Wavefield extrapolation in laterally inhomogeneous media by generalized eigenfunction transform method

Zhengsheng Yao, Gary F. Margrave

Using separation of variables the wave equation in laterally inhomogeneous media can be spatially separated into two eigen-equations corresponding to the direction of extrapolation and the other transverse direction. The two equations are connected via eigenvalues, which leads to an eigenvalue problem represented by a second order differential equation. This equation can be solved either approximately or exactly. The solutions obtained with different approximations can lead to different methods in seismic exploration seismology.