Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1890776 | Chaos, Solitons & Fractals | 2006 | 10 Pages |
Abstract
The characterization of irregular objects with fractal methods often leads to the estimation of the slope of a function which is plotted versus a scale parameter. The slope is usually obtained with a linear regression. The problem is that the fit is usually not acceptable from the statistical standpoint. We propose a new approach in which we use two straight lines to bound the data from above and from below. We call these lines the upper and lower linear bounds. We propose to define these bounds as the solution of an optimization problem. We discuss the solution of this problem and we give an algorithm to obtain its solution. We use the difference between the upper and lower linear bounds to define a measure of the degree of linearity in the scaling range. We illustrate our method by analyzing the fluctuations of the variogram in a microresistivity well log from an oil reservoir in the North Sea.
Related Topics
Physical Sciences and Engineering
Physics and Astronomy
Statistical and Nonlinear Physics
Authors
Antoine Saucier, François Soumis,