Skip to main content
SpringerLink
Log in

Comparison of methods for a 3-D density inversion from airborne gravity gradiometry

  • Published:
Studia Geophysica et Geodaetica Aims and scope Submit manuscript

Abstract

In this study, we apply Tikhonov’s regularization algorithm for a 3-D density inversion from the gravity-gradiometry data. To reduce the non-uniqueness of the inverse solution (carried out without additional information from geological evidence), we implement the depth-weighting empirical function. However, the application of an empirical function in the inversion equation brings the bias problem of the regularization factor when a traditional Tikhonov’s algorithm is applied. To solve the bias problem of regularization factor selection, we present a standardized solution that comprises two parts for solving a 3-D constrained inversion equation, specifically the linear matrix transformation and Tikhonov’s regularization algorithm. Since traditional regularization techniques become numerically inefficient when dealing with large number of data, we further apply methods which include the Simultaneous Iterative Reconstruction Technique (SIRT) and the wavelet compression combined with Least Squares QR-decomposition (LSQR). In our simulation study, we demonstrate that SIRT as well as the wavelet compression plus LSQR algorithm improve the computation efficiency, while provide results which closely agree with that obtained from applying Tikhonov’s regularization. In particular, the algorithm of wavelet compression plus LSQR shows the best computing efficiency, because it combines the advantages of coefficients compression of big matrix and fast solution of sparse matrix. Similar findings are confirmed from the vertical gravity gradient data inversion for detecting potential deposits at the Kauring (near Perth, Western Australia) testing site.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Christensen A., 2013. Results from FALCON® Airborne Gravity Gradiometer surveys over the Kauring AGG test site. ASEG Extended Abstracts 2013: 23rd Geophysical Conference, DOI: 10.1071/ASEG2013ab300.

    Google Scholar 

  • Commer M., 2011. Three-dimensional gravity modelling and focusing inversion using rectangular meshes. Geophys. Prospect., 59, 966–979.

    Google Scholar 

  • Davis K. and Li Y., 2011. Fast solution of geophysical inversion using adaptive mesh, space-filling curves and wavelet compression. Geophys. J. Int., 185, 157–166.

    Article  Google Scholar 

  • DiFrancesco D., 2013. The coming of age of gravity gradiometry. ASEG Extended Abstracts 2013: 23rd Geophysical Conference, DOI: 10.1071/ASEG2013ab062.

    Google Scholar 

  • DiFrancesco D., Meyer T., Christensen A. and Fitzgerald D., 2009. Gravity gradiometry-today and tomorrow. 11th SAGA Biennial Technical Meeting and Exhibition, Swaziland, 16–18 September 2009, 80–83.

    Google Scholar 

  • Dransfield M., 2007. Airborne gravity gradiometry in the search for mineral deposits. In: Milkereit B. (Ed.), Proceedings of Exploration 07: Fifth Decennial International Conference on Mineral Exploration. Decennial Mineral Exploration Conferences, Toronto, Canada, 341–354.

    Google Scholar 

  • Dransfield M. and Zeng Y., 2009. Airborne gravity gradiometry: Terrain corrections and elevation error. Geophysics, 74, I37–I42.

    Article  Google Scholar 

  • Droujinine A., Vasilevsky A. and Evans R., 2007. Feasibility of using full tensor gradient (FTG) data for detection of local lateral density contrasts during reservoir monitoring. Geophys. J. Int., 169, 795–820.

    Article  Google Scholar 

  • Eshagh M., 2011. Sequential Tikhonov regularization: an alternative way for inverting satellite gradiometric data. Zeitschrift fur Geodasie, Geoinformation und Landmanagement, 136(2), 113–121.

    Google Scholar 

  • Fang S., Zhang X., Jia S., Duan Y., Yang Z. and Qiu S., 2003. Multi-scale decomposition of Bouguer gravity anomaly and seismic activity in north China. J. Geodesy Geodyn., 23(B12), 34–40.

    Google Scholar 

  • Golub G.H., Heath M. and Wahba G., 1979. Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics, 21, 215–223.

    Article  Google Scholar 

  • Hansen P.C., 1999. The L-Curve and its Use in the Numerical Treatment of Inverse Problems. IMM, Department of Mathematical Modelling, Technical Universityof Denmark, Lyngby, Denmark.

    Google Scholar 

  • Hansen P.C. and Saxild-Hansen M., 2012. AIR tools: a MATLAB package of algebraic iterative reconstruction methods. J. Comput. Appl. Math., 236, 2167–2178.

    Article  Google Scholar 

  • Jekeli C. and Zhu L., 2006. Comparison of methods to model the gravitational gradients from topographic data bases. Geophys. J. Int., 166, 999–1014.

    Article  Google Scholar 

  • Kirkendall B., Li Y. and Oldenburg D., 2007. Imaging cargo containers using gravity gradiometry., IEEE Trans. Geosci. Remote Sens., 45, 1786–1797.

    Article  Google Scholar 

  • Lewis A.S. and Knowles G., 1992. Image compression using the 2-d wavelet transform. IEEE Trans. Image Process., 1, 244–250.

    Article  Google Scholar 

  • Li X., 2001. Vertical resolution: Gravity versus vertical gravity gradient. The Leading Edge, 20(8), 901–904.

    Article  Google Scholar 

  • Li Y. and Oldenburg D.W., 1998. 3-D inversion of gravity data. Geophysics, 63, 109–119.

    Article  Google Scholar 

  • Li Y. and Oldenburg D.W., 2003. Fast inversion of large-scale magnetic data using wavelet transforms and a logarithmic barrier method. Geophys. J. Int., 152, 251–265.

