Cable Tangent Stacking , by Jon F. Claerbout

Velocity estimation proceeds by summation over a hyperbolic curve and then placing the sum at zero-offset time. Hyperbolas of differing velocities are tangent at zero offset. Alternately, the sum may be placed at the time of another offset. The offset can be chosen somewhere mid-cable where the hyperbola picks up most of its energy. This procedure, called cable tangent summing yields a velocity space in which interpolation and filtering are appropriately done at constant time. Equivalently, cable-tangent velocity space is a stretching transform of the usual velocity space. The stepout dt/dv of events in velocity space contains the information of reflection coefficient vrs. angle.


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