**SECTION IV**

**GENERAL THEORY AND METHODOLOGY**

**THEORIE GENERALE ET METHODOLOGIE**

**President**: P. Holota (Czech Republic)

**Secretaries**: B. Heck (Germany)

C. Jekeli (USA)

**I-Terms of Reference**

As stated in the by-laws, Section IV has primarily a methodological character. Its scope is not confined to one particular topic in Geodesy which would be peculiar to this Section only, but rather all topics are shared in one way or another with other IAG Sections, with the accent of the research pointing towards the systematic mathematical treatment of geodetic problems.

The Section keeps its basic structure as in the last period which originated from the preparatory work done by K.P. Schwarz and the decision of the Section IV Steering Committee to adopt a new organization, by establishing a novel structure in the core of the Section at that time, i.e. the Special Commission on Mathematical and Physical Foundations of Geodesy.

This Special Commission (even this name was born in Section IV) follows the original and standing concern to collect real specialists on the mathematical treatment of various geodetic problems, e.g. geodetic boundary-value problems, statistical problems in geodesy or problems in geometry, relativity, cartography, theory of orbits and dynamics of systems, and put them work on the assessment of difficult questions, open ever since many 4-years periods.

In this concept the new S.S.G.'s are on the contrary in duty to treat a much smaller range of problems, focussing on some very specific open questions to be solved as a rule in one 4-year period. Collective numerical experiments in the framework of S.S.G's are

encouraged, when possible.

**II-Structure**

Special Commission :

SC1 : Mathematical and Physical Foundations of Geodesy

President : E.W. Grafarend (Germany)

Special Study Groups :

SSG 4.168 : Inversion of Altimetric Data

Chairman : P. Knudsen (Denmark)

SSG 4.169 : Wavelets in Geodesy

Chairman : B. Benciolini (Italy)

SSG 4.170 : Integrated Inverse Gravity Modelling

Chairman : L. Ballani (Germany)

SSG 4.171 : Dynamic Isostasy

Chairman : L.E. Sjöberg (Sweden)

SSG 4.176 : Temporal Variations of the Gravity Field

Chairman : D. Wolf (Germany)

**Special Commission SC 1**

**Mathematical and Physical Foundations of Geodesy**

President : **E. W. Grafarend **(Germany)

On the occasion the XXth General Assembly held in Vienna, 1991, Special Commission #1 has been founded within Section IV. The IAG-Council appointed Erik W. Grafarend as its first President. For the XXIst General Assembly in Boulder (USA), Special Commission #1 presented a special issue of manuscripta geodaetica (Springer-Verlag) as well as a series of review papers in Section IV Bulletin (IAG). Erik W. Grafarend had been re-elected to chair Special Commission #1 in the 1995-99 period. IAG's Executive Committee renewed the objectives and the operational manner of Special Commission #1 as following :

- to encourage and promote research on the foundations of geodesy in any way possible;

- to publish, at least once every four years, comprehensive reviews of specific areas of active research in a form suitable for use in teaching as well as research reference;

- to actively promote interaction with other sciences;

- to closely cooperate with the special study groups in Section IV.

Membership of Special Commission #1 is restricted to 30 members, one third of which will be replaced every four years. Chairmen of special study groups within Section IV are automatically members of Special Commission #1. The Section IV President as well as Section IV Secretaries are ex officio members. Other members are proposed by the Commission President and approved by the Section President.

Special Commission #1 will operate in the following manner :

Within half a year after the General Assembly, the Commission President will propose a research program and operational plan based on the input of members. The research program should identify the major research objectives for the four year period between general assemblies. Overlap with the work performed by special study groups in Section IV should be minimized. In case of conflict, the matter will be referred to the Section President for decision. The operational plan should identify the scientists or working groups responsible for specific tasks and give a rough time frame for the work to be performed.

