Modeling of the regional gravitational field using first and second derivative of spherical functions

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

Supply of photogrammetric projects with reference information obtained from large-scale aerial images

Objective. Permanent growth of the volume of remote-obtained information about location sets have challenged tasks for scientists and experts concerning quality of its processing in terms of efficiency, completeness, sub...

Analysis of stability of points of automated geodetic monitoring of engineering structures Kanev HPP

Aim. As part of the project of renovation of hydropower plants on the Kanev hydropower plants (HPP) the experts of Leica Geosystems together with Ukrhydroenergo had created a system of automated geodetic monitoring compr...

Reliability of informativeness of public cadastral map of Ukraine

Purpose. Authenticity of informativeness of public cadastral map of Ukraine is an important component of an open democratic society. It allows to adopt adequate to existing realities administrative decisions of the autho...

System social and environmental assessment of anthropogenic disturbances land

Purpose. The aim of the article is to assess the anthropogenically disturbed lands according to their ecological status and the total value of the result of its socio-economic efficiency use. Methodology. Anthropogenic l...

Approbation of application of non-simultaneous bilateral trigonometric leveling taking into account vertical efraction

Purpose. Development of efficient, economic and reliable method of trigonometric leveling that would allow replace the geometric leveling without loss of precision, especially during works in mountainous areas remains ac...

Download PDF file
  • EP ID EP484450
  • DOI 10.23939/istcgcap2018.02.005
  • Views 122
  • Downloads 0

How To Cite

B. B. Dzhuman (2018). Modeling of the regional gravitational field using first and second derivative of spherical functions. Геодезія, картографія і аерофотознімання, 88(2), 5-12. https://europub.co.uk/articles/-A-484450