Seismic Waves in an Impacted Half-Space: Time Domain BEM Versus the Method of Generalized Ray

1991 ◽  
pp. 457-470 ◽  
Author(s):  
H. Antes ◽  
P. Borejko ◽  
F. Ziegler
Keyword(s):  
Half Space ◽  
Time Domain ◽  
Seismic Waves ◽  
Space Time

scholarly journals Modeling Transient Flows in Heterogeneous Layered Porous Media Using the Space–Time Trefftz Method

2021 ◽  
Vol 11 (8) ◽  
pp. 3421
Author(s):  
Cheng-Yu Ku ◽  
Li-Dan Hong ◽  
Chih-Yu Liu ◽  
Jing-En Xiao ◽  
Wei-Po Huang
Keyword(s):  
Porous Media ◽  
Time Domain ◽  
Numerical Solutions ◽  
Space Time ◽  
Two Dimensional ◽  
Transient Flows ◽  
Layered Porous Media ◽  
Time Marching ◽  
Time Basis ◽  
Marching Scheme

In this study, we developed a novel boundary-type meshless approach for dealing with two-dimensional transient flows in heterogeneous layered porous media. The novelty of the proposed method is that we derived the Trefftz space–time basis function for the two-dimensional diffusion equation in layered porous media in the space–time domain. The continuity conditions at the interface of the subdomains were satisfied in terms of the domain decomposition method. Numerical solutions were approximated based on the superposition principle utilizing the space–time basis functions of the governing equation. Using the space–time collocation scheme, the numerical solutions of the problem were solved with boundary and initial data assigned on the space–time boundaries, which combined spatial and temporal discretizations in the space–time manifold. Accordingly, the transient flows through the heterogeneous layered porous media in the space–time domain could be solved without using a time-marching scheme. Numerical examples and a convergence analysis were carried out to validate the accuracy and the stability of the method. The results illustrate that an excellent agreement with the analytical solution was obtained. Additionally, the proposed method was relatively simple because we only needed to deal with the boundary data, even for the problems in the heterogeneous layered porous media. Finally, when compared with the conventional time-marching scheme, highly accurate solutions were obtained and the error accumulation from the time-marching scheme was avoided.

Seismic Waves in a Laterally Inhomogeneous Layered Medium, Part I: Theory

1997 ◽  
Vol 64 (1) ◽  
pp. 50-58 ◽  
Author(s):  
Ruichong Zhang ◽  
Liyang Zhang ◽  
Masanobu Shinozuka
Keyword(s):  
Wave Field ◽  
Half Space ◽  
Seismic Waves ◽  
Scattered Wave ◽  
Inhomogeneous Layer ◽  
Dislocation Source ◽  
Seismic Dislocation ◽  
Body Forces ◽  
The Mean ◽  
Layered Half Space

Seismic waves in a layered half-space with lateral inhomogeneities, generated by a buried seismic dislocation source, are investigated in these two consecutive papers. In the first paper, the problem is formulated and a corresponding approach to solve the problem is provided. Specifically, the elastic parameters in the laterally inhomogeneous layer, such as P and S wave speeds and density, are separated by the mean and the deviation parts. The mean part is constant while the deviation part, which is much smaller compared to the mean part, is a function of lateral coordinates. Using the first-order perturbation approach, it is shown that the total wave field may be obtained as a superposition of the mean wave field and the scattered wave field. The mean wave field is obtainable as a response solution for a perfectly layered half-space (without lateral inhomogeneities) subjected to a buried seismic dislocation source. The scattered wave field is obtained as a response solution for the same layered half-space as used in the mean wave field, but is subjected to the equivalent fictitious distributed body forces that mathematically replace the lateral inhomogeneities. These fictitious body forces have the same effects as the existence of lateral inhomogeneities and can be evaluated as a function of the inhomogeneity parameters and the mean wave fleld. The explicit expressions for the responses in both the mean and the scattered wave fields are derived with the aid of the integral transform approach and wave propagation analysis.

scholarly journals Space-Time Domain Tensor Neural Networks: An Application on Human Pose Classification

2021 ◽  
Author(s):  
Konstantinos Makantasis ◽  
Athanasios Voulodimos ◽  
Anastasios Doulamis ◽  
Nikolaos Bakalos ◽  
Nikolaos Doulamis
Keyword(s):  
Neural Networks ◽  
Time Domain ◽  
Space Time ◽  
Human Pose

Diffraction of elastic waves by a fluid-filled crack in a fluid-saturated poroelastic half-space

2021 ◽  
Author(s):  
Zhongxian Liu ◽  
Jiaqiao Liu ◽  
Sibo Meng ◽  
Xiaojian Sun
Keyword(s):  
Half Space ◽  
Seismic Waves ◽  
Incident Angle ◽  
Excitation Frequency ◽  
Vertical Displacement ◽  
Crack Model ◽  
P Waves ◽  
Amplification Effect ◽  
Resonance Frequencies ◽  
Angle Crack

Summary An indirect boundary element method (IBEM) is developed to model the two-dimensional (2D) diffraction of seismic waves by a fluid-filled crack in a fluid-saturated poroelastic half-space, using Green's functions computed considering the distributed loads, flow, and fluid characteristics. The influence of the fluid-filled crack on the diffraction characteristics is investigated by analyzing key parameters, such as the excitation frequency, incident angle, crack width and depth, and medium porosity. The results for the fluid-filled crack model are compared to those for the fluid-free crack model under the same conditions. The numerical results demonstrate that the fluid-filled crack has a significant amplification effect on the surface displacements, and that the effect of the depth of the fluid-filled crack is more complex compared to the influence of other parameters. The resonance diffraction generates an amplification effect in the case of normally incident P waves. Furthermore, the horizontal and vertical displacement amplitudes reach 4.2 and 14.1, respectively. In the corresponding case of the fluid-free crack, the vertical displacement amplitude is only equal to 4.1, indicating the amplification effect of the fluid in the crack. Conversely, for normally incident SV waves at certain resonance frequencies, the displacement amplitudes above a fluid-filled crack may be lower than the displacement amplitudes observed in the corresponding case of a fluid-free crack.

