scholarly journals Finite-difference approximation of wave equation: a study case of the SIMA velocity model

2014 ◽  
Vol 8 ◽  
pp. 8679-8688
Author(s):  
Fadila Ouraini ◽  
Ramon Carbonell ◽  
David Marti Linares ◽  
Kamal Gueraoui ◽  
Puy Ayarza ◽  
...  
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Velocity Model ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Study Case

scholarly journals Stable and Efficient Modeling of Anelastic Attenuation in Seismic Wave Propagation

2012 ◽  
Vol 12 (1) ◽  
pp. 193-225 ◽  
Author(s):  
N. Anders Petersson ◽  
Björn Sjögreen
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Half Space ◽  
Material Model ◽  
Second Order ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Space Problem ◽  
Standard Linear Solid ◽  
Standard Linear

AbstractWe develop a stable finite difference approximation of the three-dimensional viscoelastic wave equation. The material model is a super-imposition of N standard linear solid mechanisms, which commonly is used in seismology to model a material with constant quality factor Q. The proposed scheme discretizes the governing equations in second order displacement formulation using 3N memory variables, making it significantly more memory efficient than the commonly used first order velocity-stress formulation. The new scheme is a generalization of our energy conserving finite difference scheme for the elastic wave equation in second order formulation [SIAM J. Numer. Anal., 45 (2007), pp. 1902-1936]. Our main result is a proof that the proposed discretization is energy stable, even in the case of variable material properties. The proof relies on the summation-by-parts property of the discretization. The new scheme is implemented with grid refinement with hanging nodes on the interface. Numerical experiments verify the accuracy and stability of the new scheme. Semi-analytical solutions for a half-space problem and the LOH.3 layer over half-space problem are used to demonstrate how the number of viscoelastic mechanisms and the grid resolution influence the accuracy. We find that three standard linear solid mechanisms usually are sufficient to make the modeling error smaller than the discretization error.

scholarly journals Error Analysis of An Explicit Finite Difference Approximation for the Space Fractional Wave Equations

2012 ◽  
Vol 17 (2) ◽  
pp. 245
Author(s):  
N.H. Sweilam ◽  
T.A. Assiri
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Error Analysis ◽  
Wave Equations ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Fractional Wave Equation ◽  
Fractional Wave Equations ◽  
Explicit Finite Difference ◽  
The Stability

In this paper, the space fractional wave equation (SFWE) is numerically studied, where the fractional derivative is defined in the sense of Caputo. An explicit finite difference approximation (EFDA) for SFWE is presented. The stability and the error analysis of the EFDA are discussed. To demonstrate the effectiveness of the approximated method, some test examples are presented.   

scholarly journals New Nonpolynomial Spline in Compression Method of for the Solution of 1D Wave Equation in Polar Coordinates

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Venu Gopal ◽  
R. K. Mohanty ◽  
Navnit Jha
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Mathematical Formulation ◽  
Finite Difference Approximation ◽  
Polar Coordinates ◽  
Difference Approximation ◽  
Compression Method ◽  
One Dimensional ◽  
Spline In Compression ◽  
The Stability

We propose a three-level implicit nine point compact finite difference formulation of order two in time and four in space direction, based on nonpolynomial spline in compression approximation in -direction and finite difference approximation in -direction for the numerical solution of one-dimensional wave equation in polar coordinates. We describe the mathematical formulation procedure in detail and also discussed the stability of the method. Numerical results are provided to justify the usefulness of the proposed method.

Finite Difference Approximation of Fractional Wave Equation with Concentrated Capacity

2017 ◽  
Vol 17 (1) ◽  
pp. 33-49 ◽  
Author(s):  
Aleksandra Delić ◽  
Boško S. Jovanović
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Finite Difference Approximation ◽  
Generalized Solutions ◽  
Difference Approximation ◽  
Dirac Delta ◽  
Fractional Wave Equation ◽  
Initial Boundary Value

AbstractWe consider the time fractional wave equation with coefficient which contains the Dirac delta distribution. The existence of generalized solutions of this initial-boundary value problem is proved. An implicit finite difference scheme approximating the problem is developed and its stability is proved. Estimates for the rate of convergence in special discrete energetic Sobolev norms are obtained. A numerical example confirms the theoretical results.

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