The only way to make a too complex velocity model suitable for the ray-based methods, such as the Gaussian beam or packet methods, is to smooth it.
We have smoothed the Marmousi model by choosing a coarser grid and by minimizing the relevant derivatives of the slowness. This has been performed by minimizing the relevant Sobolev norm of the slowness.
We show that minimization of the relevant Sobolev norm of the slowness is a suitable technique for preparing the optimum models for the asymptotic ray theory methods. However, the price for a model suitable for ray tracing is an increment of the difference between the smoothed and original model. Similarly, the assumed error of travel time due to the difference between the models increases as well. In a case of smoothing the Marmousi model, we have found the assumed error of travel times on the edge of acceptability.
Due to the low frequencies under consideration, we have found the Gaussian beams and packets on the edge of applicability even in models sufficiently smoothed for ray tracing.
Velocity model, smoothing, asymptotic ray theory, Gaussian beams, Lyapunov exponent, Sobolev norm.
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Zacek, K.: Smoothing the Marmousi model. Pure and Applied Geophysics, 159 (2002), 1507-1526.