Problemas Inversos em Geofísica
--- Disciplina Eletiva; 3 créditos ---
Tópicos:
- Introdução à inversão em Geofísica;
- Exemplo das etapas de um processo inverso;
- Inversão linear;
- Transformação de um problema mal-posto em bem-posto através da introdução de informação a priori;
- Regularização de Tikhonov;
- Estimadores particulares via regularização de Tikhonov.
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Bibliografia:
- Aster R., Borchers B., and Thurber C., 2004, Parameter Estimation and Inverse Problems: Elsevier Academic Press.
- Barbosa, V. C. F., Silva, J. B. C, e Medeiros, W. E., 1997, Gravity inversion of basement relief using approximate equality constraints on depths: Geophysics, v. 62, p.1745-1757.
- Beck, J. V. e Arnold, K. J., 1977, Parameter estimation in engineering and science: John Wiley and Sons.
- Bevington, P. R., 1969, Data reduction and error analysis in science: McGraw-Hill Book Co.
- Forsythe, G. E., Malcolm, M. A. e Moler, C. B., 1977, Computer methods for mathematical computations: Prentice-Hall Inc.
- Guillen, A., e Menichetti, V., 1984, Gravity and magnetic inversion with minimization of a specific functional: Geophysics, v. 49, p. 1354-1360.
- Jackson, D. D., 1972, Interpretation of inaccurate, insufficient, and inconsistent data: Geophy. J. R. Astr. Soc., v. 28, p. 97-110.
- Lanczos, C., 1961, Linear differential operators: D. Van Nostrand Co.
- Last, B. J., e Kubik, K., 1983, Compact gravity inversion: Geophysics, v. 48, p. 713-721. –
- Li, Y, and Oldenburg, D. W., 1996, 3-D inversion of magnetic data: Geophysics, v. 61, 394-408.
- Menke, W., 1984, Geophysical data analysis: discrete inverse theory: Academic Press Inc.
- Noble B. and Dainel, J. W., 1989. Álgebra Linear Aplicada. Prentice-Hall.
- Parker, R. L., 1977, Understanding inverse theory: Ann. Rev.Earth. Planet. Sci., v. 5, p. 35-64
- Strang, G., 1988. Linear Álgebra and its Application. Saunders College Publishing, Fort Worth
- Tikhonov., A. N. e Arsenin, V. Y., 1977 Solutions of ill-posed problems: John Wiley and Sons.
- Twomey, S., 1977. Introduction to the mathematics of inversion in remote sensing and indirect measurements: Elsevier Scientific Publ. Co.
- Vogel, C. R. 2002 Computational Methods for Inverse Problems (Frontiers in Applied Mathematics) SIAM.
- Zhdanov, M. S. 2002 Geophysical Inverse Theory and Regularization Problems. Elsevier Science
- Periódicos da área.