SSG 4.189 DYNAMIC THEORIES OF DEFORMATION AND GRAVITY FIELDS

Detlef Wolf, GeoForschungsZentrum Potsdam, Germany

1. Scientific program

SSG 4.189 `Dynamic theories of deformation and gravity fields' was established in response to the continuing need to develop improved dynamical models for the interpretation of time-dependent deformation and gravity fields as better data become available from GPS, VLBI and absolute gravity measurements or are expected from the satellite gravity missions CHAMP and GRACE. Whereas the development of improved theoretical models for the different types of forcing responsible for the deformation and gravity fields is defined as the principal activity of SSG 4.189, a substantial portion of its research during the period 1999-2001 also involved the application of existing theory.

2. Regular members

H. Abd-Elmotaal (University of Minia, Egypt)

J.-P. Boy (Louis Pasteur University, France)

V. Dehant (Royal Observatory of Belgium, Belgium)

R. Eanes (University of Texas, USA)

J. Engels (University of Stuttgart, Germany)

J. Fernández (Ciudad University, Spain)

G. Kaufmann (University of Göttingen, Germany)

Z. Martinec (Charles University, Czech Rebublic)

G. Milne (University of Durham, UK)

H.-P. Plag (Norwegian Mapping Authority, Norway)

G. Spada (University of Urbino, Italy)

W. Sun (University of Tokyo, Japan)

P. Varga (Geodetic and Geophysical Research Institute, Hungary)

K. Wieczerkowski (GeoForschungsZentrum, Potsdam, Germany)

D. Wolf (GeoForschungsZentrum Potsdam, Germany)

P. Wu (University of Calgary, Canada)

3. Associate members

P. Gegout (Louis Pasteur University, France)

E. Grafarend (University of Stuttgart, Germany)

J. Hinderer (Louis Pasteur University, France)

L. Sjöberg (Royal Institute of Technology, Sweden)

4. Scientific results

4.1. Fundamental theory

Sun and Sjöberg (1999a) revisited the classical problem of surface loading of a radially symmetric elastic body and studied the radial dependence of the load Love numbers and the Green functions for displacement, potential and gravity perturbations. Grafarend (2000) computed the gravity field of an arbitrary deformable body under the assumption that the topographic surface, the interfaces and the internal mass distribution vary over time. Grafarend et al. (2000) studied the relationship between the incremental Cartesian moments of the mass density, the incremental moments of inertia and the incremental gravitational potential coefficients for an arbitrary deformable body. As excitation, they considered tidal forcing, normal and tangential surface forcings and rotational variations. Dehant et al. (1999) calculated tidal Love numbers for rotating aspherical earth models. In addition to elastic earth models, they also investigated effects caused by assuming an inelastic convecting mantle.

In two papers, the problem of load-induced, viscoelastic perturbations of a compressible earth initially in hydrostatic equilibrium was considered. Whereas Wolf and Kaufmann (2000) were concerned with the plane-earth approximation of the problem, Martinec et al. (2001) considered the generalized problem for a spherical earth consisting of compositionally homogeneous shells. The density stratification was given by Darwin's law, which can be shown to satisfy the field equations governing the initial state. In another study, a systematic comparison between the solutions for load-induced perturbations of spherical, incompressible earth models with Maxwell or Burgers rheology was carried out (Göbell et al., 1999).

Attempts were also made to obtain solutions of the field equations for 2-D and 3-D incompressible viscoelastic earth models. Whereas Kaufmann and Wolf (1999) obtained an approximate analytical solution for a 2-D plane earth, Martinec and Wolf (1999) derived the exact analytical solution for two axially nested spheres. The analytical solutions are required to test more general numerical solutions for arbitrary 2-D or 3-D viscoelastic earth models (Martinec, 1999, 2000).