The research program may be subdivided into specific tasks which can be assigned to working groups within Special Commission #1. Workshops of Special Commission #1 will be organized at least once between general assemblies and specialists from other disciplines will be invited to contribute to these workshops. The speedy transfer of research results to the teaching and working environment is part of the task of Special Commission #1 and the operational plan should be structured accordingly. A special series for publication of comprehensive research reviews should be considered. Representation on scientific bodies which can contribute to the work of Special Commission #1 or which should be aware of the research results will be sought on mutual basis.

On the occasion of the XXIst General Assembly held at Boulder the President of Section IV has accepted the following Subcomissions, the Working Group and Chair Persons :

**Subcommission 1 "Statistics"**

* *Chairman : A. Dermanis (Greece)

**Subcommission 2 "Numerical and Approximation Methods"**

* *Chairman : W. Freeden (Germany)

**Working Group "Comparison of several techniques for
solving geodetic boundary value problems by means of numerical
experiments"**

* *Chairman : R. Klees (The Netherlands)

**Subcommission 3 "Boundary Value Problems" **

* *Chairman : E. Grafarend (Germany)

**Subcommission 4 Geometry, Relativity, Cartography**

* *Chairman :** **J. Zund (USA)

**Subcommission 5 Theory of Orbits and Dynamics of Systems
**

* *Chairman : R. J. You (Taiwan)

The following distinguished scientists have been invited to work in Special Commission #1 and its Subcommissions :

__Ex officio __

P. Holota (Czech Republic)

President of Section IV

B. Heck (Germany)

Secretary of Section IV

C. Jekeli (USA)

Secretary of Section IV

P. Kundsen (Denmark)

Chairman SSG 4.168 :

Inversion of altimetric data

B. Benciolini (Italy)

Chairman SSG 4.169 :

Wavelets in geodesy

L. Ballani (Germany)

Chairman SSG 4.170 :

Inverse integrated gravity modeling

L. E. Sjöberg (Sweden)

Chairman SSG 4.171 :

Dynamic isostasy

D. Wolf (Germany)

Chairman SSG 4.176:

Temporal variations of the gravity field

__Individuals__

J. Adàm (Hungary)

M. Belikov (Russia)

J. A. R. Blais (Canada)

R. Forsberg (Denmark)

E. Groten (Germany)

K. H. Ilk (Germany)

W. Keller (Germany)

K. R. Koch (Germany)

L. Kubàcek (Czech Republic)

L. Kubackova (Czech Republic)

Z. Martinec (Czech Republic)

R. Rummel (Germany)

F. Sacerdote (Italy)

F. Sansò (Italy)

B. Schaffrin (USA)

K.-P. Schwarz (Canada)

M. Sideris (Canada)

H. Sünkel (Austria)

L. Svensson (Sweden)

P. Teunissen (The Netherlands)

C. Tscherning (Denmark)

P. Vanicek (Canada)

M. Vermeer (Finland)

P. Xu (Canada)

**Subcommission 1 **

**"Statistics"**

Chairman : A. Dermanis

**Research Program **

- The theory of observables. Fundamental issues in the statistical analysis of geodetic observations.

- Linear models. Algebraic approximation versus stochastic estimation/prediction, linear observation equations subject to stochastic condition equations (dynamic system equations), fixed versus random effects, n-th incremental Kriging, stationarity on curved manifolds of non-spherical type, robust estimation, robustness by stochastic prior information.

- Nonlinear models. Polynomial approximation of nonlinear models, algebraic approximation versus stochastic estimation/prediction, nonlinear estimators-predictors, robust estimation, robustness by stochastic prior information.

- Linear and nonlinear models with integer unknowns. Discrete optimization, validation analysis (phase observations with integer ambiguities).

- Numerical least squares. Fast least squares.

- Boundary value problems for random fields. Stochastic boundary value problems with a stochastic boundary.

- Variance-covariance component estimation. Simultaneous estimation of first and second moments.

- Invariance of geodetic observation equations.

The invariance of geodetic observation equations with respect to symmetry transformations (the similarity group, the projective group) the invariace of geodetic observational functionals in geometry and gravity space, relation of invariance to estimability.

- Random tensor fields, random eigenspace, test statistics (the deformation tensor, the stress tensor, the metric tensor, the curvature tensor).

