Numerical simulation of Lebedev grid for viscoelastic media with irregular free-surface
Yang Yu1,2, Huang Jianping3, Lei Jianshe1, Li Zhenchun3, Tian Kun4, Li Qingyang3
1. Key Laboratory of Crustal Dynamics, Institute of Crustal Dynamics, Chian Earthquake Administration, Beijing, 100085, China;
2. Institute of Geophysics, China Earthquake Administration, Beijing, 100081, China;
3. School of Geosciences, China University of Petroleum (East China), Qingdao, Shandong 266580, China;
4. Geophysical Research Institute, Shengli Oilfield Branch Co., SINOPEC, Dongying, Shandong 257022, China
Abstract：Based on previous research, this paper adopts a Lebedev grid (LG) for viscoelastic media as a new kind of staggered grid scheme for finite-difference modeling. Compared to Virieux's standard staggered grid (SSG), this scheme can avoid numerical dispersion from the interpolate wavefield when dealing with equations in the curvilinear coordinates. First of all, we deduce viscoelastic media wave equations based on the generalized standard linear solid (GSLS) under the curved coordinate system. And in the process of implementation, Lebedev grid in anisotropy media is used to discretize the equations. The traction image method is used to implement free-surface conditions. And for other boundaries multi-axial convolution perfectly matched layer (MC-PML) technique is chosen to absorb waves. Based on numerical tests on synthetic data, influence of both viscosity and topography on wavefield is showed, and the MC-PML in this study is stable and can effectively absorb artificial boundary reflections. Test results show that the absorption in viscoelastic media reduces seismic energy and decreases the dominant frequency, and at the same time the velocity dispersion produces traveltime difference and waveform change.
杨宇, 黄建平, 雷建设, 李振春, 田坤, 李庆洋. Lebedev网格黏弹性介质起伏地表正演模拟[J]. 石油地球物理勘探, 2016, 51(4): 698-706.
Yang Yu, Huang Jianping, Lei Jianshe, Li Zhenchun, Tian Kun, Li Qingyang. Numerical simulation of Lebedev grid for viscoelastic media with irregular free-surface. OGP, 2016, 51(4): 698-706.
Fan Jiacan.Seismic waves is viscoelastic.Journal of Seismological Research,2001,24(4):358-362.
[2]
Walsh J B.Seismic wave attenuation in rock due to friction.JGR,1966,71(10):2591-2599.
[3]
Xu T,McMechan G A.Efficient 3-D viscoelastic modeling with application to near-surface land seismic data.Geophysics,1998, 63(2):601-612.
[4]
Yong Yundong, Wang Xiwen, Wang Yuchao et al. MPI-based seismic wave field modeling in 3-D viscoelastic random cavity medium.SEG Technical Program Expanded Abstracts,2010,29:2921-2924.
Tang Qijun,Han Liguo,Wang Enli et al.2-D three-component seismic modeling for viscoelastic monoclinic media based on background of random isotropic media. Northwestern Seismological Journal, 2009, 30(1):35-39.
Shao Zhigang,Fu Rongshan,Huang Jianhua et al.Modeling seismic wave in linear viscoelastic media.Progress in Geophysics,2007,22(4):1135-1141.
[7]
Day S M,Minster J B.Numerical simulation of attenuated wavefields using a Pade approximant method.Geophysical Journal Royal Astronomical Society,1984,78(1):105-118.
[8]
Emmerich H,Korn M.Incorporation of attenuation into time-domain computations of seismic wave fields.Geophysics, 1987,52(9):1252-1264.
[9]
Carcione J M.Viscoacoustic wave propagation simulation in the earth.Geophysics,1988, 53(6):769-777.
[10]
Carcione J M.Wave propagating in anisotropic linear viscoelastic media:theory and simulated wave-fields.Geophysical Journal International,1990,101(3):739-750.
[11]
Robertsson J O A,Blanch J O,Symes W W.Viscoelastic finite-difference modeling.Geophysics,1994, 59(9):1444-1456.
[12]
Saenger E H,Bohlen T.Finite-difference modeling of viscoelastic and anisotropic wave propagation using the rotated staggered grid.Geophysics,2004,69(2):583-591.
Yan Hongyong, Liu Yang. Rotated staggered grid high-order finite-difference numerical modeling for wave propagation in viscoelastic TTI media. Chinese Journal of Geophysics, 2012, 55(4):1354-1365.
Chu Chunlei,Wang Xiutian.Seismic modeling with a finite-difference method on irregular triangular grids.Periodical of Ocean University of China, 2005, 35(1):43-48.
Yao Dezhong,Ruan Yingzheng,Liu Guangyuan.Wave equation numerical modeling of hexagonal sample by Fourier method. Chinese Journal of Computational Physics,1994,11(1):101-106.
[17]
张慧,李振春.基于双变网格算法的地震波正演模拟.地球物理学报, 2011,54(1):77-86.
Zhang Hui,Li Zhenchun.Seismic wave simulation method based on dual-variable grid.Chinese Journal of Geophysics,2011, 54(1):77-86.
[18]
Hestholm S and Rund B.2D finite-difference elastic wave modeling including surface topography.Geophysical Prospecting,1994, 42(5):371-390.
[19]
Hestholm S and Rund B.3D finite-difference elastic wave modeling including surface topography.Geophysics,1998, 63(2):613-622.
[20]
Hestholm S,Rund B and Husebye E.3-D versus 2-D finite-difference seismic synthetics including real surface topography. Physics of the Earth and Planetary Interiors,1999,113(1-4):339-354.
[21]
Hestholm S and Rund B.2D finite-difference viscoelastic wave modeling including surface topography.Geophysical Prospecting,2000, 48(2):341-373.
Hestholm S and Rund B.3D free-boundary conditions for coordinate- tranform finite-difference seismic modeling. Geophysical Prospecting,2002, 50(5):463- 474.
Zhang Wei.Finite Difference Seismic Wave Modeling in 3D Heterogeneous Media with Surface Topography and its Implementation in Strong Ground Motion Study[D].Peking University,Beijing,2006.
[25]
Lan Haiqiang,Chen Jingyi,Liu Youshan et al.Application of the perfectly matched layer in numerical modeling of wave propagation with an irregular free surface.SEG Technical Program Expanded Abstracts, 2013, 32:3515-3520.
[26]
Lisitsa V,Vsihnevskiy D.Lebedev scheme for the numerical simulation of wave propagation in 3D anisotropic elasticity. Geophysical Prospecting,2010, 58(4):619- 635.
[27]
Levander A R.4th-order finite-difference P-SV seismograms.Geophysics, 1988, 53(11):1425-1436.
Li Na,Huang Jianping,Li Zhenchun et al.The study on numerical simulation method of Lebedev Grid with dispersion improvement coefficients in TTI media.Chinese Journal of Geophysics,2014,57(1):261-269.
[29]
Lisitsa V,Vsihnevskiy D.Numerical simulation of seismic waves in models with anisotropic formations: coupling Virieux and Lebedev finite-difference schemes.Computers & Geosciences,2012, 16(4):1135-1152.
