Combining absorbing and nonreflecting boundary conditions for elastic wave simulation

The absorbing boundary conditions and the nonreflecting boundary condition are two of the most popular solutions to the computational boundary condition problem. We report our implementations of these boundary conditions within our staggered-grid finitedifference applications and describe their features. Then we present a method combining the absorbing boundary conditions and the nonreflecting boundary condition. INTRODUCTION Computational boundary condition problems have been a persistent topic in the field of wave phenomena modelling. Migration algorithms also have to deal with boundaries. There are a lot of solutions to the boundary condition problems. The most cited method about boundary conditions is the “absorbing boundary conditions” proposed by Engquist and Majda (1977), and Clayton and Engquist (1977). Another popular method called “nonreflecting boundary condition” was presented by Cerjan, Kosloff, Kosloff, and Reshef in 1985. There are some other solutions as well, such as “transparent boundary” by Long and Liow (1990) and “perfectly matched layer” method by Collino and Tsogka (2001). This report reviews the aborbing and nonreflecting boundary conditions first, and then presents our combined boundary conditions. RIGID BOUNDARY CONDITIONS Elastic modelling method we are using is base on the Madariaga-Virieux staggeredgrid scheme (Virieux, 1986). To illustrate the boundary conditions, a subsurface model, which contains a point diffractor in a homogenous medium in z x − plane, is designed. Figure 1 shows the geometry and the P-wave velocities, although the real subsurface model parameters used by the modelling algorithm are densities and Lame coefficients. VP(m/s) 1000 m 3750 m