Wavefield Extrapolation in Pseudo-depth Domain

Extrapolating seismic waves in Cartesian coordinate is prone to uneven spatial sampling, because the seismic wavelength tends to grow with depth, as velocity increase. We transform the vertical depth axis to a pseudo one using a velocity weighted mapping, which can effectively mitigate this wavelength variation. We derive acoustic wave equations in this new domain based on the direct transformation of the Laplacian derivatives, which admits solutions that are more accurate and stable than those derived from the kinematic transformation. The anisotropic versions of these equations allow us to isolate the vertical velocity influence and reduce its impact on modeling and imaging. The major benefit of extrapolating wavefields in pseudo-depth space is its near uniform wavelength as opposed to the normally dramatic change of wavelength with the conventional approach. Time wavefield extrapolation on a complex velocity shows some of the features of this approach.