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![]() | Traveltime approximations for transversely isotropic media with an inhomogeneous background | ![]() |
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Though the expansion in terms of in the previous section allowed us to estimate traveltimes for a tilted symmetry axis, it also required
that we solve the eikonal equation for a VTI medium, which
is relatively challenging. For inversion purposes, it also required knowledge of
, which might not be possible
in TI media using initially a VTI approximation, especially if the tilt is large.
However, an expansion in
, in addition to
(from their zero values),
will result in an elliptically anisotropic background medium and it will allow us to search for both
and
, simultaneously, considering that the elliptical anisotropy model is known.
The two-parameter expansion can be obtained by substituting the following trial solution:
For and
scan
applications, the coefficients (
,
,
,
,
, and
)
need to be evaluated only once and can be used with
equation 8 to search for the best traveltime fit
to those traveltimes extracted from the data.
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![]() | Traveltime approximations for transversely isotropic media with an inhomogeneous background | ![]() |
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