The paraxial wave equation is one of the most accurate pre-stack imaging tools for seismic data . It has been shown that pre-stack paraxial wave equation migration correctly images seismic data even for very complex velocity models (such as those containing caustics). Furthermore, the fact that the paraxial approximation yields a one-way wave equation is ideal for migration and imaging since in principle it does not generate reflections as do the acoustic and elastic wave equations. Nevertheless, the formulation and implementation of the paraxial wave equation give rise to some undesirable numerical artifacts.


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