A MATLAB-Based Numerical and GUI Implementation of Cross-Gradients Joint Inversion of Gravity and Magnetic Data

Junjie Zhou^1,2*, Xingdong Zhang^1,2, Chunxiao Xiu^1,2

¹Key Laboratory of Geo-Detection (China University of Geosciences, Beijing), Ministry of Education, Beijing, China.
²School of Geophysics and Information Technology, China University of Geosciences, Beijing, China.

DOI: 10.4236/jsea.2015.82010                

Abstract

The cross-gradients joint inversion technique has been applied to multiple geophysical data with a significant improvement on compatibility, but its numerical implementation for practical use is rarely discussed in the literature. We present a MATLAB-based three-dimensional cross-gradients joint inversion program with application to gravity and magnetic data. The input and output information was examined with care to create a rational, independent design of a graphical user interface (GUI) and computing kernel. For 3D visualization and data file operations, UBC-GIF tools are invoked using a series of I/O functions. Some key issues regarding the iterative joint inversion algorithm are also discussed: for instance, the forward difference of cross gradients, and matrix pseudo inverse computation. A synthetic example is employed to illustrate the whole process. Joint and separate inversions can be performed flexibly by switching the inversion mode. The resulting density model and susceptibility model demonstrate the correctness of the proposed program.

Keywords

Joint Inversion, Cross Gradients, Gravity and Magnetic Data, Numerical Implementation, Graphic User Interface

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Zeyen, H. and Pous, J. (1993) 3-D Joint Inversion of Magnetic and Gravimetric Data with a Priori Information. Geophysical Journal International, 112, 244-256. http://dx.doi.org/10.1111/j.1365-246X.1993.tb01452.x
[2]	Gallardo, L.A., Perez-Flores, M.A. and Gomez-Trevino, E. (2005) Refinement of Three-Dimensional Multilayer Models of Basins and Crustal Environments by Inversion of Gravity and Magnetic Data. Tectonophysics, 397, 37-54.http://dx.doi.org/10.1016/j.tecto.2004.10.010
[3]	Bosch, M., Meza, R. and Jimenez, R. (2006) Joint Gravity and Magnetic Inversion in 3D Using Monte Carlo Methods. Geophysics, 71, G163-G156. http://dx.doi.org/10.1190/1.2209952
[4]	Pilkington, M. (2006) Joint Inversion of Gravity and Magnetic Data for Two-Layer Models. Geophysics, 71, L35-L42.http://dx.doi.org/10.1190/1.2194514
[5]	Shamsipour, P., Marcotte, D. and Chouteau, M. (2012) 3D Stochastic Joint Inversion of Gravity and Magnetic Data. Journal of Applied Geophysics, 79, 27-37. http://dx.doi.org/10.1016/j.jappgeo.2011.12.012
[6]	Zhdanov, M.S., Gribenko, A. and Wilson, G. (2012) Generalized Joint Inversion of Multimodal Geo-physical Data Using Gramian Constraints. Geophysical Research Letters, 39, L09301. http://dx.doi.org/10.1029/2012GL051233
[7]	Williams, N.C. (2008) Geologically-Constrained UBC-GIF Gravity and Magnetic Inversions with Ex-amples from the Agnew-Wiluna Greenstone Belt, Western Australia. Ph. D. Dissertation. The University of British Columbia, Vancouver.
[8]	Frogoso, E. and Gallardo, L.A. (2009) Cross-Gradients Joint 3D Inversion with Applications to Gravity and Magnetic Data. Geophysics, 74, L31-L42. http://dx.doi.org/10.1190/1.3119263
[9]	Gallardo, L.A. and Meju, M.A. (2004) Joint Two-Dimensional DC Resistivity and Seismic Travel Time Inversion with Cross-Gradients Constraints. Journal of Geophysical Research: Solid Earth (1978-2012), 109, B03311. http://dx.doi.org/10.1029/2003JB002716
[10]	Oldenburg, D.W. and Jones, F.H.M. (2007) Inversion for Applied Geophysics: Learning Resources about Geophysical Inversion. The University of British Columbia, Vancouver. http://www.eos.ubc.ca/ubcgif/iag/index.htm
[11]	Özgü Arisoy, M. and Dikmen, ü. (2011) Potensoft: MATLAB-Based Software for Potential Field Data Processing, Modeling and Mapping. Computers & Geosciences, 37, 935-942. http://dx.doi.org/10.1016/j.cageo.2011.02.008
[12]	Lelièvre, P.G. and Oldenburg, D.W. (2009) A Comprehensive Study of Including Structural Orientation Information in Geophysical Inversions. Geophysical Journal International, 178, 623-637. http://dx.doi.org/10.1111/j.1365-246X.2009.04188.x
[13]	Hahn, B.H. and Valentine, D.T. (2013) Essential Matlab for Engineers and Scientists. 5th Edition, Academic Press, Boston, 129-160. http://dx.doi.org/10.1016/B978-0-12-394398-9.00006-X
[14]	Eshagh, M. and Abdollahzadeh, M. (2012) Software for Generating Gravity Gradients Using a Geopotential Model Based on an Irregular Semivectorization Algorithm. Computers & Geosciences, 39, 152-160. http://dx.doi.org/10.1016/j.cageo.2011.06.003
[15]	Pidlisecky, A., Haber, E. and Knight R. (2007) RESINVM3D: A 3D Resistivity Inversion Package. Geo-physics, 72, H1-H10. http://dx.doi.org/10.1190/1.2402499
[16]	Hansen, P.C. (1994) Regularization Tools: A Matlab Package for Analysis and Solution of Discrete Ill-Posed Problems. Numerical Algorithm, 6, 1-35. http://dx.doi.org/10.1007/BF02149761