Energy conservative SBP discretizations of the acoustic wave equation in covariant form on staggered curvilinear grids

OReilly, O. J.; Petersson, N. Anders

doi:10.1016/j.jcp.2020.109386

“…Extension to coupling nonconforming elastic-acoustic interfaces can then be achieved through straightforward modifications to the penalty terms presented above using these interpolation operators, similar to what has been presented in for the acoustic case. Additionally, similar discretization technique also based on staggered grid SBP finite-difference operators has recently been extended to curvilinear grids for the acoustic wave equation (O'Reilly and Petersson, 2020). This indicates that similar extension may also be attainable for the coupled acoustic elastic wave system, which can be applied to address the irregular geometry at the ocean bottom.…”

Section: Discussionmentioning

confidence: 99%

Explicit coupling of acoustic and elastic wave propagation in finite-difference simulations

Gao

¹

,

Keyes

²

2020

GEOPHYSICS

6

0

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We present a mechanism to explicitly couple the finite-difference discretizations of 2D acoustic and isotropic elastic wave systems that are separated by straight interfaces. Such coupled simulations allow the application of the elastic model to geological regions that are of special interest for seismic exploration studies (e.g., the areas surrounding salt bodies), while with the computationally more tractable acoustic model still being applied in the background regions. Specifically, the acoustic wave system is expressed in terms of velocity and pressure while the elastic wave system is expressed in terms of velocity and stress. Both systems are posed in first-order forms and discretized on staggered grids. Special variants of the standard finite-difference operators, namely, operators that possess the summation-by-parts property, are used for the approximation of spatial derivatives. Penalty terms, which are also referred to as the simultaneous approximation terms, are designed to weakly impose the elastic-acoustic interface conditions in the finite-difference discretizations and couple the elastic and acoustic wave simulations together. With the presented mechanism, we are able to perform the coupled elastic-acoustic wave simulations stably and accurately. Moreover, it is shown that the energy-conserving property in the continuous systems can be preserved in the discretization with carefully designed penalty terms.

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“…Extension to coupling nonconforming elastic-acoustic interfaces can then be achieved through straightforward modifications to the penalty terms presented above using these interpolation operators, similar to what has been presented in for the acoustic case. Additionally, similar discretization technique also based on staggered grid SBP finite-difference operators has recently been extended to curvilinear grids for the acoustic wave equation (O'Reilly and Petersson, 2020). This indicates that similar extension may also be attainable for the coupled acoustic elastic wave system, which can be applied to address the irregular geometry at the ocean bottom.…”

Section: Discussionmentioning

confidence: 99%

Explicit coupling of acoustic and elastic wave propagation in finite difference simulations

Gao

¹

,

Keyes

²

2020

Preprint

0

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We present a mechanism to explicitly couple the finite-difference discretizations of 2D acoustic and isotropic elastic wave systems that are separated by straight interfaces. Such coupled simulations allow the application of the elastic model to geological regions that are of special interest for seismic exploration studies (e.g., the areas surrounding salt bodies), while with the computationally more tractable acoustic model still being applied in the background regions. Specifically, the acoustic wave system is expressed in terms of velocity and pressure while the elastic wave system is expressed in terms of velocity and stress. Both systems are posed in first-order forms and discretized on staggered grids. Special variants of the standard finite-difference operators, namely, operators that possess the summation-by-parts property, are used for the approximation of spatial derivatives. Penalty terms, which are also referred to as the simultaneous approximation terms, are designed to weakly impose the elastic-acoustic interface conditions in the finite-difference discretizations and couple the elastic and acoustic wave simulations together. With the presented mechanism, we are able to perform the coupled elastic-acoustic wave simulations stably and accurately. Moreover, it is shown that the energy-conserving property in the continuous systems can be preserved in the discretization with carefully designed penalty terms.

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“…From expressions (Eqs. (22) and (23)) it is seen that the inhomogeneous nature of the speed of sound will have a more significant effect on the particle velocity vector than on the acoustic pressure. This makes it possible in principle to create methods for separately measuring the contribution to the acoustic field in an inhomogeneous medium of the density of the medium and the speed of sound in it.…”

Section: Acoustic Fieldmentioning

confidence: 99%

“…These equations are viewed as a system of equations for determining the pressure and the particle velocity vector. This approach is used to model the propagation of waves in various environments, including plasma and stellar atmospheres [19][20][21][22]. These equations are widely known, but to find analytical wave solutions of such systems given an arbitrary dependence of the density and speed of sound on the coordinates is a very difficult task.…”

Section: Introductionmentioning

confidence: 99%

Green’s Function Method for Electromagnetic and Acoustic Fields in Arbitrarily Inhomogeneous Media

Dzyuba¹,

Romashko²

2021

A Collection of Papers on Chaos Theory and Its Applications

0

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An analytical method based on the Green\'s function for describing the electromagnetic field, scalar-vector and phase characteristics of the acoustic field in a stationary isotropic and arbitrarily inhomogeneous medium is proposed. The method uses, in the case of an electromagnetic field, the wave equation proposed by the author for the electric vector of the electromagnetic field, which is valid for dielectric and magnetic inhomogeneous media with conductivity. In the case of an acoustic field, the author uses the wave equation proposed by the author for the particle velocity vector and the well-known equation for acoustic pressure in an inhomogeneous stationary medium. The approach used allows one to reduce the problem of solving differential wave equations in an arbitrarily inhomogeneous medium to the problem of taking an integral.

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Energy conservative SBP discretizations of the acoustic wave equation in covariant form on staggered curvilinear grids

Cited by 19 publications

References 40 publications

Explicit coupling of acoustic and elastic wave propagation in finite-difference simulations

Explicit coupling of acoustic and elastic wave propagation in finite-difference simulations

Explicit coupling of acoustic and elastic wave propagation in finite difference simulations

Green’s Function Method for Electromagnetic and Acoustic Fields in Arbitrarily Inhomogeneous Media

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