Igor Kohút

Generalization of electromagnetic scattering by charged grains through incorporation of interband and intraband effects.

Scattering of electromagnetic radiation by electrically charged spherical particles is treated theoretically. A generalization of the approach is performed by incorporating both intraband and interband effects, while a new oscillatory term corresponding to the classical dispersion theory and the semi-quantum approach is considered. It is shown through a set of numerical experiments that interband effects may reduce the amplitude of resonant peaks for scattering, Q(sca), and absorption, Q(abs), and cause a shift of peak positions to longer wavelengths. In general, the resonant features due to interband and intraband effects can occur at different frequencies; thus, both together may result in qualitatively and quantitatively new optical signatures of electrically charged particles. This is a motivating factor for experimentalists who can use the particles as targeted probes, for example, in mapping the electric fields in different media based on scattering and/or absorption properties of electrified particulate systems.

Gravity field due to a homogeneous oblate spheroid: Simple solution form and numerical calculations

Gravity field due to a homogeneous oblate spheroid: Simple solution form and numerical calculations We present a simple derivation of the interior and exterior gravitational potentials due to oblate spheroid and also its gravity field components by using the fundamental solution of the Laplace equation in oblate spheroidal coordinates. Application of the method of separation of variables provides an expression for the potential in terms of oblate spheroidal harmonics of degree n = 0, 2. This solution is more concise and suitable for the numerical calculations in comparison with infinite series in spherical harmonics. Also presented are the computations in the form of potential isolines inside and outside the spheroid, as well as for the gravity field components. These reveal some interesting properties of the gravity field of this fundamental geophysical body useful for the applied gravimetry.

Extensometric observation of Earth tides and local tectonic processes at the Vyhne station, Slovakia

Abstract The Vyhne Tidal Station of the Earth Science Institute of the Slovak Academy of Sciences is located in the former mining gallery of St. Anthony of Padua in the Vyhne valley, Štiavnické vrchy Mts., Central Slovakia. It is equipped with a 20.5 metre long quartz-tube extensometer measuring Earth’s tides, and long-term tectonic deformations of the Earth’s crust. Data between 2001 and 2015 with some diverse gaps were digitally collected, processed and analysed. The effects of the local conditions, such as structure of the observatory, cavity effect, topography and geological features of the surrounding rocks, were investigated in detail and these effects were taken into consideration during the interpretation of the results of the data analysis. Tidal analysis of the extensometric data between 2005 and 2015 revealed that the measured tidal amplitudes are close to the theoretical values. The tidal transfer of the observatory was also investigated by coherence analysis between the theoretical and the measured extensometric data. The coherence is better than 0.9 both in the diurnal and semidiurnal band. The effect of the free core nutation resonance was also investigated in the case of the K1 and P1 tidal components. Since the K1/O1 ratio was about the theoretical value 0.8, than the P1/O1 was between 1.0 and 1.15 instead of the theoretical value of 0.9. The rate of the long-term strain rate was also investigated and the obtained −0.05 μstr/y shows a good agreement with the strain rate inferred from GPS measurements in the Central European GPS Reference Network.

Three-dimensional colour functions for stress state visualisation

Three-dimensional colour functions were designed for visually agreeable and computationally efficient stress state visualisation in failure analysis. The colours they generate depend on three aspects of the stress state: the distance to failure, the stress character (compressive or tensile), and the relative magnitude of the intermediate principal stress. Thus, the colour of a single pixel carries information about all three scalar components of the stress tensor at a point. By discarding the intermediate principal stress information, a three-dimensional colour function degenerates to a family of two-dimensional colour functions with free palette choice parameter. We demonstrate the performance of our colouring technique in the application example - visualisation of the stress field in the Brazilian test.

The Estimation of the Cavity Effect by Higher Degree Finite Element Approximation

The measurements of tide-induced tilts and deformations are usually performed in underground cavities (mostly man-made). Therefore, the data obtained must be debugged of the influence of the cavity itself (cavity effect) and of the effect of elastic parameter inhomogeneities in the vicinity of the point of measurement (geological effect), if they are to he presented. Since these effects are reflected as a modulation of tidal waves (in both amplitude and phase), the only way to perform this can be modelling of the strain and stress field around the cavity as precisely as possible. The finite element method (F.E.M.) seems to be a very useful tool for this purpose. To justify some conclusions in this paper, a number of numerical runs of the F.E.M. models of the tide-induced strains and stresses (in two dimensions) were performed. A higher degree of approximation (up to the value of 7) was used in these calculations. To estimate the cavity effect, the correction factors (relative changes of particular strain components due to the presence of the cavity) were determined and plotted in the cavitys close neighbourhood. The distribution of the deformation energy (and also the work of external forces) over the whole domain of interest is given, and the conclusions for subsequent error estimation are drawn. An attempt was made to compare the real tilt data to the theoretical deduced from the numerical model.

