  We have undertaken a spectral-line imaging survey of a 6 x 6 arcmin^2 area
around Sgr B2 near the centre of the Galaxy, in the range from 30 to 50 GHz,
using the Mopra telescope. The spatial resolution varies from 1.0 to 1.4 arcmin
and the spectral resolution from 1.6 to 2.7 km s^-1 over the frequency range.
We present velocity-integrated emission images for 47 lines: 38 molecular lines
and 9 radio recombination lines. There are significant differences between the
distributions of different molecules, in part due to spatial differences in
chemical abundance across the complex. For example, HNCO and HOCO^+ are found
preferentially in the north cloud, and CH_2NH near Sgr B2 (N). Some of the
differences between lines are due to excitation differences, as shown by the
36.17 and 44.07 GHz lines of CH_3OH, which have maser emission, compared to the
48.37 GHz line of CH_3OH. Other major differences in integrated molecular line
distribution are due to absorption of the 7-mm free-free continuum emission
(spatially traced by the radio recombination line emission) by cool intervening
molecular material, causing a central dip in the molecular line distributions.
These line distribution similarities and differences have been statistically
described by principal component analysis (PCA), and interpreted in terms of
simple Sgr B2 physical components of the cooler, lower density envelope, and
dense, hot cores Sgr B2 (N), (M) and (S).
