The implementation of the sea-level equation (SLE) describing the redistribution of melt water in the oceans is complicated in conjunction with the Laplace-transform method conventionally used to model glacial-isostatic adjustment (GIA). The recently developed spectral finite-element method (Martinec, 2000) solves the field equations governing GIA in the time domain and, thus, eliminates the need of applying the Laplace-transform method. Moreover, the spectral finite-element approach allows us to solve the SLE when modeling GIA for a 3-D self-gravitating, incompressible, viscoelastic earth model. Using the MacCullagh formula, we solve the linearized Liouville equation for the variation of earth rotation (VER) and the incremental centrifugal potential, which also enters into the SLE. The present calculations are restricted to radially symmetric viscosity models consisting of a fluid core, a Maxwell-viscoelastic lower and upper mantle and an elastic lithosphere.
Moreover we investigate the influence of model input. Using three viscosity stratifications and three different ice models we compare the calculated results to demonstrate the sensitivity to this input. Additional we test the influence of the approximation of the ocean description and the VER on present rate of sea-level rise due to GIA.
We present applications like prediction of global geoid rise, reduction of tide-gauge data and predictions of radial velocities at Canadian GPS stations. With this selection of application we demonstrate the method of tide-gauge data reduction and also we show possibilities to qualify earth/ice model input for this duty in the future.
References:
Martinec, Z., 2000. Spectral-finite element approach to three-dimensional viscoelastic relaxation in a spherical earth. Geophys. J. Int., 142, 117-141.