Stability of the Staggered‐Grid High‐Order Difference Method for FIRST‐Order Elastic Wave Equation

Dong, Liangguo; Ma, Zaitian; Cao, Jing-Zhong

doi:10.1002/cjg2.107

Cited by 52 publications

(49 citation statements)

References 6 publications

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“…Equation (8) indicates that and are nonrotational pure P-wave field and nondispersed pure S-wave field, respectively, and they are the divergence field and curl field embedded in (7). It means that our method can achieve dual elastic wave numerical simulation with pure Pand S-modes.…”

Section: Basic Principlementioning

confidence: 97%

“…For typical grid cell ( , ), take the first-order spatial and temporary derivatives in (7); we have [6,7] +1/2…”

Section: Numerical Discretionmentioning

confidence: 99%

“…At present, using first-order velocity-stress elastic wave equation is the most prevailing and appropriate modeling method [6,7]. This can be solved using high-order staggeredgrid finite-difference scheme.…”

Section: Introductionmentioning

confidence: 99%

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Finite-Difference Simulation of Elastic Wave with Separation in Pure P- and S-Modes

Chen

2014

Journal of Computational Methods in Physics

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Elastic wave equation simulation offers a way to study the wave propagation when creating seismic data. We implement an equivalent dual elastic wave separation equation to simulate the velocity, pressure, divergence, and curl fields in pure P-and Smodes, and apply it in full elastic wave numerical simulation. We give the complete derivations of explicit high-order staggeredgrid finite-difference operators, stability condition, dispersion relation, and perfectly matched layer (PML) absorbing boundary condition, and present the resulting discretized formulas for the proposed elastic wave equation. The final numerical results of pure P-and S-modes are completely separated. Storage and computing time requirements are strongly reduced compared to the previous works. Numerical testing is used further to demonstrate the performance of the presented method.

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Section: Basic Principlementioning

confidence: 97%

“…For typical grid cell ( , ), take the first-order spatial and temporary derivatives in (7); we have [6,7] +1/2…”

Section: Numerical Discretionmentioning

confidence: 99%

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Finite-Difference Simulation of Elastic Wave with Separation in Pure P- and S-Modes

Chen

2014

Journal of Computational Methods in Physics

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“…The stability analysis method generally applies Fourier theory. Dong et al(2000) 20 derived high-order staggered-grid stability conditions for the difference equations as follows:…”

Section: Stability Conditionsmentioning

confidence: 99%

Numerical simulation of ultrasonic wave transmission experiments in rocks of shale gas reservoirs

et al. 2017

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Shale gas reservoirs have risen in importance in China’s new power source exploration and development program. The investigation of the propagation of ultrasonic waves in shale forms the basis for the full waveform application of acoustic logging data to the exploration of shale gas. Using acoustic wave theory, initial conditions, vibration source conditions, and stability conditions are developed in combination with experimental background of ultrasonic wave transmission. With improved boundary conditions, we performed numerical simulations of the ultrasound transmission experiments in shale using the high-order staggered-grid finite difference method (second-order in the time domain and fourth-order in the space domain). With programs developed within MatLab, the results obtained from numerical simulations agree well with experimental results based on physical models. In addition, using snapshots of the wave field that give a microscopic perspective, the propagation laws for ultrasonic waves can be analyzed. Using this method, human error is avoided, transmission experiments costs can be reduced and efficiency improved. This method extends the scope of experimental investigations regarding the transmission of ultrasonic waves in a shale gas reservoir with increasing stratification, and thus has great theoretical value and practical significance.

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“…Chen (2007) stated some high-order time discretizations in seismic modeling. Arbitrary staggered finite-difference formulas have also been developed for simulation of elastic waves (Dong et al, 2000;Pei, 2004).…”

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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Stability of the Staggered‐Grid High‐Order Difference Method for FIRST‐Order Elastic Wave Equation

Cited by 52 publications

References 6 publications

Finite-Difference Simulation of Elastic Wave with Separation in Pure P- and S-Modes

Finite-Difference Simulation of Elastic Wave with Separation in Pure P- and S-Modes

Numerical simulation of ultrasonic wave transmission experiments in rocks of shale gas reservoirs

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

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