Free-surface boundary conditions for elastic staggered-grid modeling schemes

I present an accurate, stable, and simple implementation of the elastic free surface for staggered-grid modeling schemes. The method is based on the presumption that the elastic Hooke's tensor on the free surface can be taken as similar to a transversely isotropic medium. The anisotropic elastic properties are then analyzed. The final scheme is isotropic, but with modified elastic properties on the free surface. The proposed scheme shows good agreement with an analytical solution. It is shown that the Rayleigh wave can not be properly resolved at two gridpoints per shortest wavelength if the shortest wavelength is calculated as the Rayleigh-wave velocity over the maximum frequency. The Rayleigh wave is exponentially damped away from the free surface and requires denser sampling than purely propagating waves.