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.     

A geoelectrical survey of an area under construction near the Moscow–St. Petersburg highway

The results of a geoelectrical survey of the Mshentsy area located in Tver oblast near the Moscow–St. Petersburg express road, which is under construction, are presented. In order to obtain information about the geological composition of the area and the processes that occur in it (karst and water flow zones ), we performed our measurements using the electrical resistivity imaging, self potential survey, water electrical conductivity and temperature measurements. Using petrophysical resistivity modeling of the rocks, taking the geoelectric data into account, we completed a lithology differentiation of the section and calculated the hydraulic conductivity values of the rocks. By interpreting this data, we found a wide distribution of fractured carbonates that compose the lower part of the section of the studied territory. The conclusion was drawn that the Mshentsy area belongs to the intense local karst zone.     

Multi-decadal synthesis of benthic–pelagic coupling in the western arctic: Role of cross-shelf advective processes

Using geographic information systems (GIS) software and geostatistical techniques, we utilized three decades of water-column chlorophyll a data to examine the relative importance of autochthonous versus allochthonous sources of reduced carbon to benthic communities that occur from the northern Bering to the eastern Beaufort Sea shelf. Spatial trend analyses revealed areas of high benthic biomass (>300 g m⁻²) and chlorophyll (>150 mg m⁻²) on both the southern and northern Chukchi shelf; both areas are known as depositional centers for reduced organic matter that originates on the Bering Sea shelf and is advected northward in Anadyr and Bering shelf water masses. We found a significant correlation between biomass and chlorophyll a in the Chukchi Sea, reflective of the strong benthic–pelagic coupling in a system that is utilized heavily by benthic-feeding marine mammals. In contrast, there was no significant correlation between biomass and chlorophyll in the Beaufort Sea, which by comparison, is considerably less productive (biomass and chlorophyll, <75 g m⁻² and <50 mg m⁻², respectively). One notable exception is an area of relatively high biomass (50–100 g m⁻²) and chlorophyll (80 mg m⁻²) near Barter Island in the eastern Beaufort Sea. Compared to other adjacent areas in the Beaufort Sea, the chlorophyll values in the vicinity of Barter Island were considerably higher and likely reflect a long-hypothesized upwelling in that area and close coupling between the benthos and autochthonous production. In the Bering Sea, a drop in benthic biomass in 1994 compared with previous measurements (1974–1993) may support earlier observations that document a decline in biomass that began between the 1980s and 1990s in the Chirikov Basin and south of St. Lawrence Island. The results of this study indicate that the benthos is an excellent long-term indicator of both local and physical advective processes. In addition, this work provides further evidence that secondary production on arctic shelves can be significantly augmented by reduced carbon advected from highly productive adjacent shelves.     

Solving the problem of shock wave attenuation in an obstacle during a contact explosion of a high-energy material charge

A problem of estimation of shock wave attenuation in an obstacle under an explosion of a high-energy material (explosive) charge on its surface is considered. An algorithm for its solution is proposed using the analytical and semiempirical dependences generally recognized in explosion physics.     

Electrical and electromagnetic surveys to locate possible causes of water seepage to ground surface at a quarry open pit near Helwan city,Egypt

Water seepage to ground surface at a limestone quarry located at Wadi Garawy about 20 km south-east of Helwan city in Egypt posed a real threat to the mining activity at the quarry. The quarry area is known to be very dry for decades and away from water utilities and infrastructures that may cause water leaks to the quarry. Geophysical investigation including 1D Vertical Electrical Sounding (VES), 2D Electrical Resistivity Tomography (ERT) and 1D Transient Electromagnetic (TEM) surveys were conducted to characterize the rock sequence and locate what could be a possible source of water seepage to the quarry. The resistivity profiles generated from the VES and TEM surveys mapped the rock units in the area down to depths exceeded 100 m. The ERT profiles acquired from the quarrying zone close to the water seepage spot have imaged the top of groundwater level at few meters below the ground surface at the quarry open pit. The spot of groundwater seepage seemed to occur at an area of limestone dissolution that were filled by finer sediments. The finer sediments acted as a hydrological conduit that allowed an upward seepage of groundwater to ground surface under the capillary action effect.     

