Packing dimensions of the images of Gaussian random fields

Let X={X(t):t∈RN} be a Gaussian random field with values in Rd and let E⊆RN be a Borel set. We determine the packing dimension of the image set X(E) in terms of the packing dimension profiles in the canonical metric ρ of X, which are extensions of the packing dimension profiles of Falconer and Howroyd (1997) and the box-counting dimension profiles of Howroyd (2001).