Efficient Modeling of Gravity Fields Caused by Sources with Arbitrary Geometry and Arbitrary Density Distribution

We present a brief review of gravity forward algorithms in Cartesian coordinate system, including both space-domain and Fourier-domain approaches, after which we introduce a truly general and efficient algorithm, namely the convolution-type Gauss fast Fourier transform (Conv-Gauss-FFT) algorithm, for 2D and 3D modeling of gravity potential and its derivatives due to sources with arbitrary geometry and arbitrary density distribution which are defined either by discrete or by continuous functions. The Conv-Gauss-FFT algorithm is based on the combined use of a hybrid rectangle-Gaussian grid and the fast Fourier transform (FFT) algorithm. Since the gravity forward problem in Cartesian coordinate system can be expressed as continuous convolution-type integrals, we first approximate the continuous convolution by a weighted sum of a series of shifted discrete convolutions, and then each shifted discrete convolution, which is essentially a Toeplitz system, is calculated efficiently and accurately by combining circulant embedding with the FFT algorithm. Synthetic and real model tests show that the Conv-Gauss-FFT algorithm can obtain high-precision forward results very efficiently for almost any practical model, and it works especially well for complex 3D models when gravity fields on large 3D regular grids are needed.     

Stochastic evaluation of simple pairing approaches to reconstruct incomplete rainfall time series

Two-station pairing approaches are routinely used to infill missing information in incomplete rainfall databases. We evaluated the performance of three simple methodologies to reconstruct incomplete time series in presence of variable nonlinear correlation between data pairs. Nonlinearity stems from the statistics describing the marginal peak-over-threshold (POT) values of rainfall events. A Monte Carlo analysis was developed to quantitatively assess expected errors from the use of chronological pairing (CP) with linear and nonlinear regression and frequency pairing (FP). CP is based on a priori selection of regression functions, while FP is based on matching the probability of non-exceedance of an event from one time series with the probability of non-exceedance of a similar event from another time series. We adopted a generalized Pareto (GP) model to describe POT events, and a t-copula algorithm to generate reference nonlinearly correlated pairs of random temporal distributions distributed according with the GP model. The results suggest that the optimal methodology strongly depends on GP statistics. In general, CP seems to provide the lowest errors when GP statistics were similar and correlation became linear; we found that a power-2 function performs well for the selected statistics when the number of missing points is limited. FP outperforms the other methods when POT statistics are different and variables are markedly nonlinearly correlated. Ensemble-based results seem to be supported by the analysis of observed precipitation at two real-world gauge stations.     

Long-term Geomechanical Observation in the Jeroným Mine

Geomechanical measurements have been carried out in the medieval Jeroným Mine since 2001. At first quarterly observation and later also continual monitoring by distributed measurement network were used. The network includes a number of different sensors that have been installed in selected places of underground spaces. There have not been any manifestations documenting dangerous changes of stability during the period of monitoring (2001–2015). The results of accomplished measurements from all convergence profiles confirm the total stability of all underground spaces. However, a number of places have been documented as potentially unstable. Measured values of selected parameters are presented in the paper, namely, movements along fractures, changes of stress tensor and fluctuations in the level of mine water table.     

About Hypothesis of the Superconducting Origin of the Saturn’s Rings

Hypothesis of possible superconductivity of the iced matter of the rings of Saturn (based on the data of Voyager and Pioneer space missions) allow us to explain many phenomena which have not been adequately understood earlier. Introducing into planetary physics force of magnetic levitation of the superconducting iced particle of the rings, which interact with magnetosphere of the planet, becomes to be possible to explain origin, evolution, and dynamics of the rings; to show how the consequent precipitation of the rings’ matter upon the planet was concluded; how the rings began their rotation; how they were compressed by the magnetic field into the thin disc, and how this disc was fractured into hundreds of thousands of separated rings; why in the ring B do exist “spokes”; why magnetic field lines have distortion near by ring F; why there is a variable azimuth brightness of the ring A; why the rings reflected radio waves so efficiently; why exists strong electromagnetic radiation of the rings in the 20.4 kHz–40.2 MHz range and Saturnian kilometric radiation; why there is anomalous reflection of circularly polarized microwaves; why there are spectral anomalies of the thermal radiation of the rings; why the matter of the various rings does not mix but preserves its small-scale color differences; why there is an atmosphere of unknown origin nearby the rings of Saturn; why there are waves of density and bending waves within Saturn’s rings; why planetary rings in the solar system appear only after the Belt of Asteroids (and may be the Belt of Asteroids itself is a ring for the Sun); why our planet Earth has no rings of its own.     

