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Modeling soil variability as a random field

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Abstract

The observed variability in the spatial distribution of soil properties suggests that it is natural to describe such distribution as a random field. One of the ways to study engineering problems in such a stochastic setting is by the use of the Monte-Carlo simulation procedure. Application of this technique requires the capability to generate a large number of realizations of a given random field. A numerical procedure for the generation of such realizations in two-dimensional space is introduced as a finite difference approximation of a stochastic differential equation. The equation used was that suggested by Heine (1955). The resulting procedure is essentially similar to other autoregressive procedures used for the same purpose (Whittle, 1954; Smith and Freeze, 1979). However, contrary to these procedures, the present one is defined in terms of physically significant parameters:r 0, the autocorrelation distance;Δ, the discretization size; and the standard deviation, σ. Formulating the simulation procedure in terms of the physically significant parameters (r 0,Δ, σ) greatly simplifies the task of generating realizations that are compatable with a given soil deposit.

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Baker, R. Modeling soil variability as a random field. Mathematical Geology 16, 435–448 (1984). https://doi.org/10.1007/BF01886325

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Key words

  • spatial variability
  • two dimensional random field
  • Monte-Carlo simulation