Inversion of surface gravity data for 3-D density modeling of geologic structures using total variation regularization
详细信息 查看全文
- 作者：Alireza Sobouti ; Mahdi Motagh ; Mohammad Ali Sharifi
- 关键词：inverse gravimetric problem ; total variation regularization ; PP ; TSVD algorithm ; genetic algorithm ; geologic structures
- 刊名：Studia Geophysica et Geodaetica
- 出版年：2016
- 出版时间：January 2016
- 年：2016
- 卷：60
- 期：1
- 页码：69-90
- 全文大小：933 KB
- 参考文献：Aster R.C., Borchers B. and Thurber C.H., 2005. Parameter Estimation and Inverse Problems. Elsevier Academic Press, London, U.K.
Barnes G. and Barraud J., 2012. Imaging geological surfaces by inverting gravity gradient data with depth horizons. Geophysics, 77, G1–G11, DOI: 10.1190/geo2011-0149.1.CrossRef
Barrodale I. and Roberts F.D.K., 1978. An efficient algorithm for discrete l1 linear approximation with linear constraints. SIAM J. Numer. Anal., 15, 603–611, DOI: 10.1137/0715040.CrossRef
Bertete-Aguirre H., Cherkaev E. and Oristaglio M., 2002. Non-smooth gravity problem with total variation penalization functional. Geophys. J. Int., 149, 499–507, DOI: 10.1046/j.1365-246X.2002.01664.x.CrossRef
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.
Farquharson C.G. and Oldenburg D.W., 1998. Nonlinear inversion using general measures of data misfit and model structure. Geophys. J. Int., 134, 213–227, DOI: 10.1046/j.1365-246x.1998.00555.x.CrossRef
Farquharson C.G., 2008. Constructing piecewise-constant models in multidimensional minimumstructure inversions. Geophysics, 73, K1–K9, DOI: 10.1190/1.2816650.CrossRef
Fedi M., Hansen P.C. and Paoletti V., 2005. Tutorial: Analysis of depth resolution in potential field inversion. Geophysics, 70, A1–A11.CrossRef
Hansen P.C., 1987. The truncated svd as a method for regularization. Bit, 27, 534–553, DOI: 10.1007/BF01937276.CrossRef
Hansen P.C., 1998. Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion. SIAM, Philadelphia, PA.CrossRef
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.CrossRef
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.
Hastie T., Tibshirani R. and Friedman J.H., 2009. The Elements of Statistical Learning. 2nd Edition. Springer-Verlag, New York.CrossRef
Isakov V., 1990. Inverse Source Problems. Mathematical Surveys and Monographs, 34. American Mathematical Society, Providence, RI.CrossRef
Kress R., 1989. Linear Integral Equations. Springer-Verlag, Berlin.CrossRef
Lavrentiev M.M., Romanov V.G. and Shishatsky S.P., 1980. Ill-Posed Problems in Mathematical Physics and Analysis. Nauka, Moscow, Russia.
Li Y. and Oldenburg D.W., 1996. 3-D inversion of magnetic data. Geophysics, 61, 394–408, DOI: 10.1190/1.1443968.CrossRef
Li Y. and Oldenburg D.W., 1998. 3-D inversion of gravity data. Geophysics, 63, 109–119, DOI: 10.1190/1.1444302.CrossRef
Li Y. and Oldenburg D.W., 2000. Joint inversion of surface and three-component borehole magnetic data. Geophysics, 65, 540–522, DOI: 10.1190/1.1444749.CrossRef
Martins C.M., Lima W.A., Barbosa V.C.F. and Silva J.B.C, 2011. Total variation regularization for depth-to-basement estimate: Part 1 - Mathematical details and applications. Geophysics, 76, I1–I12, DOI: 10.1190/1.3524286.CrossRef
Mohammadzadeh M., 2012. Solving Inversion of Gravity Anomaly Using Ant Colony Optimization Algorithm. University of Tehran, Tehran, Iran.
Motagh M., Klotz J., Tavakoli F., Djamour Y., Arabi S., Wetzel H. and Zschau J., 2006. Combination of precise leveling and InSAR data to constrain source parameters of the Mw=6.5, 26 December 2003 Bam earthquake. Pure Appl. Geophys., 163, 1–18, DOI: 10.1007/s00024-005-0005-y.CrossRef
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.CrossRef
Nagy D., Papp G. and Benedek J., 2000. The gravitational potential and its derivatives for the prism. J. Geodesy, 74, 552–560, DOI: 10.1007/s001900000116.CrossRef
Paoletti V., Hansen P.C., Hansen M.F. and Fedi M., 2014. A computationally efficient tool for assessing the depth resolution in potential-field inversion. Geophysics, 79, A33–A38, DOI: 10.1190/GEO2014-0017.1.CrossRef
Paoletti V., Ialongo S., Florio G., Fedi M. and Cella F., 2013. Self-constrained inversion of potential fields. Geophys. J. Int., 195, 854–869, DOI: 10.1093/gji/ggt313.CrossRef
Rudin L.I., Osher S. and Fatemi E., 1992. Nonlinear total variation based noise removal algorithms. Physica D, 60, 259–268, DOI: 10.1016/0167-2789(92)90242-F.CrossRef
Tikhonov A.N. and Arsenin V.Y., 1977. Solutions of Ill-Posed Problems. Wiley and Sons, New York.
Uieda L. and Barbosa V.C.F., 2012. Robust 3D gravity gradient inversion by planting anomalous densities. Geophysics, 77, G55–G66, DOI: 10.1190/geo2011-0388.1.CrossRef
Van Zon A.T., 2006. Implicit Structural Inversion for Lithology Using a Gridded Model. Utrecht University, Utrecht, The Netherland.
Van Zon A.T., Ditmar P., Chowdhury K. and Mondt J., 2007. Lithotype discrimination within a gridded model by inverting gravity data. Geophys. J. Int., 170, 481–491, DOI: 10.1111 /j.1365-246X.2007.03357.x.CrossRef
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.
Vogel C.R. and Oman M.E., 1996. Iterative methods for total variation denoising. SIAM J. Sci. Comput., 17, 227–238, DOI: 10.1137/0917016.CrossRef - 作者单位：Alireza Sobouti (1)
Mahdi Motagh (1) (2)
Mohammad Ali Sharifi (1) (3)
1. School of Surveying and Geospatial Engineering, College of Engineering, University of Tehran, 14395-515, Tehran, Iran
2. GFZ German Research Centre for Geosciences, 14473, Potsdam, Germany
3. Research Institute of Geo-information Technology (RIGT), College of Engineering, University of Tehran, 14395-515, Tehran, Iran - 刊物类别：Earth and Environmental Science
- 刊物主题：Earth sciences
Geophysics and Geodesy
Structural Geology
Meteorology and Climatology - 出版者：Springer Netherlands
- ISSN：1573-1626
文摘
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. Keywords inverse gravimetric problem total variation regularization PP-TSVD algorithm genetic algorithm geologic structures