Least-squares migration of incomplete reflection data

A least-squares migration algorithm is presented that reduces the migration artifacts arising from incomplete data. Instead of migrating data with the adjoint of the forward modeling operator, the normal equations are inverted by using a preconditioned linear conjugate gradient scheme that employs regularization. The modeling operator is constructed from an asymptotic acoustic integral equation, and its adjoint is the Kirchhoff migration operator. Numerical results show that the least-squares migrated sections are typically more focused than the corresponding Kirchhoff migrated sections and their reflectivity frequency distributions are closer to those of the true model frequency distribution.