 RELAXATION OF SMALL CRATERS AT PHOENIX LANDING SITE LATITUDES ON MARS.  A. J. Dombard1 and E. Z. Noe Dobrea2, 1Dept. of Earth & Environmental Sciences, University of Illinois at Chicago, Chicago, IL 60607 (adombard@uic.edu), 2Planetary Science Institute, Tucson, AZ 85719.   Introduction:  The high-latitude regions of Mars constitute an unique latitudinal band where water ice is inferred to occur at shallow depths in significant quantities [1, 2]. The ice-rich regolith found in the northern plains at latitudes poleward of 60º has been documented and investigated in situ by the Phoenix lander [3], which found ice at an average depth of only 4.6 cm. Although the depth of stability of water ice at these latitudes was expected from modeling work [e.g., 4], there are still a few important unknowns with regards to the state of water ice at these latitudes.  Two important unknowns that would greatly contribute toward our understanding of the genesis and history of ice at high latitudes are 1) the abundance of ice in the regolith, and 2) the thickness of the ice-bearing layer.  Water ice abundance values of ~60% by mass have been inferred from epithermal neutron data [1], which considering local variations and regional averages, is reasonably consistent with the values of 30% +/- 20% inferred from landed measurements during the Phoenix mission [5].  An abundance of 60% water ice by mass (> 80% by volume) is perplexing, as it implies abundances greater than pore-filling and is inconsistent with emplacement by water vapor only.  In a previous investigation [6-9], we performed an in-depth study of the morphology of small (km-scale and smaller) craters over a 4000 km2 region that included the Phoenix landing ellipse with the objective of constraining depositional rates, abundance of ice in the subsurface, and the thickness of ground ice layer.  Our study resulted in two major findings. First, we found that there is a weakly consolidated layer ~40-70 m thick that does not produce ejecta boulders when it is impacted. When given the geomorphic and compositional results from other investigations, we suggested that this layer consists of ice-cemented soils. Second, we found a clear association between morphology and degree of crater degradation, which allowed us to place constraints on the rate of degradation.  Based on observations of intracrater deposits, small craters (20 to 200 m in diameter) were found to lose volume due to slow infilling, resulting in the loss of these small craters over time scales of 5 - 100 kyr.  Larger craters, which did not exhibit evidence for infilling, developed networks of concentric and radial fractures as the relief was lost, and were interpreted to lose topography due to viscous creep.  Crater retention ages for these larger craters were found to be of the order of a few to tens of Myr.  This latter interpretation is intriguing and raises the question of whether craters only a few hundred meters in diameter are capable of viscously relaxing at these latitudes over time scales of a few million years. Modeling of topographic relaxation in the Southern Polar Layered Deposits (SPLD) suggested a 2 km diameter crater could relax in a few Myr [10], and scaling to 200 m suggests relaxation time scales of several tens of Myr, on the high side of the time scales for the craters at Phoenix latitudes. There are, however, competing factors that affect relaxation at these latitudes, when compared to the SLPD. First, the surface temperature is higher than in the SLPD, which would accelerate relaxation. Conversely, the dust content of the ice is likely higher, which would impede the viscous flow. Additionally, the relaxing features in the SLPD could reasonably be modeled as existing on an icy half space, while the ice at Phoenix latitudes might be restricted to a layer ~40-70 m thick, which again would impede the viscous flow. Here, we specifically model the viscous relaxation of craters 200-1000 m in diameter at Phoenix latitudes, in order to test whether the sometimes extreme shallowing of these craters can be attributed to relaxation and to begin to place constraints on ice abundance. Methods: Following our past work [e.g., 11-13], we use the MSC.Marc finite element package utilizing a viscoelastic rheology to explore the relaxation of Martian craters 200-1000 m in diameter that sit on an icy layer 40-70 m thick. (For now, we assume the substrate is rocky and therefore stiff.) We assume material parameters consistent with a mixture of water ice and basaltic silicates, assuming a volume fraction of stiff silicate particulates. Notably, Durham et al. [14] measured the stiffening effect of particulates on the viscous flow of water ice; we apply this effect to the viscous rheology of water ice that includes grain boundary sliding, diffusion creep, and dislocation