Exploration seismologists base their interpretation, skill, and judgment largely on the study of primary reflections for selected key horizons on time sections. These horizons are normally available in either CDP-stacked (i.e., unmigrated form) or time-migrated form. In regions of complex structure, the two forms of reflection can be markedly different; that is, at a common surface location the associated traveltimes to a particular reflector can differ considerably. Properly time-migrated sections can be expected to provide more realistic pictures of the geologyߝpictures which may not be simply inferred from their unmigrated counterparts, the CDP-stacked sections. The underlying principles of time migration are well described in the literature. We will, therefore, discuss only those ray-theoretical aspects that will assist later in better understanding problems related to computing interval velocities from migration velocities.
Various time migration schemes are used nowadays to transform either a CDP stacked section or common-offset sections obtained along a seismic line into a time-migrated section. One basic approach (known variously as Kirchhoff migration, Huygens-Fresnel migration, and diffraction migration) involves sum-ming scattered signals (in a weighted manner) into the apex of diffraction curves. This approach is founded on the Kirchhoff integral solution to the wave equation. It can be implemented in various ways, all of which lead to almost identical results. In the presence of strong lateral velocity gradients, however, such schemes fail to position reflections correctly (sometimes grossly so) and in that sense fail to serve the desired function of migration. The terminology originated, however, at a time when
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“Over the years, ray theory has furnished the exploration geophysicist with most of the working tools for understanding and interpreting events observed on reflection seismic sections. Even today, notwithstanding the pace at which the more powerful acoustic wave theory is introducing its new tools, ray theory, in the hands of the authors, retains its preeminence for providing insights into fundamental problems in reflection seismology. Professor Krey's earlier contributions are part of ray theory's rich heritage. Alongside C. Hewitt Dix and Hans Durbaum, he elucidated relationships between interval velocity and observed reflection moveout.”