1:45 PM - 3:15 PM
[SSS06-P11] Area-Displacement (A-D) relationship for earthquake, slow slip, and laboratory stick-slip
Keywords:Earthquake, Slow slip, Stick-slip, Scaling relationship
Among the parameters of the seismic moment Mo, the relationship between the fault area A and the (average) displacement D can be expressed as D~A0.5 if the stress drop is constant (e.g., Kanamori and Anderson, 1975). Such self-similarity is known to hold for a wide range of spatial scales, from earthquakes to acoustic emissions (AEs) (e.g., Abercrombie, 1995; Goodfellow and Young, 2014; Yoshimitsu et al., 2014). However, these studies analyzed small events with a point source model, and the discussion was based on corner frequency analysis assuming a constant rupture velocity. Therefore, they are not considered to be readily comparable to slow slip (slow earthquakes), which have much slower rupture velocities, or to stick-slip in laboratory experiments.
In this study, we summarize and discuss the A-D relationships for earthquakes, slow slip, and laboratory stick-slip. First, we perform a general orthogonal regression on data from a previous study (Thingbaijam et al., 2017), which compiled a finite fault model for earthquakes above moderate magnitude (Mw 5.4-9.2), without distinguishing between reverse, normal, and strike-slip faults. The result is D~A0.56. The same analysis is also performed on data from a previous study (Gao et al., 2012) that investigated scaling laws for slow slip (Mw 4.1-7.7), and the result is D~A0.54. Based on the above, it can be assumed that both earthquakes above moderate magnitude and slow slip are self-similar, although the amount of stress drop is different. Comparing the regression results, for the same A, D for earthquakes is about 101.5 times larger than D for slow slip. Furthermore, based on a number of previous studies of stick-slip in laboratory experiments, a similar analysis of the slip area A of the experimental samples and the displacement D of the representative results in the papers shows that stick-slip is systematically larger in D than the extension of the regression line for earthquakes and slow-slip. For example, for the same A, the D for stick-slip is about 102 times larger than the D for earthquakes. This may reflect the difference between natural and laboratory conditions (boundary conditions or stiffness), but the large spatial scale gap between moderate earthquakes and stick-slip requires investigation of intermediate-scale phenomena.
Therefore, we include finite fault models of small earthquakes in our study. Specifically, we consider two small earthquakes: mining earthquakes with Mw 0.6-1.4 (Yamada et al., 2005) and small repeating earthquakes with Mw 2.0-2.1 (Dreger et al., 2007). We examine the A-D relationship of these earthquakes and find that D is systematically larger than the regression line extension of earthquakes above moderate magnitude, and approximately intermediate between moderate earthquakes and stick-slip on the A-D relationship diagram. As an experiment, we regress the data of earthquakes including small ones and stick-slip together, and find D~A0.40. Note that compared to this regression line, stick-slip has still larger D. It is not necessarily clear at this point what these results mean. One thought might be that the small earthquakes considered reflect more localized frictional properties than moderate or large earthquakes, and are closer to laboratory stick-slip conditions. In other words, the self-similarity of natural earthquakes and slow slip may only be found on faults with sufficiently high heterogeneity that local frictional properties are no longer dominant.
In this study, we summarize and discuss the A-D relationships for earthquakes, slow slip, and laboratory stick-slip. First, we perform a general orthogonal regression on data from a previous study (Thingbaijam et al., 2017), which compiled a finite fault model for earthquakes above moderate magnitude (Mw 5.4-9.2), without distinguishing between reverse, normal, and strike-slip faults. The result is D~A0.56. The same analysis is also performed on data from a previous study (Gao et al., 2012) that investigated scaling laws for slow slip (Mw 4.1-7.7), and the result is D~A0.54. Based on the above, it can be assumed that both earthquakes above moderate magnitude and slow slip are self-similar, although the amount of stress drop is different. Comparing the regression results, for the same A, D for earthquakes is about 101.5 times larger than D for slow slip. Furthermore, based on a number of previous studies of stick-slip in laboratory experiments, a similar analysis of the slip area A of the experimental samples and the displacement D of the representative results in the papers shows that stick-slip is systematically larger in D than the extension of the regression line for earthquakes and slow-slip. For example, for the same A, the D for stick-slip is about 102 times larger than the D for earthquakes. This may reflect the difference between natural and laboratory conditions (boundary conditions or stiffness), but the large spatial scale gap between moderate earthquakes and stick-slip requires investigation of intermediate-scale phenomena.
Therefore, we include finite fault models of small earthquakes in our study. Specifically, we consider two small earthquakes: mining earthquakes with Mw 0.6-1.4 (Yamada et al., 2005) and small repeating earthquakes with Mw 2.0-2.1 (Dreger et al., 2007). We examine the A-D relationship of these earthquakes and find that D is systematically larger than the regression line extension of earthquakes above moderate magnitude, and approximately intermediate between moderate earthquakes and stick-slip on the A-D relationship diagram. As an experiment, we regress the data of earthquakes including small ones and stick-slip together, and find D~A0.40. Note that compared to this regression line, stick-slip has still larger D. It is not necessarily clear at this point what these results mean. One thought might be that the small earthquakes considered reflect more localized frictional properties than moderate or large earthquakes, and are closer to laboratory stick-slip conditions. In other words, the self-similarity of natural earthquakes and slow slip may only be found on faults with sufficiently high heterogeneity that local frictional properties are no longer dominant.