11:00 AM - 1:00 PM
[SCG44-P19] Three different scaling relations for tremor migrations beneath the Kii Peninsula, Japan
Keywords:Scaling law, Deep tectonic tremor, Tremor migration, Kii Peninsula
The slow earthquakes have a large observation gap for phenomena with durations between ten seconds and one day. Some previous studies attempted to investigate scaling relations for the events within the durations (e.g. Bletery et al., 2017; Aiken and Obara, 2021), but the scaling law in the gap has not been sufficiently understood yet. When we investigate tremor migrations that have durations of several minutes to several days and move at speeds of 1000 km/day to 10 km/day, it is possible to fill the observation gap of the slow earthquakes by assuming the ETS (Bletery et al., 2017). In this study, estimating seismic energies, durations, and rupture areas for tremor migrations beneath the Kii Peninsula, Japan, we investigate scaling laws among the three parameters. In particular, we show that it is significant to focus on temporal evolutions of rupture areas to understand rupture processes behind tremor migrations.
We used tremor migrations objectively extracted by a space-time Hough transform (Sagae et al., 2021, JpGU). The estimated durations of these migrations range between 10 minutes and 24 hours. We calculated accumulated seismic energy (E) at 2–8 Hz for tremors included in each tremor migration and estimated a rupture area (A) using the convex hull (de Berg et al., 2008) to surround the tremor locations. Moreover, we calculated scaled energy as a ratio between a seismic moment of a short-term SSE listed in the AIST-SSE catalog (e.g. Itaba and Ando 2011) and accumulated seismic energy at 2–8 Hz for tremors corresponding to the SSE. Finally, we obtained a mean value of the scaled energy (1.3410-10) by averaging scaled energies over eight SSEs. In the following analysis, this average of scaled energy was used to convert the seismic energy to the seismic moment.
From observation results, we found complicated relations such as bending of scaling laws among seismic energy (E), rupture area (A), and duration (T). To understand those complicated scaling relations, we proposed three models of scaling laws based on physical interpretation. We assumed the scaled energy and stress drop were constant for all models. The first one is a case that the rupture area grows diffusively without any geometric restrictions. This model predicts scaling relations of E∝A1.5, A∝T, and E∝T1.5. The second one is a case that the rupture area grows diffusively with the fault width geometrically limited (saturated). This second model predicts the scaling relations of E∝A2, A∝T0.5, and E∝T. Finally, the third one is a case that the rupture speed is constant. This applies to tremor migrations with speeds of 10 km/hr or more, and predicts scaling relations of E∝A1.5, A∝T2, and E∝T3, which are similar to the regular earthquake.
Following these models, we grouped tremor migrations into the three classes by taking the fine structures such as the fault width and the migration speed into consideration. Then, we estimated exponents of scaling relations between E and A, A and T, E and T by three-dimensional principal component analysis using log10E, log10A, and log10T. The estimated exponents for these classes were consistent with what our models predicted within two standard deviations. These results show that the classifications according to our models are reasonable. In particular, the scaling relations for the first and second models are newly proposed in this study. Those models suggest that tremor migrations follow a physical process in which a fault rupture grows diffusively with a low constant stress drop (2–235 kPa). Moreover, we understand that investigating the rupture growth from the relation between the rupture area and the duration is necessary to understand those complicated scaling relations.
We used tremor migrations objectively extracted by a space-time Hough transform (Sagae et al., 2021, JpGU). The estimated durations of these migrations range between 10 minutes and 24 hours. We calculated accumulated seismic energy (E) at 2–8 Hz for tremors included in each tremor migration and estimated a rupture area (A) using the convex hull (de Berg et al., 2008) to surround the tremor locations. Moreover, we calculated scaled energy as a ratio between a seismic moment of a short-term SSE listed in the AIST-SSE catalog (e.g. Itaba and Ando 2011) and accumulated seismic energy at 2–8 Hz for tremors corresponding to the SSE. Finally, we obtained a mean value of the scaled energy (1.3410-10) by averaging scaled energies over eight SSEs. In the following analysis, this average of scaled energy was used to convert the seismic energy to the seismic moment.
From observation results, we found complicated relations such as bending of scaling laws among seismic energy (E), rupture area (A), and duration (T). To understand those complicated scaling relations, we proposed three models of scaling laws based on physical interpretation. We assumed the scaled energy and stress drop were constant for all models. The first one is a case that the rupture area grows diffusively without any geometric restrictions. This model predicts scaling relations of E∝A1.5, A∝T, and E∝T1.5. The second one is a case that the rupture area grows diffusively with the fault width geometrically limited (saturated). This second model predicts the scaling relations of E∝A2, A∝T0.5, and E∝T. Finally, the third one is a case that the rupture speed is constant. This applies to tremor migrations with speeds of 10 km/hr or more, and predicts scaling relations of E∝A1.5, A∝T2, and E∝T3, which are similar to the regular earthquake.
Following these models, we grouped tremor migrations into the three classes by taking the fine structures such as the fault width and the migration speed into consideration. Then, we estimated exponents of scaling relations between E and A, A and T, E and T by three-dimensional principal component analysis using log10E, log10A, and log10T. The estimated exponents for these classes were consistent with what our models predicted within two standard deviations. These results show that the classifications according to our models are reasonable. In particular, the scaling relations for the first and second models are newly proposed in this study. Those models suggest that tremor migrations follow a physical process in which a fault rupture grows diffusively with a low constant stress drop (2–235 kPa). Moreover, we understand that investigating the rupture growth from the relation between the rupture area and the duration is necessary to understand those complicated scaling relations.