Dispersion analysis of Rayleigh waves in viscoelastic media

摘要

Multichannel Analysis of Surface Waves (MASW) is one of the most widely used techniques in environmental and engineering geophysics for the measurement of shear wave velocity and dynamic properties. This method is based on the elastic layer system theory. However, wave propagation in the earth has been recognized as viscoelastic and the propagation of Rayleigh waves presents substantial differences in viscoelastic media compared with in elastic media. Therefore, it is necessary to carry out numerical simulation and dispersion analysis of Rayleigh waves in viscoelastic media. In this paper, we apply a pseudospectral method to calculate the spatial derivatives with a Chebyshev difference operator in the vertical direction and a Fourier difference operator in the horizontal direction based on the velocity-stress elastodynamic equations and relation of linear viscoelastic solids. This approach stretches the spatial discrete grid to have a minimum grid size near the free surface such that high accuracy and resolution are achieved at the surface, and allows an effective incorporation of the free surface boundary conditions since the Chebyshev method is nonperiodic. We first use an elastic homogeneous half-space model to demonstrate the accuracy of pseudospectral method comparing with the analytical solution. We then simulate the viscoelastic half-space model and two-layer models to analysis dispersive-energy characteristics by high-resolution linear Radon transform for near-surface application. Results demonstrate that the phase velocity of Rayleigh waves in viscoelastic media is relatively higher than in elastic media due to the velocity dispersion of P- and S-waves.