Modelling the effects of diffusive-viscous waves in a 3-D fluid-saturated media using two numerical approaches

2020 ◽  
Vol 224 (2) ◽  
pp. 1443-1463
Author(s):  
Victor Mensah ◽  
Arturo Hidalgo
Keyword(s):  
Seismic Wave ◽  
Fourth Order ◽  
Seismic Waves ◽  
Time Discretization ◽  
Seismic Wave Propagation ◽  
Second Order ◽  
Finite Volume Scheme ◽  
Fluid Saturation ◽  
Runge Kutta ◽  
Saturated Medium

SUMMARY The accurate numerical modelling of 3-D seismic wave propagation is essential in understanding details to seismic wavefields which are, observed on regional and global scales on the Earth’s surface. The diffusive-viscous wave (DVW) equation was proposed to study the connection between fluid saturation and frequency dependence of reflections and to characterize the attenuation property of the seismic wave in a fluid-saturated medium. The attenuation of DVW is primarily described by the active attenuation parameters (AAP) in the equation. It is, therefore, imperative to acquire these parameters and to additionally specify the characteristics of the DVW. In this paper, quality factor, Q is used to obtain the AAP, and they are compared to those of the visco-acoustic wave. We further derive the 3-D numerical schemes based on a second order accurate finite-volume scheme with a second order Runge–Kutta approximation for the time discretization and a fourth order accurate finite-difference scheme with a fourth order Runge–Kutta approximation for the time discretization. We then simulate the propagation of seismic waves in a 3-D fluid-saturated medium based on the derived schemes. The numerical results indicate stronger attenuation when compared to the visco-acoustic case.

scholarly journals On the Accuracy and Efficiency of Transient Spectral Element Models for Seismic Wave Problems

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Sanna Mönkölä
Keyword(s):  
Fourth Order ◽  
Wave Equations ◽  
Seismic Waves ◽  
Time Discretization ◽  
Spectral Element ◽  
Higher Order ◽  
Time Stepping ◽  
Discretization Schemes ◽  
Elastic Wave Equations ◽  
Wave Problems

This study concentrates on transient multiphysical wave problems for simulating seismic waves. The presented models cover the coupling between elastic wave equations in solid structures and acoustic wave equations in fluids. We focus especially on the accuracy and efficiency of the numerical solution based on higher-order discretizations. The spatial discretization is performed by the spectral element method. For time discretization we compare three different schemes. The efficiency of the higher-order time discretization schemes depends on several factors which we discuss by presenting numerical experiments with the fourth-order Runge-Kutta and the fourth-order Adams-Bashforth time-stepping. We generate a synthetic seismogram and demonstrate its function by a numerical simulation.

On the accuracy of some explicit and implicit methods for the inviscid GRLW equation subject to initial Gaussian conditions

2016 ◽  
Vol 26 (3/4) ◽  
pp. 698-721 ◽  
Author(s):  
J I Ramos
Keyword(s):  
Finite Difference ◽  
Fourth Order ◽  
Finite Difference Methods ◽  
Second Order ◽  
Time Step ◽  
Content Type ◽  
Difference Methods ◽  
Temporal And Spatial ◽  
Runge Kutta ◽  
Grlw Equation

Purpose – The purpose of this paper is to both determine the effects of the nonlinearity on the wave dynamics and assess the temporal and spatial accuracy of five finite difference methods for the solution of the inviscid generalized regularized long-wave (GRLW) equation subject to initial Gaussian conditions. Design/methodology/approach – Two implicit second- and fourth-order accurate finite difference methods and three Runge-Kutta procedures are introduced. The methods employ a new dependent variable which contains the wave amplitude and its second-order spatial derivative. Numerical experiments are reported for several temporal and spatial step sizes in order to assess their accuracy and the preservation of the first two invariants of the inviscid GRLW equation as functions of the spatial and temporal orders of accuracy, and thus determine the conditions under which grid-independent results are obtained. Findings – It has been found that the steepening of the wave increase as the nonlinearity exponent is increased and that the accuracy of the fourth-order Runge-Kutta method is comparable to that of a second-order implicit procedure for time steps smaller than 100th, and that only the fourth-order compact method is almost grid-independent if the time step is on the order of 1,000th and more than 5,000 grid points are used, because of the initial steepening of the initial profile, wave breakup and solitary wave propagation. Originality/value – This is the first study where an accuracy assessment of wave breakup of the inviscid GRLW equation subject to initial Gaussian conditions is reported.

A NOTE ON THE PROPAGATION OF SEISMIC WAVES

Geophysics ◽  
1937 ◽  
Vol 2 (4) ◽  
pp. 319-328 ◽  
Author(s):  
Morris Muskat
Keyword(s):  
Wave Propagation ◽  
Power Series ◽  
Conventional Method ◽  
Seismic Wave ◽  
Seismic Waves ◽  
Seismic Wave Propagation ◽  
Time Distance

It is suggested that in the computation of theoretical time‐distance curves for seismic wave propagation a more tractable form of analysis is obtained if the depth is expressed as a power series in the velocity than when the converse but more conventional method is used. Several illustrations of this procedure are given.