    Article  Google Scholar 

  • Li Y. and Yang Y., 2011. Gravity data inversion for the lithospheric density structure beneath North China Craton from EGM 2008 model. Phys. Earth Planet. Inter., 189, 9–26.

    Article  Google Scholar 

  • Liu J., 2014. Airborne Gravity Gradient Tensor Data Forward Modeling and Inversion Application. Ph.D. Thesis. University of Chinese Academy of Sciences, Beijing, China.

    Google Scholar 

  • Liu Y.P., Wang Z.W., Du X.J., Liu J.H. and Xu J.S., 2013. 3D constrained inversion of gravity data based on the Extrapolation Tikhonov regularization algorithm. Chinese J. Geophys., 56(5), 1650–1659, DOI: 10.6038/cjg20130522 (in Chinese).

    Google Scholar 

  • Martin R., Monteiller V., Komatitsch D., Perrouty S., Jessell M., Bonvalot S. and Lindsay M., 2013. Gravity inversion using wavelet-based compression on parallel hybrid CPU/GPU systems: application to southwest Ghana. Geophys. J. Int., 195, 1594–1619.

    Article  Google Scholar 

  • Martinez C. and Li Y., 2012. Understanding gravity gradiometry processing and interpretation through the kauring test site data. ASEG Extended Abstracts 2012: 22nd Geophysical Conference, DOI: 10.1071/ASEG2012ab238.

    Google Scholar 

  • Meyer C.D., 2000. Matrix Analysis and Applied Linear Algebra. SIAM: Society for Industrial and Applied Mathematics, Philadeplphia, PA.

    Book  Google Scholar 

  • Murphy C.A., 2010. Recent developments with Air-FTG®. In: Lane R.J. (Ed.), Airborne Gravity 2010. Abstracts from the ASEG-PESA Airborne Gravity 2010 Workshop: Published jointly by Geoscience Australia and the Geological Survey of New South Wales, Geoscience Australia Record 2010/23 and GSNSW File GS2010/0457, 142–151.

    Google Scholar 

  • Murphy C.A. and Dickinson J.L., 2009. Exploring exploration play models with FTG gravity data, 11th SAGA Biennial Technical Meeting and Exhibition, Swaziland, 16–18 September 2009, 89–91.

    Google Scholar 

  • Paige C.C. and Saunders M.A., 1982a. Algorithm 583: LSQR: Sparse linear equations and least squares problems. ACM Trans. Math. Softw. (TOMS), 8(2), 195–209.

    Article  Google Scholar 

  • Paige C.C. and Saunders M.A., 1982b. LSQR: An algorithm for sparse linear equations and sparse least squares. ACM Trans. Math. Softw. (TOMS), 8(1), 43–71.

    Article  Google Scholar 

  • Portniaguine O. and Zhdanov M.S., 1999. Focusing geophysical inversion images. Geophysics, 64, 874–887.

    Article  Google Scholar 

  • Silva J.B. and Barbosa V.C., 2003. 3D Euler deconvolution: Theoretical basis for automatically selecting good solutions. Geophysics, 68, 1962–1968.

    Article  Google Scholar 

  • Snieder R. and Trampert J., 1999. Inverse problems in geophysics. In: Wirgin A. (Ed.), Wavefield Inversion. Springer-Verlag, Wien, Austria.

    Google Scholar 

  • Su B., Zhang Y., Peng L., Yao D. and Zhang B., 2000. Simultaneous iterative reconstruction technique for electrical capacitance tomography. J. Tsinghua Univ. Sci. Technol., 40(9), 90–92.

    Google Scholar 

  • Tikhonov A.N. and Arsenin V.Y., 1977. Solutions of Ill-Posed Problems. V.H. Winston & Sons, Washington, D.C.

    Google Scholar 

  • Wang H., Chen C. and Du J., 2013. Three-dimensional inversion methods and applications of the gravity gradient tensor data. Oil Geophys. Prospect., 48(3), 474–481 (in Chinese).

    Google Scholar 

  • Wild F. and Heck B., 2005. A comparison of different isostatic models applied to satellite gravity gradiometry. In: Jekeli C., Bastos L. and Fernandes J. (Eds), Gravity, Geoid and Space Missions. International Association of Geodesy Symposia 129, Springer-Verlag, Heidelberg, Germany, 230–235.

    Chapter  Google Scholar 

  • Zhang C., Mushayandebvu M.F., Reid A.B., Fairhead J.D. and Odegard M.E., 2000. Euler deconvolution of gravity tensor gradient data. Geophysics, 65, 512–520.

    Article  Google Scholar 

  • Zhdanov M.S., Ellis R. and Mukherjee S., 2004. Three-dimensional regularized focusing inversion of gravity gradient tensor component data. Geophysics, 69, 925–937.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Civil Engineering, Institute of Geomatics Engineering, Hefei University of Technology, Hefei Shi, Anhui Sheng, China

    Zhourun Ye

  2. Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan, China

    Zhourun Ye

  3. Department of Land Surveying and Geo-Informatics, Hong Kong Polytechnic University, Hong Kong, 181 Chatham Road South, Hung Hom, Kowloon, Hong Kong

    Robert Tenzer

  4. Institute of Geodesy, University of Stuttgart, Geschwister-Scholl-Str.24/D, Stuttgart, Germany

    Nico Sneeuw

Authors
  1. Zhourun Ye
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Robert Tenzer
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nico Sneeuw
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Robert Tenzer.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ye, Z., Tenzer, R. & Sneeuw, N. Comparison of methods for a 3-D density inversion from airborne gravity gradiometry. Stud Geophys Geod 62, 1–16 (2018). https://doi.org/10.1007/s11200-016-0492-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11200-016-0492-6

Keywords

Search

Navigation