Modeling 3D Laplace-Fourier domain acoustic wave equation with free-surface topography using finite-difference

We develop embedded boundary methods to handle arbitrarily shaped topography to ac- curately simulate acoustic seismic wave propagation in Laplace-Fourier (LF) 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 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 (FD) implementation of the problem.In realistic 3D geological settings underlying topography surfaces with a large velocity contrast between shallow and deep regions, simulation of acoustic wave propagation in LF domain using a spatially uniform grid can be computationally demanding, due to over-discretization of the high-velocity material. We introduce a discontinuous mesh (DM) method that exchanges information between regions, discretized with different grid spacings, to improve efficiency and convergence. We present a 3D second- and fourth-order velocity- pressure staggered-grid FD DM acoustic wave propagation method in LF domain for acoustic wave estimation using any spatial discretization ratio between meshes. We evaluate direct and iterative parallel solvers for computational speed, memory requirements and convergence. Benchmarks in realistic 3D models with extreme and realistic topography examples show more efficient and stable results for DM with direct solvers relative to uniform mesh with iterative solvers