4.2. Glacial loading

Th oma and Wolf (1999) interpreted a subset of the glacial-isostatic adjustment data available for Fennoscandia in terms of 1-D earth models and proposed improved bounds for the viscosity stratification. An alternative approach was followed by Wieczerkowski et al. (1999), who employed formal inverse theory to infer the viscosity stratification below Fennoscandia. More recently, Milne et al. (2001) considered GPS data from Fennoscandia. They showed that lithosphere thicknesses and asthenospere viscosities inferred from this type of data are consistent with those obtained using relative sea-level data. Kaufmann and Amelung (2000) used subsidence data from the artifical Lake Mead, Nevada, to infer the viscosity stratification in this region and found very low viscosity values. Thoma and Wolf (2001) interpreted land uplift induced by the recent melting of the Vatnajökull ice cap, Iceland, and found anomalously low values for the lithosphere thickness and asthenosphere viscosity in this region. Kaufmann and Lambeck (2000) interpreted convectively supported geoid perturbations as well as glacially induced changes of sea level, rotation and the gravity field and inferred global average values of the upper- and lower-mantle viscosities.

Wu (1999) raised the question of whether relative sea-level changes in Hudson Bay and along the Atlantic coast of North America can also be explained in terms of the glacial-isostatic adjustment of a flat earth with non-Newtonian rheology. His results show that reconciling all sea-level data is difficult for non-Newtonian rheologies. Subsequently, Wu (2001) incorporated tectonic stress and found that this modification makes the assumption of a non-Newtonian rheology more reasonable. Giunchi and Spada (2000) developed a spherical earth model with non-Newtonian rheology and concluded that, in this case, the long-wavelength signatures of glacial-isostatic adjustment become largely insensitive to the viscosity of the lower mantle.

Wu et al. (1999) discussed the question of whether deglaciation-induced stresses are sufficiently strong to have triggered paleo-earthquakes in Fennoscandia. They found that glacial-isostatic adjustment is probably the cause of the large postglacial faults observed but is unlikely to be responsible for the current seismicity in this region. Wu and Johnston (2000) studied a similar problem for North America and concluded that stresses are sufficiently strong for triggering earthquakes at locations not too far from the former ice-sheet margin. Klemann and Wolf (1999) investigated the consequences of a ductile layer inside an otherwise elastic lithosphere for glacial-isostatic adjustment. Their results show that the stress pattern is significantly affected by the presence of a ductile layer.

Milne et al. (1999) developed an improved method of accounting for the influx of ocean water to once ice-covered marine regions after melting and analyzed the implications of this effect for the interpretation of glacial-isostatic adjustment. Kaufmann (2000) predicted glacially induced variations of the gravity field due to Late-Pleistocene and present-day changes in glaciation and discussed the question of their detectability by the satellite missions CHAMP and GRACE.

Kaufmann et al. (2000) revisited the issue of glacial-isostatic adjustment in Fennoscandia. In particular, they investigated whether lateral variations in lithosphere thickness and viscosity may be resolved from the observational record. Their results show that predictions of relative sea level, uplift rates and gravity anomalies differ significantly if lateral variations are taken into account.

4.3. Surface, internal and tidal loading

Abd-Elmotaal (1999a) calculated Moho depths for a test area in Austria using the Vening Meinesz and the Airy-Heiskanen isostatic models and compared the results with seismic Moho depths. Abd-Elmotaal (1999b, 2000) reviewed the inverse Vening Meinesz isostatic problem defined as finding the Moho depth for which the isostatic gravity anomalies become zero. Sun and Sjöberg (1999b) calculated global geoid perturbations on the assumption that the topographic loads are compensated by elastic deformation only. They found positive correlations between the calculated and observed perturbations, although large differences remained for long wavelengths due to the neglect of dynamic processes. Dehant et al. (2000) computed the response of Mars to nutational, tidal and loading excitation and studied the influence of the planet's assumed material properties on its response. Arnoso et al. (2001) analyzed tidal gravity observations from Lanzarote, Canary Islands, and discussed whether they can be used to resolve structural details of the upper crust below the island. Neumeyer et al. (1999) and Hagedoorn et al. (2000) investigated the total atmospheric contribution to gravity perturbations using an elastic earth model. They found that their results are superior to those obtained by simply using empirical relationships between pressure and gravity changes.

