Table 1.

Spatial correlation functions.

Exponential	Ckk′ = e−d/ρ
Gaussian	Ckk′ = e−(d/ρ)2
Rational quadratic	$C_{k{k}^{\prime }}=\frac{1}{1+{(d∕\rho )}^2}$
Spherical	$C_{k{k}^{\prime }}=\left(1-\frac{3}{2}\frac{d}{\rho }+\frac{1}{2}{\left(\frac{d}{\rho }\right)}^3\right)1(d<\rho )$

d ≡ d(k, k′) is the spatial distance between voxels indexed by k and k′.