A multivariate variance matrix for use with emulators

Conventional emulation considers a random field as a function of position in parameter space. This
document shows how that framework may be generalized naturally to accommodate multivariate
output.
In the univariate case, a correlation matrix A is defined and the corresponding variance matrix
is 2A, where 2 is a scalar. In the multivariate generalization presented here, the variance matrix
contains a spatial component and an overall covariance component.
The two-variable case is given first, followed by some simple examples. The method generalizes
naturally to arbitrary numbers of variables.