  Based on fractional Brownian motion (fBm) simulations of 3D gas density and
velocity fields, we present a study of the statistical properties of
spectro-imagery observations (channel maps, integrated emission, and line
centroid velocity) in the case of an optically thin medium at various
temperatures. The power spectral index gamma_W of the integrated emission is
identified with that of the 3D density field (gamma_n) provided 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 gamma_C as that of the velocity field (gamma_v). Further tests with
non-fBm density and velocity fields show that this last result holds, and is
not modified either by the effects of density-velocity correlations. A
comparison is made with the theoretical predictions of Lazarian & Pogosyan
(2000).
