In this paper, we carry out a numerical dispersion analysis for the linear two-dimensional elastodynamics equations approximated by means of NURBS-based Isogeometric Analysis in the framework of the Galerkin method; specifically, we consider the analysis of harmonic plane waves in an isotropic and homogeneous elastic medium. We compare and discuss the errors associated with the compressional and shear wave velocities and we provide the anisotropic curves for numerical approximations obtained by considering B-spline and NURBS basis functions of different regularity, namely globally C^0- and C^{p−1}-continuous, p being the polynomial degree. We conclude our analysis by numerically simulating the seismic wave propagation in a sinusoidal shaped valley with discontinuous elastic parameters across an internal interface.