1887
Volume 20, Issue 3
  • ISSN: 0812-3985
  • E-ISSN: 1834-7533

Abstract

In situations in which Gaussian error assumptions are not valid, estimation procedures based on the least squares (LS) algorithm can be seriously misleading. It is then essential to use statistical procedures that are robust, in the sense of being relatively resistant or insensitive to the presence of a moderate number of outliers (abnormal data) superimposed on a common Gaussian noise background. This paper demonstrates the implementation of the robust regression M-estimate to magnetotelluric (MT) data. Like the LS estimate, the M-estimate minimizes the difference between prediction and observation, but it differs from the LS estimate in that it defines the measure of misfit in a way that does not allow a few bad points to dominate the estimate. Starting with the description of this estimate, several algorithms for computation are discussed and applied to estimate MT impedance. Using synthetic and real data, it is shown that, in comparison with the remote reference (RR) method (which is based on LS), robust procedures yield impedance estimates that are no worse than RR, and are often better.

© 1989 ASEG
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/content/journals/10.1071/EG989383
1989-06-01
2026-01-14

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References

  1. Chave, A. D., Thomson, D. J. and Ander, M. E. (1987). ‘On robust estimation of power spectra, coherences, and transfer functions’. J. Geophys. Res. 92, 633-648.
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  3. Egbert, G. D. and Booker, J. R. (1986). ‘Robust estimation of geomagnetic transfer functions’. Geophy. J. R. Astron. Soc. 87, 175-194.
  4. Gamble, T. D., Goubau, W. M. and Clarke, J. (1979). ‘Magnetotellurics with a remote reference’. Geophysics 44, 53-68.
  5. Huber, P. J. (1981). Robust statistics. Wiley, New York.
  6. Li, G. (1985). ‘Robust regression’, in, Hoaglin, D. C, Mosteller, R, and Tukey, J. W. eds., Exploring data tables, trends, and shapes. Wiley, New York, pp. 281-343.
  7. Moberg, T. F., Ramberg, J. S. and Randies, R. H. (1980). ‘An adaptive multiple regression procedure based on M-estimators’. Technometric 22, 213-224.
  8. Thomson, D. J. (1977). ‘Spectrum estimation techniques for characterization and development of WT4 waveguide’, I, Bellsyst. Tech. J. 56, 1769-1815.
  9. Wight, D. E. and Bostick, F. X. (1986). ‘Cascade decimation — A technique for real time estimation of power spectra’, in, Vozoff, K. ed., Magnetotelluric methods, Geophysics Reprint Series no. 5, Soc. Expl. Geop., pp. 215-218.
/content/journals/10.1071/EG989383
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  • Article Type: Research Article
Keyword(s): magnetotelluric impedance; robust impedance estimation

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