Analytical path-summation imaging of seismic diffractions

Conclusions

We have developed an approach for direct and analytical path-summation imaging, which improves the accuracy and significantly reduces the computation cost of numerical summation. The proposed approach is based on velocity continuation, which describes continuous image transformation with perturbation of migration velocity, and in theory can have an infinitely small velocity discretization step. As a result, path-summation migration amounts to filtering in the frequency-wavenumber domain and has a total cost equivalent to the cost of only two FFTs.

Tail artifacts inherent to path-summation migration images can be efficiently removed by a Gaussian weighting scheme. In this case, path-summation migration can still be performed analytically. Analytical evaluation formulas for double-path summation allow for efficient migration velocity extraction based on diffractions.