  We numerically investigate the metastable equilibrium structure of deep
supercooled and glassy water under pressure, covering the range of densities
corresponding to the experimentally produced high-density and very-high-density
amorphous phases. At $T = 188$ K, a continuous increase in density is observed
on varying pressure from $2.5$ to $13$ kbar, with no signs of first-order
transitions. Exploiting a recently proposed approach to the analysis of the
radial distribution function -- based on topological properties of the
hydrogen-bond network -- we are able to identify well-defined local geometries
that involve pair of molecules separated by multiple hydrogen bonds, specific
of the high and very high density structures.
