We describe the infrared properties of sources detected over ~36 deg^2 of sky in the GAMA 15-hr equatorial field, using data from both the Herschel Astrophysical Terahertz Large-Area Survey (H-ATLAS) and Wide-field Infrared Survey (WISE). With 5-sigma point-source depths of 34 and 0.048 mJy at 250 micron and 3.4 micron, respectively, we are able to identify 50.6% of the H-ATLAS sources in the WISE survey, corresponding to a surface density of ~630 deg^{-2}. Approximately two-thirds of these sources have measured spectroscopic or optical/near-IR photometric redshifts of z<1. For sources with spectroscopic redshifts at z<0.3, we find a linear correlation between the infrared luminosity at 3.4 micron and that at 250 micron, with +-50% scatter over ~1.5 orders of magnitude in luminosity, ~10^9 - 10^{10.5} L_sun. By contrast, the matched sources without previously measured redshifts (r>~20.5) have 250-350 micron flux density ratios that suggest either high-redshift galaxies (z>~1.5) or optically faint low-redshift galaxies with unusually low temperatures (T<~20). Their small 3.4-250 micron flux ratios favor a high-redshift galaxy population, as only the most actively star-forming galaxies at low redshift (e.g., Arp 220) exhibit comparable flux density ratios. Furthermore, we find a relatively large AGN fraction (~30%) in a 12 micron flux-limited subsample of H-ATLAS sources, also consistent with there being a significant population of high-redshift sources in the no-redshift sample.
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