Over the last decade, observations acquired by the Shallow Radar (SHARAD) sounder on individual passes of the Mars Reconnaissance Orbiter have revealed the internal structure of the Martian polar caps and provided new insights into the formation of the icy layers within and their relationship to climate. However, a complete picture of the cap interiors has been hampered by interfering reflections from off-nadir surface features and signal losses associated with sloping structures and scattering. Foss et al. (2017) addressed these limitations by assembling three-dimensional data volumes of SHARAD observations from thousands of orbital passes over each polar region and applying geometric corrections simultaneously. The radar volumes provide unprecedented views of subsurface features, readily imaging structures previously inferred from time-intensive manual analysis of single-orbit data (e.g., trough-bounding surfaces, a buried chasma, and a basal unit in the north, massive carbon-dioxide ice deposits and discontinuous layered sequences in the south). Our new mapping of the carbon-dioxide deposits yields a volume of 16,500 km, 11% larger than the prior estimate. In addition, the radar volumes newly reveal other structures, including what appear to be buried impact craters with no surface expression. Our first assessment of 21 apparent craters at the base of the north polar layered deposits suggests a Hesperian age for the substrate, consistent with that of the surrounding plains as determined from statistics of surface cratering rates. Planned mapping of similar features throughout both polar volumes may provide new constraints on the age of the icy layered deposits. The radar volumes also provide new topographic data between the highest latitudes observed by the Mars Orbiter Laser Altimeter and those observed by SHARAD. In general, mapping of features in these radar volumes is placing new constraints on the nature and evolution of the polar deposits and associated climate changes.

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Since its arrival in early 2006, various instruments aboard NASA's Mars Reconnaissance Orbiter (MRO) have been collecting a variety of scientific and engineering data from orbit around Mars. Among these is the SHAllow RADar (SHARAD) instrument, supplied by Agenzia Spaziale Italiana (ASI) and designed for subsurface sounding in the 15-25 MHz frequency band. As of this writing, MRO has completed over 46,000 nearly polar orbits of Mars, 30% of which have included active SHARAD data collection. By 2009, a sufficient density of SHARAD coverage had been obtained over the polar regions to support 3-D processing and analysis of the data. Using tools and techniques commonly employed in terrestrial seismic data processing, we have processed subsets of the resulting collection of SHARAD observations covering the north and south polar regions as SHARAD 3-D volumes, imaging the interiors of the north and south polar ice caps known, respectively, as Planum Boreum and Planum Australe. After overcoming a series of challenges revealed during the 3-D processing and analysis, a completed Planum Boreum 3-D volume is currently being used for scientific research. Lessons learned in the northern work fed forward into our 3-D processing and analysis of the Planum Australe 3-D volume, currently under way. We discuss our experiences with these projects and present results and scientific insights stemming from these efforts.

In this article, we discuss the numerical solution of the Bingham-Bratu-Gelfand (BBG) problem, a non-smooth nonlinear eigenvalue problem associated with the total variation integral and an exponential nonlinearity. Using the fact that one can view the nonlinear eigenvalue as a possible Lagrange multiplier associated with a constrained minimization problem from Calculus of Variations, we associate with the BBG problem an initial value problem (dynamical flow), well suited to time-discretization by operator-splitting. Various mathematical results are proved, including the convergence of a finite element approximation of the BBG problem. The operator-splitting/finite element methodology discussed in this article is robust and easy to implement. We validate the implementation by first solving the classical Bratu-Gelfand problem, obtaining and reporting results consistent with those found in the literature. We then explore the full capability of the implementation by solving the viscoplastic BBG problem, obtaining and reporting results for several values of the plasticity yield. We conclude by exhibiting and discussing the bifurcation diagrams corresponding to these same values of the plasticity yield, and by reporting and examining some finer details of the solver discovered during the course of our investigation.

We present first results from a new 3D radargram produced from 3399 Mars Reconnaissance Orbiter (MRO) Shallow Radar observations of the north polar region of Mars. While incorporating an additional 5 yr of observations relative to the prior 3D radargram, we employed surface-clutter simulations to improve the coregistration of the input data and thereby enhance the effective vertical resolution of features. Combining those improvements with the geometric corrections and an increase in signal-to-noise ratio afforded by the 3D imaging process, this data product provides new details about the interior of Planum Boreum, the Martian north polar cap. We assess the overall characteristics and compare portions of the new 3D radargram to results from prior studies that used either the prior 3D radargram or sets of 2D radargrams from individual MRO orbits. We find that the new 3D radargram has recovered essentially all of the vertical resolution inherent to the input data, and the increased coverage density has substantially reduced artifacts while enabling much greater detail in the imaging of subsurface layering and structures. These improvements extend throughout the 3D radargram, from the basal units to the shallowest subsurface layering in Planum Boreum, and out into the surrounding plains. Subsurface features such as a buried chasma, other layering structures and unconformities, and trough-bounding surfaces that offset shallow layering are now visible in unprecedented detail. A thorough analysis of this new 3D radargram and its implications for the geologic and climate history of Planum Boreum will extend over many years.

This list includes many of the hundreds of current students and scientists who have made significant contributions to Mars Polar Science in the past decade. Every name listed represents a person who asked to join the white paper or agreed to be listed and provided some comments.

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