Numerical modeling of seismic wavefields in transversely isotropic media with a compact staggered-grid finite difference scheme

2009 ◽  
Vol 6 (1) ◽  
pp. 42-49 ◽  
Author(s):  
Qizhen Du ◽  
Bin Li ◽  
Bo Hou
Keyword(s):  
Numerical Modeling ◽  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Transversely Isotropic ◽  
Staggered Grid ◽  
Transversely Isotropic Media ◽  
Isotropic Media

Finite Difference Modeling of Elastic Wave Propagation

2012 ◽  
Vol 433-440 ◽  
pp. 4656-4661
Author(s):  
Qiang Zhang ◽  
Qi Zhen Du ◽  
Xu Fei Gong
Keyword(s):  
Finite Difference ◽  
Elastic Wave ◽  
Difference Scheme ◽  
Transversely Isotropic ◽  
Second Order ◽  
Numerical Dispersion ◽  
Staggered Grid ◽  
Order Difference ◽  
Transversely Isotropic Media ◽  
Isotropic Media

We present a staggered-grid finite difference scheme for velocity-stress equations to simulate the elastic wave propagating in transversely isotropic media. Instead of the widely used temporally second-order difference scheme, a temporally fourth-order scheme is obtained in this paper. We approximate the third-order spatial derivatives with 2N-order difference rather than second-order or other fixed order difference as before. Thus, it could be possible to make a balanced accuracy of O (Δt4+Δx2N) with arbitrary N. Related issues such as stability criterion, numerical dispersion, source loading and boundary condition are also discussed in this paper. The numerical modeling result indicates that the scheme is reliable.

Finite‐difference modeling in transversely isotropic media

Geophysics ◽  
1994 ◽  
Vol 59 (2) ◽  
pp. 282-289 ◽  
Author(s):  
Eduardo L. Faria ◽  
Paul L. Stoffa
Keyword(s):  
Finite Difference ◽  
Time Derivative ◽  
Computational Cost ◽  
Vertical Component ◽  
Transversely Isotropic ◽  
Staggered Grid ◽  
Difference Operators ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Modeling Algorithm

We developed a modeling algorithm for transversely isotropic media that uses finite‐difference operators in a staggered grid. Staggered grid schemes are more stable than the conventional finite‐difference methods because the differences are actually based on half the grid spacing. This modeling algorithm uses the full elastic wave equation that makes possible the modeling of all kinds of waves propagating in transversely isotropic media. The spatial derivatives are represented by fourth‐order, finite‐difference operators while the time derivative is represented by a secondorder, finite‐difference operator. The algorithm has no limitation on the acquisition geometry or on the heterogeneity of the media. The program is currently formulated to work in a 2-D transversely isotropic medium but can readily be extended to 3-D. Snapshots can be obtained at any time with no additional computational cost. A four‐layer model is used to show the usefulness of the method. Horizontal and vertical component seismograms are modeled in transversely isotropic media and compared with seismograms modeled in the corresponding isotropic media.

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