## Resolution of prestack depth migration

**Ludek Klimes**
### Summary

The resolution of a general 3-D common-shot elastic prestack
depth migration in a heterogeneous anisotropic medium
is studied approximately, using the ray theory.
It is demonstrated that the migrated section
can approximately be represented by the convolution
of the reflectivity function
with the corresponding local resolution function.
Alternatively, it can also be approximately represented
by the convolution of the spatial distribution
of the weak-contrast displacement reflection-transmission coefficient
with the corresponding local resolution function.
The derived explicit approximate equations enable us
to predict the migration resolution approximately
without doing the whole and expensive migration.
The equations are applicable to 3-D elastic migrations
in 3-D isotropic or anisotropic, heterogeneous velocity models.

Both the reflectivity function and the spatial distribution
of the weak-contrast displacement reflection-transmission coefficient
approximately determine the linear combination
of the perturbations of elastic moduli and density
to which the migrated section is sensitive.
The imaged linear combination of the perturbations of elastic
parameters depends on the selection of the polarizations (wave types)
of the incident and back-propagated wavefields and on the directions
of propagation.

The resolution of the linear combination
of the perturbations of elastic moduli and density
in the migrated section
is determined by the above mentioned local resolution functions.
The local resolution functions
depend on the aperture and on the imaging function.
The imaging function is determined by the source time function
and by the form of the imaging functional.
The local resolution functions are considerably sensitive
to heterogeneities.
The local resolution functions in elastic media
differ from their acoustic counterparts,
especially by the existence of converted scattered waves in elastic media.

### Keywords

Elastic waves, velocity model, seismic migration, resolution,
wavefield inversion, seismic anisotropy, heterogeneous media.

### Whole paper

The reprint is available in
PDF (1456 kB).

*Stud. geophys. geod.*, **56** (2012), 457-482.