## Sobolev scalar products in the construction of velocity models.

**Petr Bulant** ** & **
**Ludek Klimes**
### Summary

The minimization of the 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 expanded abstract

The expanded abstract is available in
PostScript (7280 kB !)
and GZIPped PostScript (1194 kB !).

*XI Venezuelan Geophysical Congress Technical Programme*,
Sociedad Venezolana de Ingenieros Geofisicos (SOVG), Caracas, 2002, 8 pp.

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