Simulation of the traction-free condition is one of the key factors for the accuracy and efficiency of the FD modeling of seismic motion. And the constant Q model is very important to modeling the seismic attenuation characteristic of viscoelastic materials especially in time domain. In this paper we use the GZB to model the seismic attenuation property of real materials. And the Levenberg-Marquarat algorithm (L-M algorithm) which belongs to nonlinear optimization method is adopted to compute the viscoelastic parameter to fitting the constant Q model. When simulating the planar free surface, we use compact finite difference schemes for the points near free surface. Application of compact scheme to the z-derivatives at the grid points at and below the surface that uses no virtual values above the surface and no stress imaging.


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