A discontinuous Galerkin method for poroelastic wave propagation: The two-dimensional case

Ward, Nicholas F. Dudley; Lähivaara, Timo; Eveson, S. P.

doi:10.1016/j.jcp.2017.08.070

Cited by 34 publications

(36 citation statements)

References 57 publications

(88 reference statements)

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“…Because of the size of the system of equations, we present the discretization of each equation of the local problem (16).…”

Section: Local Problemmentioning

confidence: 99%

“…This is a clear motivation to turn to finite element methods authorizing tetrahedral meshes. Among them, discontinuous Galerkin (DG) methods 12 initially developed to solve fluid mechanics problems, have also been applied to wave propagation simulations in heterogeneous media, both in time domain [13][14][15][16] and frequency domain. 17,18 The DG methods have many advantages like good performance on unstructured and irregular meshes, thanks to hp adaptivity.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Implementation of hybridizable discontinuous Galerkin method for time‐harmonic anisotropic poroelasticity in two dimensions

Barucq

Diaz

Meyer

et al. 2021

Numerical Meth Engineering

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We apply a hybridizable discontinuous Galerkin (HDG) method to numerically solve two-dimensional anisotropic poroelastic wave equations in the frequency domain given by Biot theory. The motivation for choosing HDG method comes from the complexity of the considered equations and the high number of unknowns. The HDG method possesses all the advantages of discontinuous Galerkin method (hp-adaptivity, accuracy, ability to model complex tectonics, etc.) without a drastic increase in the number of degrees of freedom. After a description of its implementation, we illustrate the accuracy of the proposed method by comparisons with analytical solutions. We then perform a sensitivity analysis of the method as a function of stabilization parameters and frequency, and show in particular that there exists optimal values of these parameters in order to obtain a very good level of accuracy. We also show the ability of the method to reproduce the different types of poroelastic waves including the slow Biot wave.

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“…Because of the size of the system of equations, we present the discretization of each equation of the local problem (16).…”

Section: Local Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Implementation of hybridizable discontinuous Galerkin method for time‐harmonic anisotropic poroelasticity in two dimensions

Barucq

Diaz

Meyer

et al. 2021

Numerical Meth Engineering

View full text Add to dashboard Cite

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“…In this study, we operate in the Biot's high‐frequency regime for which the attenuation is controlled by the quality factor Q 0 (Carcione ; Morency and Tromp ; Dudley Ward et al . ). In the elastic layer, we have a total of three unknown physical parameters, namely density ρ e , bulk modulus K e and shear modulus μ e .…”

Section: Model Setupmentioning

confidence: 99%

“…For each sample, we compute seismic responses from multiple source locations and couple simulations with deep learning for the prediction of water‐table level and the amount of stored water. More specifically, the presented approach comprises two main components: (1)Seismic wave propagation from the source to receivers, that is, the forward problem , in coupled poroviscoelastic–elastic media is simulated using a discontinuous Galerkin (DG) and low‐storage Runge–Kutta time stepping methods (Hesthaven and Warburton ; Lähivaara and Huttunen ; Dudley Ward, Lähivaara and Eveson ). The DG method is a well‐known high‐order accurate numerical technique to numerically solve differential equations and has properties that makes it well suited for wave simulations (see, e.g., Käser and Dumbser ; de la Puente et al .…”

Section: Introductionmentioning

confidence: 99%

Estimation of groundwater storage from seismic data using deep learning

Lähivaara

Malehmir

Pasanen

et al. 2019

Geophysical Prospecting

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Convolutional neural networks can provide a potential framework to characterize groundwater storage from seismic data. Estimation of key components, such as the amount of groundwater stored in an aquifer and delineate water table level, from active‐source seismic data are performed in this study. The data to train, validate and test the neural networks are obtained by solving wave propagation in a coupled poroviscoelastic–elastic media. A discontinuous Galerkin method is applied to model wave propagation, whereas a deep convolutional neural network is used for the parameter estimation problem. In the numerical experiment, the primary unknowns estimated are the amount of stored groundwater and water table level, while the remaining parameters, assumed to be of less of interest, are marginalized in the convolutional neural network‐based solution. Results, obtained through synthetic data, illustrate the potential of deep learning methods to extract additional aquifer information from seismic data, which otherwise would be impossible based on a set of reflection seismic sections or velocity tomograms.

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“…Furthermore, other methods, such as the boundary element method by Attenborough, Berry, and Chen [1], the spectral element method [33] and [40] have been used to study this problem. Discontinuous Galerkin (DG) method also has been used to study poroelasticity, such as that of de la Puente et al [16] as well as the recent works of Chen, Luo and Feng [12], Dudley Ward, Lähivaara and Eveson [19]. Lemoine, Ou and Leveque [26] firstly used high-resolution finite volume method to model poroelasticity in the time domain, and further works on the interaction of poroelastic and fluid were in [27].…”

Section: Introductionmentioning

confidence: 99%

A discontinuous Galerkin method for wave propagation in orthotropic poroelastic media with memory terms

Xie

2019

Journal of Computational Physics

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In this paper, we investigate wave propagation in orthotropic poroelastic media by studying the timedomain poroelastic equations. Both the low frequency Biot's (LF-Biot) equations and the Biot-Johnson-Koplik-Dashen (Biot-JKD) models are considered. In LF-Biot equations, the dissipation terms are proportional to the relative velocity between the fluid and the solid by a constant. Contrast to this, the dissipation terms in the Biot-JKD model are in the form of time convolution (memory) as a result of the frequency-dependence of fluid-solid interaction at the underlying microscopic scale in the frequency domain. The dynamic tortuosity and permeability described by Darcy's law are two crucial factors in this problem, and highly linked to the viscous force. In the Biot model, the key difficulty is to handle the viscous term when the pore fluid is viscous flow. In the Biot-JKD dynamic permeability model, the convolution operator involves order 1/2 shifted fractional derivatives in the time domain, which is challenging to discretize.In this work, we utilize the multipoint Padé (or Rational) approximation for Stieltjes function to approximate the dynamic tortuosity and then obtain an augmented system of equations which avoids storing the solutions of the past time. The Runge-Kutta discontinuous Galerkin (RKDG) method is used to compute the numerical solution, and numerical examples are presented to demonstrate the high order accuracy and stability of the method.

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A discontinuous Galerkin method for poroelastic wave propagation: The two-dimensional case

Cited by 34 publications

References 57 publications

Implementation of hybridizable discontinuous Galerkin method for time‐harmonic anisotropic poroelasticity in two dimensions

Implementation of hybridizable discontinuous Galerkin method for time‐harmonic anisotropic poroelasticity in two dimensions

Estimation of groundwater storage from seismic data using deep learning

A discontinuous Galerkin method for wave propagation in orthotropic poroelastic media with memory terms

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