A comparison of P-wave phase-velocity and group-velocity in VTI media

摘要

There are essential differences between the energy-reflection and the phase-reflection in VTI (transversely isotropic with a vertical symmetry axis) medi-a, namely, the group-velocity vector and the phase-velocity vector. The group-velocity vector deviates from the phase-velocity vector. The reason is that the group-velocity propagates as waves with curve wave-fronts and it is the envelope of the phase-velocity of approximate plane wave. The stronger the anisotropy is, the larger the local curvature of the curved wave-fronts is, and consequently the larger the angle deviation of the group-velocity from the phase-velocity direction is. In this paper, the differences between the phase-velocity and the group-velocity are numerically analyzed through the calculation of the phase-velocity, the group-velocity and the time-distance curves of the P-wave phase-reflection and the energy-reflection in the VTI media. For the near-offset coverage, the angle deviation is small, but it becomes larger as the offset coverage increases, which even achieves tens of degrees for the far-offset coverage. As a result, the time-distance of the phase-reflection deviates from the time-distance of the energy-reflection. Hence, in the seismic data processing, the stacking, the migration and the imaging that is based on the phase-reflection certainly would have larger deviations for an anisotropic media.