Adaptive wavelet-based finite-difference modelling of SH-wave propagation

Operto, S.; Virieux, Jean; Hustedt, Bernhard; Malfanti, Fabrizio

doi:10.1046/j.1365-246x.2002.01573.x

Cited by 11 publications

(14 citation statements)

References 37 publications

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“…The pressure wavefield is deduced through the simple addition of the two unphysical acoustic fields P x and P z , P ( x , z , t ) = P x ( x , z , t ) + P z ( x , z , t ). The two unphysical acoustic fields P x and P z are used to account for the PML absorbing boundary conditions (see Zhang & Ballmann 1997; Operto et al 2002, for application of PML boundary conditions to the SH and P‐SV wave equations). S ( x , z , t ) is the pressure source term applied to the sum of the first two equations of outside the PML layers (in that case, the γ functions are zero): Since the pressure source term is an additive term, it can be equivalently applied either to the first or second equation of system .…”

Section: The Second‐order Finite‐difference Discretizationmentioning

confidence: 99%

“…This behaviour of the rotated staggered‐grid stencil (namely, the incomplete excitation of the pressure staggered grid when an impulsional point source is considered) suggests that its dispersion properties are less good that of the classical staggered‐grid stencil. Note, however, that a simple way to remove this artefact is to strengthen the grid coupling by smoothing the source spatial distribution, namely by spreading the point source excitation on several adjacent nodes (see also the section entitled ‘Source excitation in the wavelet domain’ in Operto et al 2002). Moreover, the space increment of along the rotated direction of spatial differentiations is greater that of the classical staggered‐grid stencil for which a space increment of 2Δ ns is considered along the unrotated direction of spatial differentiations.…”

Section: The Second‐order Finite‐difference Discretizationmentioning

confidence: 99%

“…We compare time‐domain seismograms computed with a time‐space staggered‐grid method (see Operto et al (2002) for examples of application of this code in the case of the SH ‐wave equation) and the frequency‐domain methods based on the mixed‐grid and fourth‐order staggered‐grid stencils. In Figs 15, 16 and 17, we show the comparison between the seismograms computed with the time‐space method and the frequency‐domain method.…”

Section: Numerical Examplesmentioning

confidence: 99%

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Mixed-grid and staggered-grid finite-difference methods for frequency-domain acoustic wave modelling

Hustedt

Operto

Virieux

2004

Geophysical Journal International

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284

179

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S U M M A R YWe compare different finite-difference schemes for two-dimensional (2-D) acoustic frequencydomain forward modelling. The schemes are based on staggered-grid stencils of various accuracy and grid rotation strategies to discretize the derivatives of the wave equation. A combination of two O( x 2 ) staggered-grid stencils on the classical Cartesian coordinate system and the 45 • rotated grid is the basis of the so-called mixed-grid stencil. This method is compared with a parsimonious staggered-grid method based on a fourth-order approximation of the first derivative operator. Averaging of the mass acceleration can be incorporated in the two stencils. Sponge-like perfectly matched layer absorbing boundary conditions are also examined for each stencil and shown to be effective.The deduced numerical stencils are examined for both the wavelength content and azimuthal variation. The accuracy of the fourth-order staggered-grid stencil is slightly superior in terms of phase velocity dispersion to that of the mixed-grid stencil when averaging of the mass acceleration term is applied to the staggered-grid stencil.For fourth-order derivative approximations, the classical staggered-grid geometry leads to a stencil that incorporates 13 grid nodes. The mixed-grid approach combines only nine grid nodes. In both cases, wavefield solutions are computed using a direct matrix solver based on an optimized multifrontal method. For this 2-D geometry, the staggered-grid strategy is significantly less efficient in terms of memory and CPU time requirements because of the enlarged bandwidth of the impedance matrix and increased number of coefficients in the discrete stencil.Therefore, the mixed-grid approach should be suggested as the routine scheme for 2-D acoustic wave propagation modelling in the frequency domain.Modelling seismic wave propagation is essential for understanding complex wave phenomena in a realistic heterogeneous medium. Numerical results from finite-difference (FD) modelling are particularly useful since they provide the complete wavefield response. Frequency-domain forward modelling is of special interest for multisource experiments, such as tomographic experiments, because of its computational efficiency (Pratt & Worthington 1990;Štekl & Pratt 1998). Moreover, realistic rheology is easily incorporated into the modelling scheme by introducing complex velocities. The key step in frequency-domain finite-difference (FDFD) modelling that controls computational efficiency is the numerical inversion of a massive matrix equation. The matrix structure depends on the spatial derivative approximations. We shall discuss what the useful features of this matrix are for wave modelling accuracy and for computational efficiency.Elastodynamic finite-difference time-domain (FDTD) techniques moved from second-order approximations of spatial derivatives (Madariaga 1976;Virieux 1984Virieux , 1986 to higher-order approximations (Dablain 1986;Levander 1988) using staggered-grid stencils with a good trade-off between modelling acc...

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Section: The Second‐order Finite‐difference Discretizationmentioning

confidence: 99%

Section: The Second‐order Finite‐difference Discretizationmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

See 1 more Smart Citation

Mixed-grid and staggered-grid finite-difference methods for frequency-domain acoustic wave modelling

Hustedt

Operto

Virieux

2004

Geophysical Journal International

Self Cite

284

179

View full text Add to dashboard Cite

show abstract

“…In this case, only the important physics of a problem are precisely studied, a cost-effective modeling. Once the grid is adapted, the solution is obtained by some other common schemes, (e.g., the finite difference [4,[30][31][32][33][34][35][36][37][38], or finite volume [39][40][41][42][43] method) in the physical space. The wavelet coefficients of considerable values concentrate in the vicinity of high-gradient zones.…”

Section: Introductionmentioning

confidence: 99%

“…wave propagation in the nano-composites [53]. The non-projection methods were also employed for wave-propagation problems, one can refer to [35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%