The pseudo-spectral "phase-shift+interpolation" (PSPI) method (Gazdag and Sguazzero, 1984) has traditionally been considered as heuristic (Bonomi et al., 1998) and low accuracy depth extrapolation explicit scheme (Biondi, 2006) in case of heterogeneous medium. High accuracy implicit schemes such as FFD (Ristow and Rühl, 1994) involve numerical solution of a lot of linear equation systems with tri-diagonal matrices by employing special matrix algorithm known as double-sweep or Thomas method. Such matrix algorithm is difficult to parallelize to be used on modern high-performance supercomputing platforms. A method is proposed to construct explicit pseudo-spectral schemes similar to PSPI but with high-order approximation. The method is an efficient tool to develop wave-equation pseudospectral 3D depth migration on high performance parallel computing platform that use GPU acceleration and CUDA technology.