  In this paper, we characterize the infrared spectral energy distributions
(SEDs) of mid-IR selected z~0.3-3.0 and L_IR~10^11-10^13Lsun galaxies, and
study how their SEDs differ from those of local and high-z analogs. Our mid-IR
flux-limited sample of 191 sources is unique in size, and spectral coverage,
including Spitzer mid-IR spectroscopy. Here we add Herschel photometry at
250um, 350um, and 500um, which allows us to obtain accurate total IR
luminosities, as well as constrain the relative contributions of AGN and
starbursts to those luminosities. Our sample constitutes ~23% AGN (i.e. where
the AGN contributes >50% of L_IR), ~30% starbursts (where AGN contributes <20%
of L_IR and the mid-IR spectra are starburst-like); and ~47% composites (which
show both significant AGN and starburst activity). The AGN-dominated sources
divide into ones that show a strong silicate 9.7um absorption feature, implying
highly obscured systems, and ones that do not. The high-tau_9.7 sources are
half of our z>1.2 AGN, but show SEDs that are extremely rare among local AGN.
The SEDs of our z~2 starburst-dominated ULIRGs are much closer to those of
local LIRGs than ULIRGs. This is consistent with our earlier finding that,
unlike local ULIRGs, our high-z starbursts are typically only in the early
stages of a merger. The SEDs of the composite sources are most similar to the
local archetypal warm ULIRG, Mrk231. In summary, our results show that there is
strong evolution in the SEDs between local and z~2 IR-luminous galaxies, as
well as that there is a wide range of SEDs among high redshift IR-luminous
sources. The publicly-available SED templates we derive from our sample will be
particularly useful for infrared population synthesis models, as well as in the
interpretation of other mid-IR high-z galaxies in particular those detected by
the recent all sky WISE survey.
