Postdoctor LIU Hongwei and his teacher LIU Hong present the idea of solving one-way wave equation (OWE) using the Fourier integral method, which represents OWE as a Fourier integral equation and solves it in dual spaces (both space and wave-number domains).

By doing this, they can propagate wave-fields up to nearly 90 angle from the vertical direction in the presence of lateral velocity variations. The proposed method is stable, does not suffer from the numerical dispersion, and overcomes the azimuthal anisotropy problem when extended to three dimensions. They take advantages of the Graphic Processing Unit (GPU) and use the matrix multiplication technique to accelerate the algorithm.

Fig. 1. Modulus of the whole wave-field extrapolation operator. (Image by LIU)

Fig. 2. Tiled-calculation principle of the matrix multiplication for the Fourier integral method. (Image by LIU)

Fig. 3. Sigsbee 2A model tests. Migration results of PSPI and the GPU-based FI methods. The improvement of FI over the other two methods is obvious, especially in the enlarged area. (Image by LIU)

Liu et al. A Fourier integral algorithm and its GPU/CPU collaborative implementation for one-way wave equation migration.Computers & Geosciences. 2012, 45: 139-148 (Download Here)