251
Views
13
CrossRef citations to date
0
Altmetric
Original Articles

Iteratively adaptive regularization in inverse modeling with Bayesian outlook – application on geophysical data

Pages 655-670 | Received 12 Oct 2004, Accepted 04 May 2005, Published online: 22 Aug 2006

  • Tarantola, A, 1987. Inverse Problem Theory. Amsterdam. 1987.
  • Menke, W, 1989. Geophysical Data Analysis: Discrete Inverse Theory. Sandiego. 1989.
  • Sen, MK, and Stoffa, PL, 1995. Global Optimization Methods in Geophysical Inversion. Amsterdam. 1995.
  • Kirkpatrik, S, Gelatt, CD, and Vecchi, MP, 1983. Optimization by simulated annealing, Science 220 (1983), pp. 671–680.
  • Sen, MK, and Stoffa, PL, 1991. Nonlinear one-dimensional seismic waveform inversion using simulated annealing, Geophysics 56 (1991), pp. 1624–1638.
  • Holland, JH, 1992. Adaptation of Natural and Artificial Systems: An introductory Analysis with Applications to Biology, Controls and Artificial Intelligence. Ann Arbor. 1992.
  • Sambridge, MS, and Drijkoningen, GG, 1992. Genetic algorithm in seismic waveform inversion, Geophysical Journal International 109 (1992), pp. 323–342.
  • Mockus, JB, 1990. Bayesian Approach to Global Optimization: Theory and Applications. New York. 1990.
  • Stuckman, BE, 1998. A search method for optimizing nonlinear systems, IEEE Transactions of Systems, Man and Cybernetics 18 (1998), pp. 965–977.
  • Ruján, P, 1988. Searching for optimal configuration by simulated tunneling, Zeitschrift Für Physik B 73 (1988), pp. 391–416.
  • Baumketner, A, Shimizu, H, Isobe, M, and Hiwatari, Y, 2002. Stochastic tunneling minimization by molecular dynamics: an application to heteropolymer models, Physica A 310 (2002), pp. 139–150.
  • Horst, R, and Tuy, H, 1990. Global Optimization: Deterministic Approaches. Berlin. 1990.
  • Al-Khyaal, A, and Sherali, HD, 2000. On finitely terminating branch and bound algorithms for some global optimization problems, SIAM Journal on Optimization 10 (2000), pp. 1049–1057.
  • Causse, E, 1994. "Comparison of steepest descent and conjugate gradient algorithms in 2D finite difference migration/inversion. In:". In: Extended Abstracts, 56th Mtg., Eur. Assn. Expl. Geophys, Vienna. 1994, 6–10 June.
  • Luenberger, DG, 1984. Introduction to Linear and Nonlinear Programming. Massachusetts. 1984.
  • Dai, YH, and Yuan, Y, 1999. A nonlinear conjugate gradient method with a strong global convergence property, SIAM Journal on Optimization 10 (1999), pp. 177–182.
  • Mao, WJ, and Gubbins, D, 1995. Simultaneous determination of time delays and stacking weights in seismic array beam forming, Geophysics 60 (1995), pp. 491–502.
  • More, JJ, 1978. The Levenburg-Marquardt Algorithm: Implementation and Theory. Vol. 630. Berlin. 1978. p. pp. 105–116, Lecture Notes in Mathematics.
  • Inman, JR, 1975. Reistivity inversion with ridge regression, Geophysics 40 (1975), pp. 798–816.
  • Dennis, JE, and Schnabel, RB, 1996. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Philadelphia. 1996.
  • Pratt, RG, Chengshu, Shin, and Hicks, GJ, 1998. Gauss-Newton and full Newton methods in frequency-space seismic waveform inversion, Geophysical Journal International 133 (1998), pp. 341–362.
  • Ramlau, R, 2002. A steepest descent algorithm for the global minimization of the Tikhonov functional, Inverse Problems 18 (2002), pp. 381–403.
  • Roy, IG, 2002. A robust descent type algorithm for geophysical inversion through adaptive regularization scheme, Applied Mathematical Modelling 26 (2002), pp. 619–634.
  • Engl, HW, 1987. Discrepancy principles of Tikhonov regularization of ill-posed problems leading to optimal convergence rates, Journal of Optimization Theory and Applications 52 (1987), pp. 209–215.
  • Tikhonov, AN, and Arsenin, VY, 1977. Solutions of Illposed Problems. Washington, DC. 1977.
  • Hansen, PC, 1992. Analysis of discrete ill-posed problems by means of L-curve, SIAM Review 34 (1992), pp. 561–580.
  • Haber, E, and Oldenburg, DW, 2000. A GCV based method for nonlinear ill-posed problems, Computational Geosciences 4 (2000), pp. 41–63.
  • MacKay, DJC, 1992. Bayesian interpolation, Inverse Problems in Science and Engineering 4 (1992), pp. 415–447.
  • Yagola, AG, Leonov, AS, and Titarenko, VN, 2002. Data errors and an error estimation for ill-posed problems, Inverse Problems in Science and Engineering 10 (2002), pp. 117–129.
  • Sen, MK, and Roy, IG, 2003. Computation of differential seismograms and iteration adaptive regularization in pre-stack waveform inversion, Geophysics 68 (2003), pp. 2026–2039.
  • Parasnis, DS, 1986. Principles of Applied Geophysics. New York. 1986, 4th Edn.
  • Morozov, IB, 2004. Null-space and statistical significance of first arrival travel-time inversion, Geophysical Journal International 156 (2004), pp. 549–554.
  • Dobrin, MB, and Savit, CH, 1988. Introduction to Geophysical Prospecting. New York. 1988, 4th Edn.
  • Gaul, L, Hurlebaus, S, and Jacobs, LJ, 2001. Localization of synthetic acoustic emission source on the surface of fatigue specimen, Research in Nondestructive Evaluation 13 (2001), pp. 105–117.
  • Guptasarma, D, 1982. Optimization of short digital linear filters for increased accuracy, Geophysical Prospecting 30 (1982), pp. 501–514.
  • Malischewsky, PG, 2004. A note on Rayleigh wave velocity as a function of the material parameters, Geofisica Internacional 43 (2004), pp. 407–509.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.