Non-Linear Theory and Power-Law Models for Information Integration and Mineral Resources Quantitative Assessments

Singular physical or chemical processes may result in anomalous amounts of energy release or mass accumulation that, generally, are confined to narrow intervals in space or time. Singularity is a property of different types of non-linear natural processes including cloud formation, rainfall, hurricanes, flooding, landslides, earthquakes, wildfires, and mineralization. The end products of these non-linear processes can be modeled as fractals or multifractals. Hydrothermal processes in the Earth’s crust can result in ore deposits characterized by high concentrations of metals with fractal or multifractal properties. Here we show that the non-linear properties of the end products of singular mineralization processes can be applied for prediction of undiscovered mineral deposits and for quantitative mineral resource assessment, whether for mineral exploration or for regional, national and global planning for mineral resource utilization. In addition to the general theory and framework for the non-linear mineral resources assessment, this paper focuses on several power-law models proposed for characterizing non-linear properties of mineralization and for geoinformation extraction and integration. The theories, methods, and computer system discussed in this paper were validated using a case study dealing with hydrothermal Au mineral potential in southern Nova Scotia, Canada.     

Inversely-Mapped Analytical Solutions for Flow Patterns around and within Inclined Elliptic Inclusions in Fluid-Saturated Rocks

In this paper, an inverse mapping is used to transform the previously-derived analytical solutions from a local elliptical coordinate system into a conventional Cartesian coordinate system. This enables a complete set of exact analytical solutions to be derived rigorously for the pore-fluid velocity, stream function, and excess pore-fluid pressure around and within buried inclined elliptic inclusions in pore-fluid-saturated porous rocks. To maximize the application range of the derived analytical solutions, the focal distance of an ellipse is used to represent the size of the ellipse, while the length ratio of the long axis to the short one is used to represent the geometrical shape of the ellipse. Since the present analytical solutions are expressed in a conventional Cartesian coordinate system, it is convenient to investigate, both qualitatively and quantitatively, the distribution patterns of the pore-fluid flow and excess pressure around and within many different families of buried inclined elliptic inclusions. The major advantage in using the present analytical solution is that they can be conveniently computed in a global Cartesian coordinate system, which is widely used in many scientific and engineering computations. As an application example, the present analytical solutions have been used to investigate how the dip angle of an inclined elliptic inclusion affects the distribution patterns of the pore-fluid flow and excess pore-fluid pressure when the permeability ratio of the elliptic inclusion is of finite but nonzero values.     

Hierarchical decomposition of variance with applications in environmental mapping based on satellite images

A quadtree-based image segmentation procedure (HQ) is presented to map complex environmental conditions. It applies a hierarchical nested analysis of variance within the framework of multiresolution wavelet approximation. The procedure leads to an optimal solution for determining mapping units based on spatial variability with constraints on the arrangement and shape of the units. Linkages to geostatisiics are pointed out, but the HQ decomposition algorithm does not require any homogeneity criteria. The computer implementation can be parameterized by either the number of required mapping units or the maximum within-unit variance, or it can provide a spectrum of significances of nested ANOVA. The detailed mathematical background and methodology is illustrated by a salt-affected grassland mapping study (Hortobágy, Hungary), where heterogeneous environmental characteristics have been sampled and predicted based on remotely sensed images using these principles.     

Energy balance of simple elastodynamic sources

Complete relations are derived for energy and energy flux of elastic waves generated by an isotropic and double-couple source in a perfectly elastic, homogeneous, isotropic, and unbounded medium. In the energy balance of elastodynamic sources near-field waves play an essential role, transforming static energy into wave energy, andvice versa. For explosive and dislocation sources, the sources surface radiates a positive wave energy that is partially distributed to the medium transforming into static energy. For implosive and antidislocation sources, the source surface generates elastic waves, but it does not necessarily imply that it also radiates a positive wave energy. The energy transported by waves can originate in gradual transformation of the static-to-wave energy during propagation of waves through a stressed medium.On leave from Geophysical Institute, Czech Academy of Sciences, Boní II/1401, 41 31, Praha 4 Czech Republic     

Redefining active volcanoes: a discussion

The analysis of the current definitions of active volcanoes indicates that they are empirical, conventional, inaccurate, nongeological, and arbitrarily constraining. Redefinition is therefore needed. One possible approach is to refine the current empirical definitions. A statistically reasonable and practical redefinition using a geologically based time convention-Holocene or 10000 years-is suggested. A set of time conditions according to volcano typology-i.e. 1000; 10000 and 100000 years for high-frequency basaltic shields, andesitic-dacitic composite volcanoes and low-frequency large silicic calderas, respectively-as further refinement of the empirical definition is also envisaged. Devising a phenomenological definition as a theoretical approach is another possibility, but in practice extant diagnostic means are still unsatisfactory to discriminate accurately between dormant and extinct volcanoes. As a consequence of the redefinition, a classification of volcanoes according to their eruptive status is proposed. Redefinition of active volcanoes might increase accuracy in the usage of basic terms in volcanology and influence volcanic hazard assessment and risk mitigation projects.     

