Modeling Earth's post‐glacial rebound

Abstract

Efforts to mathematically model the Earth's post‐glacial rebound, or, in general, long‐term planetary‐scale viscoelastic deformations, have been ongoing for several decades. Unfortunately, research in the post‐glacial rebound community has not been characterized by much exchange of knowledge. Groups around the world have developed their code independently, sometimes with profoundly different approaches, occasionally leading to inconsistent results [e.g., Boschi et al., 1999]. Postglacial Rebound Calculator (TABOO) is a post‐glacial rebound software that is being made freely available (through Samizdat Press at http://samizdat.mines.edu/taboo/) in the hope that it might become a common reference for all post‐glacial rebound researchers. TABOO is portable and has been tested on Unix, Linux, and Windows systems; all it requires is a Fortran90 compiler supporting quadruple precision. The software is easy to use. It comes with a detailed guide that can work as a quick reference cookbook, and it is also accompanied by a textbook, The Theory Behind TABOO, collecting the most significant theoretical results from post‐glacial rebound literature. TABOO is not a “black‐box,” although it may easily be used as such. The entire source code is provided and should be easy to understand for intermediate‐level Fortran programmers.

Using the Post-Widder formula to compute the Earth's viscoelastic Love numbers

“…The results are readily extended to finite-size surface loads (Spada et al 2004). The results are readily extended to finite-size surface loads (Spada et al 2004).…”

“…For an incompressible and self-gravitating earth including an elastic lithosphere and an inviscid fluid core, the secular equation is an algebraic equation of degree M = 4L, where L is the number of distinct mantle viscoelastic layers that characterize the earth model (see Spada et al 2004). For an incompressible and self-gravitating earth including an elastic lithosphere and an inviscid fluid core, the secular equation is an algebraic equation of degree M = 4L, where L is the number of distinct mantle viscoelastic layers that characterize the earth model (see Spada et al 2004).…”

“…(11) (see e. g. Spada et al 2004). We note that in the PWG approach, the computation of Love numbers pertaining to different time histories is straightforward, as it is sufficient to specify f (s) in the Gaver sequence (16); in the normal-mode method, the further step of a time convolution is needed to construct the Love numbers by eq.…”

“…models that consist of many homogeneous layers). Namely, (i) for an incompressible model, the number of roots of the secular equation increases linearly with increasing number of layers (Wu & Ni 1996;Spada et al 2004), while a denumerably infinite number of modes appear even for a homogeneous earth if compressibility is accounted for (Vermeersen et al 1996b); In particular, they have suggested that non-modal contributions simply reflect numerical inaccuracies in the time-domain methods, and that the normal-mode technique indeed allows to compute the response of an earth model whose rheological parameters are effectively continuous with depth (but it remains to be established to what extent a fine stratification is a good analogue for continuous variations with depth).…”

Scatter of mass changes estimates at basin scale for Greenland and Antarctica

“…GIA corrections are based on 5-layered incompressible Earth models without lateral heterogeneities. We compute the solid Earth Green's functions (Love numbers) according to the analytical approach described in the benchmark of Spada et al (2011) with the benchmarked code TABOO (Spada et al, 2004). The sea level equation is solved self-consistently with the pseudo-spectral approach (Mitrovica and Peltier, 1991) implemented in the optimized code TSec01 developed for Barletta andSpada (2011, 2012b) and benchmarked in Spada et al (2012).…”