Waves and Rays in Elastic Continua

Slawiński, Michael A.

doi:10.1142/9431

Cited by 56 publications

(42 citation statements)

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“…The anisotropic Hooke's matrix H ð0Þ a for an orthotropic material, presented in a coordinate system that is not necessarily aligned with the natural coordinate system is given as The Hooke's matrix H ð0Þ a consists of 21 independent terms and can be rewritten as a transformation of the orthotropic Hooke's matrix H ð0Þ , defined by nine entries in its natural coordinate system, by multiplication with a Bond matrix A e (Carcione, 2007;Slawinski, 2010), such that…”

Section: Introductionmentioning

confidence: 99%

A method for characterisation of the static elastic properties of the porous frame of orthotropic open-cell foams

Kelen

Cuenca

Göransson

2015

International Journal of Engineering Science

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Section: Introductionmentioning

confidence: 99%

A method for characterisation of the static elastic properties of the porous frame of orthotropic open-cell foams

Kelen

Cuenca

Göransson

2015

International Journal of Engineering Science

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“…The existence of waves in anisotropic media is governed by the Christoffel equation; its solubility condition is (e.g. Slawinski , Section 7.3)

det [\sum_{j = 1}^{3} \sum_{ℓ = 1}^{3} c_{i j k ℓ} p_{j} p_{ℓ} - δ_{i k}] = 0, i, k = 1, 2, 3,

where

c_{i j k ℓ}

is a density‐scaled elasticity tensor and

boldp

is the wavefront‐slowness vector. The three roots of this cubic equation in p 2 can be stated as the expressions for the wavefront speeds of the qP , qSV and

S H

waves; herein,

p^{2} = boldp \cdot boldp

is the squared magnitude of the slowness vector.…”

Section: Christoffel Equation In Backus Mediamentioning

confidence: 99%

On Christoffel roots for nondetached slowness surfaces

Bos

Slawiński

Stanoev

2019

Geophysical Prospecting

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The only restriction on the values of the elasticity parameters is the stability condition. Within this condition, we examine the Christoffel equation for nondetached qP slowness surfaces in transversely isotropic media. If the qP slowness surface is detached, each root of the solubility condition corresponds to a distinct smooth wavefront. If the qP slowness surface is nondetached, the roots are elliptical but do not correspond to distinct wavefronts; also, the qP and qSV slowness surfaces are not smooth.

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“…ρ es la densidad del medio. Debido a que la onda elástica se propaga en un medio isótropo, C 11 , C 12 y C 44 corresponden a los parámetros de Lamé, por la simetría del medio [4].…”

Section: Definición Del Fenómenounclassified

3D seismic modeling using hybrid arquitectures

Nino

Carreño

Trigos

et al. 2015

2015 10th Computing Colombian Conference (10CCC)

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This paper explains the wave phenomenon that was worked and the medium in which the propagation occurs. A differential equation of the elastic wave in isotropic and heterogeneous media is solved using a finite difference method with staggered mesh with second order accuracy in time and fourth grade in space, aiming for greater stability and efficiency.The solution of the equation was implemented in C. Scons was used for compiling the programs and Madagascar (seismic data processing software) to control the flow of data and perform seismic simulation. The testbed was the GUANE-1 architecture.OpenMP was used to accelerate the application, running the algorithm on 24 CPUs on one node. CUDA was used to run the solution in a hybrid architecture with CPU and GPU, using only global memory on the graphic processors. Finally an analysis and comparison of metrics and runtime acceleration of the two models of parallelization is used to check the processing power that can be achieved with hybrid architectures. Keywords-Seismic modelling, elastic wave equation, isotropic media, FDTD, computational geophysics, hybrid architectures, OpenMP, CUDA, 3D visualization.Resumen-En este trabajo se presenta la explicación del fenómeno ondulatorio que se trabajó y del medio en el que se propaga. Se soluciona la ecuación diferencial de la onda elástica en medios isótropos y heterogéneos, haciendo uso de un método de diferencias finitas con malla intercalada con segundo orden de precisión en el tiempo y cuarto orden de precisión en el espacio, para obtener una mayor estabilidad y eficiencia.La solución de la ecuación se implementó con código C, Scons para complilar los programas y Madagascar (un paquete de código libre de procesamiento de datos sísmicos) para controlar los flujos de datos y realizar la simulación sísmica, utilizando la arquitectura de GUANE-1.

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Waves and Rays in Elastic Continua

Cited by 56 publications

References 0 publications

A method for characterisation of the static elastic properties of the porous frame of orthotropic open-cell foams

A method for characterisation of the static elastic properties of the porous frame of orthotropic open-cell foams

On Christoffel roots for nondetached slowness surfaces

3D seismic modeling using hybrid arquitectures

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