Arbitrary order numerical solutions conserving the Jacobi constant in the motion near the equilibrium points

In the paper a modification of the polynomial extrapolation for solving the problem of motion nearby the equilibrium points is presented. It appears that the modification yields a better approximation of the exact solution than the convential polynomial extrapolation and other methods. Moreover, the modification conserves the Jacobi constant of motion. Computer examples for orbits nearby the equilibrium points of the Sun-Jupiter system are given.     

Gypsum facies transitions in basin-marginal evaporites: middle Miocene (Badenian) of west Ukraine

In the middle Miocene Badenian gypsum basin of the Carpathian Foredeep, west Ukraine, three main zones of gypsum development occur in the peripheral parts of the basin. Zone I consists entirely of stromatolitic gypsum formed in a nearshore zone. Zone II is located more basinward and is characterized by stromatolitic gypsum in the lower part of the section, overlain by a sabre gypsum unit. Zone III occurs in still more basinward areas and is characterized by giant gypsum intergrowths (or secondary nodular gypsum pseudomorphs of these) in the lowermost part, overlain by stromatolitic gypsum, sabre gypsum and then by clastic gypsum units. Correlation between these facies and zones has been achieved using lithological marker beds and surfaces. Of particular importance for correlation is a characteristic marker bed (usually 20–40 cm thick) of cryptocrystalline massive gypsum occurring in zones II and III. The marker was not distinguished in zone I, possibly because this bed is older than the entire gypsum section of that zone. These new results strongly suggest that the deposition of giant gypsum intergrowth facies and stromatolitic gypsum facies was coeval. In some sections of zones I and II, limestone intercalations have been recorded within the upper part of the gypsum sections. Considerable scatter of the δ¹⁸O and δ¹³C values of these limestones indicates variable diagenetic overprints of marine carbonates, but a marine provenance of the limestones is confirmed by microfacies analysis. Some of the limestones are coeval with an intercalation of gypsarenitic, mostly laminated gypsum occurring in the sabre gypsum unit of zones II and III. Badenian gypsum formed in extremely shallow‐water to subaerial environments on broad, very low relief areas of negligible brine depth, which could be affected by rapid transgressions. Stable isotope (δ³⁴S, δ¹⁸O) studies of the gypsum demonstrate that the sulphate was of sea‐water origin or was derived from dissolution of Miocene marine evaporites. Investigations of individual inclusions in the gypsum indicate decreased water salinity when compared with modern marine‐derived, calcium sulphate‐saturated water. Groundwater influences are indicated by high calcium sulphate contents of the brines in the evaporite basin. The chemical composition of Badenian waters was thus a mixture of relic sea water (depleted in NaCl), groundwater (enriched in calcium sulphate) and surface run‐off.     

Diffraction by plane sectors and polygons

Time-domain theory of edge and edge-and-vertex diffraction is briefly reviewed and its applications to diffraction by polygons, pyramids and curved reflectors are discussed. The time-domain theory is based on canonical functions defined in terms of inverse trigonometric and algebraic functions, which ensures its numerical efficiency.     

The influence of industrial immissions on the magnetic susceptibility of soils in upper Silesia

Summary Samples of metallurgical dusts and fly ashes from coal power plants and iron works in Upper Silesia as well as soil profiles in the close vicinity of these plants and in Ojcow National Park (ca. 25 km east of the industrial area) have been studied magnetically and mineralogically. The metallurgical dusts and fly ashes are highly enriched in ferromagnetic minerals. The topsoils from profiles collected near the plants have very high values of magnetic susceptibility while susceptibility in the fermentation and humic subhorizons in soil profiles from Ojcow National Park is considerably increased. The magnetic properties of the metallurgical dusts and fly ashes such as frequency dependence of susceptibility, saturation remanence or coercivity are similar to those observed in the top horizons of the soils. They are mostly related to the occurrence of large (multidomain) grains of non-stoichiometric magnetite ranging from 1 to 20 μm. The similarity of the magnetic particles in the soils is taken as evidence of an anthropogenic origin. They are responsible for the high soil susceptibilities in Upper Silesia and in adjacent areas. Some of the magnetic particles carry substantial quantitities of trace elements such as Pb, Ni, Zn and Cu. Field and laboratory susceptibility measurements can therefore be used as a simple and costeffective method of detecting the presence of heavy metals in the soils of this area.     

