## Sobolev scalar products in the construction of velocity models - smoothing the
regional model of Bohemian Massif for ray tracing

**Petr Bulant**
### Abstract

Minimization of a Sobolev norm during linearized
inversion of given data enables to control the model
parameters unresolved by the data being fitted.

Even if a reasonably looking model can be obtained
without minimizing the Sobolev norm, it may be too rough
for some computational methods. We may construct
models optimally smooth for given computational
methods by minimizing the corresponding Sobolev norm
during the inversion.

Probably the smoothest models are required by the ray
methods. The efficiency of ray tracing 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 model, which allows models optimum for ray tracing to
be constructed.

### Whole paper

The expanded abstract is available in
PDF (843 kB),
PostScript (2 591 kB !) and
GZIPped PostScript (288 kB).

*Expanded Abstracts of 11th Int. Congress of SBGf (Salvador 2009)
(CD-ROM)*, Brazilian Geophysical Society, 2009, 4 pp.

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