Inversion of surface gravity data for 3-D density modeling of geologic structures using total variation regularization
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We develop an inversion procedure using the total variation (TV) regularization method as a stabilizing function to invert surface gravity data to retrieve 3-D density models of geologic structures with sharp boundaries. The developed inversion procedure combines several effective algorithms to solve the TV regularized problem. First, a matrix form of the gradient vector is designed using the Kronecker product to numerically approximate the 3-D TV function. The piecewise polynomial truncated singular value decomposition (PP-TSVD) algorithm is then used to solve the TV regularized inverse problem. To obtain a density model with depth resolution, we use a sensitivity-based depth weighting function. Finally, we apply the Genetic Algorithm (GA) to select the best combination of the PP-TSVD algorithm and the depth weighting function parameters. 3-D simulations conducted with synthetic data show that this approach produces sub-surface images in which the structures are well separated in terms of sharp boundaries, without the need of a priori detailed density model. The method applied to a real dataset from a micro-gravimetry survey of Gotvand Dam, southwestern Iran, clearly delineates subsurface cavities starting from a depth of 40 m within the area of the dam reservoir.
Keywordsinverse gravimetric problem total variation regularization PP-TSVD algorithm genetic algorithm geologic structures
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- Aster R.C., Borchers B. and Thurber C.H., 2005. Parameter Estimation and Inverse Problems. Elsevier Academic Press, London, U.K.Google Scholar
- Du Y., Aydin A. and Segall P., 1992. Comparison of various inversion techniques as applied to the determination of a geophysical deformation model for the 1983 Borah Peak earthquake. Bull. Seismol. Soc. Amer., 82, 1840–1866.Google Scholar
- Hansen P.C, Jacobsen M., Rasmussen J.M. and Sørensen H., 2000. The PP-TSVD algorithm for image reconstruction problems. In: Hansen P.C., Jacobsen B.H. and Mosegaard K. (Eds), Methods and Applications of Inversion. Lecture Notes in Earth Science Series, 92. Springer-Verlag, Berlin, Germany, 171–186.CrossRefGoogle Scholar
- Hansen P.C. and Mosegaard K., 1996. Piecewise polynomial solutions to linear inverse problems. In: Jacobsen B.H., Mosegaard K. and Sibani P. (Eds), Inverse Methods. Lecture Notes in Earth Sciences, 63, Spinger-Verlag, Berlin, Germany, 284–294, DOI: 10.1007/BFb0011787.Google Scholar
- Lavrentiev M.M., Romanov V.G. and Shishatsky S.P., 1980. Ill-Posed Problems in Mathematical Physics and Analysis. Nauka, Moscow, Russia.Google Scholar
- Mohammadzadeh M., 2012. Solving Inversion of Gravity Anomaly Using Ant Colony Optimization Algorithm. University of Tehran, Tehran, Iran.Google Scholar
- Motagh M., Schurr B., Anderssohn J., Cailleau B., Walter T.R., Wang R. and Villotte J.P., 2010. Subduction earthquake deformation associated with 14 November 2007, Mw 7.8 Tocopilla earthquake in Chile: Results from InSAR and aftershocks. Tectonophysics, 490, 66–68, DOI: 10.1016/j.tecto.2010.04.033.CrossRefGoogle Scholar
- Tikhonov A.N. and Arsenin V.Y., 1977. Solutions of Ill-Posed Problems. Wiley and Sons, New York.Google Scholar
- Van Zon A.T., 2006. Implicit Structural Inversion for Lithology Using a Gridded Model. Utrecht University, Utrecht, The Netherland.Google Scholar
- Vogel C.R., Nonsmooth regularization. In: Engl H.W., Louis A.K. and Rundell W. (Eds), Inverse Problems in Geophysical Applications. SIAM, Philadelphia, PA, 1–11.Google Scholar