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| The SIM2D Procedure | 
| Introduction to Spatial Simulation | 
The purpose of spatial simulation is to produce a set of partial realizations of a spatial random field (SRF)  in a way that preserves a specified mean
 in a way that preserves a specified mean  and covariance structure
 and covariance structure  . The realizations are partial in the sense that they occur only at a finite set of locations
. The realizations are partial in the sense that they occur only at a finite set of locations  . These locations are typically on a regular grid, but they can be arbitrary locations in the plane.
. These locations are typically on a regular grid, but they can be arbitrary locations in the plane. 
PROC SIM2D produces simulations for continuous processes in two dimensions by using the lower-upper (LU) decomposition method. In these simulations the possible values of the measured quantity  at location
 at location  can vary continuously over a certain range. An additional assumption, needed for computational purposes, is that the spatial random field
 can vary continuously over a certain range. An additional assumption, needed for computational purposes, is that the spatial random field  is  Gaussian. The section Details: SIM2D Procedure provides more information about different types of spatial simulation and associated computational methods.
 is  Gaussian. The section Details: SIM2D Procedure provides more information about different types of spatial simulation and associated computational methods. 
Spatial simulation is different from spatial prediction, where the emphasis is on predicting a point value at a given grid location. In this sense, spatial prediction is local. In contrast, spatial simulation is global; the emphasis is on the entire realization  .
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Given the correct mean  and covariance structure
 and covariance structure  , SRF quantities that are difficult or impossible to calculate in a spatial prediction context can easily be approximated by functions of multiple simulations.
, SRF quantities that are difficult or impossible to calculate in a spatial prediction context can easily be approximated by functions of multiple simulations. 
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