PUBLICATIONS
Geophysical Research Letters
RESEARCH LETTER
10.1002/2016GL071104
Key Points:
• Higher stress-drop megathrust
earthquakes produce fewer
aftershocks than lower stress-drop
events of similar magnitude
• Productivity increases with stress drop
and moment-scaled radiated energy
for events with similar main shock
rupture area
• Large megathrust earthquakes
located in western Pacific subduction
zones have higher aftershock
productivity than in eastern Pacific
zones
Supporting Information:
• Supporting Information S1
• Text S1
• Text S2
• Text S3
• Table S1
• Table S2
• Figure S1
• Figure S2
• Figure S3
• Figure S4
• Figure S5
• Figure S6
• Figure S7
• Figure S8
Correspondence to:
N. Wetzler,
[email protected]
Citation:
Wetzler, N., E. E. Brodsky, and T. Lay
(2016), Regional and stress drop effects
on aftershock productivity of large
megathrust earthquakes, Geophys. Res.
Lett., 43, doi:10.1002/2016GL071104.
Received 6 SEP 2016
Accepted 6 OCT 2016
Accepted article online 8 OCT 2016
©2016. American Geophysical Union.
All Rights Reserved.
WETZLER ET AL.
Regional and stress drop effects on aftershock
productivity of large megathrust earthquakes
Nadav Wetzler1,2, Emily E. Brodsky1, and Thorne Lay1
1
Department of Earth and Planetary Sciences, University of California, Santa Cruz, California, USA, 2Geological Survey of
Israel, Jerusalem, Israel
Abstract
The total number of aftershocks increases with main shock magnitude, resulting in an
overall well-defined relationship. Observed variations from this trend prompt questions regarding
influences of regional environment and individual main shock rupture characteristics. We investigate
how aftershock productivity varies regionally and with main shock source parameters for large
(Mw ≥ 7.0) circum-Pacific megathrust earthquakes within the past 25 years, drawing on extant finite-fault
rupture models. Aftershock productivity is found to be higher for subduction zones of the western
circum-Pacific than for subduction zones in the eastern circum-Pacific. This appears to be a
manifestation of differences in faulting susceptibility between island arcs and continental arcs.
Surprisingly, events with relatively large static stress drop tend to produce fewer aftershocks than
comparable magnitude events with lower stress drop; however, for events with similar coseismic
rupture area, aftershock productivity increases with stress drop and radiated energy, indicating a
significant impact of source rupture process on productivity.
1. Introduction
Almost all earthquakes produce aftershocks. Aftershocks are commonly defined as an earthquake sequence
superimposed on a background level of activity bounded by temporal and/or spatial windowing with respect
to a main shock. The suddenly increased rate of seismicity following a main shock reflects the level of the
stress perturbation around the source region. This leads to an aftershock sequence that decays with time
(i.e., Omori’s law). In general, aftershock productivity, Naft, is well established to be a function of main shock
magnitude following a power law:
Naft ¼ K10αðMm Mc Þ
(1)
where α is a constant commonly measured to be ~1, Mm is the main shock magnitude, Mc is the lower limit on
measured aftershock magnitude, and the prefactor K is usually assumed to be a constant [Utsu, 1970; Ogata,
1988; Reasenberg and Jones, 1989; Felzer et al., 2004; Helmstetter et al., 2005]. Here we focus on the variability
of the prefactor K, which we call aftershock productivity, and what it can reveal about the physical controls on
aftershock generation.
Previous studies have shown that variations in aftershock production exist. For instance, Singh and Suárez
[1988] examined 30 day aftershock sequences (with mb ≥ 5.0) for 45 circum-Pacific main shocks with
Mw ≥ 7.0. They found systematically higher aftershock productivity for events in the western circumPacific relative to the eastern circum-Pacific. Scholz and Campos [1995, 2012] infer higher seismic
coupling in eastern Pacific zones than in western zones, which may affect both background levels and
aftershock productivity. A difference is also found in temporal evolution of aftershock expansion
[Tajima and Kanamori, 1985a; Tajima and Kanamori, 1985b], with western Pacific zones generally showing
greater expansion. Yamanaka and Shimazaki [1990] found that shallow intraplate earthquakes tend to be
more productive than interplate events. Persh and Houston [2004] showed that deep earthquakes are less
productive than shallow ones. Aftershock productivity of deep earthquakes (depth > 400 km) shows
strong correlation with thermal characteristics of the slab, with colder slabs being more productive
[Wiens and Gilbert, 1996]. The specific causes of these variations are not well understood.
