Shallow layer correction for Spectral Element like methods

Capdeville, Yann; Marigo, Jean‐Jacques

doi:10.1111/j.1365-246x.2007.03703.x

Cited by 36 publications

(46 citation statements)

References 26 publications

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“…Bozdag & Trampert 2008; Ritsema et al 2009), gravity modelling (Yegorova & Starostenko 2002), forward seismic wave propagation (e.g. Capdeville & Marigo 2008), dynamic topography studies (e.g. Faccenna & Becker 2010) and location of seismic events (e.g.…”

Section: Introductionmentioning

confidence: 99%

EPcrust: a reference crustal model for the European Plate

Molinari¹,

Morelli²

2011

Geophysical Journal International

171

181

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S U M M A R YWe present a new crustal model for the European Plate, derived from collection and critical integration of information selected from the literature. The model covers the whole European Plate from North Africa to the North Pole (20 • N-90 • N) and from the Mid-Atlantic Ridge to the Urals (40 • W-70 • E). The chosen parametrization represents the crust in three layers (sediments, upper crust and lower crust), and describes the 3-D geometry of the interfaces and seismologically relevant parameters-isotropic P-and S-wave velocity, plus density-with a resolution of 0.5 • × 0.5 • on a geographical latitude-longitude grid. We selected global and local models, derived from geological assumptions, active seismic experiments, surface wave studies, noise correlation, receiver functions. Model EPcrust presents significant advantages with respect to previous models: it covers the whole European Plate; it is a complete and internally-consistent model (with all the parameters provided, also for the sedimentary layer); it is reproducible; it is easy to update in the future by adding new contributions; and it is available in a convenient digital format. EPcrust could be used to account for crustal structure in seismic wave propagation modelling at continental scale or to compute linearized crustal corrections in continental scale seismic tomography, gravity studies, dynamic topography and other applications that require a reliable crustal structure. Because of its resolution, our model is not suited for local-scale studies, such as the computation of earthquake scenarios, where more detailed knowledge of the structure is required. We plan to update the model as new data will become available, and possibly improve its resolution for selected areas in the future.

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Section: Introductionmentioning

confidence: 99%

EPcrust: a reference crustal model for the European Plate

Molinari¹,

Morelli²

2011

Geophysical Journal International

171

181

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“…High‐order homogenization in the dynamical, non‐periodic case, has been tackled by Capdeville & Marigo (2007, 2008) for wave propagation in stratified media. More recently, Capdeville et al (2010a) proposed another method to understand how to upscale the wave equation, in 1‐D; in that paper, they suggested a homogenization procedure that can be generalized to a higher dimension in space.…”

Section: Introductionmentioning

confidence: 99%

2-D non-periodic homogenization of the elastic wave equation: SH case

Guillot¹,

Capdeville²,

Marigo

2010

Geophysical Journal International

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International audienceIn the Earth, seismic waves propagate through 3-D heterogeneities characterized by a large variety of scales, some of them much smaller than their minimum wavelength. The costs of computing the wavefield in such media using purely numerical methods, are very high. To lower them, and also to obtain a better geodynamical interpretation of tomographic images, we aim at calculating appropriate effective properties of heterogeneous and discontinuous media, by deriving convenient upscaling rules for the material properties and for the wave equation. To progress towards this goal we extend our successful work from 1-D to 2-D. We first apply the so-called homogenization method (based on a two-scale asymptotic expansion of the field variables) to model antiplane wave propagation in 2-D periodic media. These latter are characterized by short-scale variations of elastic properties, compared to the smallest wavelength of the wavefield. Seismograms are obtained using the 0th-order term of this asymptotic expansion, plus a partial first-order correction. Away from boundaries, they are in excellent agreement with solutions calculated at a much higher computational cost, using spectral elements simulations in the reference media. We then extend the homogenization of the wave equation, to 2-D non-periodic, deterministic media

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“…We consider asymptotic interface conditions which are only accurate to first-order with respect to τ and neglect all terms which areO(τ 2 ). Higher-order models would require the use of special FEs with increased regularity, unless one commits a"variational crime" as in Capdeville and Marigo (2008). The papers by Benveniste and Berdichevsky (2010) and Benveniste (2006b) do include interface conditions for higher orders in τ.…”

Section: Mathematical Model For the Interface Problemmentioning

confidence: 99%

Hybrid asymptotic-numerical modeling of thin layers for dynamic thermal analysis of structures

Tuval

Givoli

Behar

2016

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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Purpose -The purpose of this paper is to propose a computational model for thin layers, for problems of linear time-dependent heat conduction. The thin layer is replaced by a zero-thickness interface. The advantage of the new model is that it saves the need to construct and use a fine mesh inside the layer and in regions adjacent to it, and thus leads to a reduction in the computational effort associated with implicit or explicit finite element schemes. Design/methodology/approach -Special asymptotic models have been proposed for linear heat transfer and linear elasticity, to handle thin layers. In these models the thin layer is replaced by an interface with zero thickness, and specific jump conditions are imposed on this interface in order to represent the special effect of the layer. One such asymptotic interface model is the first-order Bövik-Benveniste model. In a paper by Sussmann et al., this model was incorporated in a FE formulation for linear steady-state heat conduction problems, and was shown to yield an accurate and efficient computational scheme. Here, this work is extended to the time-dependent case. Findings -As shown here, and demonstrated by numerical examples, the new model offers a costeffective way of handling thin layers in linear time-dependent heat conduction problems. The hybrid asymptotic-FE scheme can be used with either implicit or explicit time stepping. Since the formulation can easily be symmetrized by one of several techniques, the lack of self-adjointness of the original formulation does not hinder an accurate and efficient solution. Originality/value -Most of the literature on asymptotic models for thin layers, replacing the layer by an interface, is analytic in nature. The proposed model is presented in a computational context, fitting naturally into a finite element framework, with both implicit and explicit time stepping, while saving the need for expensive mesh construction inside the layer and in its vicinity.

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Shallow layer correction for Spectral Element like methods

Cited by 36 publications

References 26 publications

EPcrust: a reference crustal model for the European Plate

EPcrust: a reference crustal model for the European Plate

2-D non-periodic homogenization of the elastic wave equation: SH case

Hybrid asymptotic-numerical modeling of thin layers for dynamic thermal analysis of structures

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