SIMULATION SEISMIC WAVE PROPAGATION IN TOPOGRAPHIC STRUCTURES USING ASYMMETRIC STAGGERED GRIDS

Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (7): 751-760.

SIMULATION SEISMIC WAVE PROPAGATION IN TOPOGRAPHIC STRUCTURES USING ASYMMETRIC STAGGERED GRIDS

孙卫涛^1,2, 杨慧珠¹

1. Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P. R. China;
2. Department of Computer Science &Technology, Tsinghua University, Beijing 100084, P. R. China

收稿日期:2002-10-25 修回日期:2004-03-25 出版日期:2004-07-18 发布日期:2004-07-18
基金资助:
the Chinese National Petroleum Corporation-Tsinghua Foundation (2002CXKF-4)

SIMULATION SEISMIC WAVE PROPAGATION IN TOPOGRAPHIC STRUCTURES USING ASYMMETRIC STAGGERED GRIDS

SUN Wei-tao ^1,2, Yang Huizhu¹

1. Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P. R. China;
2. Department of Computer Science &Technology, Tsinghua University, Beijing 100084, P. R. China

Received:2002-10-25 Revised:2004-03-25 Online:2004-07-18 Published:2004-07-18
Supported by:
the Chinese National Petroleum Corporation-Tsinghua Foundation (2002CXKF-4)

摘要/Abstract

摘要： A new 3D finite-difference(FD) method of spatially asymmetric staggered grids was presented to simulate elastic wave propagation in topographic structures.The method approximated the first-order elastic wave equations by irregular grids finite difference operator with second-order time precise and fourth-order spatial precise.Additional introduced finite difference formula solved the asymmetric problem arisen in non-uniform staggered grid scheme.The method had no interpolation between the fine and coarse grids.All grids were computed at the same spatial iteration.Complicated geometrical structures like rough submarine interface,fault and nonplanar interfaces were treated with fine irregular grids.Theoretical analysis and numerical simulations show that this method saves considerable memory and computing time,at the same time,has satisfactory stability and accuracy.

关键词: finite difference, asymmetric staggered grid, seismic wave

Abstract: A new 3D finite-difference(FD) method of spatially asymmetric staggered grids was presented to simulate elastic wave propagation in topographic structures.The method approximated the first-order elastic wave equations by irregular grids finite difference operator with second-order time precise and fourth-order spatial precise.Additional introduced finite difference formula solved the asymmetric problem arisen in non-uniform staggered grid scheme.The method had no interpolation between the fine and coarse grids.All grids were computed at the same spatial iteration.Complicated geometrical structures like rough submarine interface,fault and nonplanar interfaces were treated with fine irregular grids.Theoretical analysis and numerical simulations show that this method saves considerable memory and computing time,at the same time,has satisfactory stability and accuracy.

Key words: finite difference, asymmetric staggered grid, seismic wave

中图分类号:

孙卫涛;杨慧珠. SIMULATION SEISMIC WAVE PROPAGATION IN TOPOGRAPHIC STRUCTURES USING ASYMMETRIC STAGGERED GRIDS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(7): 751-760.

SUN Wei-tao;Yang Huizhu. SIMULATION SEISMIC WAVE PROPAGATION IN TOPOGRAPHIC STRUCTURES USING ASYMMETRIC STAGGERED GRIDS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(7): 751-760.

