Elastic wave propagation in heterogeneous media

1970 ◽  
Vol 60 (3) ◽  
pp. 769-784 ◽  
Author(s):  
Paul R. Beaudet
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Seismic Waves ◽  
Heterogeneous Media ◽  
Heterogeneous Medium ◽  
Test Site ◽  
Nuclear Test ◽  
Field Observations ◽  
Nevada Test Site ◽  
Test Program

Abstract The wave equation is solved for the ensemble average of particle displacements produced by an explosion. The explosion is assumed to occur in a finite cavity in an infinite heterogeneous medium. The solution is applied to the seismic waves generated by an underground nuclear detonation. Field observations from the underground nuclear test program at the Nevada Test Site are in qualitative agreement with the theory.

The effect of Yucca Fault on seismic wave propagation

1971 ◽  
Vol 61 (3) ◽  
pp. 697-706 ◽  
Author(s):  
Walter W. Hays ◽  
John R. Murphy
Keyword(s):  
Wave Propagation ◽  
Seismic Wave ◽  
Seismic Waves ◽  
Low Frequency ◽  
Test Site ◽  
Seismic Wave Propagation ◽  
Nevada Test Site ◽  
Basement Rocks ◽  
Geological Discontinuity ◽  
Frequency Components

abstract Yucca Fault is a major structural feature of Yucca Flat, a well-known geological province of the Nevada Test Site (NTS). The trace of the Fault extends north-south over a distance of about 32 km. The fault plane is nearly vertical and offsets Quaternary alluvium, Tertiary volcanic tuffs and pre-Cenozoic basement rocks (quartzites, shales and dolomites) with relative down displacement of several hundred feet on the east side of the fault. Data recorded from the CUP underground nuclear detonation in Yucca Flat typify the effect of the fault on near-zone (i.e., inside 10 km) seismic wave propagation. The effect of the fault is frequency dependent. It affects the frequency components (3.0, 5.0, 10.0 Hz) of the seismic waves which have characteristic wavelengths in the order of the geological discontinuity. Little or no effect is observed for low-frequency components (0.5, 1.0 Hz) which have wave-lengths exceeding the dimensions of the geological discontinuity. The effect of the fault does not represent a safety problem.

Comparison of seismic waves generated by different types of source

1963 ◽  
Vol 53 (5) ◽  
pp. 965-978 ◽  
Author(s):  
David E. Willis
Keyword(s):  
Seismic Waves ◽  
Nuclear Explosion ◽  
Test Site ◽  
Frequency Content ◽  
Nevada Test Site ◽  
Different Types ◽  
The Waves ◽  
Source Duration ◽  
Lower Frequencies

Abstract A comparison of the seismic waves generated by a nuclear explosion and an earthquake is discussed. The epicenter of the earthquake was located within the Nevada Test Site. Both events were recorded at the same station with the same type of equipment. The earthquake waves contained slightly lower frequency than the waves generated by the nuclear shot. The early P phases of the shot had larger amplitudes while the phases after Pg for the earthquake were larger. Seismic waves from collapses were generally found to be composed of lower frequencies than the waves from the original shot. Aftershocks of the Hebgen Lake earthquake were found to generate seismic waves whose frequency content was related to the magnitude of the aftershock. Spectral differences in quarry shot recordings that correlate with source duration times are also discussed.

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.

scholarly journals Simulation of elastic wave propagation across fractures using a nodal discontinuous Galerkin method—theory, implementation and validation

2019 ◽  
Vol 219 (3) ◽  
pp. 1900-1914 ◽  
Author(s):  
T Möller ◽  
W Friederich
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Elastic Wave ◽  
Discontinuous Galerkin ◽  
Heterogeneous Media ◽  
Rheological Behaviour ◽  
Displacement Discontinuity ◽  
Signal Frequency ◽  
Elastic Wave Equation ◽  
Numerical Flux

