Enriched Galerkin finite element approximation for elastic wave propagation in fractured media

Vamaraju, Janaki; Sen, Mrinal K.; Basabe, Jonás D. De; Wheeler, Mary F.

doi:10.1016/j.jcp.2018.06.049

Cited by 20 publications

(6 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where ϕ denotes the porosity. Until now, most of the fracture models used for seismic simulations (Binder et al, 2020; Chung et al, 2016;Vamaraju et al, 2018) showed simplified structures: parallel line, coin-shape or simple intersection, which help in explaining the relationship between seismic waves and fractures. From a macroscopic point of view, parallel fractures are also easy to be understood.…”

Section: Petrophysical Modellingmentioning

confidence: 99%

Microseismic wavefield propagation in a fracture‐induced anisotropic medium based on a general dislocation source model

Yao

Wang

Kong

2022

Geophysical Prospecting

View full text Add to dashboard Cite

The propagation of microseismicity in subsurface media is complex. We developed an anisotropic petrophysical model based on an empirical formula, linear slip theory and the bond transform method considering real underground conditions. Using Biot's equations, the seismic response to a general dislocation source in fracture‐induced anisotropic two‐phased media was solved using a staggered grid high‐order finite‐difference algorithm. To understand the relationship between the microseismic wave and fracture parameters, we then designed several different models to calculate the wavefield snapshots and analyse the effect of the fracture volume ratio and orientation. The modelling results indicate that the shear faulting source generates three types of waves in two‐phase media. Fractures can render homogeneous media anisotropic, and anisotropy becomes more noticeable with an increase in the fracture volume ratio. This decreases the velocity of the fast longitudinal and transverse waves in the vertical direction and increases the velocity of the slow longitudinal wave in a certain range. The fracture orientation mainly influences the moment tensor and then affects the wavefronts. These simulations lay the foundation for further studies on microseismic wave propagation in fracture‐induced anisotropic media.

show abstract

Section: Petrophysical Modellingmentioning

confidence: 99%

Microseismic wavefield propagation in a fracture‐induced anisotropic medium based on a general dislocation source model

Yao

Wang

Kong

2022

Geophysical Prospecting

View full text Add to dashboard Cite

show abstract

“…The error analysis offers the potential and flexibility for its extension to spatial approximations by enriched Galerkin methods (cf. [37,39,56,58]) or discontinuous Galerkin approaches (cf., e.g., [6,20,21,23,24,35]). Also, for the application of discontinuous Galerkin space discretizations to the quasi-static Biot system, that differs from (1.1) by neglegting the acceleration term ρ∂ 2 t u in (1.1a), we refer to [9,49].…”

Section: Introductionmentioning

confidence: 99%

“…The error analysis has the flexibility that is required to generalize the bounds (1.2) and (1.3) to enriched (or discontinuous) Galerkin approximations in space (cf. [37,39,58]) that we prefer for applications of practical interest.…”

Section: Introductionmentioning

confidence: 99%

Convergence of a continuous Galerkin method for hyperbolic-parabolic systems

Bause¹,

Köcher²,

Radu³

2022

Preprint

View full text Add to dashboard Cite

We study the numerical approximation by space-time finite element methods of a multi-physics system coupling hyperbolic elastodynamics with parabolic transport and modelling poro-and thermoelasticity. The equations are rewritten as a first-order system in time. Discretizations by continuous Galerkin methods in space and time with inf-sup stable pairs of finite elements for the spatial approximation of the unknowns are investigated. Optimal order error estimates of energy-type are proven. Superconvergence at the time nodes is addressed briefly. The error analysis can be extended to discontinuous and enriched Galerkin space discretizations. The error estimates are confirmed by numerical experiments.

show abstract

“…Recently, the discontinuous Galerkin (DG) method has also been widely used to solve the problems of modeling the propagation of seismic waves. For example, in [17,18], it is used to model the wave fields in the fractured media using an explicit fracture model. The method is also built on unstructured meshes.…”

Section: Introductionmentioning

confidence: 99%

Novel Approach to Modeling the Seismic Waves in the Areas with Complex Fractured Geological Structures

Хохлов

Stognii

2020

Minerals

View full text Add to dashboard Cite

This paper presents a novel approach to modeling the propagation of seismic waves in a medium containing subvertical fractured inhomogeneities, typical for mineralization zones. The developed method allows us to perform calculations on a structural computational grid, which avoids the construction of unstructured grids. For the calculations, the grid-characteristic method is used. We also present a comparison of the proposed method with the one described at earlier works and discuss the areas of its practical application. As an example, the numerical results for a cluster of subvertical fractures are given. A new approach for modeling fractures makes it quite easy to incorporate fractured objects into the seismic models and perform calculations without using algorithms on unstructured and curved grids.

show abstract

Enriched Galerkin finite element approximation for elastic wave propagation in fractured media

Cited by 20 publications

References 43 publications

Microseismic wavefield propagation in a fracture‐induced anisotropic medium based on a general dislocation source model

Microseismic wavefield propagation in a fracture‐induced anisotropic medium based on a general dislocation source model

Convergence of a continuous Galerkin method for hyperbolic-parabolic systems

Novel Approach to Modeling the Seismic Waves in the Areas with Complex Fractured Geological Structures

Contact Info

Product

Resources

About