Calculation of temperature distribution and rheological properties of the lithosphere along geotransect in the Red Sea region

Abstract The temperature model of the lithosphere along profile passing through the Red Sea region has been derived using 2D integrated geophysical modelling method. Using the extrapolation of failure criteria, lithology and calculated temperature distribution, we have constructed the rheological model of the lithosphere in the area. We have calculated the strength distribution in the lithosphere and constructed the strength envelopes for both compressional and extensional regimes. The obtained results indicate that the strength steadily decreases from the Western desert through the Eastern desert towards the Red Sea where it reaches its minimum for both compressional and extensional regime. Maximum strength can be observed in the Western desert where the largest strength reaches values of about 250–300 MPa within the upper crust on the boundary between upper and lower crust. In the Eastern desert we observe slightly decreased strength with max values about 200–250 MPa within upper crust within 15 km with compression being dominant. These results suggest mostly rigid deformation in the region or Western and Eastern desert. In the Red Sea, the strength rapidly decreases to its minimum suggesting ductile processes as a result of higher temperatures.

Calculation of temperature distribution and rheological properties of the lithosphere along Profile 1 passing through Aswan

Abstract The 2D integrated geophysical modelling approach has been used to determine the temperature distribution in the lithosphere along the profile passing through Aswan. Based on the temperature model and the rheological parameters, we have calculated strength distribution in the lithosphere for the studied profile. The strength envelopes have been calculated for both compressional and extensional regimes. Our results indicate that the strength is constant along the whole length of the profile passing through the Nubia plain. The largest strength can be observed within the upper crust which allows us to assume rigid deformation in this part of the lithosphere, with compressional processes predominant. Towards the lower crust and upper mantle, strength values rapidly decrease for both regimes, suggesting ductile deformations in the lower part of the lithosphere.

Surface strain rate colour map of the Tatra Mountains region (Slovakia) based on GNSS data

Abstract The surface deformation of the Tatra Mountains region in Western Carpathians can nowadays be studied directly thanks to precise geodetic measurements using the GNSS. The strain or stress tensor field is, however, a rather complex “data structure” difficult to present legibly and with sufficient resolution in the form of a classical map. A novel and promising approach to the solution of this problem is coding the three principal strain or stress values into the three colour channels (red, green, blue) of an RGB colour. In our previous study, the colour depended on the stress tensor shape descriptors. In the current study, the adapted colouring scheme uses a subset of shape descriptors common to stress and strain, which differ only in the scaling factor. In this manner, we generate the colour map of the surface strain rate field, where the colour of each grid point carries the information about the shape of the strain rate tensor at that point. The resulting strain rate colour map can be displayed simultaneously with the map of the faults or elevations and be easily checked for the data or interpolation method errors and incompatibility with the geophysical and geological expectations.

A new lithospheric model in the eastern part of the Western Carpatians: 2D integrated modelling

Abstract Using 2D integrated geophysical modelling we recalculated lithospheric model along transect KP-X in the eastern part of the Western Carpathians. Our model takes into account the joint interpretation of the heat flow, free air anomalies, topography and geoid data. A more accurate model of lithospheric structure has been created, especially the lithosphere-astenosphere boundary. Lithosphere thickness in the study region increases from the area of the Pannonian Basin where we modelled it at the depth of 80 km towards the oldest and coolest area of the European Platform where it reaches about 150 km. In the Pannonian Basin the modelled Moho depths reach about of 25 km and it decreases towards theWestern Carpathians. The Western Carpathian’s crustal thickness varies from about 30 km to 45 km. The largest crustal thickness (45 km) has been located beneath the Externides (Carpathian Foredeep) of the Western Carpathians. In the direction of the European platform a Moho depth gradually increases until the end of the profile, where the crustal thickness reaches of about 42 km. Our modelling has confirmed the existence of an anomalous body with average density of 2850 kgm−3 seated mostly in the lower crust. Its uppermost boundary reaches a depth of about 12 km. The lower crust beneath the Western Carpathian Externides is much thicker (20 km) in comparison beneath the Pannonian Basin, where it is only 8 km on average.

Surface Displacements, Deformations and Gravity Changes Due to Underground Heat Source

Thermo-elastic strains and stresses play a considerable role in the stress state of the lithosphere and its dynamics, especially at pronounced positive geothermal anomalies. Topography has a significant effect on ground deformation. Two methods for including the topographic effects in the thermo-viscoelastic model are described. First we use an approximate methodology which assumes that the main effect of the topography is due to distance from the source to the free surface and permits to have an analytical solution very attractive for solving the inverse problem. A numerical solution (for 2D plain strain case) is also computed using finite element method (FEM). The numerical method allows include the local shape of the topography in the modeling. In the numerical model the buried magmatic body is represented by a finite volume thermal source. The temperature distribution is computed by the higher-degree FEM. For analytical as well as numerical model solution only the forces of thermal origin are considered. The results show that for the volcanic areas with an important relief the perturbation of the thermo-viscoelastic solution (deformation and total gravity anomaly) due to the topography can be quite significant. In consequence, neglecting topography could give erroneous results in the estimated source parameters.