The framework of LSRTM consists of two steps; the first one is generating the Reverse-Time Migration reflectivity image, applying the Least-Squares Migration scheme on that image and update it iteratively, however, the convergence of both operations consumes a lot of time and memory amount and moreover generates oversampling when simulating the RTM data in deeper zones. Anisotropic media yields as the velocity increase with depth which distorts the Reverse-Time Migration results significantly. This problem, in addition, can be overcome also by applying the Least-squares reverse-time migration in pseudodepth domain by projecting the migration velocity and depicting a weighted and proper wavefield extrapolator. For every point in the Cartesian space (x,y,z) there is a corresponding vertical-time-point with the coordinates (, ,) 1 2 3 hence we can interpolate the reconstructed source wavefield by drawing a Cartesian-to-Pseudodepth mapping function. Extrapolation of Least-Squares Reverse-Time Migration reconstructed wavefield transformed into Pseudodepth domain treats the aliasing of seismic signals by making even sampling and allows original amplitude to be recovered in the final migrated image. At a reduced cost, the Finite-Difference Pseudodepth wavefield extrapolator acts on the Born modelled seismic data, producing accurately similar results to the classical one, yet some amplitude differences are appeared due to various implementation issues and oversampling effect in the latter. The advanced optimizations offered by the pseudodepth domain LSRTM are 1) decreasing number of vertical samples and 2) minimizing the allocated memory. J. Claerbout principle of underground reflectors' position has been achieved in synthetic examples and its application is extended to the 2D field data by optimizing the number of vertical samples and the occupied memory to extract the pre-stack LSRTM migrated images.
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