Abstract
We describe the implementation of the complete Sea Level Equation (SLE) in a Finite Element (FE) self-gravitating 3D model. The procedure, originally proposed by Wu (2004), consists of iterating the solution of the SLE starting from a non self-gravitating model. At each iteration, the perturbation to the gravitational potential due to the deformation at the density interfaces is determined, and the boundary conditions for the following iteration are modified accordingly. We implemented the computation of the additional loads corresponding to the perturbations induced by glacial and oceanic forcings at the same iteration at which such forcings are applied. This implies an acceleration of the convergence of the iterative process that occurs actually in three to four iterations so that the complete procedure, for a 6,800 elements FE grid, can be run in about two hours of computing time, on a four-core 2.2 Linux workstation. This spherical and self-gravitating FE model can be employed to simulate the deformation of the Earth induced by any kind of load (non necessarily of glacial origin) acting on the surface and/or internally.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Dal Forno G, Gasperini P, Boschi E (2005) Linear or non-linear rheology in the mantle: a 3D finite-element approach to postglacial rebound modeling. J Geodyn 39:183–195
Dal Forno G, Gasperini P (2007) Modelling of mantle postglacial relaxation in axisymmetric geometry with a composite rheology and a glacial load interpolated by adjusted spherical harmonics analysis. Geophys J Int 169:1301–1314
Farrell WE, Clark JA (1976) On postglacial sea level. Geophys J R Astron Soc 46:647–667
Gasperini P, Sabadini R (1989) Lateral heterogeneities in mantle viscosity and postglacial rebound. Geophys J 98: 413–428
Gasperini P, Yuen D, Sabadini R (1992) Postglacial rebound with a non-Newtonian upper mantle and a Newtonian lower mantle rheology. Geophys Res Lett 19:1711–1714
Gasperini P, Dal Forno G, Boschi E (2004) Linear or non-linear rheology in the Earth’s mantle: the prevalence of power-law creep in the postglacial isostatic readjustment of Laurentia. Geophys J Int 157:1297–1302
Giunchi C, Spada G (2000) Postglacial rebound in a non-newtonian spherical Earth. Geophys Res Lett 27: 2065–2068
Kaufmann G, Wu P, Wolf D (1997) Some effectes of lateral heterogeneities in the upper mantle on postglacial land uplift close to continental margins. Geophys J Int 128:175–187
Kaufmann G, Wu P, Li G (2000) Glacial isostatic adjustment in Fennoscandia for a laterally heterogeneous earth. Geophys J Int 143:262–273
Paulson A, Zhong S, Wahr J (2005) Modelling post-glacial rebound with lateral viscosity variations. Geophys J Int 163:357–371
Peltier WR (1974) The impulse response of a Maxwell earth. Rev Geophys Space Phys 12:649–669
Simulia Inc (2009) ABAQUS Version 6.7 User’s Manual, Providence, RI
Spada G, Antonioli A, Cianetti S, Giunchi C (2006) Glacial isostatic adjustment and relative sea-level changes: the role of lithospheric and upper mantle heterogeneities in a 3-D spherical Earth. Geophys J Int 165:692–702
Spada G, Stocchi P (2007) SELEN: a Fortran 90 program for solving the “sea-level equation”. Comp Geosc 33: 538–562
Tegmark, M. (1996) An icosahedron-based method for pixelizing the celestial sphere. ApJ Lett 470:L81
Wieczorek M (2005) SHTOOLS conventions. accessed on 13 October 2011, http://www.ipgp.fr/~wieczor/SHTOOLS/www/conventions
Williams CA, Richardson RM (1991) A rheologically layered three-dimensional model of the San Andreas fault in central and southern California. J Geophys Res 96:16, 597–16, 623
Wu P (1992) Deformation of an incompressible viscoelastic flat earth with power law creep: a finite element approach. Geophys J Int 108:136–142
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 (2004) Using commercial finite element packages for the study of earth deformations, sea levels and the state of stress. Geophys J Int 158:401–408
Wu P, Wang H (2008) Postglacial isostatic adjustment in a self-gravitating spherical earth with power-law rheology. J Geodyn 46:118–130
Acknowledgements
G.S. acknowledges COST Action ES0701 “Improved Constraints on Models of Glacial Isostatic Adjustment”.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Forno, G.D., Gasperini, P., Spada, G. (2012). Implementation of the Complete Sea Level Equation in a 3D Finite Elements Scheme: A Validation Study. In: Sneeuw, N., Novák, P., Crespi, M., Sansò, F. (eds) VII Hotine-Marussi Symposium on Mathematical Geodesy. International Association of Geodesy Symposia, vol 137. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22078-4_59
Download citation
DOI: https://doi.org/10.1007/978-3-642-22078-4_59
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22077-7
Online ISBN: 978-3-642-22078-4
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)