Abstract
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.
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References
Bochner, S., 1932, Vorlesungen über Fouriersche Integrale: Akad. Verlagsgeseltschaft, Leipzig, 229 p.
Grenander, U., 1963, Probabilities on algebraic structures: John Wiley & Sons, New York, 218 p.
Sprunt, B., 1972, Digital simulation of drainage basin development,in Spatial analysis in geomorphology: Methuen & Co., Ltd., London, p. 371–389.
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supported by NSF grant GJ-3100X.
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Grenander, U. Dynamic models of geomorphological patterns. Mathematical Geology 7, 267–278 (1975). https://doi.org/10.1007/BF02312724
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DOI: https://doi.org/10.1007/BF02312724