JSG T.38

JSG T.23: High-rate GNSS

Chair: Mattia Crespi (Italy)
Affiliation:Commissions 1, 3 4 and GGOS

Introduction

The gravitational field represents one of the principal properties of any planetary body. Physical quantities, e.g., the gravitational potential or its gradients (components of gravitational tensors), describe gravitational effects of any mass body. They help indirectly in sensing inner structures of planets and their (sub-)surface processes. Thus, they represent an indispensable tool for understanding inner structures and processes of planetary bodies and for solving challenging problems in geodesy, geophysics and other planetary sciences.

Various measurement principles have been developed for collecting gravitational data by terrestrial, marine, airborne or satellite sensors. From a theoretical point of view, different parameterizations of the gravitational field have been introduced. To transform observable parameters into sought parameters, various methods have been introduced, e.g., boundary-value problems of the potential theory have been formulated and solved analytically by integral transformations.

Transforms based on solving integral equations of Stokes, Vening-Meinesz and Hotine have traditionally been of significant interest in geodesy as they accommodated gravity field observables in the past. However, new gravitational data have recently become available with the advent of satellite-to-satellite tracking, Doppler tracking, satellite altimetry, satellite gravimetry, satellite gradiometry and chronometry. Moreover, gravitational curvatures have already been measured in laboratory. New observation techniques have stimulated formulations of new boundary-value problems, equally as possible considerations on a tie to partial differential equations of the second order on a two-dimensional manifold. Consequently, the family of surface integral formulas has considerably extended, covering now mutual transformations of gravitational gradients of up to the third order.

In light of numerous efforts in extending the apparatus of integral transforms, many theoretical and numerical issues still remain open. Within this JSG, open theoretical questions related to existing surface integral formulas, such as stochastic modelling, spectral combining of various gradients and assessing numerical accuracy, will be addressed. We also focus on extending the apparatus of spheroidal integral transforms which is particularly important for modelling gravitational fields of oblate or prolate planetary bodies.

Objectives

• • Study noise propagation through spherical and spheroidal integral transforms.
  • Propose efficient numerical algorithms for precise evaluation of spherical and spheroidal integral transformations.
  • Develop mathematical expressions for calculating the distant-zone effects for spherical and spheroidal integral transformations.
  • Study mathematical properties of differential operators in spheroidal coordinates which relate various functionals of the gravitational potential.
  • Formulate and solve spheroidal gradiometric and spheroidal curvature boundary-value problems.
  • Complete the family of spheroidal integral transforms among various types of gravitational gradients and to derive corresponding integral kernel functions.
  • Investigate optimal combination techniques of various gravitational gradients for gravitational field modelling at all scales.

Program of activities

• To launch a questionnaire for the above mentioned inventory of methodologies, applications and technologies.
• To open a web page with information concerning high-rate GNSS and its wide applications in science and engineering, with special emphasis on exchange of ideas, provision and updating bibliographic list of references of research results and relevant publications from different disciplines.
• To launch the proposal for two (one science and the other engineering oriented) state-of-the-art review papers in high-rate GNSS co-authored by the JSG Members.
• To organize a session at the forthcoming Hotine-Marussi symposium.
• To promote sessions and presentation of the research results at international symposia both related to Earth science (IAG/IUGG, EGU, AGU, EUREF, IGS) and engineering (workshops and congresses in structural and geotechnical engineering).

Members

Mattia Crespi (Italy), chair
Juan Carlos Baez (Chile)
Elisa Benedetti (United Kingdom)
Geo Boffi (Switzerland)
Gabriele Colosimo (Switzerland)
Athanasios Dermanis (Greece)
Roberto Devoti (Italy)
Jeff Freymueller (USA)
Joao Francisco Galera Monico (Brazil)
Jianghui Geng (Germany)
Kosuke Heki (Japan)
Melvin Hoyer (Venezuela)
Nanthi Nadarajah (Australia)
Yusaku Ohta (Japan)
Ruey-Juin Rau (Taiwan)
Eugenio Realini (Italy)
Chris Rizos (Australia)
Nico Sneeuw (Germany)
Peiliang Xu (Japan)

Bibliography

[Biblioraphy [1]]