A new class of stratified viscoelastic models by analytical techniques

Abstract

S U M M A R YMultilayer, spherically stratified, self-gravitating relaxation models with a'large number of layers (more than 100) can be dealt with analytically. Relaxatio processes are process of a realistic earth model with an incompressible Maxwell r'heology show that models containing about 30 to 40 layers have reached continuum limits on all timescales and for all harmonic degrees up to at least 150 whenever an elastic lithosphere is present, irrespective of the viscosity profile in the mantle. In particular, fine-graded stratification of the shallow layers proves to be important for high harmonic degrees in these models. The models produce correct long-time (fluid) limits. It is shown that differences in the transient behaviour of the various models are due to the applied volume-averaging procedure of the rheological parameters. Our earlier proposed hypothesis that purported shortcomings in the fundamental physics of (discrete) normalmode theory are artificial consequences of numerical inaccuracies, theoretical misinterpretations and the use of incomplete sets of normal modes is reinforced by the results presented. We show explicitly that the models produce both continuous behaviour resulting from continuous rheological stratifications and discrete behaviour resulting from sharp density contrasts, as at the outer surface and the core-mantle boundary. The differences between volume-averaged models and fixed-boundary contrast models are outlined. Reducing many-layer models with a volume-averaging procedure before employing a normal mode analysis is both economical and highly accurate on all timescales and for all spherical harmonic degrees. The procedure minimizes the chances of missing contributing modes, while using models with more layers will not result in any substantial increase of accuracy.

Glacial isostatic adjustment in the static gravity field of Fennoscandia

“…The GIA model is based on the normal mode method ] for a multilayer model [Vermeersen and Sabadini, 1997] with self-consistent sea levels [Mitrovica and Peltier, 1991]. Details are given in van der Wal et al [2009].…”

Ocean contribution to seismic gravity changes: the sea level equation for seismic perturbations revisited

“…For that reason the largest influence of being able to distinguish between marine and terrestrial areas is expected for the 2010 Maule earthquake, for which reason we take this earthquake as a case study. Solid Earth deformation and gravity potential changes have been computed by the analytical normal mode method (Vermeersen & Sabadini 1997;Sabadini & Vermeersen 2004) which treats the Earth as a radially stratified, compressible and self-gravitating spherical body. Earth properties are derived from PREM (Dziewonski & Anderson 1981), and are listed in Table S1.…”

The European Gravity Field and Steady-State Ocean Circulation Explorer Satellite Mission: Its Impact on Geophysics

“…These two cases are chosen in such a way as to compare the potential contributions of GRACE and GOCE on the interpretation of the GIA data. The results are based on a 31-layer Earth viscoelastic model (Vermeersen and Sabadini, 1997), while the loading history is based on the ICE-3G ice model (Tushingam and Peltier, 1991). The lithospheric thickness is 120 km, while the viscosity in the lower mantle is kept fixed at 10 21 Pa s (Pascal second).…”