A 3-D hybrid finite-difference—finite-element viscoelastic modelling of seismic wave motion

SUMMARY We have developed a new hybrid numerical method for 3-D viscoelastic modelling of seismic wave propagation and earthquake motion in heterogeneous media. The method is based on a combination of the fourth-order velocity–stress staggered-grid finite-difference (FD) scheme, that covers a major part of a computational domain, with the second-order finite-element (FE) method which can be applied to one or several relatively small subdomains. The FD and FE parts causally communicate at each time level in the FD–FE transition zone consisting of the FE Dirichlet boundary, FD–FE averaging zone and FD Dirichlet zone. The implemented FE formulation makes use of the concept of the global restoring-force vector which significantly reduces memory requirements compared to the standard formulation based on the global stiffness matrix. The realistic attenuation in the whole medium is incorporated using the rheology of the generalized Maxwell body in a definition equivalent to the generalized Zener body. The FE subdomains can comprise extended kinematic or dynamic models of the earthquake source or the free-surface topography. The kinematic source can be simulated using the body-force term in the equation of motion. The traction-at-split-node method is implemented in the FE method for simulation of the spontaneous rupture propagation. The hybrid method can be applied to a variety of problems related to the numerical modelling of earthquake ground motion in structurally complex media and source dynamics.

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