Geostatistics pp 113-141 | Cite as

Autocorrelation Functions in Geology

  • F. P. Agterberg
Part of the Computer Applications in the Earth Sciences book series


By using a method originally developed by P. Whittle, it is shown that a continuous random variable in three-dimensional space has an exponential autocorrelation function if it is subject to a property analogous to the Markov property in time-series analysis.

The problem of estimating autocorrelation functions from irregularly distributed map data is discussed. Approximate autocorrelation functions are shown for a set of 200 subsurface elevations on top of the Arbuckle Group (Cambrian-Ordovician) in Kansas. Trend-surface analysis, a method of kriging and a combination of the two procedures also are applied to the data. Areal interpolation can be done by a method that consists of three steps: (1) fitting a low-order polynomial trend surface; (2) estimation of the autocorrelation function for the residuals; (3) application of kriging to the residuals.


Control Point Autocorrelation Function Spectral Density Function Autocorrelation Coefficient Continuous Random Variable 
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Copyright information

© Plenum Press, New York 1970

Authors and Affiliations

  • F. P. Agterberg
    • 1
  1. 1.Geological Survey of CanadaCanada

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