Analytical path-summation imaging of seismic diffractions

Discussion

Path-summation images can be contaminated by tails, which come from an incomplete cancellation of hyperbolas' flanks corresponding to the lowest and highest velocities. We propose to apply Gaussian weighting scheme for tails' elimination. In that case, no additional computational cost is required besides the direct integral evaluation itself. However, the weighting approach may introduce some velocity bias into path-summation images.

Resolution of path-summation images might appear inferior to that of conventional workflows based on picking "one optimal" velocity. The loss of resolution comes from the summation over a set of diffraction images: coherent summation is not limited to the very apex of diffraction hyperbola but rather to the flat area around it. "Blurred" path-summation images naturally incorporate the uncertainty of velocity estimation. Therefore, they can be treated as diffraction probability volumes. Analytical evaluation allows path-summation imaging framework to be used to constrain the model space for diffraction imaging and inversion problems.

On the other hand, images built with velocity models from division of double path-summation integral by not weighted path-summation integral have a relatively high resolution and are not blurred. In the examples provided in this paper those images appear to be optimally focused. In the analytical double-path-summation technique, no picking is required.

Analytical path-summation imaging of seismic diffractions