Interpreting polygonal terrain network arrangements on Earth and Mars using spatial point patterns

Details Interpreting polygonal terrain network arrangements on Earth and Mars using spatial point patterns Interpreting polygonal terrain network arrangements on Earth and Mars using spatial point patterns

Dec 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010phdt.......179h&link_type=abstract

ProQuest Dissertations And Theses; Thesis (Ph.D.)--McGill University (Canada), 2010.; Publication Number: AAT NR68527; ISBN: 978

Mathematics

Logic

Scientific paper

Polygonal terrain is one of the most common landforms found throughout the periglacial environments of Earth and Mars. These networks of interconnected trough-like features form through a complex interaction of climatological and rheological processes and often signify the presence of ground ice deposits. Previous comparisons of morphological similarities amongst sites on both planets have typically relied upon qualitative techniques. In some cases, limited quantitative metrics have been utilized, but there remains no objective, repeatable method by which to compare terrestrial and Martian polygonal terrain. The overarching goal of this work is to assess the utility of a particular statistical method -- Spatial Point Pattern Analysis (SPPA) -- for analyzing polygonal network geometries at sites on Earth and Mars. Based around four sets of experimental results, the objectives addressed by this thesis are to: (i) demonstrate that SPPA is an effective means by which qualitative, observable variations in polygonal morphology can be quantified; (ii) examine the effects of different input data collection methods on the output of the statistical model; (iii) establish that the analytical results of SPPA as applied to polygonal terrain are rooted in terrestrial geomorphic theory, and; (iv) perform a case study in which SPPA is used to reconstruct the landscape history of a particular region of Mars. Our results show that SPPA successfully differentiates between the geometric patterns observed at various sites, simultaneously providing data pertaining to the cumulative distribution of trough segment lengths and the overall network arrangement. In providing guidelines for future applications of this technique, we demonstrate that SPPA results are the most reliable when using data derived from ground-based terrain surveys or GIS-based analysis of high-resolution (≤ 0.5m/pixel) satellite or aerial images. Moreover, extensive fieldwork in the Canadian High Arctic illustrates that the observed point pattern of a given site is linked to its substrate composition and relative stage of development. Finally, using the field results as an analogical source to inform the interpretation of Martian geomorphic processes, a landscape evolution model is proposed to explain the development of a poorly-understood landform (scalloped depressions) in the ice-rich terrains of the Martian northern latitudes.

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