Journal ArticleDOI
Wave propagation in heterogeneous porous media formulated in the frequency-space domain using a discontinuous Galerkin method
TLDR
In this article, the authors derived the discrete linear system in the frequency domain for a discontinuous finite-element method, known as the nodal discontinuous Galerkin method, for modeling the Biot wave in the diffusive/propagative regimes, enhancing the importance of frequency effects.Abstract:
Biphasic media with a dynamic interaction between fluid and solid phases must be taken into account to accurately describe seismic wave amplitudes in subsurface and reservoir geophysical applications. Consequently, the modeling of the wave propagation in heteregeneous porous media, which includes the frequency-dependent phenomena of the fluidsolid interaction, is considered for 2D geometries. From the Biot-Gassmann theory, we have deduced the discrete linear system in the frequency domain for a discontinuous finite-element method, known as the nodal discontinuous Galerkin method. Solving this system in the frequency domain allows accurate modeling of the Biot wave in the diffusive/propagative regimes, enhancing the importance of frequency effects. Because we had to consider finite numerical models, we implemented perfectly matched layer techniques. We found that waves are efficiently absorbed at the model boundaries, and that the discretization of the medium should follow the same rules as in the elastodynamic case, that is, 10 grids per minimum wavelength for a P0 interpolation order. The grid spreading of the sources, which could be stresses or forces applied on either the solid phase or the fluid phase, did not show any additional difficulties compared to the elastic problem. For a flat interface separating two media, we compared the numerical solution and a semianalytic solution obtained by a reflectivity method in the three regimes where the Biot wave is propagative, diffusive/propagative, and diffusive. In all cases, fluid-solid interactions were reconstructed accurately, proving that attenuation and dispersion of the waves were correctly accounted for. In addition to this validation in layered media, we have explored the capacities of modeling complex wave propagation in a laterally heterogeneous porous medium related to steam injection in a sand reservoir and the seismic response associated to a fluid substitution.read more
Citations
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Journal ArticleDOI
Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media
TL;DR: A Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where basis functions are constructed from multiple local problems for both the boundaries and interior of a coarse node support or coarse element.
Journal ArticleDOI
Seismoelectric wave propagation numerical modelling in partially saturated materials
Sheldon Warden,Stéphane Garambois,Laurence Jouniaux,Daniel Brito,Pascal Sailhac,Clarisse Bordes +5 more
TL;DR: In this paper, an extension of Pride's equations aiming to take into account partially saturated materials, in the case of a water-air mixture, was incorporated into an existing seismoelectric wave propagation modeling code, originally designed for stratified saturated media.
Journal ArticleDOI
Time domain numerical modeling of wave propagation in 2D heterogeneous porous media
TL;DR: This paper deals with the numerical modeling of wave propagation in porous media described by Biot's theory, where the viscous efforts between the fluid and the elastic skeleton are assumed to be a linear function of the relative velocity.
Journal ArticleDOI
Large tectonic earthquakes induce sharp temporary decreases in seismic velocity in Volcán de Colima, Mexico
TL;DR: In this paper, the authors used the ambient noise cross-correlation and stretching methods to calculate variations in seismic velocities in the region of Volcan de Colima, Mexico.
Journal ArticleDOI
Seismic noise monitoring of the water table in a deep-seated, slow-moving landslide
TL;DR: In this paper, daily correlations of ambient seismic noise on a large landslide at Utiku, New Zealand, reveal seismic velocity changes up to ± 1.5% that follow a summer/winter cycle consistent with the pore-water pressures monitored at the basal slip surface in the landslide.
References
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Journal ArticleDOI
A perfectly matched layer for the absorption of electromagnetic waves
TL;DR: Numerical experiments and numerical comparisons show that the PML technique works better than the others in all cases; using it allows to obtain a higher accuracy in some problems and a release of computational requirements in some others.
Journal ArticleDOI
Theory of Propagation of Elastic Waves in a Fluid‐Saturated Porous Solid. I. Low‐Frequency Range
TL;DR: In this article, a theory for the propagation of stress waves in a porous elastic solid containing compressible viscous fluid is developed for the lower frequency range where the assumption of Poiseuille flow is valid.
Journal ArticleDOI
Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. II. Higher Frequency Range
TL;DR: In this paper, the theory of propagation of stress waves in a porous elastic solid developed in Part I for the low-frequency range is extended to higher frequencies, and the breakdown of Poiseuille flow beyond the critical frequency is discussed for pores of flat and circular shapes.
Book ChapterDOI
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
TL;DR: Triangle as discussed by the authors is a robust implementation of two-dimensional constrained Delaunay triangulation and Ruppert's Delaunayer refinement algorithm for quality mesh generation, and it is shown that the problem of triangulating a planar straight line graph (PSLG) without introducing new small angles is impossible for some PSLGs.
Book
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Jan S. Hesthaven,Tim Warburton +1 more
TL;DR: The text offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential equations.