An analytic signal based accurate time-domain visco-acoustic wave equation from the Constant-Q theory

Geophysics ◽  
2021 ◽  
pp. 1-58
Author(s):  
Hongwei Liu ◽  
Yi Luo
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Time Domain ◽  
Seismic Waves ◽  
Heterogeneous Media ◽  
Relaxation Property ◽  
Analytic Signal ◽  
Acoustic Wave Equation ◽  
Real Component ◽  
Frequency Components

We present a concise time-domain wave equation to accurately simulate wave propagation in visco-acoustic media. The central idea behind this work is to dismiss the negative frequency components from a time-domain signal by converting the signal to its analytic format. The negative frequency components of any analytic signal are always zero, meaning we can construct the visco-acoustic wave equation to honor the relaxation property of the media for positive frequencies only. The newly proposed complex-valued wave equation (CWE) represents the wavefield with its analytic signal, whose real part is the desired physical wavefield, while the imaginary part is the Hilbert transform of the real component. Specifically, this CWE is accurate for both weak and strong attenuating media in terms of both dissipation and dispersion and the attenuation is precisely linear with respect to the frequencies. Besides, the CWE is easy and flexible to model dispersion-only, dissipation-only or dispersion-plus-dissipation seismic waves. We have verified these CWEs by comparing the results with analytical solutions, and achieved nearly perfect matching. Except for the homogeneous Q media, we have also extended the CWEs to heterogeneous media. The results of the CWEs for heterogeneous Q media are consistent with those computed from the nonstationary operator based Fourier Integral method and from the Standard Linear Solid (SLS) equations.

Seismic waves from a horizontal stress discontinuity in a layered solid

1982 ◽  
Vol 72 (5) ◽  
pp. 1483-1498
Author(s):  
F. Abramovici ◽  
E. R. Kanasewich ◽  
P. G. Kelamis
Keyword(s):  
Half Space ◽  
Seismic Waves ◽  
Horizontal Stress ◽  
Radial Component ◽  
Elastic Half Space ◽  
Homogeneous Layer ◽  
Approximate Methods ◽  
Crustal Layer ◽  
Finite Fault ◽  
Stress Discontinuity

abstract The displacement components for a horizontal stress discontinuity along a buried finite fault in an elastic homogeneous layer on top of an elastic half-space are given analytically in terms of generalized rays. For a particular case of a concentrated horizontal force pointing in an arbitrary direction, detailed time-dependent expressions are given. For a simple model of a “crustal” layer over a “mantle” half-space, the numerical seismograms in the near- and intermediate-field show some interesting features. These include a prominent group of compressional waves whose radial component is substantial at distances four times the crustal thickness. All the dominant shear arrivals (s, SS, and sSS) are important and show large variations of amplitude as the source depth and receiver distance are varied. Some of the prominent individual generalized rays are shown, and it is found that they can be grouped naturally into families based on the number of interactions with the boundaries. The subdivision into individual generalized rays is useful for analysis and for checks on the numerical stability of the synthetic seismograms. Since the solution is analytic and the numerical evaluation is complete up to any desired time, the results are useful in comparing other approximate methods for the computation of seismograms.

scholarly journals Viscoelastic Boundary Conditions for Multiple Excitation Sources in the Time Domain

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Chen Xia ◽  
Chengzhi Qi ◽  
Xiaozhao Li
Keyword(s):  
Finite Element ◽  
Seismic Response ◽  
Time Domain ◽  
Seismic Waves ◽  
Three Dimensional ◽  
Seismic Loads ◽  
Element Analysis ◽  
Artificial Boundaries ◽  
The Time Domain ◽  
Transmitting Boundaries

Transmitting boundaries are important for modeling the wave propagation in the finite element analysis of dynamic foundation problems. In this study, viscoelastic boundaries for multiple seismic waves or excitations sources were derived for two-dimensional and three-dimensional conditions in the time domain, which were proved to be solid by finite element models. Then, the method for equivalent forces’ input of seismic waves was also described when the proposed artificial boundaries were applied. Comparisons between numerical calculations and analytical results validate this seismic excitation input method. The seismic response of subway station under different seismic loads input methods indicates that asymmetric input seismic loads would cause different deformations from the symmetric input seismic loads, and whether it would increase or decrease the seismic response depends on the parameters of the specific structure and surrounding soil.

Time-domain Modeling of Constant-Q Seismic Waves Using Fractional Derivatives

2002 ◽  
pp. 1719-1736 ◽  
Author(s):  
José M. Carcione ◽  
Fabio Cavallini ◽  
Francesco Mainardi ◽  
Andrzej Hanyga
Keyword(s):  
Time Domain ◽  
Fractional Derivatives ◽  
Seismic Waves ◽  
Domain Modeling ◽  
Time Domain Modeling
Sign in / Sign up

Export Citation Format

Share Document