Visual Computing of Global Postglacial Rebound in a Spherical Domain Ladislav Hanyk 1, Ctirad...
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Visual Computing of Global Postglacial Rebound in a Visual Computing of Global Postglacial Rebound in a Spherical Domain Spherical Domain Ladislav Hanyk 1 , Ctirad Matyska 1 and David A. Yuen 2 e-mail: [email protected], 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 HOMOGENEOUS SPHERE INCOMPRESSIBLE COMPRESSIBLE CORE - MANTLE - LITHOSPHERE INCOMPRESSIBLE horiz. displacement vertical displacement ICE LOADING HISTORY BY ICE-4G APPROXIMATION OF THE LOADING HISTORY INCOMPRESSIBLE - isoviscous 10 21 Pa s - 120-km lithosphere COMPRESSIBLE - isoviscous 10 21 Pa s - 120-km lithosphere COMPRESSIBLE - lower mantle 2.10 22 Pas - LV 10 19 Pas - lithosphere height 0 90 100 150 onset of the gravitational instability of the homogeneous compressible sphere on the time scale of 10 4 yr [3] horiz. displacement vertical displacement 90 kyr loading phase 10 kyr unloading phase 50 kyr free decay 90 kyr 100 kyr 150 kyr 20 kyr 50 kyr 80 kyr horiz. displacement vertical displacement 90 kyr 100 kyr 150 kyr 90 kyr 100 kyr 150 kyr 90 kyr 100 kyr 150 kyr 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 21 kyr B.P. 8 kyr B.P. present 100 kyr 90 kyr PREM-BASED MODELS 90 kyr 100 kyr 150 kyr time [kyr] 0 kyr Displacement: red - down or from the axis blue - up or towards the axis exaggerated by a factor - of 100 vertically - of 500 horizontally radius 15 max. height 3500 m simple responses of homogeneous incompressible models a fast collapse of homogeneous compressible models horiz. displacement vertical displacement horiz. displacement vertical displacement
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Transcript of Visual Computing of Global Postglacial Rebound in a Spherical Domain Ladislav Hanyk 1, Ctirad...
Visual Computing of Global Postglacial Rebound in a Spherical Visual Computing of Global Postglacial Rebound in a Spherical DomainDomainLadislav Hanyk1, Ctirad Matyska1 and David A. Yuen2
e-mail: [email protected], www: http://geo.mff.cuni.cz/~lh1 Department of Geophysics, Faculty of Mathematics and Physics, Charles University, Prague, Czech
Republic2 University of Minnesota Supercomputing Institute and Department of Geology and Geophysics,
MinneapolisOBJECTIVEvisual tour of postglacial rebound processes
PHYSICAL MODELa pre-stressed self-gravitating spherical EarthMaxwell viscoelastic rheologyarbitrary parameter stratificationboth compressible and incompressible modelscyclic loading and unloading
MATHEMATICAL MODELinitial value approach (no Laplace transform) [1,2]momentum equation, Poisson equation, constitutive relationspherical harmonic decompositionset 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 probleminversion of sparse (block diagonal) matrices
OUTPUTtime-dependent Love numbersphysical fields: displacement vector
perturbed gravitational potential stress tensor components
VISUALIZATION HARDWAREIntel Pentium IV 2 GHzRIMM 512 MB 800 MHznVIDIA GeForce4 MX 440 64 MB graphics card
VISUALIZATION SOFTWAREAmira v. 2.3visualization of scalar and vector fields in 3-D space and timeextensive set of input data formatseasy color scaling, zooming and adjusting the view directionmovies preparation capabilityscripting language
DATA PREPARATIONtime series of binary Amira Mesh files with curvilinear coordinates and line segments generated by a fast Fortran-90 codea coordinate mesh deformed by exaggerated displacementcolor rendering of the physical fieldshollow 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 WEBhttp://www.msi.umn.edu/~lilli … links to larry_movieshttp://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.
HOMOGENEOUS SPHEREINCOMPRESSIBLE COMPRESSIBLE
CORE - MANTLE - LITHOSPHEREINCOMPRESSIBLE
hori
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dis
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ICE LOADING HISTORY BY ICE-4G APPROXIMATION OF THE LOADING HISTORY
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
heig
ht
0 90 100 150
onset of the gravitational instability of the homogeneous compressible
sphereon the time scale of 104 yr [3] h
ori
z. d
ispla
cem
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t
vert
ical
dis
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90 kyr loading phase10 kyr unloading phase50 kyr free decay
90 kyr 100 kyr 150 kyr
20 kyr 50 kyr 80 kyr
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isp
lace
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vert
ical
dis
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90 kyr 100 kyr 150 kyr 90 kyr 100 kyr 150 kyr 90 kyr 100 kyr 150 kyr
non-monotonic depth-dependenceof 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
21 kyr B.P. 8 kyr B.P. present
100 kyr
90 kyr
PREM-BASED MODELS
90 kyr 100 kyr 150 kyr
time [kyr] 0 kyr
Displacement:red - down or from the axisblue - up or towards the axisexaggerated by a factor
- of 100 vertically- of 500 horizontally
radius 15max. height 3500 m
simple responses of homogeneous incompressible modelsa fast collapse of homogeneous compressible models
hori
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ispla
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vert
ical
dis
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cem
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hori
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ispla
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