Prestack wavefield approximations

The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations chief among them is the singularity associated with horizontally propagating waves. I introduce approximations free of such singularities, and are highly accurate. Specifically, I use Pade expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable coefficient to balance the series order and normalize the singularity. For the higher order Pade approximation the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant angle gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction.