Nonstationary phase shift (NSPS) for TI media

Robert James Ferguson, Gary F. Margrave

Nonstationary phase shift (NSPS) can be modified, using vertical and horizontal slowness, to extrapolate wavefields through media that are transversely isotropic (TI), and whose elastic parameters vary laterally. No restriction is placed on the weakness of the anisotropy, or the angle of TI symmetry. The significance of this method lies in the fact that velocity variation is allowed simultaneously in space and spatial frequency, and that wavefield extrapolation proceeds using only phase velocity.

We present impulse responses for P-waves for a number of different TI media. The first, weathered gypsum, was chosen due to its extreme P-wave anisotropy (82%). The second, Mesaverde shale, was chosen due to its more typical anisotropy (13%). Impulse responses are computed for the isotropic, vertical TI and TI with different axes of symmetry (-45 degrees for weathered gypsum, 60 degrees for Mesaverdeshale). The responses for the weathered gypsum show significant anisotropic effects, particularly for dipping angle of symmetry. The Mesaverde shale responses are less significant due to the lower level of anisotropy.

To demonstrate NSPS for materials with lateral variation in anisotropy, we presenta scenario where two spatially separate impulses are extrapolated simultaneously through a 300-meters of Gypsum and Mesaverde shale. The weathered Gypsumgrades abruptly into Mesaverde shale, both having different axis of YI symetry. The resulting responses match those from the constant anisotropy cases.