Generalized Image-Domain Inversion
Generalized Image-Domain Inversion: The gradient formula is derived for the generalized image objective function and the h-offset moveout curve in the extended image domain; in practice the objective function has an extra summation over all model points in the subsurface. The summation is over the subsurface offset indices. The result shows that Y(y) is a summation of three gradients: a low-wavenumber generalized semblance optimization (H-DSO) gradient, the intermediate-wavenumber gradient associated with differential semblance optimization (DSO), and a high-wavenumber gradient associated with full-waveform inversion (FWI). This image-domain gradient has multi-scale features similar to those of wave-equation-traveltime waveform inversion in the data domain, and it can be used to partly overcome the cycle-skipping problem with FWI.