Dynamics of the plasmasphere in the dusk sector as observed in the outer ionosphere

Summary Direct measurements of the thermal plasma parameters in the topside ionosphere reveal variations of the plasmasphere boundary in the dusk sector. The ACTIVE satellite's near-polar orbits at altitudes of 500 – 1800 km around winter solstice 1989 were used to study the bulge region of the plasmasphere during intervals with different levels of geomagnetic agitation. The narrow, sharply defined trough in electron concentration corresponding to the plasmapause under quiet conditions situated at L = 6 – 7 moved to lower L-values with increasing geomagnetic activity. This narrow trough can be found in all main ion constituents. During periods of moderate geomagnetic activity, following the onset of a weak magnetic storm, a portion of the plasmaspheric bulge region was separated from the main plasmaspheric body. This can be seen in the outer ionosphere as an inner narrow trough at lower L-value. Troughs in light ions need no longer coincide with this in electron concentration. He⁺ is the most sensitive constituent reflecting the dusk sector plasmaspheric situation at this altitude.Dedicated to the Memory of Professor Karel P     

Paleogeothermal gradient in the boskovice furrow

Summary A coalification data set from the first seam of the Rosice-Oslavany coal district in the Boskovice furrow was used to estimate the temperature gradient prevailing within the furrow during Autunian sedimentation. An appreciable scatter of the data reflects the complicated history of the sedimentary region. The northern part of the district displays a higher degree of coalification. The results of the evaluation suggest that the region ceased to subside in the upper Autunian, and that the extent of the post-Autunian erosion does not exceed 500 metres. This version of the burial history, which is consistent with geological data, yields a temperature paleogradient of 76 mK/m for the northern part and of 72 mK/m for the southern part of the district. The gradients estimated are higher than those prevailing during the Carboniferous sedimentation in the Central Bohemian Basin (45 – 53 mK/m), lower than values found for the Ostrava Formation in the Upper Silesian Basin during its Namurian A sedimentation (about 95 mK/m), but comparable with values evaluated for the Karviná Formation of the same basin deposited during the Namurian B - C and Westphalian A (60 – 77 mK/m).Dedicated to the Memory of Professor Karel P     

Behavioural-geographical aspects of environmental quality

The behavioural approach in human geography accentuates the view of quality of the environment through man and his value orientations. The quality of environment from the point of view of human experience raises behavioural-geographical questions that are the core of the presented topic. Aspects of environmental imaginations and sensations as well as human value system are presented as variables affecting the structure of the perceived environment and human spatial behaviour. In this context, the authors present results of two behavioural studies that correspond to new models of man and environment from the viewpoint of a behavioural approach. The suggested humanistic approach in behavioural geography emphasizes above all the emotional aspect of the relationship between man and environment, which through environmental values, spatial sensations, and meanings, leads to human spatial behaviour.     

Seismic hazard of Egypt

Earthquake hazard parameters such as maximum expected magnitude,M _max, annual activity rate,, andb value of the Gutenberg-Richter relation have been evaluated for two regions of Egypt. The applied maximum likelihood method permits the combination of both historical and instrumental data. The catalogue used covers earthquakes with magnitude 3 from the time interval 320–1987. The uncertainties in magnitude estimates and threshold of completeness were taken into account. The hazard parameter determination is performed for two study areas. The first area, Gulf of Suez, has higher seismicity level than the second, all other active zones in Egypt.b-values of 1.2 ± 0.1 and 1.0 ± 0.1 are obtained for the two areas, respectively. The number of annually expected earthquakes with magnitude 3 is much larger in the Gulf of Suez, 39 ± 2 than in the other areas, 6.1 ± 0.5. The maximum expected magnitude is calculated to be 6.5 ± 0.4 for a time span of 209 years for the Gulf of Suez and 6.1 ± 0.3 for a time span of 1667 years for the remaining active areas in Egypt. Respective periods of 10 and 20 years were reported for earthquakes of magnitude 5.0 for the two subareas.     

Once more on quasar periodicities

In an earlier paper Arp, Bi, Chu and Zhu investigated various quasar samples and recognized a periodicity of remarkable degree in them. Their conclusion was that the existence of such a periodicity is a counterevidence against the cosmological origin of quasar redshifts. Since this question is of great importance in a cosmological context, here we reanalyze some of the samples together with a galaxy sample of the pencil-beam survey of Broadhurstet al. Our result is that on the plane of cosmological parameters (₀, ₀) there is a non-negligible region where two quasar samples and the galaxy sample are simultaneously fairly periodic. Pure periodicity is still compatible with cosmological principles, at least on length scales much longer than the period length. So the regularities can fit into a cosmological context.