Mathematics – Logic
Scientific paper
Sep 1997
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997icar..129..232s&link_type=abstract
Icarus, Volume 129, Issue 1, pp. 232-244.
Mathematics
Logic
21
Scientific paper
The very high correlation of geoid height and topography on Venus, along with the high geoid topography ratio, can be interpreted as local isostatic compensation and/or dynamic compensation of topography at depths ranging from 50 to 350 km. For local compensation within the lithosphere, the swell-push force is proportional to the first moment of the anomalous density. Since the long-wavelength isostatic geoid height is also proportional to the first moment of the anomalous density, the swell push force is equal to the geoid height scaled by -g^2/2piG. Because of this direct relationship, the style (i.e., thermal, Airy, or Pratt compensation) and depth of compensation do not need to be specified and can in fact vary over the surface. Phillips (1990) showed that this simple relationship between swell-push force and geoid also holds for dynamic uplift by shear traction on the base of the lithosphere caused by thermal convection of a! n isoviscous, infinite half-space mantle. Thus for all reasonable isostatic models and particular classes of dynamic models, the geoid height uniquely determines the magnitude of the swell-push body force that is applied to the venusian lithosphere. Given this body force and assuming Venus can be approximated by a uniform thickness thin elastic shell over an inviscid sphere, we calculate the present-day global strain field using equations given in Banerdt (1986); areas of positive geoid height are in a state of extension while areas of negative geoid height are in a state of compression. The present-day model strain field is compared to global strain patterns inferred from Magellan-derived maps of wrinkle ridges and rift zones. Wrinkle ridges, which are believed to reflect distributed compressive deformation, are generally confined to regions with geoid of less than 20m while rift zones are found primarily along geoid highs. Moreover, much of the observed deformation matches the present-day model strain orientations suggesting that most of the rifts on Venus and many of the wrinkle ridges formed in a stress field similar to the present one. In several large regions, the present-day model strain pattern does not! match the observations. This suggests that either the geoid has changed significantly since most of the strain occurred or our model assumptions are incorrect (e.g., there could be local plate boundaries where the stress pattern is discontinuous). Since the venusian lithosphere shows evidence for limited strain, the calculation also provides an estimate of the overall strength of the lithosphere in compression and extension which can be compared with rheological models of yield strength versus depth. At the crests of the major swells, where evidence for rifting is abundant, we find that the temperature gradient must be at least 7K/km.
Bilotti Frank
Johnson Catherine L.
Sandwell David T.
Suppe John
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