A support‐operator method for viscoelastic wave modelling in 3‐D heterogeneous media

SUMMARY We apply the method of support operators (SOM) to solve the 3‐D, viscoelastic equations of motion for use in earthquake simulations. SOM is a generalized finite‐difference method that can utilize meshes of arbitrary structure and incorporate irregular geometry. Our implementation uses a 3‐D, logically rectangular, hexahedral mesh. Calculations are second‐order in space and time. A correction term is employed for suppression of spurious zero‐energy modes (hourglass oscillations). We develop a free surface boundary condition, and an absorbing boundary condition using the method of perfectly matched layers (PML). Numerical tests using a layered material model in a highly deformed mesh show good agreement with the frequency‐wavenumber method, for resolutions greater than 10 nodes per wavelength. We also test a vertically incident P wave on a semi‐circular canyon, for which results match boundary integral solutions at resolutions greater that 20 nodes per wavelength. We also demonstrate excellent parallel scalability of our code.