Modeling of the regional gravitational field using first and second derivative of spherical functions
Journal Title: Геодезія, картографія і аерофотознімання - Year 2018, Vol 88, Issue 2
Abstract
Aim. The main task of the geodesy is to determine the shape and size of the Earth and its changes over time. An integral part of determining the shape and size of the Earth is the construction of a geoid surface model, both global and regional. Today larger and more precise arrays of input data (geopotential functionals) appear to construct such a model, methods for their processing are rapidly becoming generated. One of such methods is an extention in a series of spherical functions on a spherical trapezium. Since the functionals of the gravitational field are mostly obtained using the differentiation operator, for the use of this method it is necessary to investigate the first and second derivatives of spherical functions on a spherical trapezium, which is the purpose of this work. Method. Spherical functions on a spherical trapezium can not be presented in explicit form, nor do they have simple recurrence relations. To calculate them, the extention in a hypergeometric series should be used. Therefore, to calculate the first and second derivative from the above-mentioned functions, the derivative from the hypergeometric series should be used. Results. As a result of certain mathematical transformations, we obtain an expression for finding the first and second derivatives of spherical functions on a spherical trapezium, as well as a comparatively obtained result with spherical Legendre functions of the first kind. The scientific novelty and practical significance. The expression for the first and second derivative of spherical functions on a spherical trapezium was first determined. The result obtained with the spherical Legendre functions of the first kind is comparative. This enables the use of such functions as a basic system of functions on a spherical trapezium for modelling of regional gravitational or magnetic fields.
Authors and Affiliations
B. B. Dzhuman
Keywords
Related Articles
- EP ID EP484450
- DOI 10.23939/istcgcap2018.02.005
- Views 123
- Downloads 0
Planning of hard coal underground mining operations in the aspect of GIS tools
Purpose. This article will discuss the general problems in planning hard coal underground mining operations. The conditions of Upper Silesian Coal Basin perfectly illustrate the complexity of that process. The exemplary...
The substantiation of land plot configuration data at peer exchange
Purpose. In current social and economic conditions configuration of land plots is one of the most important characteristics of peer land exchange. The purpose of the research is data substantiation which allows to contra...
Determination of the mass graves of World War II using GIS technology
Aim of the work is determined graphically visualize historical data fragment of territory-based regiment of Yakutsk, is located in Kremenets of Ternopil region in the first half of the twentieth century on modern maps. W...
Technological features of creation of a large-scale topographical plan of Lviv city landfill using combined method
Purpose. The compliance with maintenance requirements of a landfill is an important factor that have affects on its functioning. The functioning of Lviv city landfill started in 1959 and continued till 2016. According t...
Comparison of the wet component of zenith tropospheric delay derived from GNSS observations with corresponding value from radio soundings
The purpose of this paper is to evaluate an accuracy of the wet component of zenith tropospheric delay obtained by the data of six GNSS stations in comparison with radio sounding data. The determination of hydrostatic an...