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One of the most suitable methods for modeling fully dynamic earthquake cyclesimulations is the spectral boundary integral element method (sBIEM), whichtakes advantage of the fast Fourier transform (FFT) to make a complex numericaldynamic rupture tractable. However, this method has the serious drawback ofrequiring a flat fault geometry due to the FFT approach. Here we present ananalytical formulation that extends the sBIEM to a mildly non-planar fault. Westart from a regularized boundary element method and apply a small-slopeapproximation of the fault geometry. Making this assumption, it is possible toshow that the main effect of non-planar fault geometry is to change the normaltraction along the fault, which is controlled by the local curvature along thefault. We then convert this space--time boundary integral equation of thenormal traction into a spectral-time formulation and incorporate this change innormal traction into the existing sBIEM methodology. This approach allows us tomodel fully dynamic seismic cycle simulations on non-planar faults in aparticularly efficient way. We then test this method against a regular boundaryintegral element method for both rough-fault and seamount fault geometries, anddemonstrate that this sBIEM maintains the scaling between the fault geometryand slip distribution.

Fully dynamic earthquake cycle simulations on a non-planar fault using the spectral boundary integral element method