Compensating finite‐difference errors in 3-D migration and modeling

Abstract

One‐pass three‐dimensional (3-D) depth migration potentially offers more accurate imaging results than does conventional two‐pass 3-D migration for variable velocity media. Conventional one‐pass 3-D migration, using the method of finite‐difference inline and crossline splitting, however, creates large errors in the image of complex structures. These errors are due to paraxial wave‐equation approximation of the one‐way wave equation, inline‐crossline splitting, and finite‐difference grid dispersion. To compensate for these errors, and still preserve the efficiency of the conventional finite‐difference splitting method, a phase‐correction operator is derived by minimizing the difference between the ideal 3-D migration (or modeling) and the actual, conventional 3-D migration (or modeling). For frequency‐space 3-D finite‐difference migration and modeling, the compensation operator is implemented using either the phase‐shift, or phase‐shift‐plus‐interpolation method, depending on the extent of lateral velocity variations. The compensation operator increases the accuracy of handling steep dips, suppresses the inline and crossline splitting error, and reduces finite‐difference grid dispersions.