Mathematics – Logic
Scientific paper
Aug 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000mpse.conf...51g&link_type=abstract
International Conference on Mars Polar Science and Exploration, p. 51
Mathematics
Logic
Mars (Planet), Mars Surface, Polar Caps, Ice, Gravity Anomalies, Bedrock, Differential Equations, Displacement, Atmospheric Temperature, Sea Level, Heat Flux, Mass Distribution, Rheology, Mathematical Models, Isostasy, Topography, Water, Earth Mantle
Scientific paper
The flow of the permanent north polar H20 ice cap of Mars and the isostatic depression of the underlying bedrock are investigated with the 3-d dynamic/thermodynamic ice-sheet model SICOPOLIS (1) coupled to a two-layer visco-elastic model for the lithosphere/mantle system [2,31. SICOPOLIS describes the ice as a density-preserving, heat-conducting power-law fluid with thermo-mechanical coupling due to the strong temperature dependence of the ice viscosity, and computes three-dimensionally the temporal evolution of ice extent, thickness, temperature, water content and age as a response to external forcing. The tatter must be specified by (1) the mean annual air temperature above the ice, (2) the surface mass balance (ice accumulation minus melting and evaporation), (3) the global sea level (not relevant for Martian applications) and (4) the geothermal heat flux from below into the ice body. However, owing to the now well-known surface topography on the one hand, but the shortage of information about the surface mass balance on the other, here the inverse strategy of prescribing the topography and computing the surface mass balance required to sustain the topography is pursuited. Following further the approach of, we use a conceptional, paraboloid-like ice cap, growing and shrinking between the present minimum extent within 80.5 deg north and an assumed past maximum extent southward to 75 deg north with a period of 1.3 Myr (first modulation of obliquity cycle), vary the surface temperature with the same period between its measured present distribution and a 30 C warming coinciding with the maximum ice extent, and apply a geothermal heat flux of 35 mW m-2. The lithosphere/mantle model displace comprises an elastic lithosphere of constant thickness, underlain by a Maxwell-viscoelastic half-space mantle. Both layers are treated as incompressible, and we apply terrestrial standard values for the rheological parameters: density of the lithosphere and of the mantle rho1 = rhom = 3380 kg per cubic m, shear modulus of the lithosphere mu1 = 64 GPa, shear modulus of the mantle mum = 145 GPa, viscosity of the mantle 71. = 1021 Pas [3]. The thickness of the lithosphere, HI, which is the most crucial parameter of the lithosphere/mantle system, is varied between 50 and 400 km. The field equations of displacement, stress and gravity are solved in the Hankel-wavenumber, k, and Laplace-frequency, s, domain, where they are simply a system of ordinary differential equations in the remaining vertical coordinate, z, and the results are transformed back to the space-time domain by computing the inverse Laplace and Hankel transformations. Additional information is obtained in the original extended abstract.
Greve Ralf
klemann Volker
Wolf David
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