- Space-time processes and GIS (Voronoi meshes, Delaunay triangulation on curved manifolds, stochastic geometry, quality evaluation).

- Bayesian statistics.

- Time series analysis. Signal analysis.

- Testing theory (confidence intervals for robust estimators, variance components)

- Optimal design. Reliability and integrity.

**Additional Members **

W. Caspary (Germany)

Ziqiang Ou (China)

S. Meier (Germany)

Yu. A. Rozanov (Russia)

M. Schmidt (Germany)

Yuanxi Yang (China)

**Subcommission 2 **

**"Numerical and Approximation Methods"**

Chairman : W. Freeden

**Research Program **

- The use of spherical harmonic expansions of higher and higher degree for the determination of the gravitational field and the figure of the Earth has reached its bounds for several reasons (e.g. Nyquist rate, uncertainty principle). It is not appropriate to model local behavior by non-localizing functions. The polynomial nature of these functions causes severe numerical difficulties due to their oscillatory character. The evaluation of high order spherical harmonics tends to be unstable. Therefore one should concentrate on combined models, where expansions in terms of spherical harmonics are combined with local methods, e.g. radial basis function techniques as splines, wavelets, masspoints, etc. or finite elements. In addition, new trial functions like Abel-Poisson kernels, Gauss-Weierstrass kernels and locally supported kernels should be investigated in detail. Isotropy preserving methods should be compared with non-preserving techniques.

- For the use of these methods fast algorithms are still to be developed both for synthesis and analysis, e.g. in Gabor-, Toeplitz- and wavelet- expansions.

- The demanded high accuracy of future models has to take into account the mass distribution in the upper crust and the true surface of the Earth. Therefore, numerical methods usable for non-spherical boundaries should be an important goal for future developments. This includes finite difference methods, finite element methods, all boundary element techniques as well as sphere-oriented methods (like harmonic splines or harmonic wavelets). For numerical efficiency, the use of multi-level or multi-resolution techniques is indispensable.

- The problem of combining data of different types and data coming from different heights is still a challenging one. In particular, the vectorial and tensorial nature of satellite data requires adequate approximation techniques. Future numerical methods should be able to handle such problems automatically.

*Additionnal Members*

J. Engels (Germany)

H. van Gysen (South Africa)

F.J. Narcowich (USA)

M. S. Petrovskaya (Russia)

M. Schreiner (Germany)

N. Sneeuw (Germany)

The working group "Comparison of several techniques for solvin geodetic boundary value problems by means of numerical experiments headed by R. Klees should be continued.

**Working Group**

**"Comparison of several techniques for solving geodetic
boundary value problems by means of numerical experiments**"

Chairman : R. Klees

**Research Program **

Comparison of techniques for solving geodetic boundary value problems by means of numerical experiments.

**Program of activities **

- providing additional information about the data sets

- solving the BVP using different data sets with different resolutions

- detailed description of the underlying techniques and the procedures followed validation of the results

- comparison of the different techniques

- preparing the final report

**Subcommission 3 **

**"Boundary Value Problems"**

Chairman : E. Grafarend

**Research Program **

- Pseudo-boundary value problems, reduction of observational functionals to simpler boundaries, in particular to the ellipsoid of revolution: the ellipsoidal Stokes bvp (the geoid) the ellipsoidal gradiometric bvp, datum problems in geodetic bvp, regional Wo-datum

- Stochastic boundary values, measurement errors, stochastic boundary, overdetermined bvps, regions of definition of the Poisson differential equation versus Laplace differential equation (domain of harmonicity), downward-upward continuation problems, internal bvp for the Poisson equation, the impact of extra-terrestrial masses (disconnected regions of mass distribution) time-dependent effects

- Representation of approximate solutions, deterministic versus stochastic collocation

*Additional Members *

M. Günther (Germany)

J. M. Neyman (Russia)

J. Otero (Spain)

N. Weck (Germany)

W. Wendland (Germany)

K.J. Witsch (Germany)

