scholarly journals Sponge boundary condition for frequency‐domain modeling

Geophysics ◽  
1995 ◽  
Vol 60 (6) ◽  
pp. 1870-1874 ◽  
Author(s):  
Changsoo Shin
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Rayleigh Waves ◽  
Seismic Waves ◽  
Domain Modeling ◽  
Seismic Modeling ◽  
Artificial Boundary ◽  
Diffusion Term ◽  
S Waves ◽  
Artificial Boundaries

Several techniques have been developed to get rid of edge reflections from artificial boundaries. One of them is to use paraxial approximations of the scalar and elastic wave equations. The other is to attenuate the seismic waves inside the artificial boundary by a gradual reduction of amplitudes. These techniques have been successfully applied to minimize unwanted seismic waves for time‐domain seismic modeling. Unlike time‐domain seismic modeling, suppression of edge reflections from artificial boundaries has not been successful in frequency‐domain seismic modeling. Rayleigh waves caused by coupled motions of P‐ and S‐waves near the surface have been a particularly difficult problem to overcome in seismic modeling. In this paper, I design a damping matrix for frequency‐ domain modeling that damps out seismic waves by adding a diffusion term to the wave equation. This technique can suppress unwanted seismic waves, including Rayleigh waves and P‐ and S‐waves from an artificial boundary.

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

scholarly journals Time-domain and frequency-domain modeling of nonlinear optical components at the circuit-level using a node-based approach

2012 ◽  
Vol 29 (5) ◽  
pp. 896 ◽  
Author(s):  
Martin Fiers ◽  
Thomas Van Vaerenbergh ◽  
Ken Caluwaerts ◽  
Dries Vande Ginste ◽  
Benjamin Schrauwen ◽  
...  
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Nonlinear Optical ◽  
Domain Modeling ◽  
Optical Components

4. Seismic waves

2018 ◽  
pp. 53-61
Author(s):  
Mike Goldsmith
Keyword(s):  
Seismic Wave ◽  
Rayleigh Waves ◽  
Seismic Waves ◽  
Shear Waves ◽  
Free Vibrations ◽  
Love Waves ◽  
Sound Waves ◽  
P Waves ◽  
Tectonic Plates ◽  
S Waves

Sound waves travel very easily underground, often for many thousands of kilometres. These are usually referred to as a kind of seismic wave and are most often triggered by earthquakes, which result from a sudden slip of tectonic plates, down to about 700 kilometres below the Earth’s surface. ‘Seismic waves’ describes the four types of seismic wave generated by earthquakes: P-waves (primary waves), S-waves (shear waves), Love waves (usually the most powerful and destructive of seismic waves), and Rayleigh waves, which are created when P and S waves reach the Earth’s surface together, combining to form undulating ground rolls. Free vibrations and star waves are also described.

Time-domain modeling of electromagnetic diffusion with a frequency-domain code

Geophysics ◽  
2008 ◽  
Vol 73 (1) ◽  
pp. F1-F8 ◽  
Author(s):  
Wim A. Mulder ◽  
Marwan Wirianto ◽  
Evert C. Slob
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Hermite Interpolation ◽  
Computational Grid ◽  
Skin Depth ◽  
Domain Modeling ◽  
Time Domain Modeling ◽  
Robust Multigrid ◽  
Selection Of

We modeled time-domain EM measurements of induction currents for marine and land applications with a frequency-domain code. An analysis of the computational complexity of a number of numerical methods shows that frequency-domain modeling followed by a Fourier transform is an attractive choice if a sufficiently powerful solver is available. A recently developed, robust multigrid solver meets this requirement. An interpolation criterion determined the automatic selection of frequencies. The skin depth controlled the construction of the computational grid at each frequency. Tests of the method against exact solutions for some simple problems and a realistic marine example demonstrate that a limited number of frequencies suffice to provide time-domain solutions after piecewise-cubic Hermite interpolation and a fast Fourier transform.

scholarly journals A frequency‐space 2-D scalar wave extrapolator using extended 25-point finite‐difference operator

Geophysics ◽  
1998 ◽  
Vol 63 (1) ◽  
pp. 289-296 ◽  
Author(s):  
Changsoo Shin ◽  
Heejeung Sohn
Keyword(s):  
Finite Difference ◽  
Frequency Domain ◽  
Time Domain ◽  
Difference Operator ◽  
Rapid Development ◽  
Synthetic Seismograms ◽  
Domain Modeling ◽  
Time Migration ◽  
Space Frequency ◽  
Grid Points

Finite‐difference frequency‐domain modeling for the generation of synthetic seismograms and crosshole tomography has been an active field of research since the 1980s. The generation of synthetic seismograms with the time‐domain finite‐difference technique has achieved considerable success for waveform crosshole tomography and for wider applications in seismic reverse‐time migration. This became possible with the rapid development of high performance computers. However, the space‐frequency (x,ω) finite‐difference modeling technique is still beyond the capability of the modern supercomputer in terms of both cost and computer memory. Therefore, finite‐difference time‐domain modeling is much more popular among exploration geophysicists. A limitation of the space‐frequency domain is that the recently developed nine‐point scheme still requires that G, the number of grid points per wavelength, be 5. This value is greater than for most other numerical modeling techniques (for example, the pseudospectral scheme). To overcome this disadvantage inherent in space‐frequency domain modeling, we propose a new weighted average finite‐difference operator by approximating the spatial derivative and the mass acceleration term of the wave equation. We use 25 grid points around the collocation. In this way, we can reduce the number of grid points so that G is now 2.5. This approaches the Nyquist sampling limit in terms of the normalized phase velocity.

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