Christon M A. 1999. The influence of the mass matrix on the dispersive nature of the semi-discrete, second-order wave equation. Comput. Methods Appl. Mech. Eng., 173(1): 147-166.
[2]
Du S T. 1982. Finite element numerical solution of wave propagation in non-homogeneous medium with variable velocities. Journal of East China Petroleum Institute (in Chinese), 6(2): 1-20.
[3]
Abboud N N, Pinsky P M. 1992. Finite element dispersion analysis for the three-dimensional second-order scalar wave equation. Int. J. Numer. Methods Eng., 35(6): 1183-1218.
[4]
Ainsworth M, Monk P, Muniz W. 2006. Dispersive and dissipative properties of discontinuous Galerkin finite element methods for the second-order wave equation. J. Sci. Comput., 27(1-3): 5-40.
[5]
De Basabe J D, Sen M K. 2007. Grid dispersion and stability criteria of some common finite-element methods for acoustic and elastic wave equations. Geophysics, 72(6): T81-T95.
[6]
De Basabe J D, Sen M K, Wheeler M F. 2008. The interior penalty discontinuous Galerkin method for elastic wave propagation: grid dispersion. Geophys. J. Int., 175(1): 83-93.
[7]
Guo J. 1991. A kind of fast finite element algorithm. Geophysical Prospecting for Petroleum (in Chinese), 30(2): 36-43.
[8]
Hu F Q, Hussaini M Y, Rasetarinera P. 1999. An analysis of the discontinuous Galerkin method for wave propagation problems. J. Comput. Phys., 151(2): 921-946.
[9]
He X J, Yang D H, Wu H. 2014. Numerical dispersion and wave-field simulation of the Runge-Kutta discontinuous Galerkin method. Chinese J. Geophys. (in Chinese), 57(3): 906-917,doi:10.6038/cjg20140320.
[10]
Ke B, Zhao B, Cai J, et al. 2001. 2-D finite element acoustic wave modeling including rugged topography. 71th Annual International Meeting, SEG, Expanded Abstracts, 1199-1202.
[11]
Lee R, Cangellaris A C. 1992. A study of discretization error in the finite element approximation of wave solutions. IEEE Trans. Antennas Propag., 40(5): 542-549.
[12]
Liu J B, Sharan S K, Yao L. 1994. Wave motion and its dispersive properties in a finite element model with distortional elements. Comput. Struct., 52(2): 205-214.
[13]
Liu Y, Sen M K. 2009. A new time-space domain high-order finite-difference method for the acoustic wave equation. J. Comput. Phys., 228(23): 8779-8806.
[14]
Liu T, Wei X, De Basabe J D, et al. 2012. Grid dispersion and stability of the spectral element method with triangular elements. 82th Annual International Meeting, SEG, Expanded Abstracts, 1-5.
[15]
Liu Y S, Teng J W, Liu S L, et al. 2013. Explicit finite element method with triangle meshes stored by sparse format and its perfectly matched layers absorbing boundary condition. Chinese J. Geophys. (in Chinese), 56(9): 3085-3099,doi:10.6038/cjg20130921.
[16]
Liu Y S, Teng J W, Xu T, et al. 2014. Numerical modeling of seismic wavefield with the SEM based on Triangles. Progress in Geophysics (in Chinese), 29(4): 1715-1726,doi:10.6038/pg20140430.
[17]
Lu X, Zhang S Y, Cui X W. 2014. Finite element method for 2.5D resistivity forward modeling based on anomaly electric field. Progress in Geophysics (in Chinese), 29(6): 2718-2722,doi:10.6038/pg20140637.
[18]
Li L, Liu T, Hu T Y. 2014. Spectral element method with triangular mesh and its application in seismic modeling. Chinese J. Geophys. (in Chinese), 57(4): 1224-1234,doi:10.6038/cjg20140419.
[19]
Mullen R, Belytschko T. 1982. Dispersion analysis of finite element semidiscretizations of the two-dimensional wave equation. Int. J. Numer. Methods Eng., 18(1): 11-29.
[20]
Mulder W A. 1999. Spurious modes in finite-element discretizations of the wave equation may not be all that bad. Appl. Numer. Math., 1999, 30(4): 425-445.
[21]
Saad Y. 2000. Iterative Methods for Sparse Linear Systems. Philadelphia: SIAM.
[22]
Sun C Y. 2007. Theory and Methods of Seismic Waves. Dongying: China University of Petroleum Press (in Chinese): 31-37.
[23]
Sun C Y, Gong T J, Zhang Y L, et al. 2009. Analysis on dispersion and alias in finite-difference solution of wave equation. Oil Geophysical Prospecting (in Chinese), 44(1): 43-48.
[24]
Sun C Y, Xiao Y F, Yin X Y, et al. 2010. Study on the stability of finite difference solution of visco-elastic wave equations. Acta Seismologica Sinica (in Chinese), 32(2): 147-156.
[25]
Seriani G,Oliveira S P. 2008. Dispersion analysis of spectral element methods for elastic wave propagation. Wave Motion, 45(6): 729-744.
[26]
Wang M C. 2003. Finite Element Method. Beijing: Tsinghua University press (in Chinese): 472-475.
[27]
Wu G C, Wang H Z. 2005. Analysis of numerical dispersion in wave-field simulation. Progress in Geophysics (in Chinese), 20(1): 58-65.
[28]
Wang W S, Zhang H, Li X F. 2013. Review on application of the discontinuous Galerkin method for modeling of the seismic wavefield. Progress in Geophysics (in Chinese), 28(1): 171-179,doi:10.6038/pg20130118.
[29]
Wu Z Q, Song W J. 2013. Resistivity transverse section method and its application in quantified explanation of oblique faults. Progress in Geophysics (in Chinese), 28(5): 2748-2752,doi:10.6038/pg20130559.
[30]
Wang R, Wang M Y, Di Q Y, et al. 2014. 3D1C CSAMT modeling using finite element method. Progress in Geophysics (in Chinese), 29(2): 839-845,doi:10.6038/pg20140249.
[31]
Xu S Z. 1994. Finite Element Method for Geophysics. Beijing: Science Press (in Chinese): 39-42.
[32]
Xue D C, Wang S X, Jiao S J. 2007. Wave equation finite element modeling including rugged topography and complicated medium. Progress in Geophysics (in Chinese), 22(2): 522-529.
[33]
Xue D C, Wang S X. 2008a. Wave-equation finite element prestack reverse-time migration. Oil Geophysical Prospecting (in Chinese), 43(1): 17-21.
[34]
Xue D C, Wang S X. 2008b. Using combined mass matrix to suppress numerical dispersion. Oil Geophysical Prospecting (in Chinese), 43(3): 318-320.
[35]
Xue Z, Dong L G, Li X B, et al. 2014. Discontinuous Galerkin finite-element method for elastic wave modeling including surface topography. Chinese J. Geophys. (in Chinese), 57(4): 1209-1223,doi:10.6038/cjg20140418.
[36]
Yu K Y. 1982. Numerical analysis in the construction of synthetic seismograms by the finite element method. Journal of East China Petroleum Institute (in Chinese), 6(4): 11-27.
[37]
Yue B, Guddati M N. 2005. Dispersion-reducing finite elements for transient acoustics. J. Acoust. Soc. Am., 118(4): 2132-2141.
[38]
Yin X Y, Zhou J K, Wu G C, et al. 2014. Dispersion analysis for the finite element algorithm in acoustic wave equation numerical simulation. Acta Seismologica Sinica (in Chinese), 36(5): 944-955.
