An Analysis of New Mixed Finite Elements for the Approximation of Wave Propagation Problems

Bécache, Éliane; Joly, Patrick; Tsogka, Chrysoula

doi:10.1137/s0036142998345499

Cited by 122 publications

(114 citation statements)

References 22 publications

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“…The finite elements are compatible with mass-lumping, which leads to explicit time discretization schemes. For the velocity, we use a new finite element method 33,34 and for the pressure we use 1 P discontinuous functions (this is a different choice from the one in Refs. 33-34)).…”

Section: Methodsmentioning

confidence: 99%

Simulation of seismic response in an idealized city

Tsogka

Wirgin

2003

Soil Dynamics and Earthquake Engineering

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We study the seismic response of an idealized 2D 'city', constituted by ten non equallyspaced, non equally-sized, homogenized blocks (i.e., buildings or groups of buildings) anchored in a soft soil layer overlying a hard halfspace. Our results display strong response inside the blocks and on the ground which qualitatively match the responses observed in some earthquake-prone cities. Keywords: earthquakes, cities, beating, amplification and long coda of vibrationsA noticeable feature of many earthquake-prone cities such as Kobe 1 (Japan), Izmit 2 (Turkey), Nice 3 (France), Mexico City 4-6 , Los Angeles 7-10 etc., is that they are partially or wholly built on soft soil. A straightforward 1D analysis 11 (which takes no account of the presence of the buildings) shows that the soft layer increases the seismic vulnerability of the city in that it is responsible for amplification of ground motion during an earthquake.However, the 1D model does not account either for the beating phenomena and very long codas in the building vibrations, nor for the large spatial variability of response, repeatedly observed in sites such as Mexico City 5,6 .To analyze the possible causes of these puzzling effects, we study the action of a seismic wave on a relatively-simple structural model with both geological and man-made features. Our 2D model has three components (from bottom to top in Fig.1): a hard half space (HHS), overlaid by a soft soil layer (SL), in which are partially imbedded a set of even softer blocks (SB). HHS and SL are geological features, the set of SB, which are homogenized for the purpose of the analysis (see fig.2), is man-made and constitutes the 'visible' component of an idealized city.First consider the case in which the blocks are absent. Then the stress-free surface (upper boundary of the soft layer constituting the ground) is a straight horizontal line (in Fig. 1

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Section: Methodsmentioning

confidence: 99%

Simulation of seismic response in an idealized city

Tsogka

Wirgin

2003

Soil Dynamics and Earthquake Engineering

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“…This code implements the numerical method described in [4], and the finite elements are analyzed in [5]. The infinite extent of the medium is modeled numerically with a perfectly matched absorbing layer surrounding the computational domain [25].…”

Section: Numerical Simulationsmentioning

confidence: 99%

Filtering Random Layering Effects in Imaging

Borcea

Cueto

Papanicolaou

et al. 2010

Multiscale Model. Simul.

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Abstract. Objects that are buried deep in heterogeneous media produce faint echoes which are difficult to distinguish from the backscattered field. Sensor array imaging in such media cannot work unless we filter out the backscattered echoes and enhance the coherent arrivals that carry information about the objects that we wish to image. We study such filters for imaging in strongly backscattering, finely layered media. The filters are based on a travel time transformation of the array data, the normal move-out, used frequently in connection with differential semblance velocity estimation in seismic imaging. In a previous paper [L. Borcea et al., Multiscale Model. Simul., 7 (2009), pp. 1267-1301 we showed that the filters can be used to remove coherent signals from strong plane reflectors. In this paper we show theoretically and with extensive numerical simulations that these filters, based on the normal move-out, can also remove the incoherent arrivals in the array data that are due to fine random layering in the medium.

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“…We solve the acoustic wave equation as a first order velocity-pressure system with the finite element, time domain method given in [2]. The setup is shown in Figures 2 and 3 for imaging in homogeneous and cluttered media, respectively.…”

Section: Simulation Setup and Mathematical Modelsmentioning

confidence: 99%

Subspace projection filters for imaging in random media

Borcea

Papanicolaou

Tsogka

2010

Comptes Rendus. Mécanique

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We consider the problem of selective imaging extended reflectors in cluttered media. We propose a random travel time model for simulating the array response matrix in clutter and we compare it with the full wave solution. Our simplified model captures very well the full wave random medium behavior as this is illustrated by our numerical results. The algorithm for selective array imaging uses coherent interferometry on a filtered version of the data. The filter, which is based on the singular value decomposition of the response matrix, enhances the signal reflected by the edges of the reflector. We illustrate the performance of the imaging algorithm with numerical simulations in the regime of ultrasonic non-destructive testing in concrete.

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An Analysis of New Mixed Finite Elements for the Approximation of Wave Propagation Problems

Cited by 122 publications

References 22 publications

Simulation of seismic response in an idealized city

Simulation of seismic response in an idealized city

Filtering Random Layering Effects in Imaging

Subspace projection filters for imaging in random media

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