Mathematical Geology

, Volume 26, Issue 5, pp 557–564 | Cite as

Unilateral ARMA processes on a square net by the herringbone method

  • Benjamin F. Turner
  • W. E. Sharp
Article

Abstract

Because multidimensional ARMA processes have great potential for the simulation of geological parameters such as aquifer permeability, it was important to resolve which of two proposed alternative methods should be used for determining the two-dimensional weighting parameter, φ″, for a unilateral ARMA (1, 0) process on a square net. Practical simulations demonstrates that the correct formulation is: φ″=ρ10/(1+ρ 10 2 where ρr,s is the correlation between lattice points at lagsr and s. When the simulations are performed with correlations of 0.8 or more a residual bias was detected which was found to be caused by a difference in the variance between the one- and two-dimensional models. This can be rectified by modifying the two- dimensional model as follows: zij=φ″(zi−1, j + zi, j−1) + λaij whereλ2=1/(1 +ρ 10 2 ).

Key words

autoregressive processes multidimensional time series herringbone method spatial models 

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References

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Copyright information

© International Association for Mathematical Geology 1994

Authors and Affiliations

  • Benjamin F. Turner
    • 1
  • W. E. Sharp
    • 1
  1. 1.Department of Geological SciencesUniversity of South CarolinaColumbia

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