An algorithm for the optimum distribution of a regional seismic network—I

Summary An algorithm for the optimum distribution of any number of regional seismic stations is formulated. The information needed from a given region is the relative distribution of seismic intensity and the travel times of seismic waves used in earthquake location procedure. To define the optimum distribution of a regional network, some generalization of D-planning (minimization of the ellipsoid volume of earthquake location errors) was applied. The D-optimum criterion is generalized for a case where equations describing the process are nonlinear and when the most probable values of the sought parameters (origin time and earthquake focus coordinates) are not known.As an example of the algorithm application, the optimum distribution of seismic stations in the central district of the Lublin Coal Basin in Poland is given.     

An estimate of probabilistic seismic hazard for five cities in Greece by using the parametric-historic procedure

A probabilistic procedure was applied to assess seismic hazard for the sites of five Greek cities (Athens, Heraklion, Patras, Thessaloniki and Volos) using peak ground acceleration as the hazard parameter. The methodology allows the use of either historical or instrumental data, or a combination of both. It has been developed specifically for the estimation of seismic hazard at a given site and does not require any specification of seismic sources or/and seismic zones. A new relation for the attenuation of peak ground acceleration was employed for the shallow seismicity in Greece. The computations involved the area- and site-specific parts. When assessing magnitude recurrence for the areas surrounding the five cities, the maximum magnitude, m_max, was estimated using a recently derived equation. The site-specific results were expressed as probabilities that a given peak ground acceleration value will be exceeded at least once during a time interval of 1, 50 and 100 years at the sites of the cities. They were based on the maximum peak ground acceleration values computed by assuming the occurrence of the strongest possible earthquake (of magnitude m_max) at a very short distance from the site and using the mean value obtained with the help of the attenuation law. This gave 0.24 g for Athens, 0.53 g for Heraklion (shallow) and 0.39 g Heraklion (intermediate-depth seismicity), 0.30 g for Patras, 0.35 g for Thessaloniki and 0.30 g for Volos. In addition, the probabilities of exceedance of the estimated maximum peak ground acceleration values were calculated for the sites. The standard deviation of the new Greek attenuation law demonstrates the uncertainty and large variation of predicted peak ground acceleration values.     

Point-to-curve ray tracing in complicated geological models1

Boundary-value problems (BVPs) for seismic rays generally have multiple solutions. In practical applications the number of solutions can be large. The algorithm presented below solves a one-parameter family of BVPs and makes it easy to obtain all the solutions of a BVP.     

Estimation of earthquake hazard parameters for incomplete and uncertain data files

The maximum likelihood estimation of earthquake hazard parameters (maximum regional magnitudem _max, activity rate λ, and theb parameter in the Gutenberg-Richter distribution) is extended to the cases of incomplete and uncertain data. The method accepts mixed data containing only large (extreme) events and a variable quality of complete data with different threshold magnitude values. Uncertainty of earthquake magnitude is specified by two values, the lower and upper magnitude limits. It is assumed that such an interval contains the real unknown magnitude. The proposed approach allows the combination of different quality catalog parts, e.g. those where the assignment of magnitude is questionable and those with magnitudes precisely determined. As an illustration of the method, the seismic hazard analysis for western Norway and adjacent sea area (4–8°E, 58–64°N) is presented on the basis of the strongest earthquakes felt during the period 1831–1889 and three complete catalog parts, covering the period 1890–1987.     

Polycyclic aromatic hydrocarbons as an indicator of contamination of medicinal waters in the spas in the Sudetes mountains of Southwestern Poland

Thirteen polycyclic aromatic hydrocarbons (PAH) compounds have been identified in spa waters of 10 different health sources in the Sudetes region. In some of the waters the amount of PAH exceed the standard limits set up by the World Health Organization (WHO). The results obtained show that PAH can be a sensitive indicator of pollution of underground water.