Eliminating time dispersion from seismic wave modeling

Koene, Erik; Robertsson, Johan O. A.; Broggini, Filippo; Андерссон, Фредрик

doi:10.1093/gji/ggx563

Cited by 63 publications

(59 citation statements)

References 18 publications

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“…For order

M_{t}

, we have

\begin{matrix} true \\ left u^{n + 1} - 2 u^{n} + u^{n - 1} = 2 \sum_{m = 1}^{M_{t} / 2} \frac{{(Δ t)}^{2 m}}{false(2 m false)!} \frac{\partial^{2 m} u^{n}}{\partial t^{2 m}}, \end{matrix}

\begin{matrix} true \\ left \frac{\partial^{2 m + 2} u^{n}}{\partial t^{2 m + 2}} = {bold-scriptM}^{- 1} (() \frac{\partial^{2 m} {boldf}^{n}}{\partial t^{2 m}} - bold-scriptK \frac{\partial^{2 m} {boldu}^{n}}{\partial t^{2 m}}), m \geq 0 . \end{matrix}

The superscript

n

denotes the values at time

t^{n} = n Δ t

. Higher‐order time stepping can be avoided altogether, of course, with Stork's dispersion correction method (Stork, 2013; Anderson et al ., 2015; Wang and Xu, 2015; Koene et al ., 2017; Qin et al ., 2017).…”

Section: Methodsmentioning

confidence: 99%

Research Note: On the error behaviour of force and moment sources in simplicial spectral finite elements

Mulder

2020

Geophysical Prospecting

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The representation of a force or moment point source in a spectral finite‐element code for modelling elastic wave propagation becomes fundamentally different in degenerate cases where the source is located on the boundary of an element. This difference is related to the fact that the finite‐element basis functions are continuous across element boundaries, but their derivatives are not. A method is presented that effectively deals with this problem. Tests on one‐dimensional elements show that the numerical errors for a force source follow the expected convergence rate in terms of the element size, apart from isolated cases where superconvergence occurs. For a moment source, the method also converges but one order of accuracy is lost, probably because of the reduced regularity of the problem. Numerical tests in three dimensions on continuous mass‐lumped tetrahedral elements show a similar error behaviour as in the one‐dimensional case, although in three dimensions the loss of accuracy for the moment source is not a severe as a full order.

show abstract

“…For order

M_{t}

, we have

\begin{matrix} true \\ left u^{n + 1} - 2 u^{n} + u^{n - 1} = 2 \sum_{m = 1}^{M_{t} / 2} \frac{{(Δ t)}^{2 m}}{false(2 m false)!} \frac{\partial^{2 m} u^{n}}{\partial t^{2 m}}, \end{matrix}

\begin{matrix} true \\ left \frac{\partial^{2 m + 2} u^{n}}{\partial t^{2 m + 2}} = {bold-scriptM}^{- 1} (() \frac{\partial^{2 m} {boldf}^{n}}{\partial t^{2 m}} - bold-scriptK \frac{\partial^{2 m} {boldu}^{n}}{\partial t^{2 m}}), m \geq 0 . \end{matrix}

The superscript

n

denotes the values at time

t^{n} = n Δ t

Section: Methodsmentioning

confidence: 99%

Research Note: On the error behaviour of force and moment sources in simplicial spectral finite elements

Mulder

2020

Geophysical Prospecting

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show abstract

“…We can use a leap-frog time-stepping scheme to step solutions forward in time, and we remove associated errors with time-dispersion transforms (Koene et al, 2018).…”

Section: Lebedev Grid Modeling In Two Dimensionsmentioning

confidence: 99%

Anisotropic elastic finite-difference modeling of sources and receivers on Lebedev grids

2021

Self Cite

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The Lebedev grid finite-difference (FD) method allows modeling of anisotropic elastic wave propagation. On Lebedev grids, erroneous point-source excitations can create spurious (non-physical) waves. The only known remedy for such artifacts in the literature is the Lisitsa-Vishnevsky method. This method uses a distributed array to create both point-sources and point-receivers on the FD grid. However, the Lisitsa-Vishnevsky method does not fully eliminate spurious artifacts. A novel approach is found in the FD-consistent point-source, which suppresses the spurious artifacts entirely. The method requires no array recording to create point-receivers. The advantage of this method over the Lisitsa-Vishnevsky method is demonstrated with two anisotropic modeling examples.

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“…By using this approach, we obtain the non-balanced SGFD coefficients with a minimal L2-norm error for equations As equation 30is independent of the velocity, thus there will be only one group of SGFD coefficients. Additionally, the time dispersion can be eliminated by using the method proposed by Koene et al (2017).…”

Section: Computation Of Coefficients Of the Non-balanced Sgfd Operatormentioning

confidence: 99%

A non-balanced staggered-grid finite-difference scheme for the first-order acoustic VTI equation modeling

Liang

Lan

Cao

2020

Journal of Applied Geophysics

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Eliminating time dispersion from seismic wave modeling

Cited by 63 publications

References 18 publications

Research Note: On the error behaviour of force and moment sources in simplicial spectral finite elements

Research Note: On the error behaviour of force and moment sources in simplicial spectral finite elements

Anisotropic elastic finite-difference modeling of sources and receivers on Lebedev grids

A non-balanced staggered-grid finite-difference scheme for the first-order acoustic VTI equation modeling

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