3D Viscoelastic Anisotropic Seismic Modeling with High-Order Mimetic Finite Differences
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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.
CitationFerrer, Miguel [et al.]. 3D Viscoelastic Anisotropic Seismic Modeling with High-Order Mimetic Finite Differences. A: "Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. Selected papers from the ICOSAHOM conference, June 23-27, 2014, Salt Lake City, Utah, USA". Springer, 2015, p. 217-225.
Is part ofLecture Notes in Computational Science and Engineering, 106 (2015)