Variation of stacking velocity in transversely isotropic media

Abstract

Numerical studies have been conducted to analyse how the elastic parameter d* influences the shapes of the squared travel time-offset curves (T2 versus X2) for surface seismic data and the subsequent effects on stacking velocities using reasonably large offsets typical of reflection seismology. The velocity functions of Green River shale and Mesaverde clayshale (Thomsen, 1986) used in this study represent opposite properties of P-wave propagation. As such they have been chosen to explain fully the role of d* in this analysis. A one-layer transversely isotropic solid overlying a plane reflector represents the model geometry used in the numerical studies. The axis of symmetry is vertical and both horizontal and dipping reflector cases were considered. Travel times were computed for common mid-point gathers above the reflector. The stacking velocities were computed at different offsets by fitting a tangent line to the T2-X2 plot at each X, making it possible to generate graphs of stacking velocity versus offset (X) using Green River shale and Mesaverde clayshale as representative examples. The numerical modelling results indicate that the stacking velocities not only vary significantly with offset but also differ from the vertical ray velocity depending on the sign of the anisotropic parameter d*. Hence, P-wave surface-seismic data cannot accurately predict depths to horizontal reflectors in the presence of anisotropy. This study further emphasises that interpretation of travel time graphs must consider the presence of anisotropy. The variation of the stacking velocity, with offset is expected to give rise to non-hyperbolic travel time curves, which if not taken into consideration may lead to deterioration of stacking itself. Results of the physical modelling obtained using phenolite material which simulates a transversely isotropic medium, indicate that, if anisotropy is present, the stacking velocity used in aligning the primary reflection changes with offset and may not be representative of either the vertical or horizontal velocity.