  While the possible roles of GRBs' progenitors as Gravitational Waves (GW)
sources have been extensively studied, little attention has been given to the
jet itself as a GW source. We expect the jet's acceleration to produce a GW
Memory signal. While all relativistic jet models display anti-beaming of GW
radiation away from the jet axis, thus radiating away from directions of GRBs'
gamma radiation, this effect is not overwhelming. The decrease of the signal
amplitude towards the cone of gamma-ray detectability is weak, and for some
models and parameters the GW signal reaches a significant amplitude for much of
the gamma-ray cone. Thus both signals may be jointly detected. We find
different waveforms and fourier signatures for uniform jets and structured jet
models - thus offering a method of using GW signatures to probe the internal
structure and acceleration of GRB jets. The GW signal peaks just outside the
jet (core) of a uniform (structuted) jet. Within the jet (core) the GW signal
displays wiggles, due to a polarization effect; thus for a uniform jet, the
peak amplitude accompanies a smoother signal than the peak of a structured jet.
For the most probable detection angle and for typical GRB parameters, we expect
frequencies < ~600Hz and amplitudes h~10^-25. Our estimates of the expected
signals suggest that the signals are not strong enough for a single cluster of
DECIGO nor for aLIGO's sensitivities. However, sensitivies of ~10^-25/sqrt(Hz)
in the DECIGO band should suffice to detect typical long GRBs at 2Gpc and short
GRBs at 200Mpc, implying a monthly event of a long GRB and a detection of a
short GRB every decade. In addition, we expect much more frequent detection of
GW from GRBs directed away from us, including orphan afterglows. The ultimate
DECIGO sensitivy should increase the range and enable detecting these signals
in all models even to high cosmological z.
