ISSN:
1365-2478
Source:
Blackwell Publishing Journal Backfiles 1879-2005
Topics:
Geosciences
,
Physics
Notes:
The arrival-time curve of a reflection from a horizontal interface, beneath a homogeneous isotropic layer, is a hyperbola in the x - t-domain.If the subsurface is one-dimensionally inhomogeneous (horizontally layered), or if some or all of the layers are transversely isotropic with vertical axis of symmetry, the statement is no longer strictly true, though the arrival-time curves are still hyperbola-like. In the case of transverse isotropy, however, classical interpretation of these curves fails. Interval velocities calculated from t2 - x2-curves do not always approximate vertical velocities and therefore cannot be used to calculate depths of reflectors.To study the relationship between velocities calculated from t2 - x2-curves and the true velocities of a transversely isotropic layer, we approximate t2 - x2-curves over a vertically inhomogeneous transversely isotropic medium by a three-term Taylor series and calculate expressions for these terms as a function of the elastic parameters. It is shown that both inhomogeneity and transverse isotropy affect slope and curvature of t2 - x2-curves. For P-waves the effect of transverse isotropy is that the t2 - x2-curves are convex upwards; for SV-waves the curves are convex downwards. For SH-waves transverse isotropy has no effect on curvature.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1111/j.1365-2478.1984.tb00742.x