Adaptive particle swarm optimization for optimal orbital elements of binary stars

The paper presents an adaptive particle swarm optimization (APSO) as an alternative method to determine the optimal orbital elements of the star η Bootis of MK type G0 IV. The proposed algorithm transforms the problem of finding periodic orbits into the problem of detecting global minimizers as a function, to get a best fit of Keplerian and Phase curves. The experimental results demonstrate that the proposed approach of APSO generally more accurate than the standard particle swarm optimization (PSO) and other published optimization algorithms, in terms of solution accuracy, convergence speed and algorithm reliability.     

Exact Bianchi type-II, VIII and IX perfect fluid cosmological models in Saez-Ballester theory of gravitation

Exact Bianchi type-II, VIII and IX cosmological models are obtained in a scalar tensor theory proposed by Saez and Ballester (Phys. Lett. A 113:467, 1986) with perfect fluid as a source. Some physical and geometrical properties of the models are studied. It is observed that the models are free from initial singularities and they are expanding with time.     

Stability of equilibrium points in the generalized perturbed restricted three-body problem

This paper studies the existence and stability of equilibrium points under the influence of small perturbations in the Coriolis and the centrifugal forces, together with the non-sphericity of the primaries. The problem is generalized in the sense that the bigger and smaller primaries are respectively triaxial and oblate spheroidal bodies. It is found that the locations of equilibrium points are affected by the non-sphericity of the bodies and the change in the centrifugal force. It is also seen that the triangular points are stable for 0<μ<μ _c and unstable for \(\mu_{c}\le\mu <\frac{1}{2}\), where μ _c is the critical mass parameter depending on the above perturbations, triaxiality and oblateness. It is further observed that collinear points remain unstable.     

Evaluating Natural Attentuation with Spreadsheet Analytical Fate and Transport Models

Superposition techniques can extend the capabilities of relatively simple analytical fate and transport models. Complex source geometries, simple aquifer boundaries, and electron acceptor limited biodegradation can be simulated by using superposition techniques in computer spreadsheets. Spreadsheet models are an easily used tool for interpreting sampling results and for estimating attenuation and degradation rates in relatively homogeneous aquifers. Analytical spreadsheet models are based on the Domenico analytical model and can provide results that are in close agreement with the numerical model UIOPLUMH II.     

Organic matter in the Soultz HDR granitic thermal exchanger (France): natural tracer of fluid circulations between the basement and its sedimentary cover

Organic matter has been observed in cores of the Soultz-sous-Forêts granite (Alsace, France) at depths between 2158 and 2160 m, in a highly fractured and altered zone. The granite is overlain by a 1400-m-thick sedimentary cover containing petroleum (Pechelbronn oil field). The Soultz area is devoted to Hot Dry Rock geothermics thanks to a high geothermal gradient (up to 100 °C/km). During drilling operations, an artesian source produced oil in a fractured zone of the sedimentary cover (Buntsandstein). Its gas-chromatography and mass-spectrometry (GC-MS) analysis revealed the presence of normal alkanes (n-alkanes, i.e. linear hydrocarbons) centered on C₁₇, branched alkanes with a major C₁₉ peak, and few unsaturated hydrocarbons. The aromatic fraction is present in small amounts. In the Soultz granite, where it is altered, organic matter is exclusively associated with tosudite (interstratified clay mineral) which crystallized in plagioclase sites during a hydrothermal alteration episode. Organic matter has been later displaced and concentrated along veinlets in which illite and carbonates have crystallized during another hydrothermal alteration stage. The soluble organic matter analyzed by GC-MS is composed of aliphatic acids, n-alkanes with a bimodal C₁₈ and C₂₄-C₂₅ centered distribution, alkylbenzenes and aromatic acids. Organic compounds in the granite would either originate from a single source (immature sediments) or from two sources (immature sediments and migration of the Pechelbronn oil). No real evidence was found to prove which hypothesis is the best one. The presence of organic matter in the granite shows the importance of fluid flows between the sedimentary cover and the granitic basement through major fractures. In addition, the impregnation of plagioclase pseudomorphs with organic matter is made possible due to their high interconnection degree and to the intergranular microfracturation of the granite. The succession of several hydrothermal events with different physico-chemical characteris- tics may also be inferred from the occurrence of organic matter found in association with neoformed clay minerals in the granite.