Compensating finite-difference errors in 3-D migration and modelingZhiming Li

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 finitedifference 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 frequencyspace 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.