Long-term variations in the second sectorial Stokes harmonics on the basis of TOPEX/POSEIDON altimetry between 1993 and 2000

The long-term variations in the second degree sectorial Stokes parameters of the geopotential have been determined from TOPEX-POSEIDON (T/P) satellite altimeter data, covering the period of January 1, 1993 to January 3, 2001 (T/P cycles 11-305). It is the first attempt to determine the variations in the second sectorial harmonics in the Earth’s inertia tensor due to the ocean dynamics. The variations amount to about 1 × 10⁻¹⁰ (J ₂ ⁽²⁾ ≈ 1.6 × 10⁻⁶ and S ₂ ⁽²⁾ ≈ −0.9 × 10⁻⁶). The variations are about 5% of the tidal effect. This corresponds to variations in the directions of the equatorial axes of the Earth’s inertia ellipsoid of up to 10 arc-seconds. Consequently, the annual and semi-annual variations of the Earth’s equatorial flattening is about 10⁻⁹; i.e. it corresponds to a change of 8 units of its denominator of 91 030. (The equatorial flattening ≈ 1/91 030). Since the coverage of the Earth’s ocean surface is not worldwide, and the inclination of T/P is i = 66°, it is only 58.2% (min. depth of the ocean 2 000 m) of the Earth’s surface which is processed, the torque, resulting from the seasonal transfer of masses within a sea surface layer, is not zero. It amounts up to 10¹⁶ kg m²s⁻², which is comparable to the total indirect tidal torque due to the Moon and the Sun, ∼ 3.9 × 10¹⁶ kg m²s⁻². However, the above estimate strongly depends on the adopted thickness of the sea surface layer, ΔR = 50 m. For a larger thickness of ΔR = 100 m, the seasonal torque amounts to about ∼ 2.3 × 10¹⁶ kg m²s⁻².     

Recent Advances and Difficulties of Infrasonic Wave Investigation in the Ionosphere

Acoustic waves have a remarkable ability to transfer energy from the ground up to the uppermost layers of the atmosphere. On the ground, there are many permanent sources of infrasound, and also pulsed and/or sporadic sources (e.g., sea waves, infrasonic and sonic noise of cities, lightning, earthquakes, explosions, etc.). The infrasonic waves carry away the major part of their energy upwards through the atmosphere. What are the consequences of the upward energy transfer? What heights of the atmosphere are supplied by energy from various sources of an infrasonic wave? In most cases, the answers to these questions are not well known at present. The only opportunity to monitor the propagation of an infrasonic wave to high altitudes is to watch for its influence on the ionospheric plasma. Unfortunately, most of standard equipment for ionospheric sounding, as a rule, cannot detect plasma fluctuations in the infrasonic range. Besides, the form of an infrasonic wave strongly varies during propagation due to nonlinear effects. However, the development of the Doppler method of radiosounding of the ionosphere has enabled progress to be made. Simultaneously, the ionospheric method for sensing aboveground and underground explosions has been developed. Its main advantage is the remote observation of an explosion in the near field zone by means of short radio waves, i.e., the radio sounding of the ionosphere directly above the explosion. The theory of propagation of an acoustic pulse produced by an explosion on the ground up to ionospheric heights has been developed better than the theory for other sources, and has been quantitatively confirmed by experiments. A review of some advances in the area of infrasound investigations at ionospheric heights is given and some current problems are presented.     

Ray-centred coordinate systems in anisotropic media

Whereas the ray-centred coordinates for isotropic media by Popov and Pšenčík are uniquely defined by the selection of the basis vectors at one point along the ray, there is considerable freedom in selecting the ray-centred coordinates for anisotropic media. We describe the properties common to all ray-centred coordinate systems for anisotropic media and general conditions, which may be imposed on the basis vectors. We then discuss six different particular choices of ray-centred coordinates in an anisotropic medium. This overview may be useful in choosing the ray-centred coordinates best suited for a particular application. The equations are derived for a general homogeneous Hamiltonian of an arbitrary degree and are thus applicable both to the anisotropic-ray-theory rays and anisotropic common S-wave rays.     

