Scaling relationships in intraplate fracture systems related to Red Sea rifting

Castaing, C.; Halawani, M.A.; Gervais, Florence; Chilès, Jean‐Paul; Genter, Albert; Bourgine, Bernard; Ouillon, Guy; Brosse, J.M.; Martin, P.; Genna, Antonin; Janjou, Dominique

doi:10.1016/0040-1951(95)00177-8

Cited by 76 publications

(12 citation statements)

References 40 publications

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“…As is common in these types of studies (CASTAING et al, 1996;ODLING, 1997), we selected sub-areas in zones of moderate to high degrees of fracturing. As we were not analyzing fracture spacing (CASTAING et al, 1996) or scale-dependent lacunarity (ALLAIN and CLOITRE, 1991) of the fracture pattern, the spatial location of the fractures and their mutual distances were not analyzed. During fieldwork we searched for walls of approximately 10 m horizontal and 3 m vertical dimensions, located inside the faulted zone and with a minimum of weathering.…”

Section: Methodology Fieldworkmentioning

confidence: 99%

Spatial Distribution, Scaling and Self-similar Behavior of Fracture Arrays in the Los Planes Fault, Baja California Sur, Mexico

Nieto-Samaniego

Alaniz-Álvarez

Tolson

et al. 2005

Pure appl. geophys.

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We present a case of detailed analysis of fracture arrays spanning four orders of magnitude in length; all of them measured at a single natural site by acquiring images at progressively larger scales. There is a high dispersion of cumulative-length exponents, box dimensions and fracture densities. However, the fractal analysis supports the fractal nature of fracture arrays. Our data indicate the existence of an upper limit for the density parameters, as similarly reported by other authors. We prove that box dimension is in inverse relation with fracture concentration and in direct relation with fracture density. These relations are also observed in our data and additionally there is an upper limit for the box dimensions. We interpret the dispersion in our results as more fundamental than methodological problems. It represents a truncation in the complete evolution of the fracture systems because in natural cases strain initiates overprinting of previous fracture arrays. Considering that larger fractures accommodate strain more efficiently than small fractures, the generation of small fractures is inhibited in the presence of preexisting larger fractures. Maximum values of fracture density prevent accommodating an excess of strain in a single or restricted range of scales; we claim this condition produces migration of fracturing to larger scales originating fracture scaling.

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Section: Methodology Fieldworkmentioning

confidence: 99%

Spatial Distribution, Scaling and Self-similar Behavior of Fracture Arrays in the Los Planes Fault, Baja California Sur, Mexico

Nieto-Samaniego

Alaniz-Álvarez

Tolson

et al. 2005

Pure appl. geophys.

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“…However, it has been known for a long time that real fracture networks are polydisperse [9][10][11][12][13]. Therefore, the main objective of this paper is to extend the results of Koudina et al [5] to three-dimensional fracture networks with a power-law size distribution.…”

Section: Introductionmentioning

confidence: 92%

“…The flow calculations are successively performed along the three different directions, and the macroscopic permeability of the network is derived from Eqs. (11) and (12). In this case, K is not a tensor, but for isotropic networks its statistical average is still expected to be spherical.…”

Section: Generalmentioning

confidence: 99%

Macroscopic permeability of three-dimensional fracture networks with power-law size distribution

Mourzenko

Thovert

Adler³

2004

Phys. Rev. E

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Fracture network permeability is investigated numerically by using a three-dimensional model of plane polygons uniformly distributed in space with sizes following a power-law distribution. Each network is triangulated via an advancing front technique, and the flow equations are solved in order to obtain detailed pressure and velocity fields. The macroscopic permeability is determined on a scale which significantly exceeds the size of the largest fractures. The influence of the parameters of the fracture size distribution--the power-law exponent and the minimal fracture radius--on the macroscopic permeability is analyzed. Eventually, a general expression is proposed, which is the product of a dimensional measure of the network density, weighted by the individual fracture conductivities, and of a fairly universal function of a dimensionless network density, which accounts for the influences of the fracture shapes and of the parameters of their size distribution. Two analytical formulas are proposed which successfully fit the numerical data over a wide range of network densities.

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“…Previously, the spatial fault distribution was described as a fractal set, where the fractal dimension (D) is obtained by the box-counting technique (Velde et al, 1990;Gillespie et al, 1993;Walsh and Watterson, 1993;Barton and La Pointe, 1995;Castaing et al, 1996;Rodríguez-Pascua et al, 2003). The so-called box-dimension, D, represents the fractality or complexity degree of the spatial distribution of the fractal geometry measured (Hasting and Sugihara, 1993).…”

Section: Introduction and Objectivesmentioning

confidence: 99%

Relationship between the fractal dimension anisotropy of the spatial faults distribution and the paleostress fields on a Variscan granitic massif (Central Spain): the F-parameter

Pérez‐López

Paredes

Muñoz-Martı́n

2005

Journal of Structural Geology

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The spatial distribution of faults is usually described as a fractal set characterised by the fractal dimension. In this work, we have filtered fault patterns interpreted from digital elevation models, aerial photographs and field maps, by using structural geological parameters of the stress ellipsoid (stress tensor direction and stress ratio R 0 ) and age of deformation. From these filtered structural maps, we have obtained the fractal dimension associated with the fracture patterns developed during Permo-Triassic and Alpine tectonic events on a Variscan granitic massif located in the Spanish Central System. Oriented fractal dimensions were calculated on several transects crossing the fault-filtered maps. The fractal dimension (D), calculated by 1-D box-counting, describes an ellipse on a polar plot with the short axis as the minimum value (D Hmin ) and the long axis as the maximum value (D Hmax ) of the fractal dimensions measured. From these analyses, we have defined the F-parameter as a function of the maximum value, minimum value and vertical value of fractal dimension (D z ), FZ(D z KD Hmin )/(D Hmax K D Hmin ). Finally we have established, from a local scale analysis, a perpendicular relationship between the principal axes of the ellipse of the fractal spatial anisotropy of fractures and the principal axes of the stress tensor (s Hmax , s Hmin and s z ) that generates this dynamic pattern of fractures. Furthermore, the F-parameter and the stress ratio R 0 are equivalents and, applied in this area, both show a triaxial extension.

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Scaling relationships in intraplate fracture systems related to Red Sea rifting

Cited by 76 publications

References 40 publications

Spatial Distribution, Scaling and Self-similar Behavior of Fracture Arrays in the Los Planes Fault, Baja California Sur, Mexico

Spatial Distribution, Scaling and Self-similar Behavior of Fracture Arrays in the Los Planes Fault, Baja California Sur, Mexico

Macroscopic permeability of three-dimensional fracture networks with power-law size distribution

Relationship between the fractal dimension anisotropy of the spatial faults distribution and the paleostress fields on a Variscan granitic massif (Central Spain): the F-parameter

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