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Register a new userFractal properties of isolines at varying altitude reveal different dominant geological processes on Earth
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Geometrical properties of landscapes result from the geological processes that have acted through time. The quantitative analysis of natural relief represents an objective form of aiding in the visual interpretation of landscapes, as studies on coastlines, river networks, and global topography, have shown. Still, an open question is whether a clear relationship between the quantitative properties of landscapes and the dominant geomorphologic processes that originate them can be established. In this contribution, we show that the geometry of topographic isolines is an appropriate observable to help disentangle such a relationship. A fractal analysis of terrestrial isolines yields a clear identification of trenches and abyssal plains, differentiates oceanic ridges from continental slopes and platforms, localizes coastlines and river systems, and isolates areas at high elevation (or latitude) subjected to the erosive action of ice. The study of the geometrical properties of the lunar landscape supports the existence of a correspondence between principal geomorphic processes and landforms. Our analysis can be easily applied to other planetary bodies.
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Manual interpretation of data collected from drill holes for mineral or oil and gas exploration is time-consuming and subjective. Identification of geological boundaries and distinctive rock physical property domains is the first step of interpretation. We introduce a multivariate technique, that can identify geological boundaries from petrophysical or geochemical data. The method is based on time-series techniques that have been adapted to be applicable for detecting transitions in geological spatial data. This method allows for the use of multiple variables in detecting different lithological layers. Additionally, it reconstructs the phase space of a single drill-hole or well to be applicable for further investigations across other holes or wells. The computationally cheap method shows efficiency and accuracy in detecting boundaries between lithological layers, which we demonstrate using examples from mineral exploration boreholes and an offshore gas exploration well.
In the present paper, we analyze the fractal structures in magnitude time series for a set of unprecedented sample extracted from the National Earthquake Information Center (NEIC) catalog corresponding to 12 Circum-Pacific subduction zones from Chile to Kermadec. For this end, we used the classical Rescaled Range ($R/S$) analysis for estimating the long-term persistence signature derived from scaling parameter so-called Hurst exponent, $H$. As a result, we measured the referred exponent and obtained all values of $H>0.5$, indicating that a long-term memory effect exists. The main contribution of our paper, we found a possible fractal relationship between $H$ and the $b_{s}(q)$-index which emerges from nonextensive Gutenberg-Richter law as a function of the asperity, i.e., we show that the values of $H$ can be associated with the mechanism which controls the abundance of magnitude and, therefore, the level of activity of earthquakes. Finally, we concluded that dynamics associated with fragment-asperity interactions can be emphasized as a self-affine fractal phenomenon.
In line of the intermediate-term monitoring of seismic activity aimed at prediction of the world largest earthquakes the seismic dynamics of the Earths lithosphere is analysed as a single whole, which is the ultimate scale of the complex hierarchical non-linear system. The present study demonstrates that the lithosphere does behave, at least in intermediate-term scale, as non-linear dynamic system that reveals classical symptoms of instability at the approach of catastrophe, i.e., mega-earthquake. These are: (i) transformation of magnitude distribution, (ii) spatial redistribution of seismic activity, (iii) rise and acceleration of activity, (iv) change of dependencies across magnitudes of different types, and other patterns of collective behaviour. The observed global scale seismic behaviour implies the state of criticality of the Earth lithosphere in the last decade.
We study the betweenness centrality of fractal and non-fractal scale-free network models as well as real networks. We show that the correlation between degree and betweenness centrality $C$ of nodes is much weaker in fractal network models compared to non-fractal models. We also show that nodes of both fractal and non-fractal scale-free networks have power law betweenness centrality distribution $P(C)sim C^{-delta}$. We find that for non-fractal scale-free networks $delta = 2$, and for fractal scale-free networks $delta = 2-1/d_{B}$, where $d_{B}$ is the dimension of the fractal network. We support these results by explicit calculations on four real networks: pharmaceutical firms (N=6776), yeast (N=1458), WWW (N=2526), and a sample of Internet network at AS level (N=20566), where $N$ is the number of nodes in the largest connected component of a network. We also study the crossover phenomenon from fractal to non-fractal networks upon adding random edges to a fractal network. We show that the crossover length $ell^{*}$, separating fractal and non-fractal regimes, scales with dimension $d_{B}$ of the network as $p^{-1/d_{B}}$, where $p$ is the density of random edges added to the network. We find that the correlation between degree and betweenness centrality increases with $p$.
Utilizing data available from the Kentucky Geonet (KYGeonet.ky.gov) the fossil fuel mining locations created by the Kentucky Geological Survey geo-locating oil and gas wells are mapped using ESRI ArcGIS in Kentucky single plain 1602 ft projection. This data was then exported into a spreadsheet showing latitude and longitude for each point to be used for modeling at different scales to determine the fractal dimension of the set. Following the porosity and diffusivity studies of Tarafdar and Roy1 we extract fractal dimensions of the fossil fuel mining locations and search for evidence of scaling laws for the set of deposits. The Levy index is used to determine a match to a statistical mechanically motivated generalized probability function for the wells. This probability distribution corresponds to a solution of a dynamical anomalous diffusion equation of fractional order that describes the Levy paths which can be solved in the diffusion limit by the Fox H function ansatz.
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