Wavelet and rescaled range approach for the Hurst coefficient for short and long time series

Chamoli, Ashutosh; Bansal, A. R.; Dimri, V. P.

doi:10.1016/j.cageo.2006.05.008

Cited by 91 publications

(32 citation statements)

References 15 publications

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“…The R/S analysis is non-parametric, in the sense that there are no specific assumptions or requirements for the distribution of the observables. Moreover, it has been shown to be robust even in the presence of a discrete noise level (Chamoli et al 2007). …”

Section: The α − σ Parameter Space and The Hurst Exponentmentioning

confidence: 99%

Wavelet andR/Sanalysis of the X-ray flickering of cataclysmic variables

Anzolin¹,

Tamburini

Martino³

et al. 2010

A&A

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Context. Recently, wavelets and R/S analysis have been used as statistical tools to characterize the optical flickering of cataclysmic variables. Aims. Here we present the first comprehensive study of the statistical properties of X-ray flickering of cataclysmic variables in order to link them with physical parameters. Methods. We analyzed a sample of 97 X-ray light curves of 75 objects of all classes observed with the XMM-Newton space telescope. By using the wavelets analysis, each light curve has been characterized by two parameters, α and Σ, that describe the energy distribution of flickering on different timescales and the strength at a given timescale, respectively. We also used the R/S analysis to determine the Hurst exponent of each light curve and define their degree of stochastic memory in time.Results. The X-ray flickering is typically composed of long time scale events (1.5 < ∼ α < ∼ 3), with very similar strengths in all the subtypes of cataclysmic variables (−3 < ∼ Σ < ∼ −1.5). The X-ray data are distributed in a much smaller area of the α − Σ parameter space with respect to those obtained with optical light curves. The tendency of the optical flickering in magnetic systems to show higher Σ values than the non-magnetic systems is not encountered in the X-rays. The Hurst exponents estimated for all light curves of the sample are larger than those found in the visible, with a peak at 0.82. In particular, we do not obtain values lower than 0.5. The X-ray flickering presents a persistent memory in time, which seems to be stronger in objects containing magnetic white dwarf primaries. Conclusions. The similarity of the X-ray flickering in objects of different classes together with the predominance of a persistent stochastic behavior can be explained in terms of magnetically-driven accretion processes acting in a considerable fraction of the analyzed objects.

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Section: The α − σ Parameter Space and The Hurst Exponentmentioning

confidence: 99%

Wavelet andR/Sanalysis of the X-ray flickering of cataclysmic variables

Anzolin¹,

Tamburini

Martino³

et al. 2010

A&A

View full text Add to dashboard Cite

show abstract

“…Wavelet transform was first introduced by Morlet et al (1982a, b), Grossmann and Morlet (1984) and Goupilloud et al (1984) and is being used as a powerful signal analysis tool in the different fields of applications such as denoising, compression, time-frequency analysis, climate studies etc (Foufoula-Georgiou and Kumar, 1994;Chamoli et al, 2007Chamoli et al, , 2010Torrence and Compo, 1998). Wavelet transform is a localized transform in both time and frequency, which is more relevant than conventional methods to extract information from a non-stationary signal.…”

Section: Introductionmentioning

confidence: 99%

Wavelet analysis of the seismograms for tsunami warning

Chamoli

Rani

Srivastava

et al. 2010

Nonlin. Processes Geophys.

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Abstract. The complexity in the tsunami phenomenon makes the available warning systems not much effective in the practical situations. The problem arises due to the time lapsed in the data transfer, processing and modeling. The modeling and simulation needs the input fault geometry and mechanism of the earthquake. The estimation of these parameters and other aprior information increases the utilized time for making any warning. Here, the wavelet analysis is used to identify the tsunamigenesis of an earthquake. The frequency content of the seismogram in time scale domain is examined using wavelet transform. The energy content in high frequencies is calculated and gives a threshold for tsunami warnings. Only first few minutes of the seismograms of the earthquake events are used for quick estimation. The results for the earthquake events of Andaman Sumatra region and other historic events are promising.

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“…When H is close to 1, the signal is weakly irregular, while for H close to 0, it is highly irregular. The coefficient H can be estimated by various methods, the most popular is the Rescaled-Range (R/S) analysis (Dolan and Bean, 1997;Kümpel, 1998, 1999;Malamud and Turcotte, 1999;Li, 2003;Arizabalo et al, 2004Arizabalo et al, , 2006Bansal and Dimri, 2005;Chamoli et al, 2007). In addition to the R/S analysis, wavelet-based estimators have been used very successfully for estimating Published by Copernicus Publications on behalf of the European Geosciences Union and the American Geophysical Union.…”

Section: Introductionmentioning

confidence: 99%

Local regularity analysis of strata heterogeneities from sonic logs

Gaci

Zaourar

Hamoudi

et al. 2010

Nonlin. Processes Geophys.

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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.

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Wavelet and rescaled range approach for the Hurst coefficient for short and long time series

Cited by 91 publications

References 15 publications

Wavelet andR/Sanalysis of the X-ray flickering of cataclysmic variables

Wavelet andR/Sanalysis of the X-ray flickering of cataclysmic variables

Wavelet analysis of the seismograms for tsunami warning

Local regularity analysis of strata heterogeneities from sonic logs

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