The only way to make an excessively complex velocity model suitable for application of ray-based methods, such as the Gaussian beam or Gaussian packet methods, is to smooth it.
We have smoothed the Marmousi model (Versteeg & Grau 1991) by minimizing the second spatial derivatives of the slowness. This was done by minimizing the relevant Sobolev norm of slowness.
We show that minimizing the relevant Sobolev norm of slowness is a suitable technique for preparing the optimum models for asymptotic ray theory methods. However, the price we pay for a model suitable for ray tracing is an increase of the difference between the smoothed and original model. Similarly, the estimated error in the travel time also increases due to the difference between the models. In smoothing the Marmousi model, we have found the estimated error of travel times at the verge of acceptability.
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Zacek, K: Smoothing the Marmousi model. In: Seismic Waves in Complex 3-D Structures, Report 10, pp. 41-62, Dep. Geophys., Charles Univ., Prague, 2000.
Zacek, K: Smoothing the Marmousi model. In: Seismic Waves in Complex 3-D Structures, Report 11, pp. 161-179, Dep. Geophys., Charles Univ., Prague, 2001 [to appear in Pure and Applied Geophysics, 159 (2002)].