  The Finite Difference (FD) and the Spectral Boundary Integral (SBI) methods
have been used extensively to model spontaneously propagating shear cracks in a
variety of engineering and geophysical applications. In this paper, we propose
a new modeling approach, in which these two methods are combined through
consistent exchange of boundary tractions and displacements. Benefiting from
the flexibility of FD and the efficiency of spectral boundary integral (SBI)
methods, the proposed hybrid scheme will solve a wide range of problems in a
computationally efficient way. We demonstrate the validity of the approach
using two examples for dynamic rupture propagation: one in the presence of a
low velocity layer and the other in which off-fault plasticity is permitted. We
discuss possible potential uses of the hybrid scheme in earthquake cycle
simulations as well as an exact absorbing boundary condition
