Regularising Tunnelling Algorithm in Non-Linear Gravity Problems — a Numerical Study

  • R. G. S. Sastry
  • P. S. Moharir
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 103)

Abstract

Non-linear geophysical inversion, in general and gravity inversion in particular faces mainly two problems, viz., heavy dependance on quality of initial guess and stability. The proposed method developed on concepts of tunnelling (Levy et al, 1982) and Tikhonov’s regularisation tackles both these problems in a overdetermined case of gravity inversion. The algorithm is a recursive one, which rogresses through a sequence of local minima of systematically decreasing values. The results of simulation in gravity case do indicate that even if the initial guess is far away from the true solution, the terminal solution reached, is indeed close to true one. Thus, efficacy of joint application of reglarisation and tunnelling is illustrated.

Keywords

Geophysics 

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References

  1. Kirkpatrick, S., Galatt, Jr. C. D. and Vecchi, M. P. (1983). Optimization by simulated annealing, Science, 220, 671–680.CrossRefGoogle Scholar
  2. Levy, A. V., Montalvo, A., Gomez, S. and Calderon, A. (1982). Topics in Global Optimization, Lecture Notes in Mathematics, Hennart, J. P (ed.), No. 909, 18–33, Springer-Verlag, Berlin.Google Scholar
  3. Levy, A. V and Gomez, S. (1980) The tunnelling gradient-restoration algorithm for the global minimization of non-linear functions subject to non-linear inequality constraints, IIMAS-UNAM, Communicaciones Tecnicas, Serie Naranja: Investigaciones, No. 231.Google Scholar
  4. Levy, A. V and Gomez, S. (1985) The tunnelling method applied to global optimization, Numerica/ Optimization 1984, Boggs, P.T., Byrd, R. H. and Schnabel, R. B. (eds.), SIAM, Philadelphia, 213–214.Google Scholar
  5. Levy, A. V and Montalvo, A. (1977) The tunnelling algorithm for the global optimization of functions, Dundee Bienn. Conf. Num. Ana, Dundee.Google Scholar
  6. Levy, A. V. and Montalvo, A. (1980) A modification to the tunnelling algorithm for finding the global minima of an arbitrary one-dimensional function, Communicaciones Tecnicas, Seria Naranja, No. 240, IIMAS-UNAM.Google Scholar
  7. Price, W. L. (1978) A controlled random research procedure for global opti mization, Towards Global Optimization 2, Dixon, L. C. W. and Szego, G. P (eds.), North Holland, Amsterdam, 71–84.Google Scholar
  8. Rothman, R. H. (1985) Nonlinear inversion, statistical mechanics and residual estimation, Geophy., 50, 2784–2796.CrossRefGoogle Scholar
  9. Starostenko, V. I. and Zavaretko, A. N. (1976) Application of regularising algorithm to non-linear inverse problem of gravity — Methodology and results, Geophizicheski Sbornik, 71, 29–40.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • R. G. S. Sastry
    • 1
  • P. S. Moharir
    • 2
  1. 1.Department of Earth SciencesUniversity of RoorkeeRoorkeeIndia
  2. 2.National Geophysical Research InstituteHyderabadIndia

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