Least-squares diffraction imaging using shaping regularization by anisotropic smoothing |

To solve for a seismic diffraction image , we extend the approach developed by Merzlikin and Fomel (2016) to three dimensions:

where is the objective function, and is ``observed'' data. Here, forward modeling corresponds to the chain of operators: three-dimensional path-summation integral filter (Merzlikin and Fomel, 2015,2017), azimuthal plane wave destruction (AzPWD) filter (Merzlikin et al., 2017b,2016) and three-dimensional Kirchhoff modeling . The path-summation integral filter can be treated as the probability of a diffraction at a certain location. Azimuthal plane wave destruction filter removes reflected energy perpendicular to the edges. Therefore, AzPWD emphasizes edge diffraction signature, which when measured in the direction perpendicular to the edge exhibits a hyperbolic moveout and kinematically behaves as a reflection when observed along the edge. AzPWD application is the key distinction from the 2D version of the workflow (Merzlikin and Fomel, 2016), in which plane-wave destruction filter (PWD) (Fomel, 2002) is applied along the time-distance plane (Fomel et al., 2007; Merzlikin et al., 2018). After weighting the data by path-summation integral and AzPWD filter , model fitting is constrained to most probable diffraction locations.

Least-squares diffraction imaging using shaping regularization by anisotropic smoothing |

2021-02-24