Mathematics – Logic
Scientific paper
Dec 2004
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004agufm.g43a0796d&link_type=abstract
American Geophysical Union, Fall Meeting 2004, abstract #G43A-0796
Mathematics
Logic
8122 Dynamics, Gravity And Tectonics, 8164 Stresses: Crust And Lithosphere, 5417 Gravitational Fields (1227), 6225 Mars, 1227 Planetary Geodesy And Gravity (5420, 5714, 6019)
Scientific paper
The quantification of lithospheric dynamics on Mars is of fundamental importance to the understanding of Martian geologic history and surface morphology. The global stress field associated with gravitational potential energy differences (GPE) constitutes a significant fraction of the total stress field. We have obtained 0.25 × 0.25 degree data sets of MOLA topography and crustal thickness from Zuber et al 2000. We calculate the GPE associated with the topography by vertically integrating density to a given lithospheric depth using either Airy isostasy assumptions or the crustal thickness model of Zuber et al 2000. Using a finite-element thin sheet method we solve the full 3-D force-balance equations for stress magnitudes and orientations within the lithosphere associated with the horizontal gradients in GPE. We assume ρ crust = 2900~ kg m-3, ~ρ mantle = 3500~ kg m-3, ~g = 3.7~ ms-2 and various lithospheric thicknesses. We explore both viscous and elastic rheologies. It is interesting to note that our solutions depend on the rheology only through the ratio of shear and bulk moduli for the elastic case or the shear and bulk viscosities for the viscous case. Finally, we also calculate the expected style and orientation of the associated elastic strain. To first order, all stress field solutions are consistent with a tectonically inactive region relaxing due to excess or deficit of mass. Thus topographic highs e.g., Tharsis Mons, Olympus Mons, and Alba Patera, are in deviatoric extension, while topographic lows e.g., Valles Marineras and impact basins, are in deviatoric compression. At short wavelengths, however, features are regionally supported and differences in the stress field solutions occur between the Airy isostasy and the crustal thickness models. For example, several lowlands e.g., Isidis and Argyre Planitae, are in deviatoric extension in the crustal thickness model. Increasing the lithospheric depth increases the magnitudes of stresses but does not change the deformation style. Comparisons of viscous and elastic solutions with the same ratio of the shear and bulk viscosities for the viscous case and shear and bulk moduli for the elastic case show small variations in stress magnitudes and orientations among the solutions. We compare our results with inferred fault styles and orientations e.g., Mege 2001, Montessi and Zuber 2003. The GPE variations appear to match the radial graben features on Tharsis, as well as the wrinkle ridges at lower elevations. However, they do not predict the wrinkle ridges on the flanks of Tharsis and some grabens around Alba Patera extend into the lower topography regions beyond the area where the GPE associated stresses predict extension. Calculations of Banerdt and Glombek 2000 show the importance of flexural loading on the stress field. Their flexural loading solution provides compression at higher elevations on Tharsis that may explain some of the wrinkle ridges not predicted by GPE variations. Therefore, it appears that a combined solution of GPE inferred vertically integrated deviatoric stresses and the flexurally produced stresses will provide a better fit to the fault styles and orientations observed on Mars.
Dimitrova Lada L.
Haines John Allan
Holt William E.
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