f Acoustic modelling on a grid of vertically varying spacing

In many cases the efficiency of high-order finite differencing schemes and the Fourier method for the acoustic wave equation is limited as the differencing operators are applied to a uniform grid. To improve this a differencing scheme is introduced in which the grid spacings can be extended or reduced by any integer factor at a given depth. This scheme adds more flexibility and efficiency to the acoustic modelling as the grid spacings can be changed according to the material properties and the model geometry. The time integration is done by the Rapid Expansion Method (REM). The only additional computational effort of the modelling scheme is eaused by the requirement to interpolate the pressure on a strip of the computational mesh where the grid spacings change.