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The general framework of LSRTM consists of two steps; the first one isgenerating the RTM image and the second is applying the Least-SquaresMigration, however, the convergence of both operations consumes a lot of timeto extract the final Least-Squares Reverse-Time Migration image and moreovergenerates oversampling when simulating the data. Applying Reverse-TimeMigration to seismic data will generate results with some migration artifactsdepending on the applied imaging conditions. To overcome this dilemma, theLeast-Squares Reverse-Time Migration is applied to the migrated section throughBorn modeling and Conjugate Gradient algorithm. Vertical transverse isotropy(VTI) media yielded as the velocity decreases with depth which distorts theReverse-Time Migration results significantly. This problem can be overcome byapplying the Least-Squares Reverse-Time Migration in either the Cartesian orpseudo-depth domains by applying a proper wavefield extrapolator. Extrapolationof Least-Squares Reverse-Time Migration reconstructed wavefield using the 2Dconstant-density acoustic wave equation transformed into Riemannian domaintreats the oversampling effect of seismic signals by making even sampling andallows more amplitude to be recovered in the final migrated image...At areduced cost, the Finite Difference Riemannian wavefield extrapolator acts onthe Born modelled seismic data, producing accurately similar results to theclassical LSRTM, yet some amplitude differences are appeared due to variousimplementation issues and oversampling effect in the latter. The resultssupport that the domain transformation strategy effectively reduces thecomputational time without affecting the accuracy of the conventional LSRTMresults.

The Optimization and Application of The Propagated Riemannian Wavefield  Extrapolator in VTI Media- Pseudo-Depth Domain Least-Squares Reverse-Time  Migration