Time–space domain scalar wave modeling by a novel hybrid staggered-grid finite-difference method with high temporal and spatial accuracies

Godunov, 1959, Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics, Mat. Sb., 47, 271 Harlow, 1965, Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. Fluids, 8, 2182, 10.1063/1.1761178 Pozrikidis, 1997 Pletcher, 2012 Yee, 1966, Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media, IEEE Trans. Antennas Propag., 14, 302, 10.1109/TAP.1966.1138693 Kunz, 1993 Chen, 1996, Time-domain staggered-grid finite-difference simulation of GPR data, 797 Taflove, 2005 Sullivan, 2013 Alterman, 1970, Seismic waves in a quarter and three-quarter plane, Geophys. J. Int., 20, 101, 10.1111/j.1365-246X.1970.tb06058.x Boore, 1972, Finite difference methods for seismic wave propagation in heterogeneous materials, Methods Comput. Phys., 11, 1 Kelly, 1976, Synthetic seismograms: a finite-difference approach, Geophysics, 41, 2, 10.1190/1.1440605 Madariaga, 1976, Dynamics of an expanding circular fault, Bull. Seismol. Soc. Am., 66, 639, 10.1785/BSSA0660030639 Virieux, 1984, SH-wave propagation in heterogeneous media: velocity-stress finite-difference method, Geophysics, 49, 1933, 10.1190/1.1441605 Virieux, 1986, P-SV wave propagation in heterogeneous media: velocity-stress finite-difference method, Geophysics, 51, 889, 10.1190/1.1442147 Levander, 1988, Fourth-order finite-difference P-SV seismograms, Geophysics, 53, 1425, 10.1190/1.1442422 Tam, 1993, Dispersion-relation-preserving finite difference schemes for computational acoustics, J. Comput. Phys., 107, 262, 10.1006/jcph.1993.1142 Robertsson, 1994, Galerkin-wavelet modeling of wave propagation: optimal finite-difference stencil design, Math. Comput. Model., 19, 31, 10.1016/0895-7177(94)90113-9 Saenger, 2000, Modeling the propagation of elastic waves using a modified finite-difference grid, Wave Motion, 31, 77, 10.1016/S0165-2125(99)00023-2 Virieux, 2009, An overview of full-waveform inversion in exploration geophysics, Geophysics, 74, WCC1, 10.1190/1.3238367 Liu, 2009, A new time–space domain high-order finite-difference method for the acoustic wave equation, J. Comput. Phys., 228, 8779, 10.1016/j.jcp.2009.08.027 Moczo, 2000, 3D fourth-order staggered-grid finite-difference schemes: stability and grid dispersion, Bull. Seismol. Soc. Am., 90, 587, 10.1785/0119990119 Moczo, 2010, On accuracy of the finite-difference and finite-element schemes with respect to P-wave to S-wave speed ratio, Geophys. J. Int., 182, 493 Moczo, 2011, 3-D finite-difference, finite-element, discontinuous-Galerkin and spectral-element schemes analysed for their accuracy with respect to P-wave to S-wave speed ratio, Geophys. J. Int., 187, 1645, 10.1111/j.1365-246X.2011.05221.x Moczo, 2014 Igel, 2017 Alford, 1974, Accuracy of finite-difference modeling of the acoustic wave equation, Geophysics, 39, 834, 10.1190/1.1440470 Chen, 1995, Parallel computing in prestack viscoacoustic pseudospectral modeling, 1289 Özdenvar, 1997, Algorithms for staggered-grid computations for poroelastic, elastic, acoustic, and scalar wave equations, Geophys. Prospect., 45, 403, 10.1046/j.1365-2478.1997.390275.x Liu, 2011, Scalar wave equation modeling with time-space domain dispersion-relation-based staggered-grid finite-difference schemes, Bull. Seismol. Soc. Am., 101, 141, 10.1785/0120100041 Tan, 2014, An efficient finite-difference method with high-order accuracy in both time and space domains for modelling scalar-wave propagation, Geophys. J. Int., 197, 1250, 10.1093/gji/ggu077 Long, 2013, A temporal fourth-order scheme for the first-order acoustic wave equations, Geophys. J. Int., 194, 1473, 10.1093/gji/ggt168 Graves, 1996, Simulating seismic wave propagation in 3D elastic media using staggered-grid finite differences, Bull. Seismol. Soc. Am., 86, 1091, 10.1785/BSSA0860041091 Moczo, 2002, 3D heterogeneous staggered-grid finite-difference modeling of seismic motion with volume harmonic and arithmetic averaging of elastic moduli and densities, Bull. Seismol. Soc. Am., 92, 3042, 10.1785/0120010167 Mittet, 2002, Free-surface boundary conditions for elastic staggered-grid modeling schemes, Geophysics, 67, 1616, 10.1190/1.1512752 Kristek, 2003, Seismic-wave propagation in viscoelastic