Phase transformations of enstatite in spherical shock waves

The analysis of available theoretical evaluations and experimental data reveals discrepancies and makes it possible to formulate the goals for the comprehensive study of the behavior of enstatite MgSiO₃ in shock isentropic waves of various scale and intensity. The paper presents the layout and results of an explosion experiment on the compression of an enstatite sphere with spherical shock waves and the subsequent recovery of the experimental material and its examination in discrete zones (along the sphere radius) that were produced by shock waves in the material. The latter were examined with the application of scanning electron microscopy, Raman spectroscopy, and X-ray diffraction analysis. The comparison of the systematic variations in the texture, chemistry, and phase composition of enstatite along the sphere radius with calculated pressure P(R, t) and temperature T(R, t) values led us to the following conclusions: enstatite starts melting on an isentrope upon pressure relief after shock wave compression at ?? _xx ?? 80 GPa and melts on the front of the spherically converging shock wave at ?? _xx ?? 160 GPa and T ?? 6300 K. Our laboratory experiments with shock waves were the world??s first in which enstatite was loaded with spherical converging shock isentropic waves and which provided evidence that shock wave-loaded MgSiO₃ shows certain morphological and mineralogical features never before detected in this mineral loaded with plane shock wave of smaller amplitude and duration. Goals are formulated for the further studying of shock wave-loaded materials, and the necessity is discussed for conducting an explosion experiment with a five to seven times greater spherical system in order to increase the duration of the shock wave loading impulse.     

Uncertainty as the overlap of alternate conditional distributions

An important task in modern geostatistics is the assessment and quantification of resource and reserve uncertainty. This uncertainty is valuable support information for many management decisions. Uncertainty at specific locations and uncertainty in the global resource is of interest. There are many different methods to build models of uncertainty, including Kriging, Cokriging, and Inverse Distance. Each method leads to different results. A method is proposed to combine local uncertainties predicted by different models to obtain a combined measure of uncertainty that combines good features of each alternative. The new estimator is the overlap of alternate conditional distributions.     

Simplification and Validation of a Spectral-Tensor Model for Turbulence Including Atmospheric Stability

A spectral-tensor model of non-neutral, atmospheric-boundary-layer turbulence is evaluated using Eulerian statistics from single-point measurements of the wind speed and temperature at heights up to 100 m, assuming constant vertical gradients of mean wind speed and temperature. The model has been previously described in terms of the dissipation rate \(\epsilon \), the length scale of energy-containing eddies \(\mathcal {L}\), a turbulence anisotropy parameter \(\varGamma \), the Richardson number Ri, and the normalized rate of destruction of temperature variance \(\eta _\theta \equiv \epsilon _\theta /\epsilon \). Here, the latter two parameters are collapsed into a single atmospheric stability parameter z / L using Monin–Obukhov similarity theory, where z is the height above the Earth’s surface, and L is the Obukhov length corresponding to \(\{Ri,\eta _\theta \}\). Model outputs of the one-dimensional velocity spectra, as well as cospectra of the streamwise and/or vertical velocity components, and/or temperature, and cross-spectra for the spatial separation of all three velocity components and temperature, are compared with measurements. As a function of the four model parameters, spectra and cospectra are reproduced quite well, but horizontal temperature fluxes are slightly underestimated in stable conditions. In moderately unstable stratification, our model reproduces spectra only up to a scale \(\sim \) 1 km. The model also overestimates coherences for vertical separations, but is less severe in unstable than in stable cases.     

On error bounds and initialization in satellite orbit theories

The order of magnitude of the error is investigated for a first-order von Zeipel theory of satellite orbits in an axisymmetric force field, i.e., first-order long period and short-period effects are included along with second order secular rates. The treatment is valid for zero eccentricity and/or inclination. In the case where initial position and velocity vectors are known, the in-track position error over time intervals of order 1/J ₂ is kept at 0(J ₂ ²), like the other position errors and velocity errors, by calibration of the mean motion with the aid of the energy integral. The results are specifically applicable to accuracy comparisons of the Brouwer orbit prediction method with numerical integration. A modified calibration is presented for the general asymmetric force field which includes tesseral harmonics.     

Assimilation of altimetry data in the numerical model of the circulation in the Black Sea: The model numerical experiments

The numerical algorithm of the Kalman optimum filtration generalized for the case of three-dimensional fields and a multicomponent vector of the ocean state, with level measurements discrete over space and time being available, is given. The results of model numerical experiments on the assimilation of data on the Black Sea level are given. An attempt to estimate the effect of the time interval of data input on the results of field reconstruction was made.Translated by Mikhail M. Trufanov.