Martian topography: Scaling, craters, and high-order statistics.

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The high-order structure functions of Mars topography reveal three specific ranges of scales: (1) scaling range at small scales where the structure functions exhibit scaling behavior; (2) transition range where the structure functions continue to grow but do not reveal scaling; and (3) saturation range at large scales where the structure functions saturate. The scaling and saturation ranges are explored in detail in respect to scaling and intermittency. Analysis of the Mars Orbiter Laser Altimeter (MOLA) data and computer simulations suggest that there are two potential contributors to the small-scale scaling: (i) scale-invariant surface formation; and (ii) effects of discrete morphological forms such as craters. The crater effect also provides an explanation for the large-scale intermittency revealed using the normalized structure functions within the saturation range, which cannot be explained by the 'scale-invariant' concept. Overall, the obtained results suggest that the "crater" contribution to the structure function behavior often dominates over the effect of the scale-invariant surface formation.

Original languageEnglish
Pages (from-to)337-355
Number of pages18
JournalMathematical Geology
Volume37
Issue number4
DOIs
Publication statusPublished - 2005

Keywords

  • planet surface
  • high-order structure functions
  • Mars
  • scaling
  • craters
  • intermittency
  • ORBITER LASER ALTIMETER
  • MOLA DATA
  • SELF-SIMILARITY
  • MARS TOPOGRAPHY
  • TURBULENCE
  • MULTIFRACTALITY
  • ROUGHNESS
  • SLOPES
  • VENUS
  • EARTH

Cite this

Martian topography: Scaling, craters, and high-order statistics. / Nikora, Vladimir Ivanovich; Goring, D.

In: Mathematical Geology, Vol. 37, No. 4, 2005, p. 337-355.

Research output: Contribution to journalArticle

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T1 - Martian topography: Scaling, craters, and high-order statistics.

AU - Nikora, Vladimir Ivanovich

AU - Goring, D.

PY - 2005

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N2 - The high-order structure functions of Mars topography reveal three specific ranges of scales: (1) scaling range at small scales where the structure functions exhibit scaling behavior; (2) transition range where the structure functions continue to grow but do not reveal scaling; and (3) saturation range at large scales where the structure functions saturate. The scaling and saturation ranges are explored in detail in respect to scaling and intermittency. Analysis of the Mars Orbiter Laser Altimeter (MOLA) data and computer simulations suggest that there are two potential contributors to the small-scale scaling: (i) scale-invariant surface formation; and (ii) effects of discrete morphological forms such as craters. The crater effect also provides an explanation for the large-scale intermittency revealed using the normalized structure functions within the saturation range, which cannot be explained by the 'scale-invariant' concept. Overall, the obtained results suggest that the "crater" contribution to the structure function behavior often dominates over the effect of the scale-invariant surface formation.

AB - The high-order structure functions of Mars topography reveal three specific ranges of scales: (1) scaling range at small scales where the structure functions exhibit scaling behavior; (2) transition range where the structure functions continue to grow but do not reveal scaling; and (3) saturation range at large scales where the structure functions saturate. The scaling and saturation ranges are explored in detail in respect to scaling and intermittency. Analysis of the Mars Orbiter Laser Altimeter (MOLA) data and computer simulations suggest that there are two potential contributors to the small-scale scaling: (i) scale-invariant surface formation; and (ii) effects of discrete morphological forms such as craters. The crater effect also provides an explanation for the large-scale intermittency revealed using the normalized structure functions within the saturation range, which cannot be explained by the 'scale-invariant' concept. Overall, the obtained results suggest that the "crater" contribution to the structure function behavior often dominates over the effect of the scale-invariant surface formation.

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KW - SELF-SIMILARITY

KW - MARS TOPOGRAPHY

KW - TURBULENCE

KW - MULTIFRACTALITY

KW - ROUGHNESS

KW - SLOPES

KW - VENUS

KW - EARTH

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