A stable free-surface boundary condition for two-dimensional elastic finite-difference wave simulation: SHORT NOTE

INTRODUCTION Two of the persistent problems in finite-difference solutions of the elastic wave equation are the limited stability range of the free-surface boundary condition and the boundary condition's treatment of lateral variations in velocity and density. The centered-difference approximation presented by Alterman and Karal ( 1968), for example, remains stable only for 1:1/a greater than 0.30, where 1:1 and a are the shear (S) and compressional (P) wave velocities. The one-sided approximation (Alterman and Rotenberg, 1969) and composed approximation (Ilan et al., 1975) have similar restrictions. The revisedcomposed approximation of llan and Loewenthal ( 1976) overcomes this restriction, but cannot handle laterally varying media properly. First we present a free-surface boundary approximation that is stable for all physical j:lju ratios and correct for laterally varying media. The method is implicit, but only requires a simple pentadiagonal system solver to implement. When the proposed boundary conditions are coupled with second-order and fourth-order approximations for the elastic wave equation, the overall problem is stable for 1:1/a greater than 0.01 and 1:1/u greater than 0.02, respectively. A simple numerical test of the method and a comparison with other published methods are given in the second section.