Wavefield Extrapolation in the Pseudo-depth Domain

We introduce the pseudo-depth as an extension to vertical time representation of acoustic wavefield. By formulating the mapping relations between conventional depth and pseudo-depth, we derive an acoustic wave equation for isotropic media in the pseudo-depth domain. Because of a uniform vertical wavelength in the pseudo-depth domain, wavefield extrapolation requires less number of vertical samples to avoid aliasing. Reduction of samples implies a reduction of run time for finite-difference time extrapolation. To highlight its application potentials, we performed an exploding reflector modeling and zero-offset migration using pseudo-depth wavefield extrapolation. The results agree well with conventional vertical-depth modeling and migration. The pseudo-depth wavefield extrapolation also showed its potential in eliminating multiple artifacts resulting from using a discontinuous velocity model in migration.