Code and data accompanying a paper entitled "Broad Resonance of Fault Slip under Oscillatory Normal Stress: Insights from a Microphysical Friction Model"

Earthquakes and slow-slip events can sometimes be triggered or modulated by small stress changes produced by passing seismic waves, solid-Earth tides, or seasonal variations in groundwater and surface-water loading. Precisely how these weak environmental forces influence fault behavior, however, remains poorly understood. In this study, I use a physics-based numerical model to investigate how faults respond to repeated fluctuations in the normal stress that clamps the two sides of a fault together. I perform numerical simulations using a spring–slider fault analog and a solver embedded in the commercial finite-element software COMSOL, to quantify how the shear-stress response varies with spring stiffness, perturbation period, perturbation amplitude, and the material properties of fault-filling rocks (fault gouge). The results show that these small periodic stress changes can, under favorable conditions, produce resonant fault slip—a process in which repeated forcing greatly amplifies fault motion, much like pushing a swing at the right rhythm. The enclosed code and data include: 1. CNS model with variable normal stress_COMSOL.mph — A COMSOL source file that solves the two coupled ordinary differential equations (ODEs) with time-dependent normal stress as input. 2. All Simulation Results.rar — Numerical simulation results from 109 runs. Each run contains the evolution of apparent friction coefficient (shear stress / background normal stress), normal stress, and log₁₀(slip velocity) as functions of load-point displacement. Selected runs additionally include the evolution of gouge state variable [tan(dilatancy angle)] with load-point displacement. 3. Six MATLAB source code files, "Processing, a–f…" — Used to process the simulation results sequentially. 4. Six MATLAB source code files, "Plot, stressdrop_Weakening_vs_…" — Used to extract key diagnostic parameters from the time-series results, including normalized shear-stress oscillation amplitude, peak slip velocity, phase lag, and slip recurrence period. 5. Data for Original graphs.rar — Compiled numerical results containing all intermediate processing outputs (9 files in format of .csv). 6. Data_extracted for Original graphs.rar — Compiled, cleaned numerical results ready for plotting (9 files in format of .csv). 7. Original graphs.rar — All figures generated by the MATLAB code and data, saved in PDF format, totally 18. 8. Extracted results for saturated velocity, v_max_1s.xlsx — An Excel table containing extracted saturated slip velocity under short-period forcing (T_ext = 1 s) as a function of normalized stiffness and relative modulation amplitude.地震与慢滑事件有时会被过往地震波、固体地球潮汐引发的微小应力变化，或是地下水与地表水负载的季节性变化所触发或调制。然而，这些微弱的环境作用力究竟如何影响断层活动，目前仍不甚明晰。 本研究采用基于物理原理的数值模型，探究断层如何响应将断层两侧夹持的法向应力（normal stress）的周期性重复波动。研究使用弹簧-滑块断层类比模型，以及嵌入商业有限元软件COMSOL的求解器开展数值模拟，以量化剪切应力（shear stress）响应如何随弹簧刚度、扰动周期、扰动振幅以及断层充填岩石（断层泥，fault gouge）的材料属性变化。 结果表明，在适宜条件下，这些微小的周期性应力变化可引发共振型断层滑动——即通过以恰当节律持续施力，大幅放大断层运动，这一过程与以合适节奏推动秋千的原理相似。 随附的代码与数据包含以下内容： 1. "CNS model with variable normal stress_COMSOL.mph"：该COMSOL源文件用于求解以时变法向应力为输入的两组耦合常微分方程（ODEs）。 2. "All Simulation Results.rar"：包含109次数值模拟的结果。每组模拟结果均包含表观摩擦系数（apparent friction coefficient，剪切应力/背景法向应力）、法向应力以及log₁₀(滑动速度)随加载点位移的演化过程；部分模拟额外包含断层泥状态变量[剪胀角（dilatancy angle）正切值]随加载点位移的演化过程。 3. 六个MATLAB源文件，命名为"Processing, a–f…"，用于按顺序处理模拟结果。 4. 六个MATLAB源文件，命名为"Plot, stressdrop_Weakening_vs_…"，用于从时间序列结果中提取关键诊断参数，包括归一化剪切应力振荡振幅、峰值滑动速度、相位滞后以及滑动复发周期。 5. "Data for Original graphs.rar"：包含所有中间处理输出的编译数值结果（9个.csv格式文件）。 6. "Data_extracted for Original graphs.rar"：经编译、清理后可直接用于绘图的数值结果（9个.csv格式文件）。 7. "Original graphs.rar"：所有由MATLAB代码与数据生成的图表，均以PDF格式保存，共计18张。 8. "Extracted results for saturated velocity, v_max_1s.xlsx"：包含以归一化刚度与相对调制振幅为变量的短周期扰动（T_ext=1 s）下的饱和滑动速度提取结果的Excel表格。