# JSG T.23

**JSG T.23: Spherical and spheroidal integral formulas of the potential theory for transforming classical and new gravitational observables**

Chair: *Michal Šprlák (Czech Republic)*

Affiliation:*Commission 2 and GGOS*

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### 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

- Presenting findings at international geodetic or geophysical conferences, meetings and workshops.
- Interacting with IAG Commissions and GGOS.
- Monitoring research activities of JSG members and other scientists whose research interests are related to scopes of this JSG.
- Organizing a session at the Hotine-Marussi Symposium 2022.
- Providing a bibliographic list of publications from different branches of the science relevance to scopes of this JSG.

### Members

* Michal Šprlák (Czech Republic), chair Sten Claessens (Australia) Mehdi Eshagh (Sweden) Ismael Foroughi (Canada) Peter Holota (Czech Republic) Juraj Janák (Slovakia) Otakar Nesvadba (Czech Republic) Pavel Novák (Czech Republic) Vegard Ophaug (Norway) Martin Pitoňák (Czech Republic) Michael Sheng (Canada) Natthachet Tangdamrongsub (USA) Robert Tenzer (Hong Kong) *