Modeling, migration, and inversion in the generalized source and receiver domain

conclusion

I extend the theory of Born modeling, migration and inversion from the conventional shot-profile domain to the generalized source and receiver domain, and to the plane-wave phase-encoding domain and the random phase-encoding domain in particular. One important advantage of these new domains is that computing the target-oriented Hessian no longer requires storing the Green's functions, which is a major obstacle preventing the Hessian computation in the original shot-profile domain. I also prove that the Hessians obtained in the generalized source and receiver domain are equivalent to those phase-encoded Hessians discussed in Tang (2008), and they both can be derived from the same modeling equations. To balance the accuracy and cost of computing the Hessian, I introduce a new phase encoding domain, i.e., the mixed phase-encoding scheme, which combines plane-wave phase encoding and random phase encoding. My preliminary tests shows that this new phase-encoding scheme achieves high accuracy with relatively low cost.

Modeling, migration, and inversion in the generalized source and receiver domain