A Greenʹs function time-domain boundary element method for the elastodynamic half-plane

The transient Greenʹs function of the 2-D Lambʹs problem for the general case where point source and receiver are situated beneath the traction-free surface is derived. The derivations are based on Laplacetransform methods, utilizing the Cagniard{de Hoop inversion. The Greenʹs function is purely algebraic without any integrals and is presented in a numerically applicable form for the rst time. It is used to develop a Greenʹs function BEM in which surface discretizations on the traction-free boundary can be saved. The time convolution is performed numerically in an abstract complex plane. Hence, the respective integrals are regularized and only a few evaluations of the Greenʹs function are required. This fast procedure has been applied for the rst time. The Greenʹs function BEM developed proved to be very accurate and e cient in comparison with analogue BEMs that employ the fundamental solution