4.4. Seismo-volcanic forcing

Nostro et al. (1999) compared spherical and flat earth models for computing co- and postseismic deformations in order to assess in which cases the neglect of sphericity and self-gravitation is justified. In a related study, Boschi et al. (2000) calculated the global deformation caused by a shear dislocation located in the mantle. Important points of their study were the consideration of sources below the lithosphere and effects due the presence of a low-viscosity asthenosphere. Folch et al. (2000) considered the viscoelastic deformation caused by an inflated magma chamber and investigated the errors introduced by neglecting the finite dimension of the chamber or the topography of the region. In a related study, Fernández et al. (2001) interpreted deformation and gravity change data from Long Valley Caldera, California. They showed that incorrect interpretations may result if only one type of data is used.

5. Other activities

The research carried out in SSG 4.189 was reported by several of its members and invited guests during the 7th International Winter Seminar on Geodynamics on `Viscoelastic Theories in Geodynamics' held in Sopron, Hungary, February 19-23, 2001. The meeting was financially supported by the Hungarian Academy of Science.

6. Selected publications of members: 1999-2001

Abd-Elmotaal, H., 1999a.
Inverse Vening Meinesz isostatic problem: theory and practice.
Boll. Geod. Sci. Aff., 58, 53-70.

Abd-Elmotaal, H., 1999b.
Moho depths versus gravity anomalies.
Surv. Rev., 35, 175-186.

Abd-Elmotaal, H., 2000.
Vening Meinesz inverse isostatic problem with local and global Bouguer anomalies.
J. Geod., 74, 390-398.

Arnoso, J., Fernández, J., Vieira, R., 2001.
Interpretation of tidal gravity anomalies in Lanzarote, Canary Islands.
J. Geodyn., 31, 341-354.

Boschi, L., Piersanti, A., Spada, G., 2000.
Global postseismic deformation: deep earthquakes,
J. Geophys. Res., 105, 631-652.

Dehant, V., Defraigne, P., Wahr, J.M., 1999.
Tides for a convective earth.
J. Geophys. Res., 104, 1035-1058.

Dehant V., Defraigne P., Van Hoolst T., 2000.
Computation of Mars' transfer function for nutation tides and surface loading.
Phys. Earth Planet. Inter., 117, 385-395.

Fernández, J., Charco, M., Tiampo, K. F., Jentzsch, G., Rundle, J. B., 2001.
Joint interpretation of displacements and gravity changes in volcanic
areas. A test example: Long Valley Caldera, California.
Geophys. Res. Lett., 28, 1063-1066.

Folch, A., Fernández, J., Rundle, J.B., Martí, J., 2000.
Ground deformation in a viscoelastic medium composed of a layer
overlying a half space. A comparison between point and extended sources.
Geophys. J. Int., 140, 37-50.

Giunchi, C., Spada, G., 2000.
Postglacial rebound in a non-Newtonian spherical earth.
Geophys. Res. Lett., 27, 2065-2068.

Göbell, S., Thoma, M., Wolf, D., Grafarend, E.W., 1999.
Berechnung auflastinduzierter Vertikalverschiebungen, Geoidhöhen und
Freiluft-Schwereanomalien für ein selbstgravitierendes, sphärisches Erdmodell
und unterschiedliche Rheologien.
Sci. Techn. Rep. GFZ Potsdam, STR99/24, 76 pp.

Grafarend, E.W., 2000.
The time-varying gravitational potential field of a massive, deformable body.
Stud. Geophys. Geod., 44, 364-373

Grafarend, E.W., Engels, J., Varga, P., 2000.
The temporal variation of the spherical and Cartesian multipoles of the
gravity field: the generalized MacCullagh representation.
J. Geod., 74, 519-530.

Hagedoorn, J.M., Wolf, D., Neumeyer, J., 2000.
Modellierung von atmosphärischen Einflüssen auf hochgenaue Schweremessungen
mit Hilfe elastischer Erdmodelle.
Sci. Techn. Rep. GFZ Potsdam, STR00/15, 87 pp.

Kaufmann, G., 2000.

Ice-ocean mass balance during the Late Pleistocene glacial cycles in view
of CHAMP and GRACE satellite missions.
Geophys. J. Int., 143, 142-156.

Kaufmann, G., Amelung, F., 2000.
Reservoir-induced deformation and continental rheology in vicinity of Lake Mead, Nevada.
J. Geophys. Res., 105, 16341-16358.

Kaufmann, G., Lambeck, K., 2000.
Mantle dynamics, postglacial rebound and the radial viscosity profile.
Phys. Earth Planet. Inter., 121, 301-327.