Simultaneous determination of Earth orientation parameters and station coordinates from combination of results of different observation techniques

Described is a method for non-regular combination of different techniques, where the normal equations matrix cannot be restored, to obtain a representative set of Earth orientation parameters and station coordinates. The method is based on combining station position vectors transformed to the celestial reference frame, where they are functions of both the EOP and the station coordinates. Three types of constraints are applied to stabilize the system, separate celestial pole offset from polar motion and, to tie the EOP between individual epochs. VLBI, GPS, SLR and Doris data as collected for the ‘IERS SINEX Combination Campaign’ was used to check the method. After combination, dispersion of station coordinates decreased from 0.040 to 0.031 m. The effect of the combination on EOP is of the order of 0.2 mas and it can be seen in Figs. 3 and 4 as a difference of the final and a priori values.     

Behaviour of zircon in high-grade metamorphic rocks: evidence from Hf isotopes,trace elements and textural studies

Hf isotopic data of minerals in a mafic pyroxene granulite from the southern Bohemian Massif, together with their major and trace element composition and petrological observations were used to decipher the metamorphic history and behaviour of zircon in the granulite. The Hf isotopic composition in the minerals was used to estimate whether the decompression reaction, namely the consumption of garnet and rutile, could have provided Zr for the formation of newly grown metamorphic zircon. The age of the decompression reaction indicated by the evolution of Hf isotopes in garnet and orthopyroxene is between 333 and 331 Ma, i.e. ca. 7 Ma younger than the available U–Pb zircon ages from the Moldanubian granulites and than the newly obtained 343 ± 2 Ma laser ablation ICP-MS U–Pb age of zircons. The combination of bulk and in-situ Hf isotopic data, major and trace element composition and petrological modeling of P–T evolution revealed that the formation of zircons can not be related to the decompression phase of the evolution of the mafic granulites. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Magmatic history of granite-derived mylonites from the southern Desná Unit (Silesicum, Czech Republic)

Summary In the southern part of the Hruby Jeseník Mts. (Silesicum, Bohemian Massif) granitic orthogneisses and quartz-feldspars mylonites occur that were variously deformed, metamorphosed and imbricated with the overlaying Devonian volcano-sedimentary complex during the Variscan orogeny. Based on combined mapping, petrologic and geochemical studies, three main rock groups are distinguished. The fairly primitive nature of the tonalite suite is shown by low ⁸⁷Sr/⁸⁶Sr₅₅₀ ratios (0.7034–0.7038) and positive ε _Nd ⁵⁵⁰ values (+3.8 and +3.1). Isotopic composition of the metagranite suite is similar (ε _Nd ⁵⁵⁰ = +1.9 to +2.9). Both suites probably belong to a single Cadomian calc-alkaline tonalite–granite association, which can be correlated with acid-intermediate plutonic rocks of the eastern Brunovistulicum (Slavkov Terrane). All these units are interpreted as representing dismembered fragments of the same continental margin magmatic arc system. The leucogranite suite is most likely early Variscan in age. The initial Nd isotopic composition (ε _Nd ³³⁰ = +0.8 and +2.3) is consistent with its formation by a Variscan remelting of the metaigneous Cadomian crust represented by the rocks of the tonalite–granite association. The within-plate granite affinity of the leucogranite suite is most likely related to the break-up of the Brunovistulicum during the Variscan orogeny.     

