Solution of the equations of dynamic elasticity by a Chebychev spectral method

Kosloff, Dan; Kessler, David; Filho, Anibal Queiroz; Tessmer, E.; Behle, Alfred; Strahilevitz, Ronit

doi:10.1190/1.1442885

Cited by 113 publications

(68 citation statements)

References 10 publications

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“…The method including a free surface was first introduced by Kosloff et al [23] for the 2D isotropic-elastic case. For computing spatial derivatives, the scheme is based on the Fourier and Chebyshev differential operators in the horizontal and vertical directions, respectively.…”

Section: The Pseudospectral Methodsmentioning

confidence: 99%

“…A less straightforward issue using pseudospectral differential operators is to model the freesurface boundary condition. While in finite-element methods the implementation of traction-free boundary conditions is natural -simply do not impose any constraint at the surface nodes -finitedifference and pseudospectral methods require a particular boundary treatment [14,23,25,26].…”

Section: The Pseudospectral Methodsmentioning

confidence: 99%

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Elastic surface waves in crystals – Part 2: Cross-check of two full-wave numerical modeling methods

et al. 2011

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Nathalie Favretto-Cristini. Elastic surface waves in crystals -part 2: cross-check of two full-wave numerical modeling methods. Ultrasonics, Elsevier, 2011, 51 (8) AbstractWe obtain the full-wave solution for the wave propagation at the surface of anisotropic media using two spectral numerical modeling algorithms. The simulations focus on media of cubic and hexagonal symmetries, for which the physics has been reviewed and clarified in a companion paper. Even in the case of homogeneous media, the solution requires the use of numerical methods because the analytical Green's function cannot be obtained in the whole space. The algorithms proposed here allow for a general material variability and the description of arbitrary crystal symmetry at each grid point of the numerical mesh. They are based on high-order spectral approximations of the wave field for computing the spatial derivatives. We test the algorithms by comparison to the analytical solution and obtain the wave field at different faces (stress-free surfaces) of apatite, zinc and copper. Finally, we perform simulations in heterogeneous media, where no analytical solution exists in general, showing that the modeling algorithms can handle large impedance variations at the interface.

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Section: The Pseudospectral Methodsmentioning

confidence: 99%

Section: The Pseudospectral Methodsmentioning

confidence: 99%

Elastic surface waves in crystals – Part 2: Cross-check of two full-wave numerical modeling methods

et al. 2011

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“…Tessmer et al 18 and Kosloff et al 19 apply a combined Fourier and Chebyshev method to compute wave propagation in a seismic environment with surface topography and propose a three-dimensional implementation 20 . Moreover, essentially one-dimensional multidomain formulations have been proposed for irregular domains [21][22] .…”

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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“…Several sets of two-component seismograms were computed through the lithospheric model described above using a 2-D, elastic pseudospectral code [Kosloff et al, 1990]. The model was discretized at 0.6-km intervals in both directions which, given the minimum velocity in our model (3.6 km s-•), allows for frequen- …”

Section: Synthetic Seismogramsmentioning

confidence: 99%

Multiparameter two‐dimensional inversion of scattered teleseismic body waves 2. Numerical examples

Shragge¹,

Bostock²,

Rondenay³

2001

J. Geophys. Res.

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Abstract. In this paper, we investigate the formal inversion of synthetic teleseismic P coda waves for subsurface elastic properties using a ray theoretic approach which assumes single scattering [Bostock et al., this issue]. We consider a model comprising an idealized lithospheric suture zone whose geometrical configuration is drawn from previous deep crustal seismic studies. Two-dimensional, pseudospectral synthetic seismograms representing plane waves propagating through this model are preprocessed to extract an estimate of the scattered wave field generated by short-wavelength structure. These data are employed in a series of numerical simulations which examine the dependence of multiparameter inversion results on a range of input parameters. In particular, we demonstrate (1) the contrasting sensitivity which forward and backscattered waves display to structural recovery, (2) the diminution of the problem null-space accompanied by increased source coverage, (3) improvements in model reconstruction achieved through simultaneous treatment of multiple scattering modes, and (4) the robustness of the method for data sets with noise levels and receiver geometries that approach those of field experiments.

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Solution of the equations of dynamic elasticity by a Chebychev spectral method

Cited by 113 publications

References 10 publications

Elastic surface waves in crystals – Part 2: Cross-check of two full-wave numerical modeling methods

Elastic surface waves in crystals – Part 2: Cross-check of two full-wave numerical modeling methods

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

Multiparameter two‐dimensional inversion of scattered teleseismic body waves 2. Numerical examples

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