Dynamic models of geomorphological patterns

  • Ulf Grenander


A deformation mechanism is described and analyzed. It is intended for height patterns exposed to erosion and tectonic activity. A simulation experiment is carried out for this model. Closedform expressions are derived for the covariance field, the properties of spectral estimates, and for the optimal retrospective reconstruction of earlier, unknown height patterns. For obvious reasons the author is in no position to make claims about the verisimilitude of the model. It is offered as an example of a potential application to geology of the theory of patterns developed by the author and his coworkers in recent years. It is hoped that those more qualified than the author in the subject matter area can extend and modify the analysis to make it closer to geological reality.

Key words

Fourier analysis pattern analysis geomorphology 


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  1. Bochner, S., 1932, Vorlesungen über Fouriersche Integrale: Akad. Verlagsgeseltschaft, Leipzig, 229 p.Google Scholar
  2. Grenander, U., 1963, Probabilities on algebraic structures: John Wiley & Sons, New York, 218 p.Google Scholar
  3. Sprunt, B., 1972, Digital simulation of drainage basin development,in Spatial analysis in geomorphology: Methuen & Co., Ltd., London, p. 371–389.Google Scholar

Copyright information

© Plenum Publishing Corporation 1975

Authors and Affiliations

  • Ulf Grenander
    • 1
  1. 1.Division of Applied MathematicsBrown UniversityUSA

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