Optimization of the shape of Gaussian beams

The applicability and accuracy of the Gaussian beam method depend on the proper choice of the shape of beams. Gaussian beams become inaccurate solutions of the elastodynamic equation if the velocity field changes considerably within the beam width. We present a procedure of determining the optimum initial shape of Gaussian beams based on minimizing the average squared widths of Gaussian beams and smoothing the distribution of the optimum parameters of Gaussian beams on the Hamiltonian hypersurface in the phase-space. The original method of smoothing represents an essential part of the algorithm, which is designed particularly for the optimization of the shape of Gaussian beams for Gaussian beam or packet migrations.     

Connections between the distribution of prevailing winds in the winter Northern Hemisphere, solar/geomagnetic activity and the QBO phase

The effect of solar/geomagnetic activity and QBO phase on the distribution of winds prevailing in the winter periods (January–March) in the Northern Hemisphere at the altitude of 850 mb was studied. Analysis has shown that the zonal flow over the North Atlantic under high geomagnetic activity intensifies and under low solar/geomagnetic activity weakens. Flow deviations, associated with geomagnetic activity, are more marked under the QBO-east phase, and flow deviations, associated with solar activity, are more marked under the QBO-west phase. The results reported by Venne and Dartt (1990) concerning the wind distribution in the winter (February–March) Northern Hemisphere under high and low solar activity and a QBO-west phase, have been confirmed, and supplemented with wind distributions under high and low geomagnetic activity.     

On hydromagnetic instabilities and the mean electromotive force in a non-uniformly stratified Earth’s core affected by viscosity

Linear magnetoconvection in a model of a non-uniformly stratified horizontal rotating fluid layer with a toroidal magnetic field is investigated for no-slip and finitely electrically conductive boundaries and with very thin stably stratified upper sublayer. The basic parabolic temperature profile is determined by the temperature difference between the boundaries and by the homogeneous heat source distribution in the layer. This results in a density pattern, in which a stably stratified upper sublayer is present. The developed diffusive perturbations (modes) are strongly affected by the complicated coupling of viscous, thermal and magnetic diffusive processes. The calculations were performed for various values of Roberts number (q ≪ 1 and q = O(1)). The mean electromotive force produced by the developed hydromagnetic instabilities is investigated to find the modes, which can be appropriate for creating the α-effect. It was found that the azimuthal part of the EMF is dominant for westward modes when the Elsasser number Λ ≲ O(1).     

Decomposition of the wave field into optimized Gaussian packets

The decomposition of the wave field into optimized Gaussian packets represents a crucial step of the Gaussian packet prestack depth migration algorithm. The shape of optimized Gaussian packets, in the plane perpendicular to the central ray of the packet, depends not only on the frequency, but also on the coordinate of the intersection of the central ray of a Gaussian packet with the profile, on its arrival time, and on the component of the slowness vector along the profile. We express the amplitude of a Gaussian packet in the form of an integral transform similar to the forward coherentstate transform. Our method is suitable for a smooth distribution of the parameter determining the shape of a packet in the plane perpendicular to its central ray.     

Full three-dimensional tomography: a comparison between the scattering-integral and adjoint-wavefield methods

This paper analyses the computational issues of full 3-D tomography, in which the starting model as well as the model perturbation is 3-D and the sensitivity (Fréchet) kernels are calculated using the full physics of 3-D wave propagation. We compare two formulations of the structural inverse problem: the adjoint-wavefield (AW) method, which back-propagates the data from the receivers to image structure, and the scattering-integral (SI) method, which sets up the inverse problem by calculating and storing the Fréchet kernels for each data functional. The two inverse methods are closely related, but which one is more efficient depends on the overall problem geometry, particularly on the ratio of sources to receivers, as well as trade-offs in computational resources, such as the relative costs of compute cycles to data storage. We find that the SI method is computationally more efficient than the AW method in regional waveform tomography using large sets of natural sources, although it requires more storage.     