A. I. Yanushauskas (Lituania)

**Subcommission 4 **

**"Geometry, Relativity, Cartography"**

Chairman: J. Zund

**Research Program **

Geometry

- the generalized Marussi-Hotine approach to differential geodesy, including schemes for integrating the Hotine-Marussi equations

- conceptual foundations of Gaussian differential geodesy

- the geometry of plumblines, the Newtonian form of the differential equation of plumbline (orthogonal trajectories of a family of equipotential surfaces), plumblines as geodesics in a conformally flat 3-manifold, the deviation equation (Soldner-Fermi coordinates)

- the Lagrange portrait versus the Hamilton portrait of a geodesic, symplectic manifolds, Poincare diagrams

Relativity

- the general imbedding problem for relativistic space-times

- the differential equation od a geodesic in a relativistic space-time expressed in terms of "parallel coordinates" (Soldner-Fermi coordinates), geodesic deviation, higher order series representation, space-time Riemannian coordinates, stability analysis, bifurcation theory

- the coupled Einstein-Maxwell equations applied to compute the trajectories of an electromagnetic signal travelling in a curved space-time from a satellite to the Earth's surface and back (the PRARE satellite system), geometric-optical approximation, the Gordon metric

- the analysis of relativistic gravity gradients in a local pseudo-orthogonal frame

- minimal atlas of group manifolds, e.g. SO(3), SO(1,3), application of the Lusternik-Schnirelmann category theorem

Cartography

- the Earth's topographic surface as a 2-manifold and its imbedding in an Euclidean 3-space, geodesics on the Earth's topographic surface and its Delaunay triangulation, Voronoi meshes and their curvature tensor, map projections of the Earth's topographic surface

- general analysis of Maupertuis manifolds, 3-manifolds of satellite orbit geometry, conformally flat manifolds of dimension 2, 3 and 4, the Weyl-Schouten theorem and its applications

- map projections of the geoid (Law of the Sea) in spheroidal-spherical harmonic series

- map projections of an ellipsoid of revolution: the Hotine oblique Mercator projection, pseudo-cylindrical/equiareal projections of an ellipsoid of revolution, the triple map projection: the Earth's topographic surface, ellipsoid of revolution, plane, map projections based on the second fundamental form of a surface

- map projections of a space-time manifold - in particular the Schwarzschild space-time, existence of hyperequiareal map projections

*Additional Members *

F. Bocchio (Italy)

B. Mashhoon (USA)

V. S. Schwarze (Germany)

R. Syffus (Germany)

**Subcommission 5**

**"Theory of orbits and dynamics of systems"**

Chairman : R. J. You

**Research Program **

Determination of the terrestrial gravity field by dynamic satellite geodesy

- Earth's gravity field and its time variations

- analysis of the Love number

- inverse satellite gradiometry

Precise orbit computation

- study of spin-orbit coupling of an extended satellite body's orbit

- the impact of mass centre change of satellite

- the impact of a higher order tidal field

Relativistic orbit computation

- by means of KS elements

- study of the Zeeman effect

Modeling of nongravitational forces on satellite motions

*Additional Members *

O. L. Colombo (USA)

C. Cui (Germany)

S. Ehlers (till May 1996) (England)

J. Feltens (Germany)

P. Moore (from May 1996) (England)

N. Sneeuw (Germany)

**Special Study Group 4.168**

**Inversion of Satellite Altimetry**

Chairman : **P. Knudsen** (Denmark)

**Objectives **

This Special Study Group should study various geodetic and oceanographic inversion methods and data assimilation techniques. Through a deeper understanding of such techniques new ideas may be brought in order to enhance the use of satellite altimetry.

**Activities **

1) The estimation of the marine gravity field has been highly improved with data from the geodetic missions of Geosat and ERS-1. However, most processing schemes leave parts of the medium and long wavelength parts of the gravity field unsolved.

a) How does the recovery of the gravity field and the influence of ocean variability depend on the data type (sea surface heights, slopes, or curvature data) ?

b) How can TOPEX/POSEIDON altimetry be used as reference frame for GEOSAT and ERS-1 data ?

c) Is a Global Circulation Models adequate for elimination of the sea surface topography ?

d) How to process data in a global gravity field mapping?

