Migration velocity analysis; theory and an iterative algorithm

Abstract Imaging complex structures inside the earth requires reasonable velocities that can be provided by applying prestack depth migration to multichannel seismic data. Migration velocity analysis is based on the principle that the images in the migrated data will be distorted when an erroneous velocity is used, and the difference of the imaged depths (residual moveout) at a common image gather is a measure of the error in the velocity.The imaging equations that we derive from Snell's law describe a general, quantitative relationship between migration images and migration velocity. Based on the imaging equations, we analyze properties of common-image gathers and derive analytical formulas to represent residual moveout in some cases. These formulas show what factors affect the sensitivity of velocity analysis, which is useful to assess errors involved in velocity estimates. In addition, we develop a simple-iteration algorithm to correct the layer velocities from residual moveout. The algorithm presented here is applicable to a medium that consists of constant-velocity layers separated by arbitrary smooth interfaces. Some computer implementations are presented for both synthetic data and physical-tank data. They demonstrate the effectiveness of our velocity analysis approach.