Rayleigh surface wave has been used to research the character of shallow subsurface widely, and the real geological medium is close to viscoelastic media. This paper models Rayleigh wave in viscoelastic media with planar free surface by using the staggered-grid finite-difference method based on the generalized standard linear body firstly. In the simulation process the Levenberg-Marquarat algorithm which is belonged to nonlinear optimization method is adopted to directly compute the relaxation time to fitting the constant Q model. The stress imaging method and compact finite difference scheme are combined to implement the free surface conditions exactly. Then the dispersion profile is extracted from seismic record using phase shift method. And surface wave dispersion properties of several typical model are compared and analyzed. The results indicate that viscoelasticity can influence the surface wave dispersion markedly. So the viscoelastic factors should be considered in the surface wave exploration.


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