A wraparound elimination technique for the pseudospectral wave synthesis using an antiperiodic extension of the wavefield

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The pseudospectral method (e.g., Kosloff and Baysal, 1982) is an attractive alternative to numerical modeling schemes such as finite difference or finite element because it requires several orders of magnitude less computer memory and computation time. In the pseudospectral method, the field variables are expanded in terms of Fourier interpolation polynomials which impose periodic boundary conditions on the equation of motion. Numerical differentiation is then implemented via the discrete Fourier transform. The periodicity condition causes the periodically extended wavefield on either side of the computational domain to propagate in from the sides, interfering with the actual solution. This phenomenon is called wraparound. In many current applications (e.g., Cerjan et al., 1985), an absorbing boundary condition has been used to damp the wraparound phases through a gradual reduction of the wavefield amplitude in the vicinity of the grid boundary. Such a method works effectively when the appropriate absorption coefficients are used. However, improper selection of absorption parameters can result in reflected waves of relatively large amplitude. Thus a major disadvantage of such methods is the difficulty of selecting appropriate damping parameters to suppress both the wraparound and the boundary reflected phases.