KIRCHHOFF MIGRATION USING EIKONAL EQUATION TRAVEL-TIMES

The use of ray shooting followed by interpolation of traveltimes onto a regular grid is a popular and robust method for computing diffractio n curves for Kirchhoff migration. An alternative to this method is to compute the traveltimes by directly solving the eikonal equation on a regular grid, without computing raypaths. Solving the eikonal equation on such a grid simplifies the problem of interpolating times onto the migration grid, but this method is not well defined at points where t wo different branches of the traveltime field meet. Also, computationa l and data storage issues that are relatively unimportant for performa nce in two dimensions limit the applicability of both schemes in three dimensions. A new implementation of a gridded eikonal equation solver has been designed to address these problems. A 2-D version of this al gorithm is tested by using it to generate traveltimes to migrate the M armousi synthetic data set using the exact velocity model. The results are compared with three other images: an F-X migration (a standard fo r comparison), a Kirchhoff migration using ray tracing, and a Kirchhof f migration using traveltimes generated by a commonly used eikonal equ ation solver. The F-X-migrated image shows the imaging objective more clearly than any of the Kirchhoff migrations, and we advance a heurist ic reason to explain this fact. Of the Kirchhoff migrations, the one u sing ray tracing produces the best image, and the other two are of com parable quality.