Optimization of the shape of Gaussian beams

Karel Zacek


The applicability and accuracy of the Gaussian beam method depend on the proper choice of the shape of beams. Gaussian beams become inaccurate solutions of the elastodynamic equation if the velocity field changes considerably within the beam width. We present a procedure of determinig the optimum initial shape of Gaussian beams based on minimizing the average squared widths of Gaussian beams and smoothing the distribution of the optimum parameters of Gaussian beams.

This procedure can increase the applicability of the Gaussian beam or packet method, especially in complex structures. Moreover, it can make the use of the Gaussian beam or packet method more comfortable. The presented procedure is suitable for the optimization of the shape of Gaussian beams for Gaussian beam or packet migrations.


Asymptotic ray theory, Gaussian beams, Sobolev norm.

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In: Seismic Waves in Complex 3-D Structures, Report 11, pp. 181-201, Dep. Geophys., Charles Univ., Prague, 2001.
Submitted to Geophysical Prospecting.
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