Accuracy of Finite‐difference Modeling of the Acoustic Wave Equation

Alford, R. M.; Kelly, Kenneth R.; Boore, David M.

doi:10.1190/1.1440470

Cited by 624 publications

(282 citation statements)

References 6 publications

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“…Alford et al (1974) comparou os resultados dos trabalhos usando diferenças finitas (DF) com resultados analíticos em modelos com quinas. Estes métodos atingem um alto grau de aproximação, desde que se tenha uma grade suficientemente fina.…”

Section: Introductionunclassified

Modelagem acústica bidimensional usando diferentes parametrizações de campos de velocidades

Santos

Figueiró

2006

Rev. Bras. Geof.

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ABSTRACT. The algorithm developed, in this work, is based on the finite difference method applied to the acoustic wave equation, assuming that the Earth has an acoustic behavior, that allow us to implement, in a numerical way, a seismic modeling employing regular grids in models representing two-dimensional geological media. Second derivatives with respect to space and time of wave equation are obtained by Taylor series expansion of fourth and second orders, respectively. The models are represented by two different kinds of parameterizations: blocks and trigonometric polynomials. Simulations of the wave propagation phenomenon are accomplished in several models represented by the two mentioned parameterizations, making possible to generate synthetic seismograms to be compared. Seismograms, obtained when the polynomial parameterization is used, show some undesired behaviors such as: production of artificial reflections, weakening of reflection events, suppression of diffractions, and a little alteration in calculated traveltimes and amplitudes. By the other hand, some advantages of the proposed polynomial parameterization are: economy of computer memory space (because a complicated velocity model can be represented by a few quantity of coefficients, it means: the model is not more stored in a file, but it is compressed, or contained, in a mathematical formula or an analytical representation); production of a smooth velocity model (useful to generate a time field to be used in seismic migration, for example, in reverse time migration); the polynomial coefficients are just the parameters of the model to be estimated by an inversion procedure (independently of the degree of geometrical complication of the model and how is varying the seismic velocity on it); realistic models are better represented by trigonometric polynomial than block parameterization; and the ambiguity commonly present in inversion techniques results, is reduced if sufficient data is available. Gibbs effects, present in polynomial representations, is avoided by the finite differences method by choosing conveniently the knots of the mesh or increasing the number of polynomial coefficients. RESUMO.O algoritmo desenvolvido neste trabalhoé baseado no método das diferenças finitas aplicadoà equação acústica da onda, assumindo que a Terra se comporta como um meio acústico, que permite implementar numericamente uma modelagem sísmica empregando malhas regulares em modelos que representam meios geológicos bidimensionais. As derivadas segundas presentes na equação da onda foram obtidas por expansões da série de Taylor de quarta ordem, para o caso espacial, e de segunda, para o temporal. Os modelos foram representados por dois tipos distintos de parametrizações: por blocos e polinomial trigonométrica. São apresentadas simulações do fenômeno de propagação de ondas em vários modelos, representados pelas duas parametrizações mencionadas, possibilitando, assim, a geração de sismogramas sintéticos para comparação. Os sismogramas obtidos, com a parametrização poli...

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Section: Introductionunclassified

Modelagem acústica bidimensional usando diferentes parametrizações de campos de velocidades

Santos

Figueiró

2006

Rev. Bras. Geof.

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“…Alford et al 9 model acoustic scattering with a higher order scheme and Kelly et al 10 show how complex interfaces can be incorporated into the simulations. These techniques handle most complex material geometries but are limited by numerical dispersion, preventing the modeling of waves propagating over large distances, as well as the inability to impose the correct conditions on the statevariables across material interfaces.…”

Section: Introductionmentioning

confidence: 99%

A multi-domain Chebyshev collocation method for predicting ultrasonic field parameters in complex material geometries

Nielsen¹,

Hesthaven

2002

Ultrasonics

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In many areas of acoustical imaging, such as ultrasonic non-destructive evaluation (NDE), a realistic calculation of ultrasonic field parameters and associated elastic wave scattering requires the treatment of discontinuous, layered solids in complex geometries. These facts suggest the need for an accurate and geometrically flexible numerical approach for the simulation of the ultrasonic field, rather than reliance on semi-analytic solutions.In this paper we present an approach for solving the elastic wave equation in discontinuous scattering related to ultrasonic NDE are presented as evidence of the accuracy and flexibility of the proposed computational method.

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“…This inequality bounds the maximum possible time step dt as a function of the space step size dx and of the maximum velocity v max . The second is the numerical dispersion relation [3] (15)…”

Section: The 2d Acoustic Seismic Equation and Its Numerical Modelmentioning

confidence: 99%

“…Here we assume only P-wave propagation and heterogeneous density data that are small if compared to pressure and source term variations. In this case [3,7], the seismic wave propagation can be approximated by the following equation:…”

Section: The 2d Acoustic Seismic Equation and Its Numerical Modelmentioning

confidence: 99%

“…However, if we use the same order p for all the grid points of the spatial domain, the efficiency decreases and the computational time increases. As a matter of fact the numerical dispersion depends on the local velocity, but the constraint associated to the numerical dispersion is related to the minimum velocity in the whole spatial domain (see [3]). See also [4] for a review of the recent developments in finite-difference modelling of seismic wave propagation and earthquake motion.…”

Section: Introductionmentioning

confidence: 99%

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A local adaptive method for the numerical approximation in seismic wave modelling

Galuzzi

Zampieri

Stucchi

2017

Communications in Applied and Industrial Mathematics

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We propose a new numerical approach for the solution of the 2D acoustic wave equation to model the predicted data in the field of active-source seismic inverse problems. This method consists in using an explicit finite difference technique with an adaptive order of approximation of the spatial derivatives that takes into account the local velocity at the grid nodes. Testing our method to simulate the recorded seismograms in a marine seismic acquisition, we found that the low computational time and the low approximation error of the proposed approach make it suitable in the context of seismic inversion problems.

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Accuracy of Finite‐difference Modeling of the Acoustic Wave Equation

Cited by 624 publications

References 6 publications

Modelagem acústica bidimensional usando diferentes parametrizações de campos de velocidades

Modelagem acústica bidimensional usando diferentes parametrizações de campos de velocidades

A multi-domain Chebyshev collocation method for predicting ultrasonic field parameters in complex material geometries

A local adaptive method for the numerical approximation in seismic wave modelling

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