2) The inversion of altimetry into marine geoid and sea surface topography has been improved along with the increased accuracies of the altimeter data and the geopotential models. However, in many regions the gravity models are not adequately accurate.

a) How does the a-priori spectrum for the topography look and is it homogeneous and isotropic ?

b) Which hydrodynamic flow mechanisms (geostrophy, friction, viscosity) are relevant to include and how can it be done ?

c) Which hydrodynamic constraints (mass, salt, and heat balance) are relevant to include and how can it be done ?

d) How important are other data sources (ship gravimetry, hydrography, AVHRR/ATSR surface temperature, ....) ?

3) The mapping of the ocean tides has been vastly improved in the deep ocean through the TOPEX/POSEIDON mission. However, in shelf regions major inconsistencies between the various models exist.

a) What causes the trade-off between hydrodynamics and altimetry and what is the role of errors in the bathymetry ?

b) Interpolation/extrapolation of ocean tides using empirical methods, assimilation techniques, or inversion techniques ?

c) How smooth is the ocean tides and which resolution should be used ?

d) Should other data sources (tide gauges, loadings, GPS, SAR) be included?

*Members :*

O.Ba. Andersen (Denmark)

M. Brovelli (Italy)

R. Coleman (Australia)

G.D. Egbert (USA)

G. Evensen (Norway)

O. Francis (Belgium)

Y. Fukuda (Japan)

H. van Gysen (South Africa)

R.H.N. Haagmans (The Netherlands)

W. Keller (Germany)

P. Knudsen (Denmark) - Chairman

P.J. van Leeuwen (The Netherlands)

F. Lyard (England)

P.-Y. Le Traon (France)

R.S. Nerem (USA)

N. Pavlis (USA)

R. Ray (USA)

D. Stammer (USA)

C.C. Tscherning (Denmark)

P.L. Woodworth (England)

Changyou Zhang (USA)

*Corresponding members :*

R. Feron (The Netherlands)

R.H. Rapp (USA)

F. Sansò (Italy)

V. Zlotnicki (USA)

C. Wunsch (USA)

**Special Study Group 4.169**

**Wavelets in Geodesy**

Chairman : **B. Benciolini **(Italy)

**I- Terms of Reference**

The theory of wavelets originated from the need of analysing a function with a tool able to balance localization in the space (or time) domain and localization in the frequency domain. First-generation-wavelets are families of functions derived by a single one, the mother function, by dilation and translation. Dilation and translation parameters can be considered to belong to continuous or discrete sets and correspondingly there are continuous and discrete wavelet transforms of a function.

A proper choice of the mother function and of the dilation and translation parameters allows the construction of families of wavelets that form a base (or sometime only a frame) of various functional spaces. Second-generation-wavelets are constructed with the so-called Lifting Scheme and offer more flexibility when facing with bounded domains, irregularly sampled functions, functions on curves and surfaces.

Several geodesists have already recognized the possibility of solving different geodetic problems with the help of wavelets. In particular, the ability of wavelets to represent integral operators in a very compact form allows the fast computation of such operators.

The SSG will stimulate and coordinate research activities in this field and it will also try to bring together geodesists and mathematicians for an interdisciplinary cooperation.

The theory of wavelets is now well established and mature, so that applied scientists can enter into the field and try to develop practical applications; on the other hand, it is also young enough to leave room for significant and original developments and to demand the interdisciplinary cooperation mentioned above.

Other topics strictly related to the theory of wavelets, such as multiresolution analysis and local Fourier transform, will also be of interest for the SSG.

**II- Program of Activities**

The following is a non-exhaustive list of research topics for the SSG; the list focuses on applications rather than on mathematical tools :

- analysis and reduction of geodetic and geophysical signals (e.g. gravimetric, seismic and earth rotation signals, photogrammetric and other images)

- data compression for efficient storage in geodetic data bank and GIS

- fast computation of linear operators in planar and in higher order approximation (e.g.: Stokes' integral)

- fast computation of the terrain effect

- harmonic continuation

- numerical solution of geodetic BVP's

- local and regional multiresolution gravity models

- global multiresolution gravity models (spherical wavelets)

- inverse modelling and regularization

- management of digital elevation models.

