Boundary integral equations for dynamic rupture propagation on vertical complex fault system in half-space: Theory

The boundary integral equation method (BIEM) is now widely used in numerical studies on earthquake rupture dynamics, and is proved to be a powerful tool to deal with problems on complex fault system. However, since this method heavily lies on the specific forms of Greenos function and only the Greenos function in full-space has a closed analytic expression, it is usually limited to a full-space medium. In this study, as a first step to extend this method to an arbitrary complex fault system in half-space, the boundary integral equations (BIEs) for dynamic strike-slip on vertical complex fault system in half-space are derived based on exact Greenos function for isotropic and homogeneous half-space. Effect of the geometry of the complex fault system are dealt with carefully. Final BIEs is composed of two parts: contribution from full-space, which has been thoroughly investigated by Aochi and his co-workers by using the Greenos function for full-space, and that from free surface, which is studied in detail in this study.