Abstract
Far-field formulas are derived for the point scatterer responses, the horizontal resolution limits, and the dynamic ranges of 2-D and 3-D migrated images. Numerical tests verify the validity of these formulas for practical CDP geometries. Our results show that in the far field, where the depth is much greater than the width of the recording aperture, the horizontal resolution limit for migrated images is proportional to the depth of the scatterer and inversely proportional to the wavenumber and aperture size. Given the same recording aperture size, the 2-D prestack migration image has the same horizontal resolution limit as the corresponding 2-D poststack image. For the same aperture size, the 3-D poststack migration image has twice the resolution as the 3-D prestack migration with sources and receivers distributed in fixed areas. Also, prestack migration images have a better dynamic range than poststack migration images, and dynamic range improves with an increase in width of the recording aperture. The resolution limits are based on a Rayleigh-like zero crossing criterion.
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