A few MHD simulations have been performed to study the interaction
between a propagating interplanetary shock and Earth's standing bow
shock, followed by the magnetosheath and magnetopause. They
satisfactorily explain the deceleration of the interplanetary shock in
the magnetosheath, which was observed a few dozen times by well-arranged
satellites. In this work, we perform a hybrid particle-in-cell
simulation in a similar setting with a self-consistently developed
quasi-perpendicular interplanetary shock. We track the position of the
interplanetary shock as it travels through the magnetosheath. We show
that early in the propagation through the magnetosheath, the
interplanetary shock slows down, which is in line with the conclusion of
previous studies. Later in the propagation, however, we find that -- in
the plane perpendicular to the interplanetary magnetic field -- the
interplanetary shock travels faster inside the magnetosheath than it
does in the solar wind. We also note that as the magnetic field lines
are stretched along the magnetopause, the interplanetary shock becomes
quasi-parallel close to the magnetopause.