3D Viscoelastic Anisotropic Seismic Modeling with High-Order Mimetic Finite Differences

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.The authors want to thank Repsol for the permission to publish the present research, carried out at the Repsol-BSC Research Center as a part of the Kaleidoscope Project. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 644602.Peer Reviewe