Some remarks on the estimation of fractal scaling parameters from borehole wire‐line logs

Dolan, Seán; Bean, Christopher J.

doi:10.1029/97gl00987

Cited by 33 publications

(27 citation statements)

References 10 publications

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“…filtering procedures, detrending) and to the use of several algorithms for assessing the coefficients (spectral or Hurst Exponents). Goff and Holliger (1999), covariance; (2) Jones and Holliger (1997), robust power spectrum; (3) Leonardi and Kümpel (1998), power spectrum (periodogram); (4) Leonardi and Kümpel (1998), rescaled-range; (5) Marsan and Bean (1999), power spectrum; (6) Marsan and Bean (1999), structure function, (7) Marsan and Bean (2003), power spectrum; (8) Wu et al (1994), power spectrum, (9) Dolan and Bean (1997), power spectrum; (10) Dolan and Bean (1997), rescaled-range; (11) Holliger (1996), autocovariance; (12) Maus and Dimri (1994), power spectrum; (13) Zhou and Thybo (1998), power spectrum; In our work, the obtained H values are close those derived from the previous researches. That establishes the robustness of the proposed approaches.…”

Section: Resultsmentioning

confidence: 99%

“…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%

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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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Section: Resultsmentioning

confidence: 99%

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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“…a cross-section of a surface), the equation is therefore as follows: (Huang and Turcotte, 1989;Dolan and Bean, 1997). …”

Section: Background and Previous Workmentioning

confidence: 99%

“…The Hurst number, H (or ν) is related to D by the following equation (Mandelbrot, 1985;Feder, 1988;Dolan and Bean, 1997):…”

mentioning

confidence: 99%

“…Martini et al (2005) Much of this work stems from analysis of borehole data to produce stochastic models (e.g. Bean, 1996;Holliger, 1996;Dolan and Bean, 1997;Dolan et al, 1998;Frenje and Juhlin, 1998) and analysis of topography both on land (Huang and Turcotte, 1989) and on the seafloor (Goff and Jordan, 1988). Similar approaches have been used in a number of different fields including the analysis of sedimentary cycles (Browaeys and Fomel, 2009) and in seismic oceanography (Buffett et al, 2010).…”

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confidence: 99%

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On the Use of Fractal Surfaces to Understand Seismic Wave Propagation in Layered Basalt Sequences

Nelson

Hobbs

Rusch

2014

Pure Appl. Geophys.

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Rupture dynamics and ground motions from earthquakes in 2‐D heterogeneous media

Bydlon

Dunham

2015

Geophysical Research Letters

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We perform 2‐D simulations of earthquakes on rough faults in media with random heterogeneities (with von Karman distribution) to study the effects of geometric and material heterogeneity on the rupture process and resulting high‐frequency ground motions in the near‐fault region (out to ∼20 km). Variations in slip and rupture velocity can arise from material heterogeneity alone but are dominantly controlled by fault roughness. Scattering effects become appreciable beyond ∼3 km from the fault. Near‐fault scattering extends the duration of incoherent, high‐frequency ground motions and, at least in our 2‐D simulations, elevates root‐mean‐square accelerations (i.e., Arias intensity) with negligible reduction in peak velocities. We also demonstrate that near‐fault scattering typically occurs in the power law tail of the power spectral density function, quantified by the Hurst exponent and another parameter combining standard deviation and correlation length.

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Some remarks on the estimation of fractal scaling parameters from borehole wire‐line logs

Abstract: Abstract.Well-logging provides a direct means of assessing fluctuations in petrophysical properties with depth, and thus allows for the statistical characterisation of crustal heterogeneity. Using records from three

Cited by 33 publications

References 10 publications

Local regularity analysis of strata heterogeneities from sonic logs

Local regularity analysis of strata heterogeneities from sonic logs

On the Use of Fractal Surfaces to Understand Seismic Wave Propagation in Layered Basalt Sequences

Rupture dynamics and ground motions from earthquakes in 2‐D heterogeneous media

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