606 research outputs found
Convergence of the uniaxial PML method for time-domain electromagnetic scattering problems
In this paper, we propose and study the uniaxial perfectly matched layer
(PML) method for three-dimensional time-domain electromagnetic scattering
problems, which has a great advantage over the spherical one in dealing with
problems involving anisotropic scatterers. The truncated uniaxial PML problem
is proved to be well-posed and stable, based on the Laplace transform technique
and the energy method. Moreover, the -norm and -norm error
estimates in time are given between the solutions of the original scattering
problem and the truncated PML problem, leading to the exponential convergence
of the time-domain uniaxial PML method in terms of the thickness and absorbing
parameters of the PML layer. The proof depends on the error analysis between
the EtM operators for the original scattering problem and the truncated PML
problem, which is different from our previous work (SIAM J. Numer. Anal. 58(3)
(2020), 1918-1940).Comment: 23 pages, 1 figure. arXiv admin note: text overlap with
arXiv:1907.0890
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
Wavefield Analysis of Rayleigh Waves for Near-Surface Shear-Wave Velocity
Shear (S)-wave velocity is a key property of near-surface materials and is the fundamental parameter for many environmental and engineering geophysical studies. Directly acquiring accurate S-wave velocities from a seismic shot gather is usually difficult due to the poor signal-to-noise ratio. The relationship between Rayleigh-wave phase velocity and frequency has been widely utilized to estimate the S-wave velocities in shallow layers using the multichannel analysis of surface waves (MASW) technique. Hence, Rayleigh wave is a main focus of most near-surface seismic studies. Conventional dispersion analysis of Rayleigh waves assumes that the earth is laterally homogeneous and the free surface is horizontally flat, which limits the application of surface-wave methods to only 1D earth models or very smooth 2D models. In this study I extend the analysis of Rayleigh waves to a 2D domain by employing the 2D full elastic wave equation so as to address the lateral heterogeneity problem. I first discuss the accurate simulation of Rayleigh waves through finite-difference method and the boundary absorbing problems in the numerical modeling with a high Poisson's ratio ( 0.4), which is a unique near-surface problem. Then I develop an improved vacuum formulation to generate accurate synthetic seismograms focusing on Rayleigh waves in presence of surface topography and internal discontinuities. With these solutions to forward modeling of Rayleigh waves, I evaluate the influence of surface topography to conventional dispersion analysis in 2D and 3D domains by numerical investigations. At last I examine the feasibility of inverting waveforms of Rayleigh waves for shallow S-wave velocities using a genetic algorithm. Results of the study show that Rayleigh waves can be accurately simulated in near surface using the improved vacuum formulation. Spurious reflections during the numerical modeling can be efficiently suppressed by the simplified multiaxial perfectly matched layers. The conventional MASW method can tolerate gentle topography changes with insignificant errors. Finally, many near-surface features with strong lateral heterogeneity such as dipping interfaces, faults, and tunnels can be imaged by the waveform inversion of Rayleigh waves for shallow S-wave velocities. This thesis consists of four papers that are either published (chapter 1) or in review (chapter 2, 3, and 4) for consideration of publication to peer-refereed journals. Each chapter represents a paper, and therefore inadvertently there will be a certain degree of overlap between chapters (particularly for the introduction parts, where references to many common papers occur)
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