Illumination‐based normalization for wave‐equation depth migration

Abstract

Illumination problems caused by finite‐recording aperture and lateral velocity lensing can bias amplitudes in migration results. In this paper, I develop a normalization scheme appropriate for wave‐equation migration algorithms that compensates for irregular illumination. I generate synthetic seismic data over a reference reflectivity model, using the adjoint of wave‐equation shot‐profile migration as the forward modeling operator. I then migrate the synthetic data with the same shot‐profile algorithm. The ratio between the synthetic migration result and the initial reference model is a measure of seismic illumination. Dividing the true data migration result by this illumination function mitigates the illumination problems. The methodology can take into account reflector dip as well as both shot and receiver geometries, and, because it is based on wave‐equation migration, it naturally models the finite‐frequency effects of wave propagation. The reference model should be as close to the true model as possible; good choices include the migrated image, or a synthetic image with a single known dip that corresponds to the expected dip of a reflector of interest. Computational shortcuts allow the illumination functions to be computed at about the cost of a single migration. Results indicate that normalization can significantly reduce amplitude distortions due to irregular subsurface illumination.