In this work the analytical wavefield is computed by just solving the wave equation once, differently of conventional methods that need to solve the wave equation twice: once for the source and another for the Hilbert transformed source. Our proposed method can improve the computation of wavefield separation and can bring the causal imaging condition into practice. For time extrapolation, we are using the rapid expansion method to compute the wavefield and its first order time derivative and then compute the analytical wavefield. This method is unconditionally stable and free of numerical noise. By computing the analytical wavefield, we can, therefore, separate the wavefield into down- and up-going components for each time step in an explicit way. For RTM applications, we can now employ the causal imaging condition and through a synthetic example, we could demonstrate the effectiveness of this new imaging condition. The RTM result shows that it can successfully remove the low-frequency noise which is common in the typical cross-correlation imaging condition.


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