## Smoothing 2-D model Pluto 1.5 for ray tracing
using Sobolev scalar products.

**Petr Bulant**
### Summary

The efficiency of ray tracing in a seismic model can be evaluated in terms of
the ``average Lyapunov exponent'' for the model.
The exponent may be approximated by
the square root of the corresponding
Sobolev norm of the functions describing the model.
We may thus construct models optimally smooth for ray tracing
by minimizing the Sobolev norm during the inversion of seismic data.

The model Pluto 1.5 is given in the form of 2-D grid of values
of the velocity.
If the ray method is to be used,
a continuous and smooth version of the model must be prepared.
Such representation of the model parameterized by tricubic B--splines
is obtained by velocity inversion
with minimization of the Sobolev norm.
Smoothness of the resulting model and its suitability for ray methods
is controlled by weighting factor of the Sobolev norm.
### Whole extended abstract

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### Related full papers

Bulant, P.:
Sobolev scalar products in the construction of velocity models -
application to model Hess and to SEG/EAGE Salt Model.
*Pure and appl. Geophys.*, **159** (2002), 1487-1506.

Bulant, P.:
Sobolev scalar products in the construction of velocity models -
application to model Hess, to SEG/EAGE Salt Model, and to model Pluto 1.5.
In: Seismic Waves in Complex 3-D Structures, Report 11,
pp. 133-159, Dep. Geophys., Charles Univ., Prague, 2001.

Extended Abstracts of 64th EAGE Conference (Florence),
EAGE, Houten, 2002, C023.

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