+ Summary
+ Numerical simulations of seismic cycles constitute a useful tool to
+ test the implications of various constitutive friction laws, materials
+ properties, and boundary conditions. A unique challenge of numerical
+ models of fault dynamics is the resolution of a wide range of time and
+ length scales, going from milliseconds during seismic ruptures to
+ years during seismic quiescence with a rupture front spanning a few
+ meters to fault slip distributed over multiple kilometers. A
+ well-suited approach for this problem is the boundary integral method
+ (Barbot,
+ 2019b;
+ Liu
+ & Rice, 2007;
+ Ozawa
+ & Ando, 2021;
+ Segall
+ & Bradley, 2012;
+ Wang
+ & Barbot, 2023), as the elastic medium is captured by
+ appropriate Green’s functions, and only the fault interface must be
+ sampled numerically, resulting in orders of magnitude reduction in
+ computational burden
+ (M.
+ Li et al., 2022), while still allowing realistic fault geometry
+ (D.
+ Li & Liu, 2016,
+ 2017;
+ Sathiakumar
+ et al., 2020). Using the spectral boundary integral method
+ (Lapusta
+ & Liu, 2009) reduces the numerical complexity even further,
+ allowing exploration of increasingly complex rheological models
+ (Barbot
+ et al., 2012;
+ Gauriau
+ et al., 2023;
+ Miyake
+ & Noda, 2019;
+ Noda,
+ 2022). However, the approach is often limited to a single fault
+ (Romanet
+ & Ozawa, 2022). Here, we provide a suite of numerical
+ modeling software to simulate seismic cycles on multiple parallel
+ faults combining the efficiency of Fourier methods and the complexity
+ of an interacting fault network
+ (Barbot,
+ 2021).
+ The models include semi-infinite faults in conditions of
+ two-dimensional anti-plane or in-plane strain, or along finite faults
+ embedded in a three-dimensional full space. The fault dynamics is
+ governed by a constitutive law with a slip-rate, state, and
+ temperature dependence
+ (Barbot,
+ 2019a,
+ 2022,
+ 2023). The
+ method is based on the quasi-dynamic approximation whereby the effect
+ of seismic waves is approximated by radiation damping. The stress
+ interactions are computed analytically in the Fourier domain
+ (Barbot,
+ 2021) and converted with the FFTW3 fast
+ Fourier transform
+ (Frigo
+ & Johnson, 2005). The calculations for a two-dimensional
+ domain are parallelized with OpenMP. The spectrum of fault slip,
+ including creep, slow-slip events, slow and fast earthquakes
+ ([fig:01]), is afforded
+ by adaptive time steps with the Runge-Kutta method
+ (Press
+ et al., 1996). The simulations using finite faults are
+ parallelized with MPI
+ (Gabriel
+ et al., 2004). The stress kernels allow the mechanical
+ interactions of an arbitrary number of parallel faults, allowing
+ structurally complex settings with a network of faults and multiple
+ step-overs.
+
+ Example simulation of seismic cycles on two parallel
+ faults. A) Model setup with the distribution of frictional and
+ physical properties leading to unstable slip in a 5 km-wide asperity
+ (red) surrounded by a velocity-strengthening region (blue). The thin
+ surroundings of the fault surface (yellow) is subject to a kinematic
+ boundary condition to enforce a long-term slip-rate of about 30
+ mm/yr, equivalent to 1 nm/s. The two faults are separated by 15 km.
+ Each fault is sampled with 512x512 rectangle patches of 25 m. B)
+ Sequences of fast ruptures followed by afterslip and slow-slip
+ events late in the inter-seismic period corresponding to about
+ 120,000 quasi-static time steps. The slices correspond to horizontal
+ and vertical cross-sections through each fault. The dashed lines
+ indicate the boundaries of the velocity-weakening region. C) Time
+ series of peak velocity in the unstable asperities of faults 1 and
+ 2. Velocities above 1 m/s are firmly in the seismic regime.
+ Slow-slip events are more pronounced on fault 1. The simulation
+ corresponds to the input file
+ 3d/examples/tutorials/run2f.sh.
+ ![]()
+
+
+
+ Statement of need
+ Motorcycle is a series of Fortran90
+ standalone numerical modeling tools for fault dynamics. The numerical
+ simulations are optimized for performance and stability, based on
+ automatic time-stepping and meshing. The input file allows complex
+ rheological or structural settings and the automatic exploration of
+ the parameter space. The simulation output is provided in ASCII tables
+ and netcdf files
+ (Brown
+ et al., 1993;
+ Rew
+ & Davis, 1990) for automatic visualization with typical
+ geophysical software such as the Generic Mapping Tools
+ (Wessel
+ et al., 2019).
+ Motorcycle is designed for scientists
+ conducting research in fault dynamics. Applications include the
+ nucleation of frictional instabilities (e.g., slow-slip events), the
+ propagation of earthquake ruptures (e.g., crack-like versus
+ pulse-like), and the mechanical coupling of multiple faults.
+ Successful simulation benchmarks based on comparison with other
+ software can be found in Jiang et al.
+ (2022).
+ Applications of the method include the simulation of synchronized
+ earthquakes on distant faults
+ (Barbot,
+ 2021), of complex slow-slip events generating tremors
+ (Nie
+ & Barbot, 2021), and of mainshock/aftershock sequences
+ (Nie
+ & Barbot, 2022).
+
+