## Kirchhoff prestack depth scalar migration of
complete wave field using the prevailing-frequency
approximation of the coupling ray theory

**Vaclav Bucha**
### Summary

The coupling ray theory provides more accurate polarizations
and travel times of S waves in models with weak anisotropy than
the anisotropic ray theory.
We test the application of the prevailing-frequency approximation
of the coupling ray theory to 3-D ray-based Kirchhoff prestack depth
scalar migration and compute migrated sections in two simple
inhomogeneous weakly anisotropic velocity models composed of two
layers separated by a curved interface.
The recorded complete seismic wave field is calculated using
the Fourier pseudospectral method.
We use a scalar imaging for the complete wave field
in a single-layer velocity model
with the same anisotropy as in the upper layer of the velocity model
used to calculate the recorded wave field.
We migrate reflected PP, converted PS1 and PS2 elementary waves
without the separation of the recorded complete wave field.
For migration of the S wave part we use the prevailing-frequency
approximation of the coupling ray theory and for comparison we apply
the anisotropic-ray-theory approximation. Calculations
using the prevailing-frequency approximation of the coupling ray
theory are without problems for both models. On the other hand,
for the anisotropic-ray-theory approximation in the model with weaker
anisotropy we have to use limitation of Green function maxima
otherwise the migrated sections are wrong.
In spite of complex recorded wave fields, without decomposition,
the migrated interfaces for the vertical component of the PP reflected
wave, radial and transversal components of PS1 and PS2 converted waves
are in all stacked migrated sections relatively good with exception
of spurious interface images close to the correct ones.

### Keywords

Fourier pseudospectral method, 3-D Kirchhoff prestack depth scalar
migration, anisotropic velocity model, weak anisotropy, complete
wave field, coupling ray theory

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*Seismic Waves in Complex 3-D Structures*, **31** (2022), 7-29
(ISSN 2336-3827, online at http://sw3d.cz).