@article{GaciZaourarHamoudietal.2010,
  author    = {Gaci, Said and Zaourar, Naima and Hamoudi, Mehdi and Holschneider, Matthias},
  title     = {Local regularity analysis of strata heterogeneities from sonic logs},
  issn      = {1023-5809},
  doi       = {10.5194/npg-17-455-2010},
  year      = {2010},
  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.},
  language  = {en}
}
@article{ZaourarHamoudiHolschneideretal.2013,
  author    = {Zaourar, Naima and Hamoudi, Mohamed and Holschneider, Matthias and Mandea, Mioara},
  title     = {Fractal dynamics of geomagnetic storms},
  series = {Arabian journal of geosciences},
  volume    = {6},
  journal   = {Arabian journal of geosciences},
  number    = {6},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {1866-7511},
  doi       = {10.1007/s12517-011-0487-0},
  pages     = {1693 -- 1702},
  year      = {2013},
  abstract  = {We explore fluctuations of the horizontal component of the Earth's magnetic field to identify scaling behaviour of the temporal variability in geomagnetic data recorded by the Intermagnet observatories during the solar cycle 23 (years 1996 to 2005). In this work, we use the remarkable ability of scaling wavelet exponents to highlight the singularities associated with discontinuities present in the magnetograms obtained at two magnetic observatories for six intense magnetic storms, including the sudden storm commencements of 14 July 2000, 29-31 October and 20-21 November 2003. In the active intervals that occurred during geomagnetic storms, we observe a rapid and unidirectional change in the spectral scaling exponent at the time of storm onset. The corresponding fractal features suggest that the dynamics of the whole time series is similar to that of a fractional Brownian motion. Our findings point to an evident relatively sudden change related to the emergence of persistency of the fractal power exponent fluctuations precedes an intense magnetic storm. These first results could be useful in the framework of extreme events prediction studies.},
  language  = {en}
}
@article{GaciZaourarBriqueuetal.2011,
  author    = {Gaci, Said and Zaourar, Naima and Briqueu, Louis and Holschneider, Matthias},
  title     = {Regularity analysis applied to sonic logs data a case study from KTB borehole site},
  series = {Arabian journal of geosciences},
  volume    = {4},
  journal   = {Arabian journal of geosciences},
  number    = {1-2},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {1866-7511},
  doi       = {10.1007/s12517-010-0129-y},
  pages     = {221 -- 227},
  year      = {2011},
  abstract  = {Borehole logs provide in situ information about the fluctuations of petrophysical properties with depth and thus allow the characterization of the crustal heterogeneities. A detailed investigation of these measurements may lead to extract features of the geological media. In this study, we suggest a regularity analysis based on the continuous wavelet transform to examine sonic logs data. The description of the local behavior of the logs at each depth is carried out using the local Hurst exponent estimated by two (02) approaches: the local wavelet approach and the average-local wavelet approach. Firstly, a synthetic log, generated using the random midpoints displacement algorithm, is processed by the regularity analysis. The obtained Hurst curves allowed the discernment of the different layers composing the simulated geological model. Next, this analysis is extended to real sonic logs data recorded at the Kontinentales Tiefbohrprogramm (KTB) pilot borehole (Continental Deep Drilling Program, Germany). The results show a significant correlation between the estimated Hurst exponents and the lithological discontinuities crossed by the well. Hence, the Hurst exponent can be used as a tool to characterize underground heterogeneities.},
  language  = {en}
}
@misc{ZaourarHamoudiMandeaetal.2013,
  author    = {Zaourar, Naima and Hamoudi, Mohamed and Mandea, Mioara and Balasis, Georgios and Holschneider, Matthias},
  title     = {Wavelet-based multiscale analysis of geomagnetic disturbance},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  volume    = {65},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {12},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-43691},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-436912},
  pages     = {1525 -- 1540},
  year      = {2013},
  abstract  = {The dynamics of external contributions to the geomagnetic field is investigated by applying time-frequency methods to magnetic observatory data. Fractal models and multiscale analysis enable obtaining maximum quantitative information related to the short-term dynamics of the geomagnetic field activity. The stochastic properties of the horizontal component of the transient external field are determined by searching for scaling laws in the power spectra. The spectrum fits a power law with a scaling exponent β, a typical characteristic of self-affine time-series. Local variations in the power-law exponent are investigated by applying wavelet analysis to the same time-series. These analyses highlight the self-affine properties of geomagnetic perturbations and their persistence. Moreover, they show that the main phases of sudden storm disturbances are uniquely characterized by a scaling exponent varying between 1 and 3, possibly related to the energy contained in the external field. These new findings suggest the existence of a long-range dependence, the scaling exponent being an efficient indicator of geomagnetic activity and singularity detection. These results show that by using magnetogram regularity to reflect the magnetosphere activity, a theoretical analysis of the external geomagnetic field based on local power-law exponents is possible.},
  language  = {en}
}