Some applications can be based on results already available in the theory of wavelets and require mainly an effort for the implementation of the software. Other applications will require more mathematical research.

**III -** **Membership**

*Members :*

L. Battha (Hungary)

B. Benciolini (Italy) - Chairman

G. Beylkin (USA)

J.A.R. Blais (Canada)

B.F. Chao (USA)

F. Collin (Belgium)

W. Freeden (Germany)

E.W. Grafarend (Germany)

V. Kunitsyn (Russia)

R. Lehmann (Germany)

Z. Li (Canada)

E.C. Pavlis (USA)

F. Sacerdote (Italy)

B. Schaffrin (USA)

M. Schmidt (Germany)

P. Schroeder (USA)

G. Strykowsky (Denmark)

W. Sweldens (USA)

J. Zavoti (Hungary)

H. Sünkel (Austria)

*Correponding Members :*

J. Adàm (Hungary)

D. Arabelos (Greece)

L. Ballani (Germany)

R. Barzaghi (Italy)

S. Bertoluzza (Italy)

R. Coifman (USA)

I. Colomina (Spain)

H. Denker (Germany)

J.O. Dickey (USA)

A. Geiger (Switzerland)

R. Hanssen (The Netherlands)

G.W. Hein (Germany)

B. Hofmann-Wellenhof (Austria)

W. Keller (Germany)

R. Klees (The Netherlands)

A. Marchenko (Ukraine)

W. Ming (Canada)

L. Montefusco (Italy)

C. Seegraef (Germany)

D. Sguerso (Italy)

L. Shumaker (USA)

H. van Gysen (South Africa)

**Special Study Group 4.170**

**Integrated Inverse Gravity Modelling**

Chairman : **L. Ballani** (Germany)

**I -** **Terms of Reference**

Considering the ill-posedness of the inverse gravimetric problem, the interpretation of gravity data becomes considerably more effective if it includes data from fields associated with other sources and phenomena. The possibility of joint inversions becomes more relevant with the availability of more input data of different fields and their improved resolution and accuracy. Another motivation to study the integrated inverse gravity modelling in detail comes from today's intensive investigation of geodynamic effects. In addition to the classical and important joint inversion of gravity and seismic data, new combinations appear: Gravity data are successfully inverted jointly with stress and strain data, with magnetic and heat flow data, and also coupled to kinematic and rheologic information. The modelled structures under investigation vary widely in dimension, shape and depth, and in scale. A broad spectrum of mathematical and physical models is employed connected with a diversity of solving algorithms for the inversion procedure. The methods are of deterministic and stochastic type or embedded in the frames of information theory and artificial intelligence.

**II - Program of Activities**

- Studies of the non-uniqueness (null space, inclusion of constraints, decomposition, approximation) and the instability (regularization procedures) in the inversion of potential fields, tests of different algorithms and their application to synthetic and measured data

- Study of the properties of different types of joint inversion (gravity data combined with other types of data) with respect to their implementation and the evaluation of the results

- Dependence of inversion procedures on the investigated structures (dimension, regional or global extension, layers, boundaries, depths, shape of the disturbing body, density model, etc.) and on the properties and the combination of the data

- Comparative calculations using different procedures and standard data sets

- Organization of special meetings, exchange of data and information and final publication integrating and reviewing the different aspects of the topic and the numerical results in special issue or monograph form

**III -** **Membership**

*Members*

U. Achauer (France)

L. Ballani (Germany) - Chairman

R. Barzaghi (Italy)

O. Cadèk (Czech Republic)

V.N. Glaznev (Russia)

R. Lehmann (Germany)

Z. Martinec (Czech Republic)

V.O. Mikhailov (Russia)

K. Mosegaard (Denmark)

I. Nakanishi (Japan)

M.K. Sen (USA)

