Estimating the Grain Size Distribution of Mars based on Fragmentation Theory and Observations

We present here a fundamental extension to the fragmentation theory [1] which yields estimates of the distribution of particle sizes of a planetary surface. The model is valid within the size regimes of surfaces whose genesis is best reflected by the evolution of fragmentation phenomena governed by either the process of meteoritic impacts, or by a mixture with aeolian transportation at the smaller sizes. The key parameter of the model, the regolith maturity index, can be estimated as an average of that observed at a local site using cratering size-frequency measurements, orbital and surface image-detected rock counts and observations of sub-mm particles at landing sites. Through validation of ground truth from previous landed missions, the basis of this approach has been used at the InSight landing ellipse on Mars to extrapolate rock size distributions in HiRISE images down to 5 cm rock size, both to determine the landing safety risk and the subsequent probability of obstruction by a rock of the deployed heat flow mole down to 3-5 m depth [2]. Here we focus on a continuous extrapolation down to 600 µm coarse sand particles, the upper size limit that may be present through aeolian processes [3]. The parameters of the model are first derived for the fragmentation process that has produced the observable rocks via meteorite impacts over time, and therefore extrapolation into a size regime that is affected by aeolian processes has limited justification without further refinement. Incorporating thermal inertia estimates, size distributions observed by the Spirit and Opportunity Microscopic Imager [4] and Atomic Force and Optical Microscopy from the Phoenix Lander [5], the model's parameters in combination with synthesis methods are quantitatively refined further to allow transition within the aeolian transportation size regime. In addition, due to the nature of the model emerging in fractional mass abundance, the percentage of material by volume or mass that resides within the transported fraction on Mars can be estimated. The parameters of the model thus allow for a better understanding of the regolith's history which has implications to the origin of sand on Mars. [1] Charalambous, PhD thesis, ICL, 2015 [2] Golombek et al., Space Science Reviews, 2016 [3] Kok et al., ROPP, 2012 [4] McGlynn et al., JGR, 2011 [5] Pike et al., GRL, 2011