## Sensitivity of seismic waves to the structure.

**Ludek Klimes**
### Summary

We study how the perturbations of a generally heterogeneous
isotropic or anisotropic structure manifest themselves
in the wavefield, and which perturbations can be detected
within a limited aperture and a limited frequency band.
A broad-band incident wavefield with a smooth frequency spectrum
is considered.
Infinitesimally small perturbations of elastic moduli and density
are decomposed into Gabor functions.
The wavefield scattered by the perturbations is then composed of
waves scattered by individual Gabor functions.
The scattered waves are estimated using
the first-order Born approximation with
paraxial ray approximation.

Each Gabor function generates at most 5 scattered waves,
propagating in specific directions.
A Gabor function corresponding to a low wavenumber
may generate a single broad-band unconverted wave
scattered in forward or narrow-angle directions.
A Gabor function corresponding to a high wavenumber
usually generates 0 to 5 narrow-band Gaussian packets
scattered in wide angles,
but may also occasionally generate
a narrow-band P to S converted Gaussian packet
scattered in a forward direction,
or a broad--band S to P converted wave scattered in wide angles.

For a particular source, each wave scattered by a Gabor function
at a given spatial location is sensitive to just a single linear combination
of 22 values of the elastic moduli and density
corresponding to the Gabor function.
This information about the Gabor function is lost
if the scattered wave does not fall into the aperture
covered by the receivers
and into the legible frequency band.

### Whole expanded abstract

The abstract is available in
PostScript (253 kB)
and GZIPped PostScript (31 kB).

*Extended Abstracts Book, EAGE/SEG Summer Research Workshop
on 'Processing and imaging of seismic data' Using explicit or
implicit velocity model information? (Trieste)*, T33 (4 pp.),
Eur. Assoc. Geoscientists & Engr., Houten, 2003.

SW3D
- main page of consortium ** Seismic Waves in Complex 3-D Structures **.