Least-squares reverse time migration using orthogonal dynamic encoding

Least-squares reverse time migration (LSRTM) generates better imaging result than conventional migration methods but it is computational intensive. In this paper, we present an orthogonal dynamic encoding scheme to reduce the computational cost. The inversion process is divided into stages. Each stage is composed by several subproblems which are encoded using orthogonal vectors. The result of previous subproblem is used as initial value for the next subproblem. Since the encoding function for each subproblem is orthogonal, the crosstalk introduced by encoding can be effectively canceled out by stacking gradients of subproblems in each stage. The residual crosstalk is suppressed by introducing a random phase encoding between stages. Since each super shot of subproblem is composed by several nearby single shots, the geometry of super shot is almost the same as that of single shot. Therefore, this encoding scheme is suitable for both marine data and land data. In addition, its memory requirement is almost the same as common shot LSRTM. Numerical examples on a synthetic marine streamer data show the feasibility of this method.