参考文献

[1] Alterman Z, Karal F C Jr. Propagation of elastic waves in layered media by finite difference methods[J]. Bulletin f the Seismological Society of America, 1968, 58(1):367-398.
[2] Kelly K R, Ward R W, Treiter S, et al. Synthetic seismograms, a finite difference approach[J]. Geophysics, 1976, 41(1):2-27.
[3] Virieux J. SH-wave propagation in heterogeneous media:velocity-stress finite-difference method[J]. Geophysics, 1984, 49(11):1933-1942.
[4] Virieux J. P-SV wave propagation in heterogeneous media. velocity-stress finite-difference method[J]. Geophysics, 1986, 51(4):889-901.
[5] Shortley G H, Weller R. Numerical solution of Laplace's equation[J]. J Appl Phys, 1938, 9(5):334-348.
[6] Jastram C, Tessmer E. Elastic modeling on a grid with vertically varying spacing[J]. Geophys Prosp, 1994, 42(2):357-370.
[7] Falk J. Tessmer E, Gajewski D. Tube wave modeling by the finite-differences method with varying grid spacing[J]. Pure Appl Geophys, 1996, 148(3):77-93.
[8] Tessmer E, Kosloff D, Behle A. Elastic wave propagation simulation in the presence surface topography[J]. Geophys J Internat, 1992, 108(2):621-632.
[9] Hestholm S O, Ruud B O. 2-D finite-difference elastic wave modeling including surface topography[J]. Geophys Prosp, 1994, 42(2):371-390.
[10] Oprsal I, Jiri Zahradnik. Elastic finite-difference method for irregular grids[J]. Geophysics, 1999, 64(1):240-250.
[11] Moczo P. Finite-difference technique for SH-waves in 2-D media using irregular grids-application to the seismic response problem[J]. Geophys J Internat, 1989, 99(1):321-329.
[12] Pitarka A. 3D elastic finite-difference modeling of seismic motion using staggered grids with nonuniform spacing[J]. Bull Seism Soc Am, 1999, 89(1):54-68.
[13] SUN Wei-tao, YANG Hui-zhu. Elastic wavefield calculation for heterogeneous anisotropic porous media using the 3-D irregular-grid finite-difference[J]. Acta Mechanica Solida Sinica, 2003, 16(4):283-299.
[14] SUN Wei-tao, YANG Hui-zhu. 3D irregular grids f inite difference method of elastic wave propagation in anisotropic media[J]. Chinese Journal of Geophysics, 2004, 47(2):332 - 337. (in Chinese).
[15] Levander A R. Fourth-order finite-difference P-SV seismograms[J]. Geophysics, 1988, 53(11):1425-1436.
[16] Higdon R L. Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation[J]. Mathematics of Computation, 1986, 47(141):437-459.

SIMULATION SEISMIC WAVE PROPAGATION IN TOPOGRAPHIC STRUCTURES USING ASYMMETRIC STAGGERED GRIDS

SIMULATION SEISMIC WAVE PROPAGATION IN TOPOGRAPHIC STRUCTURES USING ASYMMETRIC STAGGERED GRIDS

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	M. HAMID, M. USMAN, Zhenfu TIAN. Computational analysis for fractional characterization of coupled convection-diffusion equations arising in MHD flows[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(4): 669-692.
[2]	Yanli QIAO, Xiaoping WANG, Huanying XU, Haitao QI. Numerical analysis for viscoelastic fluid flow with distributed/variable order time fractional Maxwell constitutive models[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(12): 1771-1786.
[3]	Shitang CUI, Xiaojun NI. Propagation of combined longitudinal and torsional stress waves in a functionally graded thin-walled tube[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(12): 1717-1732.
[4]	A. ALI, M. HUSSAIN, M. S. ANWAR, M. INC. Mathematical modeling and parametric investigation of blood flow through a stenosis artery[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(11): 1675-1684.
[5]	Lingyan TANG, Songhe SONG, Hong ZHANG. High-order maximum-principle-preserving and positivity-preserving weighted compact nonlinear schemes for hyperbolic conservation laws[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(1): 173-192.
[6]	Xuyang SUN, Shaowei WANG, Moli ZHAO, Qiangyong ZHANG. Numerical solution of oscillatory flow of Maxwell fluid in a rectangular straight duct[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(11): 1647-1656.
[7]	A. RAUF, Z. ABBAS, S. A. SHEHZAD, A. ALSAEDI, T. HAYAT. Numerical simulation of chemically reactive Powell-Eyring liquid flow with double diffusive Cattaneo-Christov heat and mass flux theories[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(4): 467-476.
[8]	S. E. AHMED. Modeling natural convection boundary layer flow of micropolar nanofluid over vertical permeable cone with variable wall temperature[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(8): 1171-1180.
[9]	Hong XIA, Zhendong LUO. Optimized finite difference iterative scheme based on POD technique for 2D viscoelastic wave equation[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(12): 1721-1732.
[10]	Qingkai ZHAO, Hang XU, Longbin TAO, A. RAEES, Qiang SUN. Three-dimensional free bio-convection of nanofluid near stagnation point on general curved isothermal surface[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(4): 417-432.
[11]	Boling GUO, Qiang XU, Zhe YIN. Implicit finite difference method for fractional percolation equation with Dirichlet and fractional boundary conditions[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(3): 403-416.
[12]	Hui CHENG, Tianyou FAN, Hao WEI. Solutions for hydrodynamics of 5-and 10-fold symmetry quasicrystals[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(10): 1393-1404.
[13]	H. SALEH, I. HASHIM. Buoyant Marangoni convection of nanofluids in square cavity[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(9): 1169-1184.
[14]	Xiao-dong LI;Min JIANG;Jun-hui GAO;Da-kai LIN;Li LIU;Xiao-yan LI. Recent advances of computational aeroacoustics[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(1): 131-140.
[15]	郑子君陈璞王大钧. Unified proof to oscillation property of discrete beam[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(5): 621-636.