Reply to "Comment on 'A model of earthquake triggering probabilities and application to dynamic deformations constrained by ground motion observations' by Ross Stein"

[1] We thank Stein [2011] for pointing out the errors in the caption of Figure 1 of Gomberg and Felzer [2008], and we correct the caption appropriately herein. However, as we show below, the figure itself is not in error. We were also remiss in not providing a thorough description of how Figure 1 was created, and thus, do so in this reply. We also emphasize that the foundations of the study described by Gomberg and Felzer [2008] do not depend on its Figure 1, but instead Figure 1 simply strengthens them. The primary focus of Gomberg and Felzer [2008] was to glean some physical understanding about the processes that give rise to aftershocks, particularly the aftershock characteristics revealed in the study of Felzer and Brodsky [2006]. They showed that the aftershock density follows a continuous inverse power law decay over distances of many multiples of the rupture dimension and traditionally defined aftershock zone out to at least 50–100 km, separately for main shocks within bins M2–3, 3–4 and 5–6. Indeed, while Figure 1 of Gomberg and Felzer [2008] further corroborates the remarkable linearity of aftershock log‐density and its lack of dependence on main shock dimensions by combining results for multiple magnitudes, the premise of the paper derives from the original results of Felzer and Brodsky [2006], with or without this additional corroboration. [2] Stein’s [2011] message is that the M2–3 and M5–6 aftershock density measurements have not been correctly combined to show the continuity inferred by Gomberg and Felzer [2008]. Stein has four concerns: (1) he correctly notes errors in the caption of Figure 1, (2) he takes issue with the interpretation of the overlap between the two populations, (3) inclusion of only subsets of measurements from each population, and (4) the certainty of the correction for differences in populations due to the dependence of aftershock rate on measurement duration. We address these concerns sequentially. [3] First, Stein correctly notes that the statement “All aftershocks are M > 2 and occur in the first 5 min after their main shock” is in error, as it only applies to the M2–3 main shocks and the inequality should be M ≥ 2 (this inequality was similarly incorrectly reported by Felzer and Brodsky [2006]). In other words, we failed to note in the caption of Figure 1 that aftershocks are M ≥ 3 in the first 2 days for the M5–6 main shocks. However, these errors affect the caption only, and were accounted for in the creation of Figure 1. [4] Stein also correctly notes a second error in the caption of Figure 1 regarding the distance range of densities plotted for the M5–6 main shocks. We reported these were plotted only to distances of r < 3 km, when in fact as can be seen in Figure 1, they are plotted to 12 km and thus overlap with the M2–3 measurements from 3 to 12 km. However, we disagree that this overlap obscures the continuity between the two data sets and note that the overlap more robustly establishes continuity than had each data set been terminated at a “3 km boundary.” In addition, the overlap makes sense physically because the transition from near to far field occurs over a finite distance range, not at a sharp boundary. [5] Stein’s third concern pertains to the omission of measurements, that “outliers at distances greater than 10 km in Figure S5, and a change in slope of the data at 80–100 km in Figure S1, are excluded.”We remind Stein and the reader the latter is explained in the caption of Figure S1 of Felzer and Brodsky [2006], which states “At far distances there are more background earthquakes than aftershocks, and thus that the aftershock decay can no longer be observed. Since the main shock selection criteria only eliminated larger main shocks within 100 km (see Methods), there is contamination from aftershocks of larger mainshocks beyond 100 km, as well as contamination from other sources of background seismicity.” Careful inspection of Figure S5 reveals that in Figure 1 no points from the M5–6 data set were excluded within the 0–12 km distance range (chosen for reasons discussed above and in the caption) and the density range plotted. Stein states that the selection criteria applied to the M5–6 data set render “the M5–6 portion of theGomberg and Felzer [2008] Figure 1 irreproducible.” We note that this does not appear to be supported by the fact that Marsan and Lengline [2010] had no difficulty duplicating the results of Felzer and Brodsky [2006]. The critical point is being able to determine accurate locations for the main shock fault planes; Marsan and Lengline [2010] developed an automated algorithm for fault plane location and found that the aftershocks of a larger U.S. Geological Survey, Department of Earth and Space Sciences, University of Washington, Seattle, Washington, USA. U.S. Geological Survey, Pasadena, California, USA.