Conservative Transport Schemes for Spherical Geodesic Grids: High-Order Flux Operators for ODE-Based Time Integration

2011 ◽  
Vol 139 (9) ◽  
pp. 2962-2975 ◽  
Author(s):  
William C. Skamarock ◽  
Almut Gassmann
Keyword(s):  
Fourth Order ◽  
Time Integration ◽  
Higher Order ◽  
Second Order ◽  
Time Step ◽  
Diffusion Term ◽  
The Third ◽  
Integration Schemes ◽  
Order Scheme ◽  
Runge Kutta

Higher-order finite-volume flux operators for transport algorithms used within Runge–Kutta time integration schemes on irregular Voronoi (hexagonal) meshes are proposed and tested. These operators are generalizations of third- and fourth-order operators currently used in atmospheric models employing regular, orthogonal rectangular meshes. Two-dimensional least squares fit polynomials are used to evaluate the higher-order spatial derivatives needed to cancel the leading-order truncation error terms of the standard second-order centered formulation. Positive definite or monotonic behavior is achieved by applying an appropriate limiter during the final Runge–Kutta stage within a given time step. The third- and fourth-order formulations are evaluated using standard transport tests on the sphere. The new schemes are more accurate and significantly more efficient than the standard second-order scheme and other schemes in the literature examined by the authors. The third-order formulation is equivalent to the fourth-order formulation plus an additional diffusion term that is proportional to the Courant number. An optimal value for the coefficient scaling this diffusion term is chosen based on qualitative evaluation of the test results. Improvements using the higher-order scheme in place of the traditional second-order centered approach are illustrated within 3D unstable baroclinic wave simulations produced using two global nonhydrostatic models employing spherical Voronoi meshes.

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.

Viscoelastic amplitude variation with offset equations with account taken of jumps in attenuation angle

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. N17-N29 ◽  
Author(s):  
Shahpoor Moradi ◽  
Kristopher A. Innanen
Keyword(s):  
Seismic Waves ◽  
Steam Injection ◽  
Seismic Wave Propagation ◽  
Type I ◽  
Amplitude Variation ◽  
Volume Scattering ◽  
Amplitude Variation With Offset ◽  
S Waves ◽  
Fluid Saturation ◽  
Special Cases

Anelastic properties of reservoir rocks are important and sensitive indicators of fluid saturation and viscosity changes due (for instance) to steam injection. The description of seismic waves propagating through viscoelastic continua is quite complex, involving a range of unique homogeneous and inhomogeneous modes. This is true even in the relatively simple theoretical environment of amplitude variation with offset (AVO) analysis. For instance, a complete treatment of the problem of linearizing the solutions of the low-loss viscoelastic Zoeppritz equations to obtain an extended Aki-Richards equations (one that is in accord with the appropriate complex Snell’s law) is lacking in the literature. Also missing is a clear analytical path allowing such forms to be reconciled with more general volume scattering pictures of viscoelastic seismic wave propagation. Our analysis, which provides these two missing elements, leads to approximate reflection and transmission coefficients for the P- and type-I S-waves. These involve additional, complex terms alongside those of the standard isotropic-elastic Aki-Richards equations. The extra terms were shown to have a significant influence on reflection strengths, particularly when the degree of inhomogeneity was high. The particular AVO forms we evaluated were finally shown to be special cases of potentials for volume scattering from viscoelastic inclusions.

scholarly journals A Preconditioned 3-D Multi-Region Fast Multipole Solver for Seismic Wave Propagation in Complex Geometries

2012 ◽  
Vol 11 (2) ◽  
pp. 594-609 ◽  
Author(s):  
S. Chaillat ◽  
J.F. Semblat ◽  
M. Bonnet
Keyword(s):  
Wave Propagation ◽  
Seismic Wave ◽  
Seismic Waves ◽  
Plane Waves ◽  
Seismic Wave Propagation ◽  
Boundary Element Methods ◽  
Complex Geometries ◽  
Fast Multipole ◽  
Geological Structures ◽  
Actual Configuration

AbstractThe analysis of seismic wave propagation and amplification in complex geological structures requires efficient numerical methods. In this article, following up on recent studies devoted to the formulation, implementation and evaluation of 3-D single- and multi-region elastodynamic fast multipole boundary element methods (FM-BEMs), a simple preconditioning strategy is proposed. Its efficiency is demonstrated on both the single- and multi-region versions using benchmark examples (scattering of plane waves by canyons and basins). Finally, the preconditioned FM-BEM is applied to the scattering of plane seismic waves in an actual configuration (alpine basin of Grenoble, France), for which the high velocity contrast is seen to significantly affect the overall efficiency of the multi-region FM-BEM.

scholarly journals A Fourth-Order-Centered Finite-Volume Scheme for Regular Hexagonal Grids

2007 ◽  
Vol 135 (12) ◽  
pp. 4030-4037 ◽  
Author(s):  
Hiroaki Miura
Keyword(s):  
Finite Volume ◽  
Fourth Order ◽  
Phase Error ◽  
Second Order ◽  
Finite Volume Scheme ◽  
Flux Divergence ◽  
Surrounding Cell ◽  
Divergence Operator ◽  
Cell Corner ◽  
Hexagonal Grids

Abstract Fourth-order-centered operators on regular hexagonal grids with the ZM-grid arrangement are described. The finite-volume method is used and operators are defined at hexagonal cell centers. The gradient operator is calculated from 12 surrounding cell center scalars. The divergence operator is defined from 12 surrounding cell corner vectors. A linear combination of local or interpolated values generates cell corner values used to calculate the operators. The flux-divergence operator applies the same cell corner values as those used in the gradient and divergence operators. The fourth-order convergence of the gradient and divergence operators is obtained in numerical tests using sufficiently smooth and differentiable test functions. The flux-divergence operator is formally second-order accurate. However, the results from a cone advection test show that the flux-divergence operator performs better than a commonly used second-order flux-divergence operator. Numerical dispersion and phase error are small because mean wind advection is computed with fourth-order accuracy.

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