Free-surface Boundary Condition in Time-domain Elastic Wave Modeling Using Displacement-based Finite-difference Method

시간영역 변위근사 유한차분법의 자유면 경계조건

  • Min Dong-Joo (Global Environment Research Laboratory, Korea Ocean Research & Development Institute) ;
  • Yoo Hai Soo (Global Environment Research Laboratory, Korea Ocean Research & Development Institute)
  • 민동주 (한국해양연구원 지구환경연구본부) ;
  • 유해수 (한국해양연구원 지구환경연구본부)
  • Published : 2003.05.01


We designed a new time-domain, finite-difference, elastic wave modeling technique, based on a displacement formulation. which yields nearly correct solutions to Lamb's problem. Unlike the conventional, displacement-based, finite-difference method using a node-based grid set (where both displacements and material properties such as density and Lame constants are assigned to nodal points), in our new finite-difference method, we use a cell-based grid set (where displacements are still defined at nodal points but material properties within cells). In the case of using the cell-based grid set, stress-free conditions at the free surface are naturally described by the changes in the material properties without any additional free-surface boundary condition. Through numerical tests, we confirmed that the new second-order finite differences formulated in the cell-based grid let generate numerical solutions compatible with analytic solutions unlike the old second-order finite-differences formulated in the node-based grid set.