Mathematics – Logic
Scientific paper
Sep 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008epsc.conf...74i&link_type=abstract
European Planetary Science Congress 2008, Proceedings of the conference held 21-25 September, 2008 in Münster, Germany. Online a
Mathematics
Logic
Scientific paper
Introduction: The Magellan SAR images provide sufficient data to compile a geological map of nearly the entire surface of Venus. Such a global and selfconsistent map serves as the base to address the key questions of the geologic history of Venus. 1) What is the spectrum of units and structures that makes up the surface of Venus [1-3]? 2) What volcanic/tectonic processes do they characterize [4-7]? 3) Did these processes operated locally, regionally, or globally [8- 11]? 4) What are the relationships of relative time among the units [8]? 5) At which length-scale these relationships appear to be consistent [8-10]? 6) What is the absolute timing of formation of the units [12-14]? 7) What are the histories of volcanism, tectonics and the long-wavelength topography on Venus? 7) What model(s) of heat loss and lithospheric evolution [15-21] do these histories correspond to? The ongoing USGS program of Venus mapping has already resulted in a series of published maps at the scale 1:5M [e.g. 22-30]. These maps have a patch-like distribution, however, and are compiled by authors with different mapping philosophy. This situation not always results in perfect agreement between the neighboring areas and, thus, does not permit testing geological hypotheses that could be addressed with a self-consistent map. Here the results of global geological mapping of Venus at the scale 1:10M is presented. The map represents a contiguous area extending from 82.5oN to 82.5oS and comprises ~99% of the planet. Mapping procedure: The map was compiled on C2- MIDR sheets, the resolution of which permits identifying the basic characteristics of previously defined units. The higher resolution images were used during the mapping to clarify geologic relationships. When the map was completed, its quality was checked using published USGS maps [e.g., 22-30] and the catalogue of impact craters [31]. The results suggest that the mapping on the C2-base provided a highquality map product. Units and structures: A limited set of material units and tectonic structures describes the geological situation on the surface of Venus (Fig. 1). The globally applicable stratigraphic sequence summarizing varieties of local to regional columns consists of the following units (from older to younger), the relative ages of which are established by relationships of embayment: Tessera (t) represents elevated regions deformed by multiple sets of tectonic structures. Densely lineated plains (pdl) are dissected by numerous subparallel narrow and short lineaments. Ridged plains (pr) commonly form elongated belts of ridges. Shield plains (psh) have numerous small volcanic edifices on the surface. Regional plains were divided into the lower (pr1) and the upper (pr2) units. The lower unit has uniform and relatively low radar albedo; the upper unit is brighter and often forms flow-like occurrences. Shield clusters (sc) are morphologically similar to psh but occur as small patches that postdate regional plains. Smooth plains (ps) have uniform and low radar albedo and occur near impact craters and at distinct volcanic centers. Lobate plains (pl) form fields of lava flows that are typically undeformed by tectonic structures and are associated with major volcanic centers. Several structural assemblages complicate the surface of the material units: Tessera-forming structures (ridges and grooves), belts of ridges, belts of grooves (structural unit gb), mountain belts (structural unit mt that occurs around Lakhmi Planum), wrinkle ridges, and rift zones (structural unit rt). The higly tectonized material and structural units such as t, pdl, pr, mt, and gb predate vast plains units such as psh and rp1. Wrinkle ridges deform all units that are older than units ps and pl. Smooth and lobate plains together with rift zones and shield clusters appear to be contemporaneous and form the top of the global stratigraphic column. Crater statistics: Two factors, the