Least-squares migration with gathers

Least-Squares Migration (LSM) reduces the amplitude variations due to uneven illumination and migration operator restrictions. When posed as an inversion in the angle domain, LSM compensates the angle gather amplitudes and improves their resolution. Our LSM angle extension requires an explicit computation of the Hessian matrix or Point Spread Functions (PSFs). The algorithm applies a chain of operators and their adjoints for modeling, migration, and offset to angle transformation to a grid of point scatterers distributed through the model. It effectively incorporates the spatial and angle variability of the PSF. The angular reflectivity is recovered by solving a linear system of equations that deconvolves the multidimensional PSF from the migrated image gathers. Results from the Sigsbee model and a multisensor streamer survey acquired in the Central North Sea show how LSM improves the image resolution and Amplitude Versus Angle (AVA) reliability.