Modelling and migration with orthogonal isochron rays

For increasing time values, isochrons can be regarded as expanding wavefronts and their perpendicular lines as the associated orthogonal isochron 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 orthogonal isochron-rays 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 modelling and imaging common-offset sections. In our imaging approach, the common-offset migration is implemented as a trace-by-trace algorithm in three steps: equivalent velocity computation, data conditioning for zero-offset migration and zero-offset wave-equation migration. We apply this methodology for modelling and imaging synthetic common-offset sections using two kinds of algorithms: finite-difference and split-step wavefield extrapolation. We also 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 it permits depth migration of common-offset sections or just pieces of that by using wave-equation algorithms, it extends the use of robust zero-offset algorithms, it presents favourable features for parallel processing, it permits the creation of hybrid migration algorithms and it is appropriate for migration velocity analysis.