atmosphere screening [32-34] and the observational bias [35], appear to affect the statistics of the smaller craters on Venus. For the larger craters, these factors appear to be less important and craters >8 km were used to estimate the crater density on mapped units. The shape and size of occurrences of units may also affect the crater statistics on Venus where the total number of craters is small. To minimize influence of this factor the crater density on large and contiguous units that have quasiequidimensional occurrences was estimated. Sometimes, the small total number of craters on Venus impels to combine some units into one in order to increase the crater statistics. The generally similar nature of the heavily tectonized units (t, pdl, pr, gb) and their consistent relationships with the vast plains units permit to combine them into one, the tectonized terrains unit. Both units of regional plains were also combined. Thus, craters were counted on five units: tt (tectonized terrains: t+pdl+pr+gb), psh, rp (rp1+rp2), pl, and rt that make up ~95.8% of the map area. The mean densities (craters per 106km2) of craters on these units are as follow: tt 1.70 (±0.27, two σ); psh: 1.62 (±0.28); rp: 1.63 (±0.18); pl: 0.84 (±0.29); rt: 0.98 (±0.40). The mean density of craters (>8 km) in the map area (all units) is 1.56. If the mean crater density corresponds to the mean surface age, T [19], then the ages of the above units as fractions of T are: tt: 1.09 (±0.17, two σ) T, psh: 1.04 (±0.18) T, rp: 1.05 (±0.12) T, pl: 0.54 (±0.19) T, rt: 0.63 (±0.26) T. These results are consistent with the observed stratigraphic relationships and suggest that the visible stratigraphic record consists of two periods: Fortunian, which includes units from tessera to regional plains (densely clustered around 1.06 T) and Atlian, during which smooth and lobate plains and rift zones were emplaced. These units formed during significantly longer time interval from ~1 T and perhaps to the present. The exposed (minimal) area of the Fortunian units is ~81.7% of the map area, whereas the younger units cover ~14.1% of the surface. Depending upon the estimates of T (750 Ma [36], 500 Ma [37], 300 Ma [38]), duration of Fortunian Period can be from 300 m.y (T=750 Ma) to 120 m.y (T=300 Ma). The minimum integrated resurfacing rate (both volcanic and tectonic) at this time was from ~1.2 to ~3.1 km2/y. Duration of Atlian Period is estimated to be from 750 to 300 m.y and the integrated resurfacing rate during this period could be from ~0.2 to ~0.4 km2/y. Such a significant drop of the resurfacing rates suggests that Fortunian and Atlian periods correspond to two different geodynamic regimes that probably were related to different regimes of mantle convection and lithospheric properties. References: 1) Basilevsky, A. T. and J.W. Head, PSS, 43, 1523, 1995; 2) Basilevsky, A.T. and J.W. Head, PSS, 48, 75, 2000 3) DeShon, H.R. et al., JGR, 105, 6983, 2000; 4) Head, J.W. et al., JGR, 97, 13153, 1992; 5) Solomon, S.C. et al., JGR, 97, 13199, 1992; 6) Squyres, S.W. et al., JGR, 97, 13579, 1992; 7) Stofan, E. R. et al., JGR, 97, 13347, 1992; 8) Guest, J.E., and E.R., Icarus139, 56, 1999; 9) Basilevsky, A.T.,et al., in: Venus II, S.W. Bougher et al. eds., Univ. Arizona Press 1047, 1997; 10) Head, J.W. and A.T. Basilevsky, Geology, 26, 35, 1998; 11) Ivanov, M.A. and J.W. Head, JGR, 106, 17515, 2001; 12) Price, M. and J., Nature, 372, 756, 1994; 13) Price, M. et al., JGR, 101, 4657, 1996 14) Namiki, N. and S.C. Solomon, Science, 265, 929, 1994 15) Parmentier, E.M. and P.C. Hess, GRL, 19, 2015, 1992; 16) Head, J.W. et al., PSS, 42, 803, 1994; 17) Turcotte, D.L., JGR, 98, 127061, 1993; 18) Arkani-Hamed, J. and M.N. Toksoz, PEPI, 34, 232, 1984; 19) Solomon, S.C, LPSC (Abstr.), XXIV, 1331, 1993; 20) Phillips R.J. and V.L. Hansen, Science, 279, 1492, 1998; 21) Solomatov, S.V. and L.-N. Moresi, JGR, 101, 4737, 1996; 22) Bender, K.C., et al., USGS Map I-2620, 2000; 23) Rosenberg, E. and G. E. McGill, USGS Map I-2721, 2001; 24) Ivanov, M. A. and J. W. Head, USGS Map I-2684, 2001; 25) Ivanov, M. A. and J. W. Head, USGS Map I-2792, 2003; 26) Ivanov, M. A. and J. W. Head, USGS Map 2870,
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