Decay of aftershock density with distance indicates triggering by dynamic stress

Abstract

The majority of earthquakes are aftershocks, yet aftershock physics is not well understood. Many studies suggest that static stress changes trigger aftershocks, but recent work suggests that shaking (dynamic stresses) may also play a role. Here we measure the decay of aftershocks as a function of distance from magnitude 2-6 mainshocks in order to clarify the aftershock triggering process. We find that for short times after the mainshock, when low background seismicity rates allow for good aftershock detection, the decay is well fitted by a single inverse power law over distances of 0.2-50 km. The consistency of the trend indicates that the same triggering mechanism is working over the entire range. As static stress changes at the more distant aftershocks are negligible, this suggests that dynamic stresses may be triggering all of these aftershocks. We infer that the observed aftershock density is consistent with the probability of triggering aftershocks being nearly proportional to seismic wave amplitude. The data are not fitted well by models that combine static stress change with the evolution of frictionally locked faults.

A new estimation of the decay of aftershock density with distance to the mainshock

“…To compare our results to those of Felzer and Brodsky [2006] and Richards-Dinger et al (unpublished), we compute the linear density, still for the same intervals of mainshock magnitude and time delays, as f ij (r k ≤ r < r k+1 ) = l ijk V ik r kþ1 Àr k . This is done for the four runs of our MISD algorithm, corresponding to the four combinations of (1) dV ik computed as geometrical Euclidean shell volumes, or as the number of unconditioned earthquakes in these volumes, and (2) l 0 = 0 or 10 −3 per km 3 and day, which for both dV ik sets gives a 53% proportion of background earthquakes (see section 3).…”

“…Similarly, we test and compare the results of Felzer and Brodsky [2006] to ours by performing their analysis with different sets of (declustering) parameters. We recall that, with their approach, an earthquake is not considered as a mainshock if there exists a larger earthquake within a radius L that occurred less than T 1 before or T 2 after it.…”

“…Thick crosses indicate our method. Thin circles indicate using the approach modified from the study of Felzer and Brodsky [2006]. The plotted values and the error bars are the means and standard deviations of the logarithm of the linear density values.…”

“…We further modify the analysis of Felzer and Brodsky [2006] by accounting for background seismicity: we count the number of earthquakes occurring in time intervals with similar durations (15 min or 12 h) but taken at random, excluding the 100 days before and 100 days after the mainshock. We then estimate the rate change dl corresponding to the rate of aftershocks as the mean of the positively defined random variable X with probability density f X (x) = A R 1 0 dm f 0 (m) f (m + x), where f 0 (m) is the probability density of the background rate m, f (m + x) is the probability density of the rate of posterior earthquakes, equal to the background rate m plus the aftershock rate x, and A is a normalizing constant such that R 1 0 dx f X (x) = 1.…”

“…These methods, although very simple to implement, are known to depend on relatively arbitrary parameters. For example, Felzer et al [2004], Helmstetter et al [2005], and Felzer and Brodsky [2006] all used a selection criterion to first select mainshocks, based on their relative isolation from previous, close-by, large earthquakes, and then defined aftershocks as earthquakes occurring within a mainshock magnitude-dependent space-time window from the considered mainshock (or from previous aftershocks of this mainshock, as in Reasenberg [1985] and Helmstetter et al [2005]). In recent work, K. Richards-Dinger, R. S. Stein, and S. Toda (Test of the hyphothesis that all aftershocks are triggered by dynamic stress, in preparation; henceforth referred to as Richards-Dinger et al, unpublished) have found, in the case of the analysis conducted by Felzer and Brodsky [2006], this method does not discriminate efficiently the aftershocks from other, unrelated earthquakes, and can therefore lead to biases in both the results and their interpretation.…”