At the exploration scale, the simulation of seismic wave propagation in the subsurface requires using absorbing boundary conditions. For the last twenty years, the method of choice has been the Perfectly Matched Layer (PML) method. PML are easy to implement and remarkably accurate. However, in certain situations such as the simulation of seismic waves in anisotropic media, the PML method becomes amplifying. We present here an alternative layer method, the SMART method. This method is based on a selective damping strategy. From an eigenvalue analysis of the matrices defining the hyperbolic system, the outgoing components of the wavefield associated with P- and S-wave velocities are damped. The SMART layer has two advantages over the PML. First, the dissipation is ensured for elasto-dynamic equations in isotropic and anisotropic media (no amplification). Second, the method yields a new strategy to prevent from the generation of non physical S-waves in acoustic transverse isotropic modeling. The SMART layer method is not perfectly matched, therefore less accurate than the PML. However our numerical experiments show that the accuracy of the PML can be reached provided an increase of the layer width. The additional computational cost associated with this increase of the layer size is compensated by the fact that the SMART method is less expensive: only a zero-order term is added to the initial system of equations, no additional variables are required.