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The adjoint of the generalized beam stack operator
samples each (*t*,*x*) location in the data and stacks over a localized
window of offsets, (*x*-*l*,*x*+*l*). The trajectory of this stack is a function
designed to evaluate the local component of energy with dip equal to
the slowness parameter *p*. This energy is mapped to the model space location
.In order to
evaluate the dip, the trajectory function must have a slope at the point
(*t*,*x*) in the data equal to *p*. One function that can be
used to evaluate the local dip is a dipping line. This is often
referred to as a local slant stack Biondi (1990). The resolution of the
local slant
stack is limited by the Fresnel zone of the the linear trajectory
across the curved event. In order to increase resolution in model
space, I chose to use a parabolic trajectory for the local stack. The
parabolic trajectory estimates the local curvature of hyperbolic
events from the offset and stepout being evaluated. This estimation
of the wavefront curvature results in a larger Fresnel zone.
A hyperbolic function is also an option as a stacking trajectory but
is prohibited in the frequency domain because of time dependent
curvature. Nevertheless, the parabolic approximation of the hyperbolic
curvature is quite good for local segments of hyperbolic trajectories.

- Beam Stack Model Space and Data Space: An Illustration
- Frequency Domain Formulation
- Synthetic data
- Beam Stack Inversion

11/11/1997