Nearest-neighbor analysis of small features on Mars: Applications to tumuli and rootless cones

Details Nearest-neighbor analysis of small features on Mars: Applications to tumuli and rootless cones Nearest-neighbor analysis of small features on Mars: Applications to tumuli and rootless cones

Mar 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007jgre..11203002b&link_type=abstract

Journal of Geophysical Research, Volume 112, Issue E3, CiteID E03002

Mathematics

Logic

9

Planetary Sciences: Solid Surface Planets: Volcanism (6063, 8148, 8450), Planetary Sciences: Solar System Objects: Mars, Volcanology: Effusive Volcanism, Volcanology: Planetary Volcanism (5480, 6063, 8148), Volcanology: Instruments And Techniques

Scientific paper

Fields of low relief cones, domes, and mounds on Mars have been interpreted as tumuli, rootless cones, and pingos. The spatial distribution of such features can be characterized by their nearest-neighbor (NN) distances. The NN distributions can provide insight into the physical processes that affected field formation and can possibly provide a future diagnostic of the feature type present on Mars. The conventional approach for analyzing the observed NN distribution is based on the Poisson probability distribution and uses one statistic, c. Our simulations of spatial randomness show that there is an unrecognized bias in c that often leads to erroneous conclusions. Three alternative extensions of the Poisson distribution are proposed here. The first accounts for a minimum threshold on the size of features discerned, the second considers the scavenging of the resources necessary to form neighboring features (e.g., inflation pressurization and subsurface volatiles), and the third models self-limiting growth of the feature population. Three statistical tests are proposed to improve the conventional NN analysis. We provide the critical regions needed to perform these tests for common sample sizes of these geologic features. Our methodology is applied to tumuli at Mauna Ulu, Hawaii, and conjectured tumuli and rootless cones on Mars. Each example exhibits a different aspect of spatial randomness. These applications suggest avenues for further field and theoretical studies to develop this approach as a remote-sensing diagnostic.

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