IC SG3

JSG 0.3: Comparison of current methodologies in regional gravity field modelling

Chairs: M. Schmidt (Germany), Ch. Gerlach (Germany)
Affiliation: Comm. 2, 3

Introduction

Traditionally the gravitational potential of the Earth and other celestial bodies is modelled as a series expansion in terms of spherical harmonics. Although this representation is technically possible for ultra-high expansions, it is well-known that spherical harmonic approaches cannot represent data of heterogeneous density and quality in a proper way. In order to overcome these and other deficiencies regional modelling comes into question.

In the last years many groups have developed sophisticated approaches for regional modelling, e.g., the expansion of the gravity field or functionals of the field in terms of spherical (radial) base functions. Analogously to spherical harmonic approaches, also in regional modelling the unknown model parameters, i.e., the coefficients of the series expansion, can be either determined by means of numerical integration or as the solution of a parameter estimation process. Numerical integration techniques are widely used in the mathematical community and provide efficient and stable solutions. However, numerical integration techniques suffer from important disadvantages. Among others these methods (1) require the input data to be given on a spherical integration grid, (2) cannot provide estimated error variances and covariances of the model parameters and (3) have difficulties to handle the combination of data from different measurement techniques. Due to these disadvantages, parameter estimation is the preferred strategy in the geodetic community. Although solutions in regional modelling based on parameter estimation are generated by several groups since many years, a large number of unsolved problems and open questions still remain. They mostly arise from the condition of the normal equation system and are therefore directly connected to the parametrization of the gravity field, the type and distribution of observation data, the choice and location of base functions, possible regularisation schemes, etc.

The aim of the JSG is to find guidelines on suitable strategies for setting up the parameter estimation of regional gravity field modelling. This includes appropriate strategies for the combination of satellite, airborne and terrestrial data. The focus of the JSG is on the methodological foundation of regional gravity field modelling based on series expansions in terms of localizing base functions. Therefore, numerical studies will be concentrated on simulations based on synthetic data. It is not the aim of the JSG to process and compare solutions from real data.

Objectives

The main objectives of this JSG are:

• to collect information of available methodologies and strategies for regional modelling, including
  • the type of base functions (splines, wavelets, Slepian function, Mascons, etc.),
  • the point grids for placing the functions (standard grid, icosaeder, Reuter grid, etc. on a sphere, ellipsoid, etc.),
  • the choice and establishment of an appropriate adjustment model (combination strategy, variance component estimation, rank deficiency problems, e.g., due to downward continuation, etc.),
  • the consideration of model errors (truncation errors, edge effects, leakage, etc.),
  • the specific field of application,
• to analyze the collected information in order to find specific properties of the different approaches and to find, why certain strategies have been chosen,
• to create a benchmark data set for comparative numerical studies,
• to carry out numerical comparisons between different solution strategies for estimating the model parameters and to validate the results with other approaches (spherical harmonic models, least-squares collocation, etc.),
• to quantify and interpret the differences of the comparisons with a focus on detection, explanation and treatment of inconsistencies and possible instabilities of the different approaches,
• to create guidelines for generating regional gravity solutions,
• to outline standards and conventions for future regional gravity products.
• Comparable work outside gravity field determination, e.g., in the mathematical communities and in geomagnetic field determination will be taken into account.
• To achieve the objectives, the JSG interacts and collaborates with other ICCT JSGs as well as IAG Commission 2. As a matter of fact, the outcomes of the JSG can be also used by other IAG commissions, especially in Commission 3.
• The JSG's work will be distributed to IAG sister associations through respective members.

Program of Activities

The JSG’s program of activities will include organization of SG meetings and of one or more scientific workshops on regional modelling participation in respective symposia (EGU, AGU, etc.), publication of important findings in proper journals, maintaining a website for general information as well as for internal exchange of data sets and results, supporting ICCT activities.

Members

Michael Schmidt (Germany), chair
Christian Gerlach (Germany), chair
Katrin Bentel (Norway)
Annette Eicker (Germany)
Indridi Einarsson (Denmark)
Junyi Guo (USA)
Majid Naeimi (Germany)
Isabelle Panet (France)
Judith Schall (Germany)
Uwe Schäfer (Germany)
Frederick Simons (USA)
C.K. Shum (USA)
Matthias Weigelt (Germany)
Gongyou Wu (China)