Multi-Layer Models

Abstract

Multi-layer, spherically stratified, self-gravitating relaxation models with a large number of layers (more than 100) can be dealt with analytically once the limits posed by the procedures based on standard routines to detect a small number of modes used in several analyses (Spada et al., 1992b; Piersanti et al., 1995) are avoided by means of the bisection algorithm for detecting the modes in the s-domain. In order to let the reader become accustomed with the analytical methodologies in the normal mode approach, relaxation processes are studied in this chapter based on Vermeersen and Sabadini (1997) for both Heaviside surface loads and tidal forcings. Simulations of the relaxation process of a realistic earth model with an incompressible Maxwell rheology 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. Especially 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 transient behavior of the various models are due to the applied volume-averaging procedure of the rheological parameters.