Volume 40 Number 3
  • E-ISSN: 1365-2478



There is a general lack of awareness among ‘lay’ professionals (geophysicists included) regarding the limitations in the use of least‐squares. Using a simple numerical model under simulated conditions of observational errors, the performance of least‐squares and other goodness‐of‐fit criteria under various error conditions are investigated. The results are presented in a simplified manner that can be readily understood by the lay earth scientist. It is shown that the use of least‐squares is, strictly, only valid either when the errors pertain to a normal probability distribution or under certain fortuitous conditions. The correct power to use (e.g. square, cube, square root, etc.) depends on the form of error distribution. In many fairly typical practical situations, least‐squares is one of the worst criteria to use. In such cases, data treatment, ‘robust statistics’ or similar processes provide an alternative approach.


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  1. Bodoky, T. and Szeidovitz, Zs.1972. The effect of normal correction errors on the stacking of common‐depth point traces. Geophysical Transactions of the Hungarian Geophysical Institute Roland Eötvös20. 3–4, 47–57.
    [Google Scholar]
  2. Box, G.E.P. and Cox, D.R.1964. An analysis of transformations. Journal of the Royal Statistical Society , Series B211.
  3. Claerbout, J.F. and Muir, F.1973. Robust modelling with erratic data. Geophysics38, 826–844.
    [Google Scholar]
  4. Constable, C.G.1988. Parameter estimation in non‐Gaussian noise. Geophysical Journal of the Royal Astronomical Society94, 131–142.
    [Google Scholar]
  5. Gray, W.C.1979. Variable norm deconvolution . Ph.D. thesis, Stanford University.
  6. Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J. and Stahel, W.A.1986. Robust Statistics. John Wiley & Sons, Inc.
    [Google Scholar]
  7. Lines, L.R. and Treitel, S.1984. Tutorial: A review of least squares and its application to geophysical problems. Geophysical Prospecting32, 159–186.
    [Google Scholar]
  8. Miller, H.J. and Thomas, J.B.1972. Detector for discrete time‐signals in non‐Gaussian noise. IEEE Transactions on Information TheoryIT‐18, 241–250.
    [Google Scholar]
  9. Mood, M.A., Graybill, F.A. and Boes, D.C.1974. Introduction to the Theory of Statistics. McGraw‐Hill Book Co.
    [Google Scholar]
  10. Size, W.B.
    (editor) 1987. Use and Abuse of Statistical Methods in Earth Sciences. Oxford University Press.
    [Google Scholar]
  11. Walden, A.T.1985. Non‐Gaussian reflectivity, entropy and deconvolution. Geophysics50, 2862–2888.
    [Google Scholar]
  12. Walden, A.T.1989. Robustification of AVO time slice intercepts and gradients . Internal BP Report, EXH.
  • Article Type: Research Article
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