In the presentation we describe the mathematical basis of the Gaussian beam summation method and its applications in geophysics that concern the following topics: modelling, migration, inversion and velocity model reconstruction. For each topic we emphasize specific features of the method that lead to advantages in practical applications and demonstrate these for a number of numerical experiments with synthetic benchmark data. With regard to the migration problems, we pay special attention to the difference between the Gaussian beam migration method proposed by N.R. Hill and our Gaussian beam summation method. The numerical results presented here prove that the Gaussian beam summation method can be considered a powerful tool in a variety of geophysical applications.


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