In general, aftershock productivity is likely due to a combination of main shock forcing and regional seismic
susceptibility (the available distribution of near-failure faults [e.g., Dieterich, 1994]). Are differences in
MEGATHRUST AFTERSHOCK PRODUCTIVITY
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aftershock productivity reflective of observable main shock rupture properties, or are they entirely controlled
by the regional stress state? To the best of our knowledge, prior work has not evaluated aftershock productivity as a function of main shock source parameters other than magnitude. One might anticipate that earthquakes with larger stress changes would perturb the environment more, resulting in relatively more
aftershocks, but the affected area might be smaller, resulting in relatively fewer aftershocks. We will test this
behavior.
Our strategy is to focus on a set of uniformly characterized main shocks, first measuring relative near-source
aftershock productivity accounting for main shock magnitude scaling. We then evaluate the relationships
between aftershock productivity and regional characteristics as well as main shock properties such as stress
drop and radiated energy.
2. Main Shock Selection
The static stress drop and total seismic energy radiated from the source are important characteristics of large
earthquakes that could influence aftershock productivity. Measurements of both parameters are sensitive to
methodological choices [Ye et al., 2013] making composite data sets subject to subtle biases [Ide and Beroza,
2001]. Therefore, it is important to have a consistently derived, global data set in order to examine differences
in aftershock productivity as a function of main shock properties.
Here we utilize a recent study [Ye et al., 2016] that produced a systematic catalog of source parameters for 114
Mw ≥ 7 megathrust earthquakes between 1990 and 2015 using least squares kinematic finite fault slip inversions [e.g., Hartzell and Heaton, 1983; Kikuchi and Kanamori, 1986]. Estimates are available for each large event
for apparent stress σ a ¼ MER0 μ (where ER is the radiated energy, M0 is the seismic moment, and μ is the source
2μ
σa
¼ 2 Δσ
(Figure S1 in the
region shear modulus), static stress-drop Δσ s, and radiation efficiency ηR ¼ ME R0 : Δσ
S
S
supporting information). It is important to note that moment-scaled radiated energy (ER/M0) and static
stress-drop (Δσ s) were measured independently. These measures do not show substantial scaling with magnitude or source depth, indicating a general tendency of self-similarity for large (Mw > 7) interplate earthquakes.
However, the estimated parameters do have significant uncertainties associated with parameterization of the
rupture process (e.g., assumptions of rupture velocity and model grid) and medium properties (e.g., rigidity,
seismic attenuation, and seismic velocity structure). We therefore consider a range of parameters for each
earthquake partially spanning the uncertainties in the estimates (Table S1 in the supporting information).
3. Measuring Aftershock Productivity
To measure variations of aftershock productivity parameter K in equation (1), we count aftershocks for our
main shocks using the Advanced National Seismic System [Northern California Earthquake Data Center,
2014] catalog from 1 January 1985 to 1 June 2015 for all events above a magnitude of completeness of 5.0
(Text S1, Figure S2, and Table S2 in the supporting information), recognizing that this global value leads to
some sparse aftershock distributions even for some of the larger main shocks.
We focus on aftershocks close to the source. The aftershock time window is set to 7 days from the main shock
origin, which is the longest time window allowed for the mean background seismicity to be below a threshold of a single M5 earthquake within a radius of 1000 km from the main shock (Figure S3). To avoid underestimation of aftershocks caused by seismicity detection saturation right after the main shock we shift the 7 day
time window by 0.2 days from the origin time for all events. We develop a procedure to systematically determine an effective nearby aftershock counting radius (Figure 1). By measuring binned seismic density in annuli
around the epicenter we determine the maximum radius at which the binned aftershock density remains
resolvably above the background level (see Text S2). The resulting effective radius, which ignores isolated
remote possible aftershocks, scales with main shock magnitude with a power law of ~0.5 (Figure S4).
