2,795 research outputs found
Modeling seismic wave propagation and amplification in 1D/2D/3D linear and nonlinear unbounded media
To analyze seismic wave propagation in geological structures, it is possible
to consider various numerical approaches: the finite difference method, the
spectral element method, the boundary element method, the finite element
method, the finite volume method, etc. All these methods have various
advantages and drawbacks. The amplification of seismic waves in surface soil
layers is mainly due to the velocity contrast between these layers and,
possibly, to topographic effects around crests and hills. The influence of the
geometry of alluvial basins on the amplification process is also know to be
large. Nevertheless, strong heterogeneities and complex geometries are not easy
to take into account with all numerical methods. 2D/3D models are needed in
many situations and the efficiency/accuracy of the numerical methods in such
cases is in question. Furthermore, the radiation conditions at infinity are not
easy to handle with finite differences or finite/spectral elements whereas it
is explicitely accounted in the Boundary Element Method. Various absorbing
layer methods (e.g. F-PML, M-PML) were recently proposed to attenuate the
spurious wave reflections especially in some difficult cases such as shallow
numerical models or grazing incidences. Finally, strong earthquakes involve
nonlinear effects in surficial soil layers. To model strong ground motion, it
is thus necessary to consider the nonlinear dynamic behaviour of soils and
simultaneously investigate seismic wave propagation in complex 2D/3D geological
structures! Recent advances in numerical formulations and constitutive models
in such complex situations are presented and discussed in this paper. A crucial
issue is the availability of the field/laboratory data to feed and validate
such models.Comment: of International Journal Geomechanics (2010) 1-1
Spectral-Element and Adjoint Methods in Seismology
We provide an introduction to the use of the spectral-element method (SEM) in seismology. Following a brief review of the basic equations that govern seismic wave propagation, we discuss in some detail how these equations may be solved numerically based upon the SEM to address the forward problem in seismology. Examples of synthetic seismograms calculated based upon the SEM are compared to data recorded by the Global Seismographic Network. Finally, we discuss the challenge of using the remaining differences between the data and the synthetic seismograms to constrain better Earth models and source descriptions. This leads naturally to adjoint methods, which provide a practical approach to this formidable computational challenge and enables seismologists to tackle the inverse problem
Variational Multiscale Stabilization and the Exponential Decay of Fine-scale Correctors
This paper addresses the variational multiscale stabilization of standard
finite element methods for linear partial differential equations that exhibit
multiscale features. The stabilization is of Petrov-Galerkin type with a
standard finite element trial space and a problem-dependent test space based on
pre-computed fine-scale correctors. The exponential decay of these correctors
and their localisation to local cell problems is rigorously justified. The
stabilization eliminates scale-dependent pre-asymptotic effects as they appear
for standard finite element discretizations of highly oscillatory problems,
e.g., the poor approximation in homogenization problems or the pollution
effect in high-frequency acoustic scattering
An Overview of Recent Advances in the Iterative Analysis of Coupled Models for Wave Propagation
Wave propagation problems can be solved using a variety of methods. However, in many cases, the joint use of different numerical procedures to model different parts of the problem may be advisable and strategies to perform the coupling between them must be developed. Many works have been published on this subject, addressing the case of electromagnetic, acoustic, or elastic waves and making use of different strategies to perform this coupling. Both direct and iterative approaches can be used, and they may exhibit specific advantages and disadvantages. This work focuses on the use of iterative coupling schemes for the analysis of wave propagation problems, presenting an overview of the application of iterative procedures to perform the coupling between different methods. Both frequency- and time-domain analyses are addressed, and problems involving acoustic, mechanical, and electromagnetic wave propagation problems are illustrated
Some Applications of the Generalized Multiscale Finite Element Method
Many materials in nature are highly heterogeneous and their properties can vary at different scales. Direct numerical simulations in such multiscale media are prohibitively expensive and some types of model reduction are needed. Typical model reduction techniques include upscaling and multiscale methods. In upscaling methods, one upscales the multiscale media properties so that the problem can be solved on a coarse grid. In multiscale method, one constructs multiscale basis functions that capture media information and solves the problem on the coarse grid.
Generalized Multiscale Finite Element Method (GMsFEM) is a recently proposed model reduction technique and has been used for various practical applications. This method has no assumption about the media properties, which can have any type of complicated structure. In GMsFEM, we first create a snapshot space, and then solve a carefully chosen eigenvalue problem to form the offline space. One can also construct online space for the parameter dependent problems. It is shown theoretically and numerically that the GMsFEM is very efficient for the heterogeneous problems involving high-contrast, no-scale separation.
In this dissertation, we apply the GMsFEM to perform model reduction for the steady state elasticity equations in highly heterogeneous media though some of our applications are motivated by elastic wave propagation in subsurface. We will consider three kinds of coupling mechanism for different situations. For more practical purposes, we will also study the applications of the GMsFEM for the frequency domain acoustic wave equation and the Reverse Time Migration (RTM) based on the time domain acoustic wave equation
- …