Journal ArticleDOI
Elastic wave calculations by the Fourier method
TLDR
In this article, a two-dimensional forward modeling algorithm based on a Fourier method was proposed to handle the free surface boundary condition with a new set of wave equations which contain the stresses as unknowns instead of the displacements.Abstract:
We introduce a two-dimensional forward modeling algorithim based on a Fourier method. In order to be able to handle the free surface boundary condition with the Fourier method, a new set of wave equations are derived which contain the stresses as unknowns instead of the displacements. The solution algorithm includes a discretization in both space and time. Spatial derivatives are approximated with the use of the Fast Fourier Transform, whereas temporal derivatives are calculated with second order differencing. The numerical method is tested against the analytic solution for Lamb's problem in two dimensions.read more
Citations
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Journal ArticleDOI
A nonreflecting boundary condition for discrete acoustic and elastic wave equations
TL;DR: In this paper, a nonreflecting boundary condition for the finite-difference method is proposed, which is based on gradual reduction of the amplitudes in a strip of nodes along the boundary of the mesh.
Journal ArticleDOI
Nonlinear two-dimensional elastic inversion of multioffset seismic data
TL;DR: In this article, an elastic finite-difference method is used to perform an inversion for P-wave velocity, S-wave impedance, and density, which is based on nonlinear least squares and proceeds by iteratively updating the earth parameters.
Journal ArticleDOI
The pseudospectral method: Comparisons with finite differences for the elastic wave equation
TL;DR: The pseudospectral method has been used recently by several investigators for forward seismic modeling as discussed by the authors, in two different ways: as a limit of finite differences of increasing orders, and by trigonometric interpolation.
Journal ArticleDOI
Wave propagation simulation in a linear viscoacoustic medium
TL;DR: In this article, the Boltzmann superposition principle based on the general standard linear solid rheology is implemented in the equation of motion by the introduction of memory variables, and the propagation in time is done by a direct expansion of the evolution operator by a Chebycheff polynomial series.
Journal ArticleDOI
Computational aspects of the choice of operator and sampling interval for numerical differentiation in large-scale simulation of wave phenomena*
TL;DR: In this article, a generalized numerical dispersion analysis for wave equation computations is developed, which can then be designed by minimizing the corresponding peak relative error in group velocity within a spatial frequency band.
References
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Book
Quantitative seismology : theory and methods
Keiiti Aki,Paul Richards +1 more
TL;DR: This work has here attempted to give a unified treatment of those methods of seismology that are currently used in interpreting actual data and develops the theory of seismic-wave propagation in realistic Earth models.
Journal ArticleDOI
Spectral methods for problems in complex geometries
TL;DR: In this paper, a new iteration procedure is introduced to solve the full matrix equations resulting from spectral approximations to nonconstant coefficient boundary-value problems in complex geometries, and the work required to solve these spectral equations exceeds that of solving the lowest-order finite-difference approximation to the same problem by only O(N log N).
Journal ArticleDOI
Forward modeling by a Fourier method
Dan Kosloff,Edip Baysal +1 more
TL;DR: In this paper, a pseudospectral forward-modeling algorithm for solving the two-dimensional acoustic wave equation is presented, which utilizes a spatial numerical grid to calculate spatial derivatives by the fast Fourier transform.
Journal ArticleDOI
Modeling of the acoustic wave equation with transform methods
TL;DR: In this paper, numerical methods are described for the simulation of wave phenomena with application to the modeling of seismic data, and two separate topics are studied: the first deals with the solution of the acoustic wave equation and the second topic treats wave phenomena whose direction of propagation is restricted within ±90 degrees from a given axis.