Abstract: The authors present a method for solving the acoustic wave equation with variable density by using finite sine and cosine transforms. The method consists of four steps: (1) applying the finite sine or the finite cosine transform to the wave equation; (2) inserting the unknown acoustic field given by the sine or the cosine series into the transformed wave equation; (3) applying the finite difference or other approximations to the time and spatial derivatives that are not transformed; (4) computing the wavefield by using the inverse transforms and the coefficients obtained by solving the discrete equation. In comparison with other methods, the method presented here is suitable for computing synthetic seismograms in the models with strong lateral velocity and density variations.

Key words: finite sine and cosine transforms, seismic numerical modeling, strong velocity variation