New Uncertainty Measures for Predicted Geologic Properties from Seismic Attribute Calibration
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.
KeywordsTraining Data Attribute Vector Level Reliability Seismic Attribute Basic Probability Assignment
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