The Gaussian Beam (GB) is an asymptotic solution of the elastodynamic equation in
the paraxial vicinity of a central ray, which approaches better the wave field than the
standard zero-order ray theory. The GB regularity in the description of the wave field, as
well as its high accuracy in some singular regions of the propagation medium, provide a
strong alternative to solve seismic modeling and imaging problems. In this dissertation , I
present a new procedure for pre-stack depth migration with true-amplitude, combining
the flexibility and robustness of Kirchhoff migration type using superposition of Gaussian
beams to represent the wave field. The proposed migration algorithm comprises in two
stacking process: the first is the beam stack applied to subsets of seismic data multiplied
by a weight function defined such that stack operator has the same formulation of the
integral of the Gaussian beams superposition; the second is a weighted diffraction stack by
means of the Kirchhoff type integral having as input the stacked data. For these reasons
it is called Kirchhoff-Gaussian-Beam (KGB) migration. In order to compare the Kirchhoff
and KGB methods with respect to the sensibility on relation to the discretization length,
we apply them to the well-know 2D Marmousi dataset using four velocity grids, i.e. 60
m, 80 m, 100 m e 150 m. As result we have that both methods present a much better
image for smaller discretization interval of the velocity grid. The amplitude spectrum of
the migrated sections provide us with the spatial frequency contents of the obtained image
sections.
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