  For the period July 2003 to August 2010, the interplanetary coronal mass
ejection (ICME) catalogue maintained by Richardson and Cane lists 106
Earth-directed events, which have been measured in-situ by plasma and field
instruments onboard the ACE satellite. We present a statistical investigation
of the Earth's thermospheric neutral density response by means of accelerometer
measurements collected by the GRACE satellites, which are available for 104
ICMEs in the data set, and its relation to various geomagnetic indices and
characteristic ICME parameters such as the impact speed, southward magnetic
field strength (Bz). The majority of ICMEs causes a distinct density
enhancement in the thermosphere, with up to a factor of eight compared to the
pre-event level. We find high correlations between ICME Bz and thermospheric
density enhancements (~0.9), while the correlation with the ICME impact speed
is somewhat smaller (~0.7). The geomagnetic indices revealing the highest
correlations are Dst and SYM-H (~0.9), the lowest correlations are obtained for
kp and AE (~0.7), which show a nonlinear relation with the thermospheric
density enhancements. Separating the response for the shock sheath region and
the magnetic structure of the ICME, we find that the Dst and SYM-H reveal a
tighter relation to the Bz minimum in the magnetic structure of the ICME,
whereas the polar cap indices show higher correlations with the Bz minimum in
the shock sheath region. Since the strength of the Bz component - either in the
sheath or the magnetic structure of the ICME - is highly correlated (~0.9) with
the neutral density enhancement, we discuss the possibility of satellite
orbital decay estimates based on magnetic field measurements at L1, i.e. before
the ICME hits the Earth's magnetosphere. This will further stimulate progress
in space weather understanding and applications regarding satellite operations.
