2:45 PM - 3:00 PM
[SCG50-17] Toward understanding earthquake mechanism based on theories of strain energy
★Invited Papers
Keywords:strain energy, seismicity, multi-segment rupture
Earthquake faulting releases some strain energy from the earth. Some of the energy is dissipated on the fault and the rest of the energy radiates from the fault (e.g., Kostrov 1974; Rudnick & Freund 1981). This energy transformation is irreversible for earthquake faulting. We introduce our recent results using the theories of strain energy.
(i) Seismicity and strain energy
When the strain energy increases, the seismicity would become active. We developed a method to calculate the strain energy change caused by a dislocation in a stressed medium. Using this method, we evaluated the energy change distribution in the inland area of southwestern Japan caused by the Nankai-trough plate locking. In most of the inland area, the shear strain energy decreases by the NS compressional stress due to the plate subduction. In some areas, on the other hand, the shear strain energy increases because the plate coupling varies in space. We found that the seismicity tends to be high in the area where the shear strain energy increases (Saito et al. 2018 JGR; Noda et al. GRL 2020).
(ii) Minimum stress necessary for earthquake faulting
Since the amount of the released strain energy is identical to the sum of the energy dissipated on the fault and the radiated energy (e.g. Kostrov 1974), the strain energy, represented by the seismic moment, the initial stress, and the stress drop, needs to be larger than the radiated energy (Terakawa et al. 2018; Noda et al. 2020 GRL). Using this relationship, the minimum initial stress necessary for the earthquake generation can be derived (Saito and Noda 2020 GJI). Note that elastic dislocation theory predicts that seismic waves radiated from the fault are independent of the initial stress (e.g., Aki and Richards 2002). However, we can constrain the minimum initial stress by considering the energy transformation from the elastic energy to the radiated energy (e.g., Yoshida et al. 2020 JGR).
(iii) Necessary conditions for multi-segment ruptures.
If we assume a simple slip-weakening law in the energy conservation, we can estimate the fracture energy from the available energy and the radiated energy (Abecrombi and Rice 2005). The fracture energy is reported to be increased with the seismic moment (e.g., Viesca et al. 2015).
The available energy needs to be larger than the radiated energy for earthquake generation. We propose a necessary condition for multi-segment ruptures (Noda et al. 2020 EGU). We first estimated the stress rate distribution along the Nankai Trough by analyzing GNSS records (Noda et al. 2018 JGR) and recognized 4 peak stress-rate areas (off Cape Muroto, off Kii channel, Kumano-nada, and Enshu-nada) as asperity. We created various rupture scenarios including multi-segment ruptures of these asperities and evaluated available energy. If the stress accumulation rate is constant during the intersismic period, the available energy increases with the square of time since both average slip and the stress drop increases linearly. On the other hand, the fracture energy empirically increases more slowly than the available energy (e.g. Viesca et al. 2015; Ye et la. 2016). The available energy evaluated for each scenario increases with time, and eventually becomes larger than the fracture energy. Based on this idea, we introduce a necessary stress-accumulation time for each multi-segment rupture.
We presented the energy conservation for an earthquake. It is also important to consider energy conservation over seismic cycles. Since the Nankai Trough has historical earthquake data, it is important to evaluate the energy balance taking into account the historical events for creating possible rupture scenarios (Noda and Saito 2021JpGU).
(i) Seismicity and strain energy
When the strain energy increases, the seismicity would become active. We developed a method to calculate the strain energy change caused by a dislocation in a stressed medium. Using this method, we evaluated the energy change distribution in the inland area of southwestern Japan caused by the Nankai-trough plate locking. In most of the inland area, the shear strain energy decreases by the NS compressional stress due to the plate subduction. In some areas, on the other hand, the shear strain energy increases because the plate coupling varies in space. We found that the seismicity tends to be high in the area where the shear strain energy increases (Saito et al. 2018 JGR; Noda et al. GRL 2020).
(ii) Minimum stress necessary for earthquake faulting
Since the amount of the released strain energy is identical to the sum of the energy dissipated on the fault and the radiated energy (e.g. Kostrov 1974), the strain energy, represented by the seismic moment, the initial stress, and the stress drop, needs to be larger than the radiated energy (Terakawa et al. 2018; Noda et al. 2020 GRL). Using this relationship, the minimum initial stress necessary for the earthquake generation can be derived (Saito and Noda 2020 GJI). Note that elastic dislocation theory predicts that seismic waves radiated from the fault are independent of the initial stress (e.g., Aki and Richards 2002). However, we can constrain the minimum initial stress by considering the energy transformation from the elastic energy to the radiated energy (e.g., Yoshida et al. 2020 JGR).
(iii) Necessary conditions for multi-segment ruptures.
If we assume a simple slip-weakening law in the energy conservation, we can estimate the fracture energy from the available energy and the radiated energy (Abecrombi and Rice 2005). The fracture energy is reported to be increased with the seismic moment (e.g., Viesca et al. 2015).
The available energy needs to be larger than the radiated energy for earthquake generation. We propose a necessary condition for multi-segment ruptures (Noda et al. 2020 EGU). We first estimated the stress rate distribution along the Nankai Trough by analyzing GNSS records (Noda et al. 2018 JGR) and recognized 4 peak stress-rate areas (off Cape Muroto, off Kii channel, Kumano-nada, and Enshu-nada) as asperity. We created various rupture scenarios including multi-segment ruptures of these asperities and evaluated available energy. If the stress accumulation rate is constant during the intersismic period, the available energy increases with the square of time since both average slip and the stress drop increases linearly. On the other hand, the fracture energy empirically increases more slowly than the available energy (e.g. Viesca et al. 2015; Ye et la. 2016). The available energy evaluated for each scenario increases with time, and eventually becomes larger than the fracture energy. Based on this idea, we introduce a necessary stress-accumulation time for each multi-segment rupture.
We presented the energy conservation for an earthquake. It is also important to consider energy conservation over seismic cycles. Since the Nankai Trough has historical earthquake data, it is important to evaluate the energy balance taking into account the historical events for creating possible rupture scenarios (Noda and Saito 2021JpGU).