Existence of the solution of Szebehely's equation in three dimensions using a two-parametric family of orbits

The three-dimensional inverse problem is investigated. A quasi-linear system of partial differential equations is derived for the determination of the potential. The solution of this system is studied by a method of differential geometry. A necessary condition for the solution is derived and the determination of the potential is reduced to algebraic equations written in vectorial form. A few examples are also given.     

Inversion of magnetic measurements of the CHAMP satellite over the Pannonian Basin

The Pannonian Basin is a deep intra-continental basin that formed as part of the Alpine orogeny. In order to study the nature of the crustal basement we used the long-wavelength magnetic anomalies acquired by the CHAMP satellite. The anomalies were distributed in a spherical shell, some 107,927 data recorded between January 1 and December 31 of 2008. They covered the Pannonian Basin and its vicinity. These anomaly data were interpolated into a spherical grid of 0.5° × 0.5°, at the elevation of 324 km by the Gaussian weight function. The vertical gradient of these total magnetic anomalies was also computed and mapped to the surface of a sphere at 324 km elevation. The former spherical anomaly data at 425 km altitude continued downward to 324 km. To interpret these data at the elevation of 324 km we used an inversion method. A polygonal prism forward model was used for the inversion. The minimum problem was solved numerically by the Simplex and Simulated annealing methods; a L₂ norm in the case of Gaussian distribution parameters and a L₁ norm was used in the case of Laplace distribution parameters. We interpret that the magnetic anomaly was produced by several sources and the effect of the sable magnetization of the exsolution of hemo-ilmenite minerals in the upper crustal metamorphic rocks.     

Granulometric investigations of loess profiles in Hungary

The granulometric analysis of loess varieties is meant to contribute to the subdivision of loess sequences, to the reconstruction of the environments of loess formation (identifying areas of loess origin [from where the dust derives], geographical obstacles to transport, contemporary wind directions [through drawing isokatharoses lines connecting points with identical FG values] and even wind velocities) and subsequent changes in climatic and geographical conditions. It was investigated whether loesses and loess-like deposits can be described by a generalised grain size parameter (fineness grade, FG) or to what extent other granulometric indices can lead to a more differentiated picture of grain size variation. Fineness grade was used to denominate sediments and to identify finer and coarser sections in the series;K _d index indicates the lithostratigraphical positions of cold stages (maximum values) and warm stages (minimum values); finesorting (S _o) points to eolian accumulation, while fluvial deposits (bedload, saltated and suspended load) are poorly sorted;kurtosis (K) allows conclusions for the reworking of the deposit andasymmetry (S_k) indicates the factor active in the accumulation of the deposit.The paper concentrates primarily on the study of variation in the vertical profile of deposits. Along with other indices, fineness grade was found useful in distinguishing between loess varieties and other sediments and could even replace the function of the conventional index median value (M_d).