In this paper an analysis of data coordinate systems from selenographic catalogues and space missions was carried out. The lunar macrorelief models were made on basis of the software package ASNI USTU using method of the spherical harmonic expansion. These models accurately describe the global features of the lunar figure. To construct these models the following sources of topographic information were used: “Clementine” and “KАGUYА” (Selena, Japan mission) missions, “KSC-1162” (Kazan selenocentric catalogue), “Kiev” (selenodesic catalogue), “SAI” (Chuikova (1975)), “Bills, Ferrari”, “ULCN” (The Unified Lunar Control Network 2005). Direct comparison hypsometric information “KSС-1162” catalogue data with “Clementine” mission was carried out. These researches confirmed a good agreement of the hypsometric information of compared systems. The normalized coefficients were obtained on basis of the hypsometric information expansion for eight sources. The displacement of the lunar center of mass (LCM) relatively to the lunar center of figure (LCF) was obtained by using topographic data selenodetical catalogues and space missions.

We describe a method to construct a reference selenocentric catalogue in the lunar libration zone using the marginal zone maps "Kazan" and Watts, as well as the data from the "Full maps of the moon" (SAI).

Construction of a global reference network on the lunar surface is one of the most important problems of modern selenodesy. We describe main approaches to modeling the reference selenocentric coordinate system in the center of mass and principal axes of inertia of the Moon based on the combination of space and ground-based observations.

This article examines the use of adaptive dynamic regressions describing the change latitudes.

An accuracy of geocenter motion estimation is strongly dependent on the geodetic network size and stations distribution over the Earth's surface. From this point of view DORIS system has an advantage, as its ground network of beacons consists of more than 50 sites, equally distributed over the Earth's surface. Aiming to study variations of the geocenter movements, the results of DORIS data analysis for the time span 1993.0-2009.0 (inawd06.snx series), performed at the Analysis Centre of the Institute of astronomy of the Russian Academy of Sciences, have been used. DORIS data processing was made with GIPSY/OASIS II software, developed by Jet Propulsion Laboratory and modified for DORIS data processing by Institute Geographique National. Standard deviations of stations coordinates are estimated at the level 0.5-4.0 cm (internal consistency), depending on the number of satellites used in the solution. RMS of estimated components of the DORIS satellites orbits, compared with the solutions of other IDS analysis centres, do not exceed 1-2 cm. Weekly solutions for coordinates have been transformed from free network solutions (inawd06.snx series) to a well defined terrestrial reference frame ITRF2005 with the use of seven parameters of Helmert transformation, which were examined with a view to study variations of the geocenter movements (ina05wd01.geoc time series). In order to estimate linear trend, amplitudes, periods and phases of geocenter variation a method of linear regression was applied. The evaluated amplitudes of annual variations are of the order of 5-7 mm for X and Y components and 27-29 mm for Z component. Semi-annual amplitudes are also noticeable in all components (1-34 mm for X, Y and Z components). Secular trends in the DORIS geocenter coordinates are: -1.2, -0.1 and -0.3 mm/year for X, Y and Z directions respectively.Spectral analysis of the same set of DORIS data (1993.0-2009.0) with the method of dynamic regression modeling allowed to find out several other harmonics with periods of 2, 3, 5 years and valuable amplitudes (1-3 mm for X, Y components and about 10 mm for Z component) and to develop a model of the geocenter dynamics. The simulated values of geocenter coordinates, estimated for the 2008 year with the use of shortcut model, limited by 1993-2007 data, coincide with "observable" (calculated with use of DORIS measurements) data with the correlation coefficient 0.7-0.8. (C) 2010 COSPAR. Published by Elsevier Ltd. All rights reserved.

Based on the uniform catalogue of earthquakes of the minimum energy class 8.5 for 1962–2008, multiharmonic models of seismic activity in Kamchatka are developed. The main harmonic components with periods from a few days to 12 years are identified. Both the entire catalogue and its modified versions obtained by the elimination of aftershocks and clusters, as well as nonoverlapping time series were used to study the stability of the models. The forward-prediction testing showed that in the models with weekly averaged initial data, periods of increased and reduced seismic activity lasting for several weeks are predicted with high confidence on an interval of up to 1.8% of the education period. This testifies for the presence of deterministic components in the seismic activity.

Gravimetrical Measurements revealing particularities of the gravitational field, play an important role in a research after oil thanks to their capacity to reduce the cost of reconnaissance work. Graphic generalization of the field is given by gravimetrical maps of the field anomalies, drawn out with the corresponding software on the basis of one or other version of interpolation formula. Mathematical models of the trend forming regional reference-surface, can extend the capabilities of graphic generalization of measurements. With these models and corresponding contour maps, the local particularities of the gravitational field reveal themselves more clearly. The use of models in the manner of truncated decompositions in Fourier series on spherical surfaces is offered for practical geophysical tasks. An algorithm of adaptive statistical modelling which allows optimum mathematical models to be built is considered. In the last section we describe the developed software that allows us to build the statistical potential field models. The corresponding field maps of residual anomalies are described.

The coordinates of 171 objects of the reverse side and marginal zone, and 42 objects of the visible side of the Moon's Western hemisphere in survey zone from the automatical interplanet stations of ‘Zond 6 and 8’ type are presented. While dealing with the measuring information, systematical errors arising from the breakdown of orthogonality in coordinate transformation were taken into account, as well as original geometry of the Moon's limb as measured from the space.

The existing models of different orders that describe surface and gravitational fields of planets contain a redundant number of members with no useful information, which makes it difficult to describe physical phenomena. The possibility of using statistical (regressive) modelling as an effective means of obtaining adequate relief and gravitational field models is considered. A concrete numerical example shows that the use of regression modelling in the task of describing the Moon surface by expansion on spherical functions permits us to obtain approximate models with the harmonics less than a half in number compared to the traditional approach; the precision of “shortened” model approximations being higher or, at least, not lower than the precision description for the usual number of harmonics that correspond to the expansion order taken.