Applied Geophysics, 11(2), 139−148.
[25]
Wang, H. R., Chen C., and Du, J. S., 2013, 3-D inversion method and application of gravity gradient tensor data: Oil Geophysical Prospecting, 48(3), 475−481.
[26]
Wedge, D., 2013, Mass anomaly depth estimation from full tensor gradient gravity data: Applications of Computer Vision, IEEE workshop, 526−533.
[27]
Zhdanov, M.S., Ellis, R.G., Mukherjee,S., et al, 2002, Regularized focusing inversion of 3-D gravity tensor data: 72nd Ann. Soc. Expl. Geophys. Mtg., Expanded Abstracts, 751−754.
[28]
Zhdanov, M. S., Robert Ellis, and Souvik Mukherjee, 2004, Three-dimensional regularized focusing inversion of gravity gradient tensor component data: Geophysics, 69(4), 925−937.
2015, Vol. 12 
