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Trigonal meshes in diffraction tomography with optimum regularization: an application forcarbon sequestration monitoring
E.T.F. SANTOS1 ,
J.M. HARRIS2 ,
A. BASSREI3 ,
J.C. COSTA4
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1
Federal Center of Technological Education of Bahia (CEFET-BA), Salvador, BA, Brazil. eduardot@cefetba.br,
2
Department of Geophysics, Stanford University, Stanford, CA, U.S.A.,
3
Institute of Physics & Research Center in Geophysics and Geology, Federal University of Bahia, Caixa Postal 1001, 40001-970 Salvador, BA, Brazil.,
4
Faculty of Geophysics, Federal University of Pará, Belém, PA, Brazil.,
JSE 2009, 18(2), 135–156;
Submitted: 18 May 2008 | Accepted: 30 December 2008 | Published: 1 April 2009
© 2009 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract
Santos, E.T.F., Harris, J.M., Bassrei, A. and Costa, J.C., 2009. Trigonal meshes in diffraction tomography with optimum regularization: an application for carbon sequestration monitoring. Journal of Seismic Exploration, 18: 135-156. Diffraction tomography is an inversion technique that provides the reconstruction of a subsurface velocity field from scattered acoustic field data. High-resolution imaging conventionally requires estimation of a large number of parameters. A trigonal mesh is applied in the study described in this paper, in order to strongly reduce the number of parameters. Thus, instead of a velocity-estimate for each cell in a regular grid, the velocity is estimated only at triangle vertices, which act as control points for the interpolation of velocity field within each triangle. Regularization is required to avoid sharp artifacts due to trigonal elements. A synthetic model is adopted to test the feasibility of the proposed method for reservoir monitoring.
Keywords
inverse problems
diffraction tomography
regularization
trigonal meshes
CO2 sequestration
References
- Ajo-Franklin, J.B., Urban, J.A. and Harris, J.M., 2006. Using resolution-constrained adaptivemeshes for traveltime tomography. J. Seismic Explor., 14: 371-392.
- Bassrei, A. and Rodi, W.L., 1993. Regularization and inversion of linear geophysical data. 3rd
- Internat. Congr. Brazil. Geophys. Soc., Rio de Janeiro, Brazil, I: 111-116.
- Belge, M., Kilmer, M.E. and Miller, E.L., 2002. Efficient determination of multiple regularizationparameters in a generalized L-curve framework. Inverse Problems, 18: 1161-1183.
- Bottema, O., 1982. On the area of a triangle in barycentric coordinates. Crux Mathematic., 8:228-231.156 SANTOS, HARRIS, BASSREI & COSTA
- Devaney, A.J., 1984. Geophysical diffraction tomography.Inst. Electr. Electron. Engin. Transact.Geosci. Remote Sens., 22: 3-13.
- Hansen, P.C., 1992. Analysis of discrete ill-posed problems by means of the I-curve. Soc. Industr.Appl. Mathemat. Rev., 34: 561-580.
- Hansen, P.C., 1998. Rank-Deficient and Discrete Ill-Posed Problems. Soc. Industr. Appl.Mathemat, Philadelphia.
- Hansen, P.C. and O’Leary, D.P., 1993. The use of the L-curve in the regularization of discreteill-posed problems. Soc. Industr. Appl. Mathemat. J. Scientif. Computat., 14: 1487-1503.
- Harris, J.M., 1987. Diffraction tomography with discrete arrays of sources and receivers. Inst.
- Electr. Electron. Engin. Transact. Geosci. Remote Sens., 25: 448-455.
- Kilmer, M.E., O’Leary, D.P., 2001. Choosing Regularization Parameters in Iterative methods forill-posed problems. Soc. Industr. Appl. Mathemat. J. Matrix Analys. Applic., 22:1204-1221.
- Lanczos, C., 1961. Linear Differential Operators. Van Nostrand, London.
- Levenberg, K., 1944. A method for the solution of certain non-linear problems in least-squares.Quart. Appl. Mathemat., 2: 164-168.
- Lo, T.-W. and Inderwiesen, P.L., 1994. Fundamentals of Seismic Tomography. GeophysicalMonograph Series, SEG, Tulsa, OK.
- Marquardt, D.W., 1963. An algorithm for least-squares of nonlinear parameters. J. Soc. Industr.Appl. Mathemat., 11: 431-441.
- Penrose, R., 1955. A generalized inverse for matrices. Proc. Cambridge Philosoph. Soc., 51:406-413.
- Persson, P.-O. and Strang, G., 2004. A simple mesh generator in MATLAB. Soc. Industr. Appl.Mathemat. Rev., 46: 329-345.
- Reiter, T.D. and Rodi, W., 1996. Nonlinear waveform tomography applied to crosshole seismicdata. Geophysics, 61: 902-913.
- Rocha Filho, A.A., Harris, J.M. and Bassrei, A., 1996. A simple matrix formulation diffractiontomography algorithm. 39th Congr. Brasil. Geol., Salvador, BA, Brasil, 2: 312-315.
- Santos, E.T.F., Bassrei, A. and Costa, J., 2006. Evaluation of L-curve and @-curve approaches forthe selection of regularization parameter in anisotropic traveltime tomography. J. SeismicExplor., 15: 245-272.
- Santos, E.T.F. and Bassrei, A., 2007. L- and @-curve approaches for the selection of regularizationparameter in geophysical diffraction tomography. Comput. Geosci., 33: 618-629.
- Thompson, D.R., Rodi, W. and Tokséz, M.N., 1994. Nonlinear seismic diffraction tomographyusing minimum structure constraints. J. Acoust. Soc. Am., 95: 324-330.
- Titterington, D.M., 1985. General structure of regularization procedures in image reconstruction.Astron. Astrophys., 144: 381-387.
- Twomey, S., 1963. On the numerical solution of Fredholm integral equations of the first kind bythe inversion of the linear system produced by quadrature. J. Assoc. Comput. Mach., 10:97-101.
- Wu, R.-S. and Toks6z, M.N., 1987. Diffraction tomography and multisource holography appliedto seismic imaging. Geophysics, 52: 11-25.
