1887
Volume 43 Number 2
  • E-ISSN: 1365-2478

Abstract

Abstract

A new information criterion, the extended information criterion (EIC) was applied in order to determine an optimum solution in simultaneous iterative reconstruction technique (SIRT) P‐wave velocity tomography. The EIC is derived from information theory and statistics, and it measures the goodness‐of‐fit between the true (unknown) data distribution and the observed data distribution: the former gives the probability of data realization from the true (unknown) model, whereas the latter gives a probability of data realization calculated from a particular model of which parameters are estimated. The EIC is calculated using bootstrap statistics, a numerical technique for calculating statistical estimators. Bootstrap statistics enables us to obtain the bias between the log likelihood and the expected log likelihood, and then to obtain the expected log likelihood from the log likelihood. Since the EIC is obtained numerically, we can use it for most problems of model parameter estimation without employing the maximum likelihood method. Taking weak anisotropy into account, we reconstructed the P‐wave velocity structure of a rock sample during water infiltration under differential stress loading conditions. The results indicate that we can remove unrealistic solutions sometimes encountered when too many iterations are made. In spite of much computation time, the EIC is a promising technique for the near future, prompted by the rapid progress in current computer technology.

Loading

Article metrics loading...

/content/journals/10.1111/j.1365-2478.1995.tb00129.x
2006-04-28
2024-03-28
Loading full text...

Full text loading...

References

  1. BackusG. and GilbertF.1970). Uniqueness in the inversion of inaccurate gross Earth data. Philosophical Transactions of the Royal Society of LondonA266, 123–192.
    [Google Scholar]
  2. DiaconisP. and EfronB.1983). Computer‐intensive methods in statistics. Scientific American248, 96–108.
    [Google Scholar]
  3. EfronF.1983). Estimating the error rate of a prediction rule: improvement on cross‐validation. Journal of the American Statistical Association78, 316–331.
    [Google Scholar]
  4. IshiguroM. and SakamotoY.1991). WIC: An estimator‐free information criterion. The Institute of Statistical Mathematics, Research Memorandum No. 410, 1–22.
  5. IvanssonS.1983). Remarks on an earlier proposed iterative tomographic algorithm. Geophysical Journal of the Royal Astronomical Society75, 855–860.
    [Google Scholar]
  6. KitagawaG.1991. On the bootstrap of likelihood. In: Report of the Institute of Statistical Mathematics No. 31, “Theory and Application of Estimation about Time Series”, pp. 175–179(in Japanese).
  7. MasudaK., NishizawaO., KusunoseK., SatohT., TakahashiM. and KranzR.1990). Positive feedback fracture process induced by nonuniform high‐pressure water flow in dilatant granite. Journal of Geophysical Research95, 21583–21592.
    [Google Scholar]
  8. MurataY.1993). Estimation of optimum average surficial density from gravity data: an objective approach. Journal of Geophysical Research98, 12097–12109.
    [Google Scholar]
  9. MurataY. and NoroH.1993). Optimization of estimation procedure of Bouger density by use of the ABIC‐minimization method. Butsuritansa46, 120–127 (in Japanese).
    [Google Scholar]
  10. NishizawaO. and NoroH.1994). Bootstrap statistics for finding an optimum model in SIRT. Journal of Seismic Exploration3, 157–171.
    [Google Scholar]
  11. OgataY., ImotoM. and KatsuraK.1991). 3D spatial variation of b‐values of magnitude‐frequency distribution beneath the Kanto district, Japan. Geophysical Journal International104, 135–146.
    [Google Scholar]
  12. SakamotoY., IshiguroM. and KitagawaG.1986. Akaike Information Criterion Statistics. D. Reidel Pub. Co.
    [Google Scholar]
  13. TamuraY., SatoT., OoeM. and TshiguroM.1991). A procedure for tidal analysis with a Bayesian information criterion. Geophysical Journal International104, 507–516.
    [Google Scholar]
  14. TarantolaA.1987. Inverse Problem Theory. Elsevier Science Publishing Co.
    [Google Scholar]
  15. TarantolaA. and ValetteB.1982). Inverse problems = Quest for information. Journal of Geophysics50, 159–170.
    [Google Scholar]
  16. TauxeL., KylstraN. and ConstableC.1991). Bootstrap statistics for paleomagnetic data. Journal of Geophysical Research96, 11723–11740.
    [Google Scholar]
  17. WongH.W.1983). A note on the modified likelihood for density estimation. Journal of the American Statistical Association78, 461–463.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/j.1365-2478.1995.tb00129.x
Loading
  • Article Type: Research Article

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error