SUMMARY An existing nodal discontinuous Galerkin (NDG) method for the simulation of seismic waves in heterogeneous media is extended to media containing fractures with various rheological behaviour. Fractures are treated as 2-D surfaces where Schoenberg’s linear slip or displacement discontinuity condition is applied as an additional boundary condition to the elastic wave equation which is in turn implemented as an additional numerical flux within the NDG formulation. Explicit expressions for the new numerical flux are derived by considering the Riemann problem for the elastic wave equation at fractures with varying rheologies. In all cases, we obtain further first order differential equations that fully describe the temporal evolution of the particle velocity jump at the fracture. Our flux formulation allows to separate the effect of a fracture from flux contributions due to simple welded interfaces enabling us to easily declare element faces as parts of a fracture. We make use of this fact by first generating the numerical mesh and then building up fractures by selecting appropriate element faces instead of adjusting the mesh to pre-defined fracture surfaces. The implementation of the new numerical fluxes into NDG is verified in 1-D by comparison to an analytical solution and in 2-D by comparing the results of a simulation valid in 1-D and 2-D. Further numerical examples address the effect of fracture systems on seismic wave propagation in 1-D and 2-D featuring effective anisotropy and coda generation. Finally, a study of the reflective and transmissive behaviour of fractures indicates that reflection and transmission coefficients are controlled by the ratio of signal frequency and relaxation frequency of the fracture.

Multiscale modeling of acoustic wave propagation in 2D media

Geophysics ◽  
2014 ◽  
Vol 79 (2) ◽  
pp. T61-T75 ◽  
Author(s):  
Richard L. Gibson ◽  
Kai Gao ◽  
Eric Chung ◽  
Yalchin Efendiev
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Acoustic Wave ◽  
Heterogeneous Media ◽  
Coarse Grid ◽  
Basis Functions ◽  
Seismic Survey ◽  
Fine Scale ◽  
Acoustic Wave Propagation ◽  
Fine Grid

Conventional finite-difference methods produce accurate solutions to the acoustic and elastic wave equation for many applications, but they face significant challenges when material properties vary significantly over distances less than the grid size. This challenge is likely to occur in reservoir characterization studies, because important reservoir heterogeneity can be present on scales of several meters to ten meters. Here, we describe a new multiscale finite-element method for simulating acoustic wave propagation in heterogeneous media that addresses this problem by coupling fine- and coarse-scale grids. The wave equation is solved on a coarse grid, but it uses basis functions that are generated from the fine grid and allow the representation of the fine-scale variation of the wavefield on the coarser grid. Time stepping also takes place on the coarse grid, providing further speed gains. Another important property of the method is that the basis functions are only computed once, and time savings are even greater when simulations are repeated for many source locations. We first present validation results for simple test models to demonstrate and quantify potential sources of error. These tests show that the fine-scale solution can be accurately approximated when the coarse grid applies a discretization up to four times larger than the original fine model. We then apply the multiscale algorithm to simulate a complete 2D seismic survey for a model with strong, fine-scale scatterers and apply standard migration algorithms to the resulting synthetic seismograms. The results again show small errors. Comparisons to a model that is upscaled by averaging densities on the fine grid show that the multiscale results are more accurate.

Interface conditions for acoustic and elastic wave propagation

Geophysics ◽  
1991 ◽  
Vol 56 (2) ◽  
pp. 168-181 ◽  
Author(s):  
J. S. Sochacki ◽  
J. H. George ◽  
R. E. Ewing ◽  
S. B. Smithson
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Elastic Wave ◽  
Heterogeneous Media ◽  
Elastic Wave Propagation ◽  
Integration Scheme ◽  
Acoustic Wave Equation ◽  
Sh Wave ◽  
Numerical Schemes ◽  
Tangential Stresses

The divergence theorem is used to handle the physics required at interfaces for acoustic and elastic wave propagation in heterogeneous media. The physics required at regular and irregular interfaces is incorporated into numerical schemes by integrating across the interface. The technique, which can be used with many numerical schemes, is applied to finite differences. A derivation of the acoustic wave equation, which is readily handled by this integration scheme, is outlined. Since this form of the equation is equivalent to the scalar SH wave equation, the scheme can be applied to this equation also. Each component of the elastic P‐SV equation is presented in divergence form to apply this integration scheme, naturally incorporating the continuity of the normal and tangential stresses required at regular and irregular interfaces.

Sign in / Sign up

Export Citation Format

Share Document