media with material discontinuities: a 3D fourth-order staggered-grid finite-difference modeling, Bull. Seismol. Soc. Am., 93, 2273, 10.1785/0120030023 Komatitsch, 2007, An unsplit convolutional perfectly matched layer improved at grazing incidence for the seismic wave equation, Geophysics, 72, SM155, 10.1190/1.2757586 Kristek, 2009, A brief summary of some PML formulations and discretizations for the velocity-stress equation of seismic motion, Stud. Geophys. Geod., 53, 459, 10.1007/s11200-009-0034-6 Moczo, 2019, A discrete representation of material heterogeneity for the finite-difference modelling of seismic wave propagation in a poroelastic medium, Geophys. J. Int., 216, 1072, 10.1093/gji/ggy412 Luo, 1990, Parsimonious staggered grid finite-differencing of the wave equation, Geophys. Res. Lett., 17, 155, 10.1029/GL017i002p00155 Saenger, 2004, Finite-difference modeling of viscoelastic and anisotropic wave propagation using the rotated staggered grid, Geophysics, 69, 583, 10.1190/1.1707078 Di Bartolo, 2015, Theory of equivalent staggered-grid schemes: application to rotated and standard grids in anisotropic media, Geophys. Prospect., 63, 1097, 10.1111/1365-2478.12210 Liu, 2013, Time–space domain dispersion-relation-based finite-difference method with arbitrary even-order accuracy for the 2D acoustic wave equation, J. Comput. Phys., 232, 327, 10.1016/j.jcp.2012.08.025 Tan, 2014, A staggered-grid finite-difference scheme optimized in the time–space domain for modeling scalar-wave propagation in geophysical problems, J. Comput. Phys., 276, 613, 10.1016/j.jcp.2014.07.044 Chen, 2016, A k-space operator-based least-squares staggered-grid finite-difference method for modeling scalar wave propagation, Geophysics, 81, T45, 10.1190/geo2015-0090.1 Ren, 2017, Modeling of the acoustic wave equation by staggered-grid finite-difference schemes with high-order temporal and spatial accuracy, Bull. Seismol. Soc. Am., 107, 2160, 10.1785/0120170068 Berkhout, 1982 Claerbout, 1985 Pei, 2004, Numerical modeling using staggered-grid high order finite difference of elastic wave equation on arbitrary relief surface, Oil Geophys. Prospect., 39, 629 Wang, 2016, Effective finite-difference modelling methods with 2-D acoustic wave equation using a combination of cross and rhombus stencils, Geophys. J. Int., 206, 1933, 10.1093/gji/ggw250 Zhou, 2011, Prefactored optimized compact finite-difference schemes for second spatial derivatives, Geophysics, 76, WB87, 10.1190/geo2011-0048.1 Liu, 2014, Optimal staggered-grid finite-difference schemes based on least-squares for wave equation modelling, Geophys. J. Int., 197, 1033, 10.1093/gji/ggu032 Zhou, 2021, Elastic wave modeling with high-order temporal and spatial accuracies by a selectively modified and linearly optimized staggered-grid finite-difference scheme, IEEE Trans. Geosci. Remote Sens. Wang, 2021, Acoustic wave propagation with new spatial implicit and temporal high-order staggered-grid finite-difference schemes, J. Geophys. Eng., 18, 808, 10.1093/jge/gxab053 Zhang, 2013, Optimized explicit finite-difference schemes for spatial derivatives using maximum norm, J. Comput. Phys., 250, 511, 10.1016/j.jcp.2013.04.029 Yan, 2016, Optimal staggered-grid finite-difference schemes by combining Taylor-series expansion and sampling approximation for wave equation modeling, J. Comput. Phys., 326, 913, 10.1016/j.jcp.2016.09.019 He, 2019, Determining the optimal coefficients of the explicit finite-difference scheme using the Remez exchange algorithm, Geophysics, 84, S137, 10.1190/geo2018-0446.1 Zhou, 2021, Optimizing orthogonal-octahedron finite-difference scheme for 3D acoustic wave modeling by combination of Taylor-series expansion and Remez exchange method, Explor. Geophys., 52, 335, 10.1080/08123985.2020.1826890 Ren, 2015, Acoustic and elastic modeling by optimal time-space-domain staggered-grid finite-difference schemes, Geophysics, 80, T17, 10.1190/geo2014-0269.1 De Hoop, 1960, A modification of Cagniard's method for solving seismic pulse problems, Appl. Sci. Res., B, 8, 349, 10.1007/BF02920068 Castagna, 1993 Jiang, 2021, TTI equivalent medium parametrization method for the seismic waveform modelling of heterogeneous media with coarse grids, Geophys. J. Int., 227, 2016, 10.1093/gji/ggab310