Journal cover Journal topic
Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
Journal topic

Journal metrics

IF value: 1.558
IF1.558
IF 5-year value: 1.475
IF 5-year
1.475
CiteScore value: 2.8
CiteScore
2.8
SNIP value: 0.921
SNIP0.921
IPP value: 1.56
IPP1.56
SJR value: 0.571
SJR0.571
Scimago H <br class='widget-line-break'>index value: 55
Scimago H
index
55
h5-index value: 22
h5-index22
Volume 17, issue 5
Nonlin. Processes Geophys., 17, 455–466, 2010
https://doi.org/10.5194/npg-17-455-2010
© Author(s) 2010. This work is distributed under
the Creative Commons Attribution 3.0 License.

Special issue: Complexity and extreme events in geosciences

Nonlin. Processes Geophys., 17, 455–466, 2010
https://doi.org/10.5194/npg-17-455-2010
© Author(s) 2010. This work is distributed under
the Creative Commons Attribution 3.0 License.

  20 Sep 2010

20 Sep 2010

Local regularity analysis of strata heterogeneities from sonic logs

S. Gaci1, N. Zaourar1, M. Hamoudi1, and M. Holschneider2 S. Gaci et al.
  • 1Département Géophysique – FSTGAT, Université des Sciences et de la Technologie Houari Boumediene (USTHB), BP 32 El Alia, 16111, Algiers, Algeria
  • 2Institute for Mathematics, University of Potsdam, Am Neuen Palais 10, 14469 Potsdam, Germany

Abstract. Borehole logs provide geological information about the rocks crossed by the wells. Several properties of rocks can be interpreted in terms of lithology, type and quantity of the fluid filling the pores and fractures.

Here, the logs are assumed to be nonhomogeneous Brownian motions (nhBms) which are generalized fractional Brownian motions (fBms) indexed by depth-dependent Hurst parameters H(z). Three techniques, the local wavelet approach (LWA), the average-local wavelet approach (ALWA), and Peltier Algorithm (PA), are suggested to estimate the Hurst functions (or the regularity profiles) from the logs.

First, two synthetic sonic logs with different parameters, shaped by the successive random additions (SRA) algorithm, are used to demonstrate the potential of the proposed methods. The obtained Hurst functions are close to the theoretical Hurst functions. Besides, the transitions between the modeled layers are marked by Hurst values discontinuities. It is also shown that PA leads to the best Hurst value estimations.

Second, we investigate the multifractional property of sonic logs data recorded at two scientific deep boreholes: the pilot hole VB and the ultra deep main hole HB, drilled for the German Continental Deep Drilling Program (KTB). All the regularity profiles independently obtained for the logs provide a clear correlation with lithology, and from each regularity profile, we derive a similar segmentation in terms of lithological units. The lithological discontinuities (strata' bounds and faults contacts) are located at the local extrema of the Hurst functions. Moreover, the regularity profiles are compared with the KTB estimated porosity logs, showing a significant relation between the local extrema of the Hurst functions and the fluid-filled fractures. The Hurst function may then constitute a tool to characterize underground heterogeneities.

Publications Copernicus
Download
Citation