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Here, I consider the simplest and probably most practical anisotropic model,
that is, a transversely isotropic (TI)
medium with a vertical symmetry axis.
Although more complicated kinds of
anisotropies can exist (i.e., orthrohombic anisotropy), the large
amount of shales
present in the subsurface implies
that the TI model has the most influence on P-wave data ().
In homogeneous transversely isotropic media with a vertical symmetry axis (VTI media),
P- and SV-waves can be described by the vertical velocities
VP0 and VS0 of P- and S-waves, respectively, and two
dimensionless parameters and ().
() demonstrated that P-wave velocity and
traveltime are practically independent of VS0, even for strong anisotropy.
This implies that, for practical purposes, P-wave kinematic signatures is
a function of just three parameters: VP0, , and .
() further demonstrated that a new representation in terms of
just two parameters is sufficient for performing all time-related processing,
such as normal moveout correction (including non-hyperbolic moveout correction, if necessary),
dip-moveout correction, and prestack and post-stack time
migration. These two parameters are the normal-moveout velocity for a horizontal reflector
| |
(117) |
and the anisotropy coefficient ,
| |
(118) |
where Vh is the horizontal velocity. Instead of , I will use v
to represent the interval NMO velocity in both isotropic and TI media. The midpoint-offset
traveltime equations, like any other
time-domain equations, are expected to be dependent on these to parameters as well.
Next: The midpoint-offset traveltime equation
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Stanford Exploration Project
7/5/1998