## Moveout approximations for P- and SV-waves
in transversely isotropic media with vertical
axis of symmetry

**Veronique Farra** **&**
**Ivan Psencik**
### Summary

We propose alternative expressions for the P- and SV-wave moveout
formulae in VTI media based on the weak-anisotropy approximation.
Our moveout formulae represent expansions with respect to small
parameters, which are related to deviations of anisotropy
from isotropy. First-order P-wave formulae depend on four parameters,
two-way zero offset traveltime *T*_{0} related to
the vertical velocity α,
the depth *H* of the single horizontal reflector and two
weak-anisotropy (WA) parameters ε and δ.
The first-order SV-wave
formulae depend on three parameters, again on *T*_{0}
now related to the SV-wave vertical velocity β,
depth *H* and the WA version of parameter σ.
The second-order formulae are slightly more complicated.
Both P- and SV-wave formulae depend on an additional parameter *r*,
the ratio of the SV- and P-wave velocities. The SV-wave formula depends,
in addition, on the WA parameter ε. Since the dependence of
the moveout formulae on *r* is very weak,
*r* can be specified as a typical SV- to P-wave velocity ratio
and the number of parameters necessary to specify
the second-order formulae is four for both waves. The formulae are
relatively simple, highly accurate around zero offset and yield exact
long offset asymptote. Their accuracy at intermediate offsets depends on
deviations of ray and phase-velocity directions. The proposed formulae are
also applicable in cases when the reflected ray is situated in a plane
of symmetry of an orthorhombic medium, whose another symmetry plane
is horizontal. This also includes any HTI medium with axis of symmetry
in the plane containing the reflected ray.

### Whole paper

The paper is available in
PDF (176 kB).

In: Seismic Waves in Complex 3-D Structures, Report 23,
pp. 81-103, Dep. Geophys., Charles Univ., Prague, 2013.