MIGRATION OF REFLECTION SEISMIC DATA IN ANGLE-MIDPOINT COORDINATES

The earth's subsurface may be imaged by migrating reflection seismic data in angle-midpoint sections. An angle-midpoint trace is the part of a common midpoint gather (the set of all seismic recordings with the same source-receiver midpoint) with the same time-offset slope. An angle-midpoint section is the collection of such traces from a row of common midpoint gathers.; Migration in angle-midpoint coordinates has theoretical and practical advantages over most existing migration methods. These include improvements in sub-surface images and velocity analysis. The most widely used migration method is to migrate the hyperbolic stacks of common midpoint gathers. Although this method is very practical, the migration equations are inaccurate for steep dips, wide offsets, and reflectors of different dips in the same location. The alternative of migrating shot profiles (recordings spaced at various distances from the same shot) is theoretically sound, but is hurt by aliasing and truncation. The other method of migrating constant offset sections (one offset from each profile) is more workable, but makes dip, angle, or velocity approximations in its migration equations. The angle-midpoint migration equations make none of these approximations and have workable implementations.; There are three ways of transforming a into angle-midpoint coordinates: (1) Slant stacking sums across the common midpoint gather along a slanted linear trajectory. (2) Radial traces are extracted from the common midpoint gather along diagonal lines. (3) Snell traces are extracted from the common midpoint gather along the line formed by the part of each reflection hyperbola that has the same slope. The migration equations in each case have different accuracy and practical limitations. Slant stacks are the most accurate, while radial traces are the least accurate. However, the slant stacking often has numerical artifacts, while the radial trace transformation is very workable. Snell traces are a good compromise both in theory and practice.