Heterogeneity spectrum and scale‐anisotropy in the upper crust revealed by the German Continental Deep‐Drilling (KTB) Holes

Abstract

Crustal heterogeneities and their statistical characteristics bear important information about the dynamic processes and evolution of the crust. The velocity well‐log data from the German Continental Deep Drilling Project (KTB) offer a rare opportunity to measure directly the properties of crustal heterogeneities. In this study, we first estimated the power spectrum of crustal heterogeneities from the P‐velocity well‐logs of the two holes. For the first time, a power‐law spectrum of crustal heterogeneities was directly observed in the spatial wavelength range from a few meters to a few kilometers. The slope of the vertical 1D power spectrum of the random velocity perturbations is about 1.1, corresponding to a flicker‐noise random medium. The scale‐anisotropy ratio (aspect ratio) and the horizontal spectral slope of crustal heterogeneities were also estimated by cross‐correlation analysis between these two holes to be about 1.8 and 2.0, respectively.

Local regularity analysis of strata heterogeneities from sonic logs

“…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.…”

“…Furthermore, the three techniques are implemented to study multifractionality properties of the P-and S-waves sonic measurements recorded in the KTB pilot and main boreholes. The KTB offers a unique opportunity to investigate the properties of crustal heterogeneities and many studies have been devoted to analyze the well log measurements (Leary, 1991;Maus and Dimri, 1994;Wu et al, 1994;Kneib, 1995;Holliger, 1996;Jones and Holliger, 1997;Li, 1998;Dolan et al, 1998;Zhou and Thybo, 1998;Kümpel, 1998, 1999;Bean, 1999, 2003;Goff and Holliger, 1999;Fedi, 2003;Fedi et al, 2005;Gaci and Zaourar, 2010).…”

Well-Logs Data Processing Using the Fractal Analysis and Neural Network

“…It is commonly observed that well log measurements exhibit scaling properties, and are usually described and modelled as fractional Brownian motions (Pilkington & Tudoeschuck , 1991;Wu et al 1994;Kneib 1995;Bean, 1996;Holliger 1996 , we have shown that well logs fluctuations in oil exploration display scaling behaviour that has been modelled as self affine fractal processes. They are therefore considered as fractional Brownian motion (fBm), characterized by a fractal k- power spectrum model where k is the wavenumber and  is related to the Hurst parameter (Hermman,1997; Ouadfeul and Aliouane, 2011).…”

“…Geophysical well-logs often show a complex behavior which seems to suggest a fractal nature (Pilkington & Tudoeschuck, 1991;Wu et al, 1994;Turcotte, 1997;Ouadfeul, 2006; Ouadfeul and Aliouane 2011; Ouadfeul et al, 2012). They are geometrical objects exhibiting an irregular structure at any scale.…”

Scaling and multifractal fields in the solid earth and topography

“…It is perhaps surprising that for many geophysical 3/28/07 7 parameters the vertical structure is better known than the horizontal due to the large number of borehole analyses. Examples of scaling spectra from boreholes (gamma emission, rock density, magnetic susceptibility, sonic velocity, porosity, electrical resistivity) are Pilkington and Todoeschuck (1990), Todoeschuck et al (1990), Todoeschuck and Jensen (1991), Bean and McCloskey (1993), Molz and Boman (1993); Molz and Liu (1997), Wu et al (1994), Hollinger (1996), Leary (1997), Dolan et al (1998), Leonardi and Kümpel (1999), Tchiguirinskaia (2002), Leary (2003a), Bean (1999, 2003), Dimri (2005). Other parameters such as thermal conductivities (Dimri and Vedanti, 2005) have also been shown to be scaling using other analysis techniques.…”