Least-Squares Wave Equation Migration With Angle Gathers

Least-Squares migration (LSM) produces high-resolution images ready for reservoir characterization. It corrects the image amplitudes from the migration operator limitations and the uneven illumination created by a complex model. When posed as a reflectivity inversion in the angle domain, LSM compensates the angle gathers amplitudes. Our LSM algorithm explicitly computes a Hessian matrix or point spread functions (PSF) with an extra angle dimension. It applies a chain of operators and their adjoints for modeling, migration, and angle generation to a grid of point scatterers distributed through the model. The angular reflectivity is recovered by solving a linear system of equations that deconvolves the multidimensional PSF from the migrated image gathers. The implementation is efficient and effectively incorporates the spatial variability of the PSF. Results from Sigsbee2A model and a multisensor streamer survey from the Central North Sea show how our procedure improves the image resolution and the AVA reliability.