Full elastic constant tensors of three high-pressure polymorphs of sil
ica: stishovite, CaCl2-type and columbite-type (alpha-PbO2 structure);
are determined at lower mantle pressures from first-principles using
the plane wave pseudopotential method within the local density approxi
mation. The calculated sere pressure athermal elastic moduli are withi
n a few percent of the experiments. We find that the elastic propertie
s of silica are strongly pressure dependent. The shear wave velocity d
ecreases rapidly (by 60 %) and the anisotropy increases rapidly (by a
factor of five) between 40 and 47 GPa prior to the transition from sti
shovite to the CaCl2 structure at 47 GPa. At this phase transition, th
e isotropically averaged shear wave velocity changes discontinuously b
y 60 %, while the S-wave polarization anisotropy decreases by a factor
of two. The transformation of the CaCl2 phase to the columbite phase
at 98 GPa is accompanied by a discontinuous change of 1-2 % in elastic
wave velocity and decrease by a factor of two in anisotropy. We sugge
st that even a small amount of silica in the lower mantle may contribu
te significantly to observed seismic anisotropy, and may provide an ex
planation of observed seismic reflectivity near 1000 km.