A grey system approach for estimating the hölderian regularity with an application to algerian well log data

Said Gaci, Orietta Nicolis

Research output: Contribution to journalArticlepeer-review

Abstract

The Hölderian regularity is an important mathematical feature of a signal, connected with the physical nature of the measured parameter. Many algorithms have been proposed in lit-erature for estimating the local Hölder exponent value, but all of them lead to biased estimates. This paper attempts to apply the grey system theory (GST) on the raw signal for improving the accuracy of Hölderian regularity estimation. First, synthetic logs data are generated by the succes-sive random additions (SRA) method with different types of Hölder functions. The application on these simulated signals shows that the Hölder functions estimated by the GST are more precise than those derived from the raw data. Additionally, noisy signals are considered for the same ex-periment, and more accurate regularity is obtained using signals processed using GST. Second, the proposed technique is implemented on well log data measured at an Algerian exploration bore-hole. It is demonstrated that the regularity determined from the well logs analyzed by the GST is more reliable than that inferred from the raw data. In addition, the obtained Hölder functions al-most reflect the lithological discontinuities encountered by the well. To conclude, the GST is a powerful tool for enhancing the estimation of the Hölderian regularity of signals.

Original languageEnglish
Article number86
JournalFractal and Fractional
Volume5
Issue number3
DOIs
Publication statusPublished - Sep 2021

Keywords

  • Fractal
  • Grey system theory
  • Hölder exponent
  • Well logs

ASJC Scopus subject areas

  • Analysis
  • Statistical and Nonlinear Physics
  • Statistics and Probability

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