3D Viscoelastic Anisotropic Seismic Modeling with High-Order Mimetic Finite Differences Miguel Ferrer, Josep de la Puente, Albert Farrés, and José E. Castillo Abstract We present a scheme to solve three-dimensional viscoelastic anisotropic wave propagation on structured staggered grids. The scheme uses a fully-staggered grid (FSG) or Lebedev grid (Lebedev, J Sov Comput Math Math Phys 4:449– 465, 1964; Rubio et al. Comput Geosci 70:181–189, 2014), which allows for arbitrary anisotropy as well as grid deformation. This is useful when attempting to incorporate a bathymetry or topography in the model. The correct representation of surface waves is achieved by means of using high-order mimetic operators (Castillo and Grone, SIAM J Matrix Anal Appl 25:128–142, 2003; Castillo and Miranda, Mimetic discretization methods. CRC Press, Boca Raton, 2013), which allow for an accurate, compact and spatially high-order solution at the physical boundary condition. Furthermore, viscoelastic attenuation is represented with a generalized Maxwell body approximation, which requires of auxiliary variables to model the convolutional behavior of the stresses in lossy media. We present the scheme’s accuracy with a series of tests against analytical and numerical solutions. Similarly we show the scheme’s performance in high-performance computing platforms. Due to its accuracy and simple pre- and post-processing, the scheme is attractive for carrying out thousands of simulations in quick succession, as is necessary in many geophysical forward and inverse problems both for the industry and academia. 1 Introduction Seismic waves occur when the subsurface is excited, by an internal event (e.g. an earthquake, an underground explosion) or an external event (e.g. the impact of a meteorite, a landslide). The behaviour of such waves can be described by means of a M. Ferrer () • J. de la Puente • A. Farrés Computer Applications in Science and Engineering, Barcelona Supercomputing Center, Jordi Girona 29, 08034 Barcelona, Spain e-mail: miguel.ferrer@bsc.es; josep.delapuente@bsc.es; albert.farres@bsc.es J.E. Castillo Computational Science Research Center, San Diego State University, 5500 Campanile Drive, San Diego, CA 92182-7720, USA e-mail: jcastillo@mail.sdsu.edu © Springer International Publishing Switzerland 2015 R.M. Kirby et al. (eds.), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014, Lecture Notes in Computational Science and Engineering 106, DOI 10.1007/978-3-319-19800-2_18 217 jcastillo@mail.sdsu.edu