  The forerunners preceding the main tunneling signal of the wave created by a
source with a sharp onset or by a quantum shutter, have been generally
associated with over-the-barrier (non-tunneling) components. We demonstrate
that, while this association is true for distances which are larger than the
penetration lenght, for smaller distances the forerunner is dominated by
under-the-barrier components. We find that its characteristic arrival time is
inversely proportional to the difference between the barrier energy and the
incidence energy, a tunneling time scale different from both the phase time and
the B\"uttiker-Landauer (BL) time.
