Modeling and imaging with isochron rays

Isochron rays are lines perpendicular to isochrons, which represent surfaces of constant two-way traveltime. The image of a temporal sequence of seismic impulses is a sequence of isochrons in depth. The later the time impulse the deeper the isochron. The term isochron ray arises from an analogy between the isochron “movement” and the wave propagation. While isochrons behave as wavefronts, its perpendicular lines can be regarded as rays. The speed of the isochron movement depends on the medium velocity and the source-receiver position. We introduce the term equivalent-velocity to refer to the speed of isochron movement. In the particular case of zero-offset data, the equivalent velocity is half of the medium velocity. We use the concepts of isochronrays and equivalent velocity to extend the application of the exploding reflector model to non-zero offset imaging problems. In particular, we employ these concepts to extend the use of zero-offset wave-equation algorithms for modeling and imaging commonoffset sections. In our imaging approach, the common-offset migration is implemented as a trace-by-trace algorithm in three steps: 1) equivalent velocity computation, 2) data-conditioning for zero-offset migration, and 3) zero-offset wave-equation migration. We apply this methodology for modeling and imaging synthetic common-offset sections using two kinds of algorithms: finite-difference and split-step wavefield extrapolation. We illustrate the isochron-ray imaging methodology with a field-data example and compare the results with conventional common-offset Kirchhoff migration. This methodology is attractive because (1) it permits depth migration of commonoffset sections or just pieces of that by using wave-equation algorithms, (2) it extends the use of robust zero-offset algorithms, (3) it presents favorable features for parallel processing, (4) it permits the creation of hybrid migration algorithms, and (5) it is appropriate for migration velocity analysis.