creep [15]. Because the increase in temperature associated with Mars's geothermal gradient is minimal over such shallow depths (< 1 K), we employ a constant temperature equal to the surface value (185 K). At the contact between the icy layer and the stiff substrate, we test both extremes of a welded contact and one of free-slip. Results and Discussion:  We begin with a test of a crater 200 m in diameter (the small end of our range), because relaxation is generally slower for smaller craters. We consider 2 cases for a crater sitting on an icy layer 70 m thick: (1) a "hard" case, with a welded base, a relatively large ice grain size of 1 mm, and a larger volume fraction of silicate particulates of 50% (~25% ice by mass, comparable to the Phoenix results [5]); and a "soft" case, with a free-slip base, a grain size of 0.1 mm, and a particulate volume fraction of 25% (~50% ice by mass, closer to the neutron data [1]). The blue curve in Fig. 1 shows the "hard" case after a simulated time of 10 Myr. This crater has lost a significant amount (about half) of its initial topography in that time.  This "hard" case is designed to limit the amount of relaxation, yet it still relaxes significantly within the relevant time scales. As expected then, the "soft" case relaxes much faster (red curve in Fig. 1), seeing comparable amounts of relaxation, but in only 100 kyr (100 times faster).   Figure 1. Radial elevation profiles of a relaxed 200 m diameter crater. The black curve is the initial shape, the blue curve is a mechanical stiff case after 10 Myr, and the red curve is a weaker case after 100 kyr.   Clearly, relaxation is a process that can affect these craters, though a more thorough exploration of the parameter space (e.g., crater diameter, layer thickness, etc.) is needed for a more definitive conclusion. We can determine some implications from these preliminary results, though. The "soft" case explored an ice content even below the value inferred from neutron data [1] and was strongly relaxed in only 100 kyr. This simulated crater would be near completely flat after 1 Myr, the lower bound of the expected age range. If such high ice contents are prevalent throughout the layer, then these craters should almost uniformly be completely relaxed, in contrast with the observations.  Consequently, the ice content of this layer likely cannot be uniformly this high across this latitude band as indicated by the epithermal neutron data [1]. One possible resolution to this dilemma is that ice contents are only this high in the uppermost meter or so where the neutrons are generated. Another observation associated with these apparently relaxed craters is the network of concentric and radial fractures. Strongly relaxed craters can develop faulting on the crater floor [11], and future work can explore this phenomenon. Specifically, the viscoelastic rheological model can be extended to include plasticity, a continuum approximation of brittle failure, with which we can predict the size and orientation of tectonic features associated with relaxation. The discovery of water ice in the shallow subsurface of the northern plains of Mars bears significant importance towards our understanding of the geologic state of water on Mars, the climatological history of Mars, and the effects of water on the modern geology climatological processes of the planet.  By expanding on previous hypotheses [6-9] regarding the thickness of the ice table and the abundance of ice in the regolith and comparing observations of craters in this icy latitude band to simulations of relaxing craters, it may be possible to constrain the state of water ice on Mars and its role in modern geological processes. References: [1] Maurice S. W. et al. (2011) JGR, 116, doi:10.1029/2011JE003810. [2] Mellon M. T. et al. (2008) JGR, 113, doi:10.1029/2007JE003067. [3] Smith, P.H. (2009) PhD Dissertation, U. Arizona. [4] Mellon M. T. et al. (2004) Icarus, 169, doi:10.1016/j.icarus.2003.10.022. [5] Cull S. et al. (2010)  GRL, 37, doi:10.1029/2010GL045372. [6] Noe Dobrea E. Z. et al. (2015) Workshop on Issues in Crater Studies and the Dating of Planetary Surfaces, LPI Contrib. No. 1841, Abstract #9035. [7] Noe Dobrea E. Z. et al. (2015) LPS XLVI, Abstract #2511. [8] Noe Dobrea E. Z. et al. (2016) Icarus, submitted. [9] Noe Dobrea E. Z. et al. (2016) LPS XLVII, ibid. [10] Pathare A. V. et al. (2005) Icarus, 174, 396-418. [11] Dombard A. J. and McKinnon W. B. (2006), JGR, 111, doi:10.1029/2005JE002445. [12] Dombard A. J. and Gillis J.J. (2001), JGR, 106, 27,901-27,910. [13] Karimi M. et al. (2016), Icarus, in press. [14] Durham W. B. et al. (1992) JGR, 97, 20,883-20,897. [15] Goldsby D. L. and Kohlstedt D. L. (2001) JGR, 106, 11,017-11,030. -30 -20 -10 010 0 50 100 150 200 Initial "Hard" - 10 Myr "Soft" - 100 kyr Ele va tio n (m )Radius (m) 
