Visual Computing of Global Postglacial Rebound in a Spherical Domain

1. Visual Computing of Global Postglacial Rebound in a Spherical Domain Ladislav Hanyk1, Ctirad Matyska1 and David A. Yuen2 e-mail: ladislav.hanyk@mff.cuni.cz, www: http://geo.mff.cuni.cz/~lh 1 Department of Geophysics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic 2 University of Minnesota Supercomputing Institute and Department of Geology and Geophysics, Minneapolis • OBJECTIVE • visual tour of postglacial rebound processes • PHYSICAL MODEL • a pre-stressed self-gravitating spherical Earth • Maxwell viscoelastic rheology • arbitrary parameter stratification • both compressible and incompressible models • cyclic loading and unloading • MATHEMATICAL MODEL • initial value approach (no Laplace transform) [1,2] • momentum equation, Poisson equation, constitutive relation • spherical harmonic decomposition • set of differential equations in time and radial direction [4,5] • pseudospectral discretization in the radial direction • on multi-domain Chebyshev radial grids [4,5] • numerically stiff initial value problem • inversion of sparse (block diagonal) matrices • OUTPUT • time-dependent Love numbers • physical fields: displacement vector • perturbed gravitational potential • stress tensor components • VISUALIZATION HARDWARE • Intel Pentium IV 2 GHz • RIMM 512 MB 800 MHz • nVIDIA GeForce4 MX 440 64 MB graphics card • VISUALIZATION SOFTWARE • Amira v. 2.3 • visualization of scalar and vector fields in 3-D space and time • extensive set of input data formats • easy color scaling, zooming and adjusting the view direction • movies preparation capability • scripting language • DATA PREPARATION • time series of binary Amira Mesh files • with curvilinear coordinates and line segments • generated by a fast Fortran-90 code • a coordinate mesh deformed by exaggerated displacement • color rendering of the physical fields • hollow data objects allow to spare a degree of freedom • in the data format for handling many various models • with an interactive speed • MOVIES ON THE WEB • http://www.msi.umn.edu/~lilli … links to larry_movies • http://geo.mff.cuni.cz/~lh … links to references • REFERENCES • [1] Hanyk L., Yuen D. A. and Matyska C., 1996. Initial-value and modal approaches for transient viscoelastic responses with complex viscosity profiles, Geophys. J. Int., 127, 348-362. • [2] Hanyk L., Matyska C. and Yuen D. A., 1998. Initial-value approach for viscoelastic responses of the Earth's mantle, in Dynamics of the Ice Age Earth: • A Modern Perspective, ed. by P. Wu, Trans Tech Publ., Switzerland, pp. 135-154 • [3] Hanyk L., Matyska C. and Yuen D. A., 1999. Secular gravitational instability • of a compressible viscoelastic sphere, Geophys. Res. Lett., 26, 557-560. • [4] Hanyk L., Matyska C. and Yuen D.A., 2000. The problem of viscoelastic relaxation of the Earth solved by a matrix eigenvalue approach based on discretization in grid space, Electronic Geosciences, 5,http://link.springer.de/link/service/journals/10069/free/discussion/evmol/evmol.htm. • [5] Hanyk L., Matyska C. and Yuen D.A., 2002. Determination of viscoelastic spectra by matrix eigenvalue analysis, in Ice Sheets, Sea Level and the Dynamic Earth, ed. by J. X. Mitrovica and B. L. A. Vermeersen, Geodynamics Research Series Volume, American Geophysical Union, pp. 257-273. ICE LOADING HISTORY BY ICE-4G APPROXIMATION OF THE LOADING HISTORY height 0 90 100 150 0 kyr time [kyr] 90 kyr loading phase 10 kyr unloading phase 50 kyr free decay 90 kyr radius 15 max. height 3500 m 21 kyr B.P. 8 kyr B.P. present HOMOGENEOUS SPHERE INCOMPRESSIBLE COMPRESSIBLE CORE - MANTLE - LITHOSPHERE INCOMPRESSIBLE 100 kyr Displacement: red - down or from the axis blue - up or towards the axis exaggerated by a factor - of 100 vertically - of 500 horizontally horiz. displacement vertical displacement horiz. displacement vertical displacement 20 kyr 50 kyr 80 kyr simple responses of homogeneous incompressible models a fast collapse of homogeneous compressible models onset of the gravitational instability of the homogeneous compressible sphere on the time scale of 104 yr [3] 90 kyr 100 kyr 150 kyr 90 kyr 100 kyr 150 kyr PREM-BASED MODELS non-monotonic depth-dependence of the vertical displacement in realistic models opposite signs of the surface horizontal displacement beneath the load in the compressible case large horizontal deformations in the low-viscosity zone INCOMPRESSIBLE - isoviscous 1021 Pa s - 120-km lithosphere COMPRESSIBLE - isoviscous 1021 Pa s - 120-km lithosphere COMPRESSIBLE - lower mantle 2.1022 Pas - LVZ 1019 Pas - lithosphere horiz. displacement vertical displacement horiz. displacement vertical displacement horiz. displacement vertical displacement 90 kyr 100 kyr 150 kyr 90 kyr 100 kyr 150 kyr 90 kyr 100 kyr 150 kyr