Numerical modeling of acoustic wave propagation is challenging for both classical finite difference methods and finite element approaches in the presence of irregular free surface topography and anomalies with high velocity contrasts. There is inaccuracy in modeling irregular boundaries in finite difference methods and time-consuming mesh generation for finite element methods. We present a hybrid approach to address these issues within the framework of the generalized multiscale finite element method (GMsFEM). In particular, we propose an efficient procedure to perform finite element based simulations without tedious mesh generation processes. The approach applies the GMsFEM to reduce computational complexity by utilizing two automatically generated grid systems. Using a complicated, 2D salt dome model, we demonstrate the accuracy of the GMsFEM solutions and the associated reduction in computing time by an order of magnitude.
The classical time domain finite difference methods that have been successfully applied to numerical modeling of seismic wave propagation (Virieux, 1986, 1984; Saenger et al., 2007; Lombard et al., 2008; Symes et al., 2009) typically face significant difficulties when free surface topographies exist. A staircase approximation of the irregular surface elevation results in artificial scattering, and several approaches have been proposed to address this difficulty: conforming grid techniques (Hestholm and Ruud, 1994; Appelö and Petersson, 2009) applying a grid mapping that changes the governing equations, and embedded boundary methods (Kreiss and Petersson, 2006; Li et al., 2010) that introduce new ghost points.
Finite element approaches such as continuous Galerkin, spectral element and discontinuous Galerkin methods can deal with topography by employing triangular or quadrilateral elements. The meshing, however, requires a description of the geometry of the entire domain, which may be too complicated. If the domain contains irregularly shaped anomalies with high velocity contrasts such as karsts and salt domes, mesh generation which honors the boundaries of these anomalies can be difficult and time-consuming.