Finite‐difference modeling in transversely isotropic media

Faria, Eduardo L.; Stoffa, Paul L.

doi:10.1190/1.1443590

Cited by 46 publications

(29 citation statements)

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“…They also provide necessary wavefield solutions for imaging (especially, reverse time migration) and full waveform inversion. Many numerical methods have been proposed to solve wave equations, among which the finite-difference method has been a popular choice (e.g., Kelly et al, 1976;Virieux, 1984Virieux, , 1986Levander, 1988;Faria and Stoffa, 1994;Igel et al, 1995;Wu et al, 1996;Saenger and Bohlen, 2004;Etgen and O'Brien, 2007). Another commonly used method is the pseudospectral method (e.g., Gazdag, 1981;Kosloff and Baysal, 1982;Kosloff et al, 1984;Fornberg, 1987;Reshef et al, 1988aReshef et al, , 1988bCarcione et al, 1992;Carcione, 1999).…”

Section: Introductionmentioning

confidence: 98%

Determination of finite-difference weights using scaled binomial windows

2012

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The finite-difference method evaluates a derivative through a weighted summation of function values from neighboring grid nodes. Conventional finite-difference weights can be calculated either from Taylor series expansions or by Lagrange interpolation polynomials. The finite-difference method can be interpreted as a truncated convolutional counterpart of the pseudospectral method in the space domain. For this reason, we also can derive finite-difference operators by truncating the convolution series of the pseudospectral method. Various truncation windows can be employed for this purpose and they result in finite-difference operators with different dispersion properties. We found that there exists two families of scaled binomial windows that can be used to derive conventional finite-difference operators analytically. With a minor change, these scaled binomial windows can also be used to derive optimized finite-difference operators with enhanced dispersion properties.

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Section: Introductionmentioning

confidence: 98%

Determination of finite-difference weights using scaled binomial windows

2012

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“…The wave-field snapshots in the xy plane (transverse plane) for the displacement three components, shown in Figures 8a, 9a, and 10a, show that the wavefronts of P and S waves are a circle in the VTI medium, whereas other snapshots in Figures 8,9,and 10 show that the wavefronts of P-and S-waves are an ellipse and the qP and qSV waves show the directional dependence on propagation velocity. The qSV wavefronts can have cusps and triplications depending on the value of c 13 (Faria and Stoffa, 1994). Triplications can be observed in the horizontal component qSV wavefronts (shown in Figs.…”

Section: Wave Fields Modelingmentioning

confidence: 94%

Optimally Accurate Nearly Analytic Discrete Scheme for Wave-Field Simulation in 3D Anisotropic Media

Yang

Song

2007

Bulletin of the Seismological Society of America

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We present a new numerical method for elastic wave modeling in 3D isotropic and anisotropic media, which is called the 3D optimal nearly analytic discrete method (ONADM) in this article. This work is an extension of the 2D ONADM (Yang et al., 2004) that models acoustic and elastic waves propagating in 2D media. The formulation is derived by using a multivariable truncated Taylor series expansion and high-order interpolation approximations. Our 3D ONADM enables wave propagation to be simulated in three dimensions through isotropic and anisotropic models. Promising numerical results show that the error of the ONADM for the 3D case is less than those of the conventional finite-difference (FD) method and the so-called Lax-Wendroff correction (LWC) schemes, measured quantitatively by the rootmean-square deviation from analytical solution. The seismic wave fields in the 3D isotropic and anisotropic media are simulated and compared with those obtained by using the fourth-order LWC method and exact solutions for the acoustic wave case. We show that, compared with the conventional FD method and the LWC schemes, the ONADM for the 3D case can reduce significantly the storage space and computational costs. Numerical experiments illustrate that the ONADM provides a useful tool for the 3D large-scale isotropic and anisotropic problems and it can suppress effectively numerical dispersions caused by discretizing the 3D wave equations when too-coarse grids are used, which is the same as the 2D ONADM. Numerical modeling also implies that simultaneously using both the wave displacement and its gradients to approximate the high-order derivatives is important for both decreasing the numerical dispersion caused by the discretization of wave equations and compensating the important wave-field information included in wave-displacement gradients.

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“…The methods to solve the propagation of seismic waves mainly include wave-field simulation (Carcione et al 1992;Lan and Zhang 2011;Liu et al 2014a, b), seismic ray tracing (Cerveny 2001;Cardarelli and Cerreto 2002;Xu et al 2006Xu et al , 2008Xu et al , 2010Xu et al , 2014 and traveltime calculation using eikonal equation (Faria and Stoffa 1994;Lan and Zhang 2013a, b). Compared with the method of traveltime calculation using eikonal equation, ray tracing methods not only can obtain the traveltime of the seismic wave field, but also can get the ray trajectories in the ground (Shearer and Chapman 1989;Cerveny 2001).…”

Section: Introductionmentioning

confidence: 99%

Ray tracing of turning wave in elliptically anisotropic media with an irregular surface

Zhang

Bai

et al. 2017

Earthq Sci

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Seismic ray tracing in anisotropic media with irregular surface is crucial for the exploration of the fine crustal structure. Elliptically anisotropic medium is the type of anisotropic media with only four independent elastic parameters. Usually, this medium can be described by only the vertical phase velocity and the horizontal phase velocity for seismic wave propagation. Model parameterization in this study is described by flexible triangular grids, which is beneficial for the description of irregular surface with high degree of approximation. Both the vertical and horizontal phase velocities are defined in the triangular grids, respectively, which are used for the description of phase velocity distribution everywhere in the model by linear interpolation. We develop a shooting ray tracing method of turning wave in the elliptically anisotropic media with irregular surface. Runge-Kutta method is applied to solve the partial differential equation of seismic ray in elliptically anisotropic media. Linearly modified method is used for adjusting emergent phase angles in the shooting scheme. Numerical tests demonstrate that ray paths coincide well with analytical trajectories in transversely homogeneous elliptically anisotropic media. Seismic ray tracing results in transversely inhomogeneous elliptically anisotropic media demonstrate that our method is effective for further first-arrival tomography in elliptically anisotropic media with an irregular surface.

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Finite‐difference modeling in transversely isotropic media

Cited by 46 publications

References 0 publications

Determination of finite-difference weights using scaled binomial windows

Determination of finite-difference weights using scaled binomial windows

Optimally Accurate Nearly Analytic Discrete Scheme for Wave-Field Simulation in 3D Anisotropic Media

Ray tracing of turning wave in elliptically anisotropic media with an irregular surface

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