Weathering: Toward a Fractal Quantifying   总被引：1，自引：0，他引：1  

Klaudia Oleschko  Jean-Francois Parrot  Gerardo Ronquillo  Sergey Shoba  Georges Stoops  Vera Marcelino 《Mathematical Geology》2004,36(5):607-627

Weathering occurs over a wide range of scales. To link features through these scales is a major challenge for interdisciplinary weathering studies. Fractal approach seems to be specially useful for this purpose. We introduce a multistep fractal weathering assessment scheme devoted to extract fractal weathering classifiers from texture analysis of the mineral's image. Our scheme enables to quantitatively estimate the global and local information about the geometry of the weathering pattern. This information is basic to develop geometrical indices of weathering, which can significantly enrich the common qualitative and semiquantitative weathering assessment schemes. To justify the fractal approach, a strong statistical self-similarity has been documented for both the weathering and fresh features of two common silica minerals: quartz and biogenic A-opal (phytolith) over four orders of length scales. The procedure is fast, drastically reduces thresholding bias, promises to be universal, it is valid for genetically different minerals and rock types, scale independent, and specially useful for monitoring the changes in the mineral's roughness during the alteration. Two of the proposed classifiers seem to be potentially useful for direct application in the field and be used by nonspecialist.  相似文献   

A simple geometric model of sedimentary rock to connect transfer and acoustic properties     

Gabor Korvin  Klavdia Oleschko  Abdulazeez Abdulraheem 《Arabian Journal of Geosciences》2014,7(3):1127-1138

A simple rock model is presented which reproduces the measured hydraulic and electric transport properties of sedimentary rocks and connects these properties with each other, as well as with the acoustic propagation velocities and elastic moduli. The model has four geometric parameters (average coordination number Z of the pores, average pore radius r, average distance between nearest pores d, and average throat radius δ) which can be directly determined from the measured porosity Φ, hydraulic permeability k, and cementation exponent m of the rock via simple analytic expressions. Inversion examples are presented for published sandstone data, and for cores taken from Saudi Arabian, Upper Jurassic and Permian carbonate reservoirs. For sandstone, the inversion works perfectly; for carbonates, the derived rock model shows order-of-magnitude agreement with the structure seen in thin sections. Inverting the equations, we express the transfer properties Φ, k, and m as functions of r, d, δ, and Z. Formulae are derived for the bulk density D _b, formation factor F, and P-wave velocity in terms of the proposed geometrical parameters.  相似文献   

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

A. F.?Nieto-SamaniegoEmail author  S. A.?Alaniz-Alvarez  G.?Tolson  K.?Oleschko  G.?Korvin  S. S.?Xu  J. A.?Pérez-Venzor 《Pure and Applied Geophysics》2005,162(5):805-826

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 pre-existing 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.  相似文献