Solar energetic events in the years 1996–2004. The analysis of their geoeffectiveness

Data concerning solar energetic events, published in 1996–2004 by the USAF/NOAA in the form of daily reports, have been collected. The analysis of the particular event types indicates that the degree of their geoeffectiveness depends on their size and on their solar disc location. The mere information that a solar X-flare (XRA) event or a Long Duration XRA Event (LDE) has occurred on the solar disc is insufficient to produce a relevant forecast of geomagnetic disturbances. The probability increases if the XRA is of class X which has occurred on the solar disk in central region (30 °E, 30 °W; 30 °S, 30 °N). XRAs associated with metric type II and IV radio bursts (RSP II and RSP IV), which occurred on the solar disc in this region will very probably cause a geomagnetic disturbance not only if X class are involved, but also M class and B–C class. The Disappearance of Solar Filament (DSF) data cannot be used in forecasting geomagnetic disturbances. The geoeffective and nongeoeffective DSFs are too disproportional. jboch@ig.cas.cz fridrich@geomag.sk     

Geoeffectiveness of XRA events associated with RSP II and/or RSP IV estimated using the artificial neural network

A forecasting scheme of geomagnetic activity is presented, based on the analysis of the geoeffectiveness of X-ray flares, accompanied by Type II and/or Type IV radio bursts (RSP) observed on the solar disc in the years 1996–2004. The neural network was used to construct this scheme enabling us to determine the probability, with which flares will be followed by a geomagnetic response of a particular intensity. The successfulness of forecasts produced after the fact depended on the flare class and on the combination of radio-burst types. In the case of RSP IV, 58% of the geomagnetic responses of X-ray flares of at least B class were successful. If only RSP II was observed, the forecast was successful only for flares of the X class (67% of successful forecasts). In the second step, a strong geomagnetic response was correctly forecast after geoeffective flares in 58% of the cases. The results are in a good agreement with recent papers based on physical modelling. fridrich@geomag.sk ph@ig.cas.cz, jboch@ig.cas.cz     

The rigorous determination of orthometric heights

The main problem of the rigorous definition of the orthometric height is the evaluation of the mean value of the Earth’s gravity acceleration along the plumbline within the topography. To find the exact relation between rigorous orthometric and Molodensky’s normal heights, the mean gravity is decomposed into: the mean normal gravity, the mean values of gravity generated by topographical and atmospheric masses, and the mean gravity disturbance generated by the masses contained within geoid. The mean normal gravity is evaluated according to Somigliana–Pizzetti’s theory of the normal gravity field generated by the ellipsoid of revolution. Using the Bruns formula, the mean values of gravity along the plumbline generated by topographical and atmospheric masses can be computed as the integral mean between the Earth’s surface and geoid. Since the disturbing gravity potential generated by masses inside the geoid is harmonic above the geoid, the mean value of the gravity disturbance generated by the geoid is defined by applying the Poisson integral equation to the integral mean. Numerical results for a test area in the Canadian Rocky Mountains show that the difference between the rigorously defined orthometric height and the Molodensky normal height reaches ∼0.5 m.     

Magion-4 High-Altitude Cusp Study

The polar cusps have traditionally been described as narrow funnel-shaped regions of magnetospheric magnetic field lines directly connected to magnetosheath ones, allowing the magnetosheath plasma to precipitate into the ionosphere. However, recent middle- to high-altitude observations (i.e., the Interball, Hawkeye, Polar, Image, and Cluster spacecraft) reported the cusps to encompass a broad area near local noon. The present paper focuses on a statistical study of the high-altitude cusp and surrounding magnetosheath regions as well as on some peculiarities of the cusp-magnetosheath transition. For a comparison of high- and low-altitude cusp determination, we present a mapping of two-year Magion-4 (a part of the Interball project) observations of cusp-like plasma along model magnetic field lines (according to the Tsyganenko 96 model) down to the Earth’s surface. The footprint positions show a substantial latitudinal dependence on the dipole tilt angle. The dependence can be fitted by a line with a slope of 0.14° MLAT per 1° of tilt. In contrary to previously reported IMF or solar wind influences on the cusp shape or location, some differences exist: (1) a possible IMF B_X dependence of the cusp location, (2) a split cusp for B_Y≠ 0, and (3) a smaller cusp during periods of higher solar wind dynamic pressure. The conclusions following from the statistical analysis are confirmed by case studies which reveal the physical mechanisms leading to the observed phenomena. Results have shown that (1) reconnection near the cusp does not necessarily lead to observable precipitation, (2) the cusp precipitation in one hemisphere can be supplied from the conjugate hemisphere, and (3) the cusp geometry at a certain time depends on the IMF history.