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The SIM2D Procedure |

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 and
covariance structure *C*_{z}(**s**_{1}-**s**_{2}) = *cov*(*Z*(**s**_{1}),*Z*(**s**_{2})).

The realizations are partial in the sense that they occur
only at a finite set of locations (**s**_{1}, **s**_{2}, ... ,**s**_{n}).
These locations are typically on a regular grid, but they can
be arbitrary locations in the plane.

There are a number of different types of spatial simulation
and associated computational methods. PROC SIM2D
produces simulations for continuous processes
in two dimensions. This means that the possible
values of the measured quantity *Z*(**s**_{0}) at location
**s**_{0} = (*x _{0}*,

An additional assumption, needed for computational
purposes, is that the spatial random field *Z*(**s**) is
Gaussian.

Spatial simulation is different from
spatial prediction, where the emphasis
is on producing a point estimate 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 (*Z*(**s**_{1}), *Z*(**s**_{2}), ... ,*Z*(**s**_{n})).

Given the correct mean and
covariance structure *C*_{z}(**s**_{1}-**s**_{2}), SRF
quantities that are difficult or impossible
to calculate in a spatial prediction context
can easily be approximated by repeated simulations.

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