An optimal true-amplitude least-squares prestack depth-migration operator

In order to define an optimal true-amplitude prestack depth migration for m ultishot and multitrace data, we develop a general methodology based on the least-squares data misfit function associated with a forward model. The am plitude of the migrated events are restored at best for any given geometry and any given preliminary filtering and amplitude correction of the data. T he migrated section is then the gradient of the cost function multiplied by a weight matrix. A study of the Hessian associated with this data misfit s hows how efficiently to find a good weight matrix via the computation of on ly few elements of this Hessian. Thanks to this matrix,the resulting migrat ion operator is optimal in the sense that it ensures the best possible rest oration of the amplitudes among the large class of least-squares migrations . Applied to a forward model based on Born, ray tracing, and diffracting poin ts approximation, this optimal migration outperforms or at least equals the classic Kirchhoff formula, since the latter belongs to the class of least- squares migrations and is only optimal for one shot and an infinite apertur e. Numerical results illustrate this construction and confirm the above expect ations.