## Smoothing SEG/EAGE Salt Model
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 ``average Lyapunov 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 SEG/EAGE 3-D Salt Model is given in the form of 3-D velocity cube
and several triangulated interfaces. A smooth version of the model
parameterized by tricubic B--splines is obtained by velocity inversion
with minimization of the Sobolev norm. A version
containing B-spline--parameterized interfaces is obtained by including the
data for the interfaces into the inversion.

### Whole expanded 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.

Expanded Abstracts of 71st Annual Meeting (San Antonio),
Errata, SP 5.9, Soc. Explor. Geophysicists, Tulsa, 2001.

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