  The annihilation of positrons in the Galaxy's interstellar medium produces
characteristic gamma-rays with a line at 511 keV. This emission has been
observed with the spectrometer SPI on INTEGRAL, confirming a puzzling
morphology with bright emission from an extended bulge-like region, and faint
disk emission. Most plausible sources of positrons are believed to be
distributed throughout the disk of the Galaxy. We aim to constrain
characteristic spectral shapes for different spatial components in the disk and
bulge with the high-resolution gamma-ray spectrometer SPI, based on a new
instrumental background method and detailed multi-component sky model fitting.
We confirm the detection of the main extended components of characteristic
annihilation gamma-ray signatures at 58$\sigma$ significance in the line. The
total Galactic line intensity amounts to
$(2.7\pm0.3)\times10^{-3}~\mathrm{ph~cm^{-2}~s^{-1}}$ for our assumed spatial
model. We derive spectra for the bulge and disk, and a central point-like and
at the position of Sgr A*, and discuss spectral differences. The bulge shows a
511 keV line intensity of
$(0.96\pm0.07)\times10^{-3}~\mathrm{ph~cm^{-2}~s^{-1}}$ and an
ortho-positronium continuum equivalent to a positronium fraction of
($1.08\pm0.03$). The 2D-Gaussian representing the disk has an extent of
$60^{+10}_{-5}$ deg in longitude and a latitudinal extent of
$10.5^{+2.5}_{-1.5}$ deg; the line intensity is
$(1.7\pm0.4)\times10^{-3}~\mathrm{ph~cm^{-2}~s^{-1}}$ with a marginal detection
of ortho-positronium and an overall diffuse Galactic continuum of
$(5.85\pm1.05)\times10^{-5}~\mathrm{ph~cm^{-2}~s^{-1}~keV^{-1}}$ at 511 keV.
The disk shows no flux asymmetry between positive and negative longitudes,
although spectral details differ. The flux ratio between bulge and disk is
($0.6\pm0.1$). The central source has an intensity of
$(0.8\pm0.2)\times10^{-4}~\mathrm{ph~cm^{-2}~s^{-1}}$.
