Regression modelling in selenodesy

Abstract

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.

The ARM-Approach Based Local Modelling of the Gravitational Field

“…∆C nm cos mλ + ∆S nm sin mλ P nm (cos θ) (1) where GM = G (M 0 + M atm )-is geocentric gravitational constant, taking into account the Earth atmosphere, abig half-axis of the Earth ellipsoid; r,θ=90 0ϕ, λ -are spherical coordinates of the point -accordingly geocentric distance, arctic distance (ϕ -geocentric width), geographical longitude;∆C nm , ∆S nm -are differences of factors of normalizing spherical functions of real and normal fields; P nm (cos θ) -are normalized joined Legendre functions of n degree and m order.…”

“…On the basis of the theory and computing experiments with great data arrays, we had proved that standard decompositions on spherical functions with MoLS-evaluations of amplitudes of harmonics do not fully correspond to real measurements, on which they are built [1]. The main reason of this fact is the redundancy of mathematical model, containing multiple (up to 60% and more) noise harmonicas.…”

“…We offered to use a statistical approach in the manner of adaptive regression modelling [1] for deciding a problem of adequacy of global models and accordingly gravimetrical contour maps of anomalies of power of gravity. This approach allows to raise the accuracy of identification of structures up to several times already at the stage of elimination of noises.…”

“…This approach allows to raise the accuracy of identification of structures up to several times already at the stage of elimination of noises. Experiments on its using under comparatively small orders of decomposition are described in [1].…”

“…Using ARM-approach, based on adaptive regression modelling [1] the following is planned: 1) determination of global and regional components of the geopotential by a great multifunction array of measurements (overland and satellite data); 2) revision of normal field of the Earth; 3) building of regional and local mathematical models in the manner of optimum decompositions by Fourier series based on the overland gravimetrical measurements.…”