Kaufmann, G., Wolf, D., 1999.
Effects of lateral viscosity variations on postglacial rebound: an analytical approach.
Geophys. J. Int., 137, 489-500.

Kaufmann, G., Wu, P., Li, G., 2000.
Glacial isostatic adjustment in Fennoscandia for a laterally heterogeneous earth.
Geophys. J. Int., 143, 262-273.

Klemann, V., Wolf, D., 1999.
Implications of a ductile crustal layer for the deformation caused by the Fennoscandian ice sheet.
Geophys. J. Int., 139, 216-226.

Martinec, Z., 1999.
Spectral, initial value approach for viscoelastic relaxation of a spherical earth
with a three-dimensional viscosity - I. Theory.
Geophys. J. Int., 137, 469-488.

Martinec, Z., 2000.
Spectral-finite element approach to three-dimensional viscoelastic
relaxation in a spherical earth.
Geophys. J. Int., 142, 117-141.

Martinec, Z., Wolf, D., 1999.
Gravitational viscoelastic relaxation of eccentrically nested spheres.
Geophys. J. Int., 138, 45-66.

Martinec, Z., Thoma, M., Wolf, D., 2000.
Material versus local incompressibility and its influence on glacial-isostatic adjustment.
Geophys. J. Int., 143, 1-25.

Milne, G.A., Mitrovica, J.X., Davis, J.L., 1999.
Near-field hydro-isostasy: the implementation of a revised sea-level equation.
Geophys. J. Int., 139, 464 -483.

Milne, G.A., Davis, J.L., Mitrovica, J.X., Scherneck, H.-G., Johansson, J.M.,
Vermeer, M., Koivula, H., 2001.
Space-geodetic constraints on glacial isostatic adjustment in Fennoscandia.
Science, 291, 2381-2385.

Neumeyer, J., Barthelmes, F., Wolf, D., 1999.
Estimates of environmental effects in superconducting gravimeter data,
Bull. Inf. Mare 'es Terr., 131, 10153-10159.

Nostro, C., Piersanti, A., Antonioli, A., Spada, G., 1999.
Spherical versus flat models of coseismic and postseismic deformations.
J. Geophys. Res., 104, 13115-13134.

Sun, W., Sjöberg, L.E., 1999a.
Gravitational potential changes of a spherically symmetric earth model
caused by a surface load.
Geophys. J. Int., 137, 449-468.

Sun, W., Sjöberg, L.E., 1999b.
A new global topographic-isostatic model.
Phys. Chem. Earth, 24, 27-32.

Thoma, M., Wolf, D., 1999.
Bestimmung der Mantelviskosität aus Beobachtungen der Landhebung und Schwere in Fennoskandien,
Sci. Techn. Rep. GFZ Potsdam, STR99/02, 101 pp.

Thoma, M., Wolf, D., 2001.
Inverting land uplift near Vatnajökull, Iceland, in terms of lithosphere
thickness and viscosity stratification.
in: Gravity, Geoid and Geodynamics 2000, Springer, Berlin, in press.

Wieczerkowski, K., Mitrovica, J., Wolf, D., 1999.
A revised relaxation-time spectrum for Fennoscandia,
Geophys. J. Int., 139, 69-86.

Wolf, D., Kaufmann, G., 2000.
Effects due to compressional and compositional density stratification on
load-induced Maxwell-viscoelastic perturbation.
Geophys. J. Int., 140, 51-62.

Wu, P., 1999.
Modeling postglacial sea-levels with power law rheology and realistic
ice model in the absence of ambient tectonic stress.
Geophys. J. Int., 139, 691-702.

Wu, P., 2001.
Postglacial induced surface motion and gravity in Laurentia for uniform mantle
with power-law rheology and ambient tectonic stress.
Earth Planet. Sci. Lett., 186, 427-435.

Wu, P., Johnston, P., 2000.
Can deglaciation trigger earthquakes in N. America?
Geophys. Res. Lett., 27, 1323-1326.

Wu, P., Johnston, P., Lambeck, K., 1999.
Postglacial rebound and fault instability in Fennoscandia.
Geophys. J. Int., 139, 657-670.