We develop embedded boundary methods to handle arbitrarily shaped topography to accurately simulate acoustic seismic wave propagation in Laplace-Fourier domain. The purpose is to use this method to enhance accurate wave simulation near the surface. Unlike most existing methods such as the ones using curvilinear grids to fit irregular surface topography, we use regular Cartesian grid system without suffering from staircasing error, which occurs in the conventional implementations.
In this improved embedded-boundary method, we use the method of images to account for an arbitrarily curved surface by imposing ghost nodes above the surface and approximating their acoustic pressures using linear extrapolation, quadratic interpolation, or cubic interpolation. Implementing this method instead of using curvilinear grids near the boundaries greatly reduces the complexity of preprocessing procedures and the computational cost. Furthermore, using numerical examples, we show the accuracy gain and performance of our embedded-boundary methods in comparison with conventional finite-difference implementation of the problem.