Abstract：There are mainly two issues when carrying out numerical modeling of elastic wave on arbitrary relief surface,the first is how to solve elastic wave equation;the second is how to handle free-boundary condition.First,started from the expression of Taylor's series,the paper deduced the expression of staggered-grid first spatial derivative having arbitrary even-order precision and relative computing formula of differential coefficients as well as solved equation of first hyperbolic staggered-grid stress-velocity elastic wave equation that the difference format has arbitrary even-order precision.Second,the free-boundary is handled by using combination of the zero-velocity method with the general ghost-image method and fourth-order difference format is used in free-boundary.The numerical modeling tests are carried out for smooth relief model and arbitrary relief model by using above mentionedmethods.The results showed that the methods described by the paper are characteristics of good stability and high precision of modeling,which is suitable for modeling of elastic wavefield on arbitrary relief surface.
