Arbitrary source and receiver positioning in finite‐difference schemes using Kaiser windowed sinc functions

Hicks, G.

doi:10.1190/1.1451454

Cited by 133 publications

(93 citation statements)

References 17 publications

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“…The source was represented as a tapered sinc, a variant of the one proposed by Hicks (2002). For the mass-lumped finite elements, we only considered the augmented element of degree 3, type 2 (Chin-Joe-Kong et al, 1999), which has a more favourable time-stepping stability limit than type 1 (Zhebel et al, 2011).…”

Section: Methodsmentioning

confidence: 99%

A Comparison of Continuous Mass-lumped Finite Elements and Finite Differences for 3D

Zhebel¹,

Minisini²,

Kononov³

et al. 2012

Proceedings

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SUMMARYThe finite-difference method is widely used for time-domain modelling of the wave equation because of its ease of implementation of high-order spatial discretization schemes, parallelization and computational efficiency. However, finite elements on tetrahedral meshes are more accurate in complex geometries near sharp interfaces. We compared the fourth-order finite-difference method to fourth-order continuous masslumped finite elements in terms of accuracy and computational cost. The results show that for simple models like a cube with constant density and velocity, the finite-difference method outperforms the finite-element method by at least an order of magnitude. For a model with interior complexity and topography, however, the finite elements are about two orders of magnitude faster than finite differences.

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Section: Methodsmentioning

confidence: 99%

A Comparison of Continuous Mass-lumped Finite Elements and Finite Differences for 3D

Zhebel¹,

Minisini²,

Kononov³

et al. 2012

Proceedings

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show abstract

“…The window's properties are dictated by the combination of r and the control parameter b, where Hicks [18] provides an analysis into selecting optimal values for these. Two common options are b = 6.31 for r = 4 and b = 12.53 for r = 8 (Fig.…”

Section: Sinc Function Truncation Using Kaiser Windowsmentioning

confidence: 99%

Accurate seabed modeling using finite difference methods

et al. 2017

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Finite difference is the most widely used method for seismic wavefield modeling. However, most finitedifference implementations discretize the Earth model over a fixed grid interval. This can lead to irregular model geometries being represented by 'staircase' discretization, and potentially causes mispositioning of interfaces within the media. This misrepresentation is a major disadvantage to finite difference methods, especially if there exist strong and sharp contrasts in the physical properties along an interface. The discretization of undulated seabed bathymetry is a common example of such misrepresentation of the physical properties in finite-difference grids, as the seabed is often a particularly sharp interface owing to the rapid and considerable change in material properties between fluid seawater and solid rock. There are two issues typically involved with seabed modeling using finite difference methods: firstly, the travel times of reflections from the seabed are inaccurate as a consequence of its spatial mispositioning; secondly, artificial diffractions are generated by the staircase representation of dipping seabed bathymetry. In this paper, we propose a new method that provides a solution to these two issues by positioning sharp interfaces at fractional grid locations. To achieve this, the velocity The Unconventional Natural Gas Institute, China University of Petroleum (Beijing), Beijing 102249, China model is first sampled in a model grid that allows the center of the seabed to be positioned at grid points, before being interpolated vertically onto a regular modeling grid using the windowed sinc function. This procedure allows undulated seabed bathymetry to be represented with improved accuracy during modeling. Numerical tests demonstrate that this method generates reflections with accurate travel times and effectively suppresses artificial diffractions.

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“…The starting frequency for modeling in exploration seismics can be as small as 2 Hz which can lead to grid intervals as large as 200 m. In this framework, accurate implementation of point source at arbitrary position in a coarse grid is critical. One method has been proposed by Hicks (2002) where the point source is approximated by a windowed Sinc function. The Sinc function is defined by…”

Section: Source and Receiver Implementation On Coarse Gridsmentioning

confidence: 99%

“…The Sinc function is tapered with a Kaiser function to limit its spatial support (Hicks, 2002) . For multidimensional simulations, the interpolation function is built by tensor product construction of 1D windowed Sinc functions.…”

Section: Source and Receiver Implementation On Coarse Gridsmentioning

confidence: 99%

Seismic Waves - Research and Analysis

Kanao¹

2012

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Arbitrary source and receiver positioning in finite‐difference schemes using Kaiser windowed sinc functions

Cited by 133 publications

References 17 publications

A Comparison of Continuous Mass-lumped Finite Elements and Finite Differences for 3D

A Comparison of Continuous Mass-lumped Finite Elements and Finite Differences for 3D

Accurate seabed modeling using finite difference methods

Seismic Waves - Research and Analysis

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