Image-space wave-equation tomography in the generalized source domain

tomography with the encoded wavefields

It is clear from previous sections that the cost for computing the gradient of the objective function $J$ in the original shot-profile domain is at least twice the cost of a shot-profile migration, because to compute the perturbed wavefields, the background wavefields are required. Because minimizing the objective function $J$ requires a considerable number of gradient and function evaluations, image-space wave-equation tomography in the conventional shot-profile domain seems to be infeasible for large-scale 3-D applications, even with modern computer resources. To reduce the cost and make this powerful method more practical, we extend the theory of image-space wave-equation tomography to the generalized source domain, where a smaller number of synthesized shot gathers are used for computing the gradient. We discuss two different strategies to generate the generalized shot gathers, i.e., the data-space phase-encoding method and the image-space phase-encoding method, both of which can achieve considerable data reduction while still keeping the necessary kinematic information for velocity analysis.

Image-space wave-equation tomography in the generalized source domain