## Sensitivity Gaussian packets

**Ludek Klimes**
### Summary

Perturbations of elastic moduli and density
can be decomposed into Gabor functions.
The wave field scattered by the perturbations is then composed of
waves scattered by the individual Gabor functions.
The scattered waves can be estimated using
the first-order Born approximation with
the paraxial ray approximation.
For a particular source generating
a short-duration broad-band incident wave field
with a smooth frequency spectrum,
each Gabor function generates at most a few
scattered sensitivity Gaussian packets
propagating in determined directions.
Each of these scattered Gaussian packets
is sensitive to just a single linear combination
of the perturbations of elastic moduli and density
corresponding to the Gabor function.
This information about the Gabor function is lost
if the scattered sensitivity Gaussian packet does not fall
into the aperture covered by the receivers
and into the recording frequency band.
We illustrate this loss of information
using the difference between the 2-D Marmousi model
and the corresponding smooth velocity model.
We decompose the difference into Gabor functions.
For each of the 240 point shots, we consider 96 receivers.
For each shot and each Gabor function,
we trace the central ray of each sensitivity Gaussian packet.
If a sensitivity Gaussian packet arrives to the receiver array
within the recording time interval and frequency band,
the recorded wave field contains
information on the corresponding Gabor function.
We then decompose the difference into
the part influencing some recorded seismograms,
and the part on which we recorded no information
and which thus cannot be recovered from the reflection experiment.

### Keywords

Wave-field inversion,
elastic waves, elastic moduli, seismic anisotropy,
heterogeneous media, perturbation.

### Whole paper

The reprint is available in
PDF (4688 kB).

*Stud. geophys. geod.*, **65** (2021), 296-304.