Earthquake nucleation simulation：A case study of the 2023 MW 7.8 Kahramanmaraş earthquake, Turkey
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摘要:
大陆转换断层系统中的次级断层在走滑地震中优先破裂是一个广泛讨论的问题，破译其潜在机制可以增强对地震物理和地震灾害的认识。本研究引入一种新的有限元框架来模拟断层成核，该框架根据背景构造应力和断层几何形状的相互作用来识别成核。该方法将断层视为2个块体之间的摩擦接触，采用准静态模拟得到的应力−应变条件作为动态破裂模拟的初始条件，并将静态摩擦突然转变为动态摩擦。其中，动态模拟的第一步得到的最大滑移区与准静态模型中最小静摩擦区相对应，即为地震成核区。使用简化的三维弹塑性模型研究了影响2023年土耳其卡赫拉曼马拉什7.8级地震成核位置的关键因素。研究结果表明，本研究提出的地震成核模拟方法具有极高的准确性，在2023年土耳其卡赫拉曼马拉什7.8级地震中，由于次级断层（努尔达伊断层）与主断层的几何结构发生了变化，其力学耦合表现出非线性特征。次级断层的明显挠曲，特别是沿垂向深度的挠曲，会显著加速地震成核，并导致成核位置从主断层向次级断层转移。本研究提出的断层成核研究方法，解决了有限元模型在平衡静岩石压力（预应力）和重力效应过程中的高自由度问题，提高了成核模拟的准确性。同时，基于物理的模拟成功地再现了由运动学有限断层反演得到的2023年土耳其卡赫拉曼马拉什同震滑动模式，为大型走滑断层为何起源于次级断层提供了合理解释。
Abstract:Objective The preferential rupture of splay faults in continental transform fault systems during strike-slip earthquakes remains a widely debated issue. Deciphering the underlying mechanism is crucial for advancing the understanding of earthquake physics and improving seismic hazard assessment.
Methods This study introduces a novel finite element framework to simulate fault nucleation, which identifies nucleation zones based on the interaction between background tectonic stress and fault geometry. Within this framework, faults are treated as frictional contact between two blocks. Stress-strain conditions derived from quasi-static simulations serve as initial conditions for dynamic rupture simulations, with the abrupt transition from static to dynamic friction modeled. The region of maximum slip obtained in the first step of the dynamic simulation corresponds to the area of minimum static friction in the quasi-static model, thereby defining the earthquake nucleation zone. Simultaneously, we investigate the key factors impacting the nucleation site of the 2023
M W 7.8 Kahramanmaraş earthquake using a simplified 3D elastic-plastic model.Results The results show the high accuracy of the proposed earthquake nucleation simulation method and reveal that the mechanical coupling between the splay Nurdağı Fault (NF) and the main fault exhibits nonlinear characteristics, influenced by variations in the geometric structure of the NF. The pronounced deflection of the NF, especially with depth, significantly accelerates earthquake nucleation and leads to the shift of the nucleation location to the NF.
Conclusions This study addresses as the challenge of high degrees of freedom in finite element models when balancing static rock pressure (pre-stress) and gravitational effects, thereby improving the accuracy of nucleation simulation. Furthermore, our physics-based simulation successfully reproduces the coseismic slip pattern derived from kinematic finite fault inversion. This study provides a robust explanation for why large strike-slip earthquakes can nucleate on splay faults.
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图 1 摩擦衰减和滑移速率关系示意图
$\mu $. 摩擦系数；$ {{{\mu}}}_{{1}} $. 动态摩擦系数；V. 程序计算的滑移速率
Figure 1. Diagram of the friction decay and slip rate
图 2 单一断层模型示意图（g为重力加速度，下同）
在准静态模型中，边界被设置为位移边界条件，而动态模型则采用速度边界条件。该模型顶部有自由边界，底部有横向自由边界
Figure 2. Conceptual schematic of the simple fault model
图 3 2023年土耳其卡赫拉曼马拉什 7.8 级地震中断层模型示意图
Figure 3. Conceptual schematic of the fault model for the 2023 MW 7.8 Kahramanmaraş earthquake
图 4 三维有限元断层模型的边界条件
Figure 4. Boundary condition applied to the three-dimensional finite element fault model
图 5 不同时间步长的第一步动态滑移分布
由于绝对震级在不同的Δt处相差几个数量级，因此对每个模型的峰值滑移（S）进行了归一化有助于直接比较，下同
Figure 5. Initial dynamic slip distribution at different time steps
图 6 有无误差矫正的断层模型垂直位移和整体变形模式（S'. 模型稳定后100 s的滑移；下同）
a. 有无矫正误差动态模拟初始子步（0.005 s）的滑动量及稳定后（100 s）断层的右旋滑动分布；b. 断层模型内任意点有无矫正误差的垂直位移和整体位移变形模式曲线图，其中所有模型的滑移量和地表垂直变形量都进行了归一化处理；c. t = 20, 40, 60, 80 s时断面上的横向滑动
Figure 6. Vertical displacement and overall deformation pattern of fault model with and without error correction
图 7 次级断层几何形态对地震成核的影响结果
a～c. 为断层倾角80°～60°时动态模拟初始子步的滑移；d～f. 为动态模拟初始子步不同断层挠度下的滑移
Figure 7. Effect of splay faults geometric on earthquake nucleation
图 8 东安托那断层和努尔达伊断层系统的断层滑动和地表垂直变形（D. 模型稳定后100 s的垂向位移）
a. 动态模拟第一步（0.005 s）的滑移结果，即初始失稳时刻下的滑移；b. 模型稳定后（100 s）的滑移；c. 模型稳定后（100 s）的垂向位移
Figure 8. Fault slip and surface vertical deformation in the case of the EAFZ-NF system
表 1 2023年土耳其卡赫拉曼马拉什7.8级地震中断层几何参数[21，38]
Table 1. Fault geometry parameters of the 2023 MW 7.8 Kahramanmaraş earthquake
断层部位 F1-1 F1-2 F2 F3 F4 F5 F6 走向/(°) 202 210 248 231 31 23 247 倾向/(°) 80 铲状 80 80 80 80 70 
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表 2 模型参数
Table 2. Model parameters
模型参数及单位 取值 重力加速度g/(m·s−2) 9.81 密度ρ/(kg·m−3) 2700 杨氏模量E/Pa 3.40×1010 泊松比r 0.3 时间子步/s 0.005 摩擦系数μ 0.6 $ \alpha $(逆冲型参数) 3 $ \alpha $(走滑型参数) 1.2 $ \alpha $(正断层型参数) 0.75
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