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The free-surface boundary condition is a crucial aspect in numerical modeling of (visco)elastic wave equations, especially when using a finite-difference (FD) method in the presence of surface topography. The parameter-modified method is a widely used approach to solve this problem. In this regard, the adaptive Poisson's ratio parameter-modified (APM) method has proven to be effective in accurately simulating seismic surface waves within the FD discretization framework. Based on the equivalent medium theory, vacuum approximation, and mathematical limit, we developed a viscoelastic parameter-modified (VPM) method for the implementation of the free-surface boundary condition in the three-dimensional (3D) viscoelastic wave equation. Our approach modifies the viscoelastic constitutive relation and density at the free surface and provides a formulation in terms of displacement and stress. We demonstrated that our VPM method is more general than the viscoelastic stress-image (VSI) method as it includes the latter as a limit case when Poisson's ratio equals zero. The presented free-surface method is represented implicitly within the FD grid, and we provide implementation details when simulating surface waves with topography in the standard staggered-grid FD scheme. We support our theory' feasibility and accuracy through numerical examples.

An accurate free-surface boundary condition is significant for seismic forward modeling and inversion. The finite-difference method (FDM) is widely used for its simplicity and efficiency. However, unlike the finite-element method (FEM) satisfying naturally the stress-free condition at the free surface, FDM needs additional treatment, particularly in the presence of irregular topography. In the elastic wave finite-difference modeling, the adaptive parameter-modified free-surface boundary condition has the advantages of high accuracy and simple operation. The viscoelastic wave equation can describe the nature of seismic waves more realistically. Based on the staggered-grid FDM, we extend the adaptive free-surface boundary condition to the viscoelastic medium with topography. This approach involves a combination of the average medium theory, vacuum approximation and limit idea. It is realized by modifying the viscoelastic constitutive relation. This method is simple enough, because three types of grid elements and in fact only two kinds of expressions are enough in the presence of topography. We only need to deal with the Lame parameters and the density at the free surface without reconstructing the existing algorithm. Viscoelastic analysis of different quality factor settings shows the viscous effect. Numerical examples display that the results of the presented method agree well with the reference solutions of spectral-element method both in crest- and trough-like model and in simplified Foothill model with irregular topography. The simulation of original Foothill model demonstrates the feasibility of our method.

The speech quality is one of the most important indexes to evaluate the communication system. The objective evaluation is the last goal that people have been pursuing. The most efficient evaluation methods based on the spectrum distortion measure was analysed. The objective evaluation method based on wavelet spectrum distortion measure was simulated on the Matlab simulation environment. The simulation results show that Matlab was very suit to analyse the speech quality. The objective evaluation rules are found out on Matlab and the objective evaluation method was achieved.

The dispersion effect of five cyclodextrins (CDs) on carbon nanotubes (CNTs) was studied. 2-HB-β-CD is the most efficient dispersing agent. The dispersing ability of CDs on the dispersion of CNTs was 2-HB-β-CD >> 6-HP-β-CD > β-CD > 6-HB-β-CD > 2-HP-β-CD. The movement in the FTIR spectra of the asymmetric and symmetric stretching vibrations of O-H of the composites means hydrogen bonding was an important factor on the dispersing ability. These results indicate that the type of interaction might be a combination of a weak interaction similar to a van der Waals type and hydrogen bonding mechanism.