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New Uncertainty Measures for Predicted Geologic Properties from Seismic Attribute Calibration

  • Chul-Sung Kim
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 80)

Abstract

Predicted geologic properties from multiple linear regression are accurate only when the true relationship between the attribute vector and the geologic property is linear. Even when the true relationship is linear, the confidence intervals of the predicted geologic properties from multiple regression models are meaningful only when certain statistical assumptions on residuals are met. Otherwise, confidence intervals computed from a regression model could give false information. In many exploration tasks, training data are often clustered into groups separated by data gaps or have insufficient coverage of the attribute space. However, we often ignore large prediction errors that could occur away from constraining data.

This paper presents a new method, called a belief model, that determines uncertainties of predicted geologic properties in terms of degrees of reliability, unreliability, and unpredictability, the values of which add up to one. For a given predicted value, comparison of these three measures will indicate that the predicted property is: (a) correct if reliability is much greater than the other two measures, (b) incorrect if unreliability is the greatest, and (c) not firmly based on training data if unpredictability is the greatest.

In this method, the training data and their residuals (xi,zi, ri), i=1,.., N, are considered as N pieces of evidence from which to evaluate the uncertainty in a predicted value z. The basic probability distribution from a piece of evidence is modeled as a modified normal distribution whose magnitude depends on the distance between the training data attribute vector and the attribute vector at the prediction point. Then, the framework of Dempster-Shafer’s theory of evidence is used to aggregate uncertainty measures on the predicted value z from each evidence (xi, zi, ri), i=1,.., N.

The Utility of this new uncertainty measure was demonstrated in assessing the reliability of the predicted geological properties, such as sand percent or porosity feet, from seismic attribute calibration of synthetic as well as real seismic data.

Keywords

Training Data Attribute Vector Level Reliability Seismic Attribute Basic Probability Assignment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Matteuci G.: Seismic attribute analysis and calibration: A general procedure and a case study, Annual Meeting Abstracts, Society of Exploration Geophysicists, p. 373–376, 1996.Google Scholar
  2. 2.
    Draper N.R. and H. Smith: Applied regression analysis, Second Edition, John Wiley & Sons, New York, 1981.Google Scholar
  3. 3.
    Shafer, G.: A mathematical Theory of Evidence, Princeton University Press, Princeton, NJ, 1976.Google Scholar
  4. 4.
    Dempster, A. P.: Upper & lower probabilities induced by a multivalued mapping, Annals Math. Statistics, Vol. 38, no. 2, p. 325–339, 1967.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Chul-Sung Kim
    • 1
  1. 1.ExxonMobil Upstream Research Co.HoustonUSA

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