Limited‐aperture migration

I establish a general theory on the true‐amplitude migration with limited aperture. The key point of this theory is to find the true‐amplitude weight function, eliminating the contribution from the boundary of the migration aperture, or edge effect. I show that the true‐amplitude weight function is a singular generalized function defined by the migration aperture. If it is used without regularization, the singular weight function reduces a diffraction stack to the distribution of the amplitude at a given traveltime to every point along a corresponding isochron. After regularization, I obtain a formula for the true‐amplitude weight function as a weak solution having the same global properties as the fundamental solution to the governing equation derived here. In comparison with other published weight functions that disregard migration aperture, this theory contains a taper function that makes the obtained weight function suitable for the migration with limited aperture. If the migration aperture goes to in...

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