Based on fractional Brownian motion (fBm) simulations of three-dimensional gas density and velocity fields, we present a study of the statistical properties of spectroimagery observations (channel maps, integrated emission, and line centroid velocity) in the case of an optically thin medium at various temperatures. The power spectral index of the integrated emission is confirmed to be that of the three-dimensional density field () provided that the medium's depth is at least of the order of the largest transverse scale in the image, and the power spectrum of the centroid velocity map is found to have the same index as that of the velocity field (). Further tests with non-fBm density and velocity fields show that this last result holds and is not modified by the effects of density-velocity correlations. A comparison is made with the theoretical predictions of Lazarian & Pogosyan (2000).