  Photons that decouple from a relativistic jet do so over a range of radii,
which leads to a spreading in arrival times at the observer. Therefore, changes
to the comoving photon distribution across the decoupling zone are encoded in
the emitted signal. In this paper, we study such spectral evolution occurring
across a pulse. We track the radiation from the deep subphotospheric regions
all the way to the observed time-resolved signal, accounting for emission at
various angles and radii. We assume a simple power-law photon spectrum
injection over a range of optical depths and let the photons interact with the
local plasma. At high optical depths, we find that the radiation exists in one
of three characteristic regimes, two of which exhibit a high-energy power law.
Depending on the nature of the injection, this power law can persist to low
optical depths and manifest itself during the rise time of the pulse with a
spectral index $\beta \approx \alpha - 1$, where $\alpha$ is the low-energy
spectral index. The results are given in the context of a gamma-ray burst jet
but are general to optically thick, relativistic outflows.
