Wave Velocity Dispersion and Attenuation in Media Exhibiting Internal Oscillations (original) (raw)
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The Journal of the Acoustical Society of America, 2011
A pseudospectral model of linear elastic wave propagation is described based on the first order stress-velocity equations of elastodynamics. k-space adjustments to the spectral gradient calculations are derived from the dyadic Green's function solution to the second-order elastic wave equation and used to (a) ensure the solution is exact for homogeneous wave propagation for timesteps of arbitrarily large size, and (b) also allows larger time steps without loss of accuracy in heterogeneous media. The formulation in k-space allows the wavefield to be split easily into compressional and shear parts. A perfectly matched layer (PML) absorbing boundary condition was developed to effectively impose a radiation condition on the wavefield. The staggered grid, which is essential for accurate simulations, is described, along with other practical details of the implementation. The model is verified through comparison with exact solutions for canonical examples and further examples are given to show the efficiency of the method for practical problems. The efficiency of the model is by virtue of the reduced point-per-wavelength requirement, the use of the fast Fourier transform (FFT) to calculate the gradients in k space, and larger time steps made possible by the k-space adjustments.
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The accurate solution of wave propagations in general two-and three-dimensional solids is still difficult and frequently impossible to achieve with the current computational schemes and computers available. We present in this paper a solution scheme that has much promise for the accurate solution of wave propagations in general solids. The procedure is based on the use of ''overlapping finite elements" and direct time integration. The overlapping finite elements are effective because the spatial dispersion error is relatively small and can be monotonically reduced using a finer mesh. Similarly, the time integration dispersion errors can also be reduced monotonically as the time step becomes smaller. Hence the key property of the solution scheme is that the total dispersion error in the simulation of multiple waves traveling through solids is monotonically reduced as the spatial discretization and time stepping become finer. We summarize the ingredients of the solution scheme and illustrate the characteristics in the solution of some wave propagation problems that are difficult to solve accurately. These solutions may be benchmark solutions to use in the evaluations of other computational schemes.
Geophysical Journal International, 2018
As recently demonstrated the most advanced finite-difference (FD) schemes are sufficiently efficient and accurate numerical-modelling tools for seismic wave propagation and earthquake ground motion especially in local surface sedimentary structures. The key advantages of the explicit FD schemes are a uniform grid, no matter what positions of material interfaces are in the grid, and one scheme for all interior points, no matter what their positions are with respect to the material interfaces. Efficiency and accuracy is determined by the grid dispersion and discrete representation of a material heterogeneity. After having developed discrete representations for the elastic and viscoelastic media, we present here a new discrete representation of material heterogeneity in the poroelastic medium. The representation is capable of subcell resolution and makes it possible to model an arbitrary shape and position of an interface in the grid. At the same time, the structure and thus the number of operations in the FD scheme are unchanged compared to the homogeneous or smoothly heterogeneous medium.