Hydrogeological characteristics of some deep siphonal springs in Serbia and Montenegro karst

In terms of hydrogeological, engineering-geological, and hydrotechnical tapping in karst in relation to ground waters, karst channels, springs and ponors, speleodiving is the only research method which enables direct observation, studying and exact geological mapping of karst channels and caverns. Data collected during speleodiving research contribute considerably to the analysis of karst evolution process in the given region, which is very important in evaluating the depth of karstification and determining the main direction of the groundwater flow. In the past 30 years in Serbia and Montenegro, speleodivers have investigated over 40 siphonal springs, active cave channels and ponors, of which more than 20 are proof of deep siphonal circulation in karstic aquifers. The karstic springs are the most interesting phenomenon from a hydrogeological view point, and their investigations need particular attention. Most of significant karstic springs are on the rims of erosion basins—perimeters of karst poljes, river valleys, sea coasts and contact areas between karst aquifers and hydrogeological barriers. General characteristics of the spring regime are the direct correlation between precipitation and spring discharge. Moreover, the hydrogeological regime of these springs also depends on the size of the catchment area, karstic aquifer retardation capacity, total porosity, as well as lithological and structural characteristics.     

Retrieval of source parameters of an event of the 2000 West Bohemia earthquake swarm assuming an anisotropic crust

We propose an inversion scheme for retrieval of characteristics of seismic point sources, which in contrast to common practice, takes into account anisotropy. If anisotropy is neglected during inversion, the moment tensors retrieved from seismic waves generated by sources situated in anisotropic media may be biased. Instead of the moment tensor, the geometry of the source is retrieved directly in our inversion; if necessary, the moment tensor can be then determined from the source geometry aposteriori. The source geometry is defined by the orientation of the slip vector and the fault normal as well as the strength of the event given by the size of the slip and the area of the fault. This approach allows direct interpretation of the source geometry in terms of shear and tensile faulting. It also makes possible to identify volumetric source changes that occur during rupturing. We apply the described algorithm to one event of the 2000 West Bohemia earthquake swarm episode. For inversion we use information of the direct P waves. The structure is approximated by three different models determined from travel-time observations. The models are inhomogeneous isotropic, inhomogeneous anisotropic, and homogeneous anisotropic. For these models we obtain seismic moments M_T = 3.2 − 3.8 × 10¹⁴ Nm and left-lateral near-vertical oblique normal faulting on a N-S trending rupture surface. The orientation of the rupture surface is consistent with fault-plane solutions of earlier studies and with the spatial distribution of other events during this swarm. The studied event seems to be accompanied by a small amount of crack opening. The amount of crack opening is slightly reduced when the inhomogeneous anisotropic model is assumed, but it persists. These results and additional independent observations seem to indicate that tensile faulting occurs as a result of high fluid pressure.     

Ray tracing for continuously rotated local coordinates belonging to a specified anisotropy

Conventional ray tracing for arbitrarily anisotropic and heterogeneous media is expressed in terms of 21 elastic moduli belonging to a fixed, global, Cartesian coordinate system. Our principle objective is to obtain a new ray-tracing formulation, which takes advantage of the fact that the number of independent elastic moduli is often less than 21, and that the anisotropy thus has a simpler nature locally, as is the case for transversely isotropic and orthorhombic media. We have expressed material properties and ray-tracing quantities (e.g., ray-velocity and slowness vectors) in a local anisotropy coordinate system with axes changing directions continuously within the model. In this manner, ray tracing is formulated in terms of the minimum number of required elastic parameters, e.g., four and nine parameters for P-wave propagation in transversely isotropic and orthorhombic media, plus a number of parameters specifying the rotation matrix connecting local and global coordinates. In particular, we parameterize this rotation matrix by one, two, or three Euler angles. In the ray-tracing equations, the slowness vector differentiated with respect to traveltime is related explicitly to the corresponding differentiated slowness vector for non-varying rotation and the cross product of the ray-velocity and slowness vectors. Our formulation is advantageous with respect to user-friendliness, efficiency, and memory usage. Another important aspect is that the anisotropic symmetry properties are conserved when material properties are determined in arbitrary points by linear interpolation, spline function evaluation, or by other means.