A new paper is added to the collection of reproducible documents: Analytical path-summation imaging of seismic diffractions
Diffraction imaging aims to emphasize small subsurface objects, such as faults, fracture swarms, channels, etc. Similarly to classical reflection imaging, velocity analysis is crucially important for accurate diffraction imaging. Path-summation migration provides an imaging method, which produces an image of the subsurface without picking a velocity model. Previous methods of path-summation imaging involve a discrete summation of the images corresponding to all possible migration velocity distributions within a predefined integration range and thus involve a significant computational cost. We propose a direct analytical formula for path-summation imaging based on the continuous integration of the images along the velocity dimension, which reduces the cost to that of only two fast Fourier transforms. The analytic approach also enables automatic migration velocity extraction from diffractions using double path-summation migration framework. Synthetic and field data examples confirm the efficiency of the proposed techniques.