Viscoelastic finite‐difference modeling

Robertsson, Johan O. A.; Blanch, Joakim O.; Symes, William W.

doi:10.1190/1.1443701

Cited by 556 publications

(310 citation statements)

References 20 publications

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“…Attenuation and dispersion is introduced to this program by application of the model of the "generalized standard linear solid" (GSLS) (Emmerich and Korn, 1987). The derivations are calculated on a standard staggered grid (SSG) (Robertsson et al, 1994).…”

Section: Resultsmentioning

confidence: 99%

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Seismic Monitoring in the Framework of the Pilot Project CLEAN

Houpt¹

2010

72nd EAGE Conference and Exhibition Incorporating SPE EUROPEC 2010

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Section: Resultsmentioning

confidence: 99%

“…3.2) (Virieux, 1986;Levander, 1988). The SSG method was first extended to viscoelastic wave propagation by Robertsson et al (1994).…”

Section: Finite-difference Methodsmentioning

confidence: 99%

Seismic Monitoring in the Framework of the Pilot Project CLEAN

Houpt¹

2010

72nd EAGE Conference and Exhibition Incorporating SPE EUROPEC 2010

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“…A line-topoint source correction (Witte, 1985) and a low-pass filter cut at 0.2 Hz are applied to the calculated wave field. Intrinsic anelasticity in pure shear is included by summing three relaxations (e.g., Robertsson et al, 1994;Blanch et al, 1995) to approximate a frequency-independent Q equal to that of PREM in the passband low-pass filter. To include the combined effects of the assumed source time function, attenuation model, and low-pass filter assumed in the pseudospectral calculation, the 2D ray-approximate method convolved the calculated pseudospectral SH wave predicted observed at 90Њ with the wave field predicted for an assumed delta-function-shaped displacement response in the far field.…”

Section: Pseudospectralmentioning

confidence: 99%

A Comparison of Synthetic Seismograms for 2D Structures: Semianalytical versus Numerical

Ni¹

2003

Bulletin of the Seismological Society of America

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Teleseismic wave fields occasionally exhibit rapid changes in travel times and waveforms over distances less than several great-circle degrees when observed at broadband arrays. These rapid changes in wave field suggest the existence of significant structural transitions occurring over scales of several hundred kilometers or less in the mid-and deep mantle. Although approximate analytical methods based on raytracing can be readily adapted to structures having arbitrarily small scale lengths, it is important to validate their accuracy against the predictions of numerical methods. Here we compare synthetics from an approximate ray-based method WKBJ modified (WKM) against the pseudospectral method for a 2D model of the S-velocity anomaly associated with the South African plume. This model consists of a uniform 3% decrease in S velocity over a broad (Ͼ10Њ) region of the mid-and deep mantle beneath South Africa, contiguous at its bottom with a thin (100-to 200-km-thick) zone of low velocity extending 30Њ westward toward South America along the coremantle boundary. Transitions between anomalous and radially symmetric structures of the test model are sharp, occurring over l0 km or less. SV and SH wave fields synthesized by the WKM and pseudospectral methods in this model generally agree with each other well. Slight mismatches in the two methods can be understood as the result of either differences in model parameterization or the effects of asymptotic approximations in the ray-based WKM method.

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“…In order to improve the accuracy and stability of a FDM in numerical modeling, many methods have been developed, including difference schemes of variable grid (Wang and Schuster, 1996;Hayashi and Burns, 1999), irregular grid (Opršal and Zahradník, 1999), standard staggered grid (Virieux, 1986;Levander, 1988;Robertsson et al, 1994;Graves, 1996), rotated staggered grid (Gold et al, 1997;Saenger and Bohlen, 2004;Bohlen and Saenger, 2006), variable time step (Tessmer, 2000), and implicit methods (Emerman et al, 1982;Zhang and Zhang, 2007).…”

Section: Introductionmentioning

confidence: 99%

Numerical modeling of wave equation by a truncated high-order finite-difference method

Liu

Sen

2009

Earthq Sci

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Finite-difference methods with high-order accuracy have been utilized to improve the precision of numerical solution for partial differential equations. However, the computation cost generally increases linearly with increased order of accuracy. Upon examination of the finite-difference formulas for the first-order and second-order derivatives, and the staggered finite-difference formulas for the first-order derivative, we examine the variation of finite-difference coefficients with accuracy order and note that there exist some very small coefficients. With the order increasing, the number of these small coefficients increases, however, the values decrease sharply. An error analysis demonstrates that omitting these small coefficients not only maintain approximately the same level of accuracy of finite difference but also reduce computational cost significantly. Moreover, it is easier to truncate for the high-order finite-difference formulas than for the pseudospectral formulas. Thus this study proposes a truncated high-order finite-difference method, and then demonstrates the efficiency and applicability of the method with some numerical examples.

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Viscoelastic finite‐difference modeling

Cited by 556 publications

References 20 publications

Seismic Monitoring in the Framework of the Pilot Project CLEAN

Seismic Monitoring in the Framework of the Pilot Project CLEAN

A Comparison of Synthetic Seismograms for 2D Structures: Semianalytical versus Numerical

Numerical modeling of wave equation by a truncated high-order finite-difference method

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