P. Smilde (Germany)

D. Stromeyer (Germany)

G. Strykowski (Denmark)

G. Toth (Hungary)

I. Tziavos (Greece)

Q. Wang (P.R. China)

T. Yegorova (The Ukraine)

H. Zeyen (Sweden)

S. Zhao (P.R. China)

*Associate Members*

A. Buyanov (Russia)

A. Geiger (Switzerland)

E.E. Klingele (Switzerland)

H. Hyvalovàa; (Czech Republic)

O. Legostaeva (The Ukraine)

H. Mikada (Japan)

A. Raevsky (Russia)

U. Schäfer (Germany)

V.N. Starostenko (Ukraine)

V.N. Strakhov (Russia)

D.W. Vasco (USA)

**Special Study Group 4.171**

**Dynamic Isostasy**

Chairman : **L.E. Sjöberg** (Sweden)

1. **Objectives**

It is well known that the classical isostatic models of Airy and Pratt do not generally fit the geoid over large portions of the Earth. Major parts of the long geoid waves are better explained by density variations in the Earth's mantle and by its core/mantle topography variations.

Isostasy may be understood in the terms of mass conservation, minimization of strain energy and mechanical equilibrium. Isostatic equilibrium may be the contribution of various mechanisms, such as crustal thickening/ thinning, thermal expansion of mantle density, postglacial rebound and plate flexure. Dynamic compensation, as opposed to static compensation, may be assigned to these latter effects.

2. **Activities**

It is the task of the group to study the dynamic effects of isostasy and to improve current isostatic models to better fit the geoid, e.g. as determined from high precision Earth gravity models.

3. **Members **

L.M. Asfaw (Ethiopia)

A. Cazenave (France)

K. Colic (Croatia)

J. Engels (Germany)

E.W. Grafarend (Germany)

B. Hager (USA)

B. Heck (Germany)

K. Heki (Japan)

X. Li (P.R. China)

Z. Martinec (Czeck Republic)

J. Mitrovica (Canada)

R. Sabadini (Italy)

L.E. Sjöberg (Sweden) - Chairman

G. Spada (Italy)

P. Vanicek (Canada)

D. Wolf (Germany)

S. Zhao (P.R. China)

*Corresponding Member :*

F. Sansò (Italy)

**Special Study Group 4.176 **

**Temporal Variations **

**of the Gravity Field**

Chairman : **D. Wolf** (Germany)

**I- Terms of References**

Recent advances in observational techniques have revealed temporal gravity variations of wide-ranging characteristic periods. Their time dependence has been related to different types of processes acting both near the Earth's surface and in its interior.

Quantitative predictions of the gravity variations require the development of dynamic Earth models.

**II- Program Of Activities**

- Classification of atmospheric, cryospheric, hydrospheric and solid-Earth processes responsible for gravity variations according to source type

- Study of conventional Love-number formalism for elementary sources (i.e. volume forces, normal and tangential surface forces)

- Development of generalized Love-number formalism for complex sources (i.e. dislocations)

- Development of generalized Love-number formalism for periodic sources (Fourier-transformed Love numbers) and aperiodic sources (Laplace-transformed Love numbers)

- Development of asymptotic approximations for large degrees and orders

- Development of viscoelastic Earth models for prediction of gravity variations

- Study of effects due to density stratification, compressibility, lateral heterogeneity, phase boundaries and rheology in mantle and core

- Prediction of gravity variations caused by atmospheric, cryospheric, hydrospheric and solid-Earth processes

**III- List of Members**

V. Dehant (Belgium)

M. Ekman (Sweden)

J. Engels (Germany)

J. Fernandez (Spain)

E.W. Grafarend (Germany)

P. Johnston (Australia)

X. Li (China)

J.B. Merriam (Canada)

J.X. Mitrovica (Canada)

S. Okubo (Japan)

L.E. Sjöberg (Sweden)

G. Spada (Italy)

L. Svensson (Sweden)

B. Vermeersen (Italy)

H.-G. Wenzel (Germany)

D. Wolf (Germany)-Chairman

*Corresponding Member*

W. Zürn (Germany)