Introduction
Hypsometric curves derived from global topography data can be used to reveal planet scale internal activity [Rosenblatt and Pinet, 1994]. Previous study revealed a domain of elevation on Earth and Venus for which the relationship between the elevation and square root of cumulative area percentage is linear, suggesting the existence of similar thermal isostasy acting at the planetary scale [Rosenblatt and Pinet, 1994]. This poster attempts to conduct the same exercise for Mars, and to extend the analysis for Venus.

Data source and analysis
5-Minute Digital Elevation Model (DEM) from NOAA National Geophysical Data Center (http://www.ngdc.noaa.gov/); 1/32 degree/pixel DEM from Mars Orbiter Laser Altimeter (MOLA) (http://wufs.wustl.edu/), 1/20 degree/pixel DEM from Magellan mission.
All data sets were projected to a cylindrical equal area projection using ArcInfo GIS software, except where noted. Earth topography was isostatically adjusted by unloading ocean water, assuming a mantle density of 3300 kg/m3. The differential hypsometric curves are constructed using 50 m bin size. The linear segment of the hypsometric curve was determined by fitting lines to different portions of the data points and selecting the one with the least root mean square error. The roughness is estimated by subtracting low pass filtered topography from the original topography.

Results and Discussion
The Earth's differential hypsometric curve is bimodal (Figure 1a), showing the difference between continent and ocean floor. On Earth, the linear domain of the cumulative hypsometric curve corresponds to the ocean floor created by sea floor spreading (Figure 1b), as depth of ocean floor is also linearly related to the square root of its age, based on thermal cooling theory. The upper bound of the linear domain (-1950m, see Table 1) is the unloaded mean elevation for the mid-ocean ridge (Figure 2a), where the thermal lithosphere thickness is equal to zero. Note that its spatial distribution also roughly includes the passive plate margins (Figure 2a). In addition, the upper peak of the differential curve is right around sea level (-50 m), which also corresponds nicely to the break in slope near sea level (-100m) of the cumulative curve (Figure 1c, see also Table 2).
On Mars, the differential hypsometric curve is also bimodal (Figure 1d), reflecting the topography dichotomy between the northern and southern hemispheres. A similar linear domain exists in its cumulative hypsometric curve (Figure 1e); however, it differs from the Earth in three ways: 1. There appear to be two linear segments below the reference elevation. 2. The extension of the higher linear segment is above the "land" portion of the hypsometry curve topography, and the extension of the lower linear segment touches the "land" portion. 3. There is no clear correlation between the differential hypsometric curve and the cumulative hypsometric curve (Table 2). These differences may have been caused by severe post-plate tectonic modification such as impact cratering. However, it is interesting to note the large slope break is close to the preferred sea level , the so-called "Contact 2," at ­3760 +_ 560m, of Head et al. [1999] and Parker et al. [1993]. There is no clear ridge system on Mars (Figure 2b). However, the black lines in Figure 2b (upper threshold of linear fit 1) between 120 and 270 longitude appear to correspond to the passive margins proposed by Sleep [1994] (Figure 3a, 3b) and the gray lines (upper threshold of linear fit 2) between 90 and 300 longitude appear to correspond to Sleep's ridge system (Figure 3a, 3b). In addition, both the gray and the black lines go into the Vallis Marineris, which could be the remnant of a rift valley.
The topographic roughness map of Earth (Figure 4a) reveals a substantial difference in the slopes of the slow-spreading Mid-Atlantic Ridge (MAR) and the fast spreading East Pacific Rise (EPR). The faster spreading of the EPR spreads the topographic relief over a larger region, thus decreasing its slope. On Venus (Figure 4b), several rift regions have been identified [Stofan et al., 1992]. The highest concentration of these is in the Beta-Atla-Themis (BAT) region. It has been noted that the three major rift provinces in the BAT region display different characteristics, including the number of associated coronae [Stoddard and Jurdy, 2001]. The rift that extends from Atla southeastwards towards Themis (AT) contains many coronae, and it has been suggested that this is therefore an active rift, whereas the rift trending north/south between Beta and Themis (BT) contains no coronae, and may therefore be less active or completely inactive [Stoddard and Jurdy, 2001]. Roughness analysis of this region shows pronounced roughness for the Beta/Themis rift, and much more subdued roughness for the Atla/Themis rift, consistent with the earlier suggestions for their relative activity. The roughness map of Mars is a representation of the topographic dichotomy and the severe modification in the southern highlands by cratering
(Figure 4c).

Conclusions
1) The hypsometric analysis shows possible remnants of passive margins and ridge systems that are consistent with an early earth-like plate tectonics process on Mars as proposed by Sleep [1994].
2) Further analysis of Venus topographic trends reveals more similarities to such trends produced by plate rifting (sea-floor spreading) on Earth.

Major References
Head, J.W., Hiesinger, H., Ivanov, M.A., Kreslavsky, M.A., Pratt, S., Thompson, B.J., 1999, Possible ancient oceans on Mars: Evidence from Mars Orbiter Laser Altimeter data, Science, 286: 2134-2137.
Parker, T.J., Gorsline, D.S., Saunders, R. S., Pieri, D.C., Schneeberger, D.M., 1991, Coastal geomorphology of the Martian northern plains, Journal of Geophysical Research, , E, Planets, 98 (6): 11,061-11,078.
Rosenblatt, P. and Pinet, P.C., 1994, Comparative hypsometric analysis of Earth and Venus, Geophysical Research Letters, 21(6): 465-468.
Sleep, N.H., 1994, Martian plate tectonics, Journal of Geophysical Research, E, Planets,
99 (3): 5639-5655.
Stoddard, P.R. and Jurdy, D.M., 2001, Orientation of coronae and relation to chasmata on Venus. XXXII Lunar and Planetary Science Conference abstract.
Stofan, E.R., Sharpton, V.L., Schubert, G.B., Gidon, B., Duane L., Janes, D.M., Squyres, S.W., 1992, Global distribution and characteristics of coronae and related features on Venus; implications for origin and relation to mantle processes, Journal of Geophysical Research, E, Planets,
97 (8): 13,347-13,378.