Abstract
The 2D topography proffers a new challenge of modeling surface waves with a 4-point finite difference (FDM) model. Topographic representation of wave propagation over a certain area will result in loss of accuracy of the numerical model. Then from this the need for appropriate modifications to reduce calculation errors. The existing approach requires value representation as an internal extrapolation solution for temporary exterior conditions. It is finally by providing boundary conditions and initial conditions in the system. However, the scheme sometimes becomes unstable for very irregular topography. 1D extrapolation along the parallel path is known to produce a simple and efficient scheme. During extrapolation, the stability of the 1D hyperbolic Schema improved by disregarding the nearest interior boundary point, which is less than half the lattice distance. Given the limited difference so that the stencils from both sides of the central evaluation point can be used as a 2D form modification if there are not enough inside points. So that in propagation space, waves that move and change according to changes in time. It will be following the wave nature of one source that travels in the x and y fields whose amplitude will change exponentially against propagation time. It is by the nature of surface wave motion.