We then count the number of aftershocks within the effective radius and divide by 10αðMm Mc Þ to get the productivity constant K from equation (1) with α set to 1. We use a fixed value of α because otherwise the covariance between K and α would make interpretation of relative measures of K ambiguous. Previous studies have
shown that for sufficiently sampled data, α is observed to be 1 [Felzer et al., 2004; Helmstetter et al., 2005]. We
use the counting method to measure the value of K rather than an Epidemic-Type-Aftershock Sequence
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Figure 1. (a) Example processing for the 17 July 2006 Mw 7.7 Java megathrust earthquake aftershock sequence (red dots)
and background seismicity over the 5 years prior to the main shock (green dots), with symbols scaled by magnitude. The
red line is the maximum radius of the seismic region, and the bold red line represents the estimated effective radius of the
aftershocks. The blue rectangle marks the dimensions of the fault model of Ye et al. [2016] projected to the surface, and the
epicenter is shown by the yellow star. Plate boundaries are shown by magenta lines, mean convergence rate is indicated by
the white arrow, and the main shock global centroid moment tensor focal mechanism solution is shown. (b) Densities of
the background activity (green curve) and aftershocks (red curve) are plotted within annuli of equal width (25 km) centered
at the epicenter, normalized by the annulus area. The dashed red line is the aftershock effective radius.
(ETAS) inversion [Ogata, 1988] because ETAS inversions are known to have strong trade-offs between K and
the Omori’s law decay exponent p [Brodsky and Lajoie, 2013]. As we want to associate an aftershock count
with a specific main shock, we avoid sequences with a second nearby main shock within the 7 day window,
which eliminates 10 of the 114 events.
The resulting compilation of aftershock productivity for 104 main shocks is in Figure 2a. A final step is to identify a threshold for main shock magnitudes, which we call Mcrt, producing a significant number of aftershocks
within the time-window considered, even for the weak productivity events or regions. This requirement is
necessary so that the statistics are not biased by our inability to resolve trends if the number of counted aftershocks is below 1. A minimum of one earthquake in a 7 day time window after the main shock is satisfied for
95% of the main shocks if the main shock magnitude is Mw 7.5 or higher (Figure 2a). The supporting information provides more details about the method (Text S2), along with information on individual main shock productivity (Table S1).
We also consider an alternative measure of productivity to probe the robustness of the results. The magnitude of the largest aftershock (M1) relative to the main shock magnitude (M0), often discussed in terms of
Bath’s law, is linked to the aftershock productivity [Mogi, 1967; Felzer et al., 2004]. Given Gutenberg-Richter
scaling, a lower value of M0-M1 should accompany a larger number of aftershocks, and therefore negatively
correlates with productivity. We use M0-M1 as a second measure of relative productivity to compare with our
primary results.
4. Observations
Of the 104 megathrust ruptures, 91 main shocks had at least one M ≥ 5 aftershock, 46 events exceed the critical magnitude (Mw 7.5), and 13 had zero M ≥ 5 aftershocks (Figure 2a). We consider trends in aftershock productivity on regional scales and as a function of main shock source parameters for all events, and for events
above Mcrt.
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Figure 2. (a) Aftershock productivity (magenta-Eastern Pacific and green-Western Pacific) plotted with respect to main
shock magnitude. The power law fit with a slope of 1 is shown by the black dashed line and separately for eastern and
western Pacific populations by the magenta and green lines, respectively. The thin dashed blue lines represent the 95%
interval. The black vertical dashed line indicates the lowest main shock magnitude threshold, Mcrt (Mw 7.5), for
aftershock detectability calculated from the 95% interval and a single aftershock (black horizontal dashed line). The
recalculated power law with a cutoff of Mcrt is represented by the thick lines (black for all data, green for western Pacific,
and magenta for eastern Pacific). Unfilled symbols with down pointing arrows mark main shocks with zero aftershock
count. Histograms show the distribution of the prefactor K (equation (1)) with the number of realizations from the
bootstrap trials of each group (green and magenta), calculated using (b1) all magnitudes and (b2) above Mcrt separately.
The dashed lines represent the 5% and 95% confidence levels, and the solid black lines indicate the mean of each group.
(c) Global relative aftershock productivity for 7 day time windows shown by both size and colored outer circles on a log
scale (log10(Naft/Npredicted), where Npredicted is the number of aftershocks evaluated from the fitted black line). Inner
dots indicate the relative stress drop with respect to the median, with blue indicating a relatively low value, red a
relatively high value, and white is with ±10% from the median. Stress-drop distribution is shown in Figure S1.
4.1. Regional Variations of Aftershock Productivity
Significant regional variations in aftershock productivity exist (Figures 2a–2c). The prefactor K (equation (1)) for the
western Pacific (including Sumatra) is higher than for eastern circum-Pacific zones both for all events (Figure 2b1)
and for main shocks above Mcrt (Figure 2b2). The western region tends to be more productive by a factor of ~1.5.
For example, three megathrust events located in the northern South-America subduction zone (21 February
1996 Mw 7.5 Peru, 19 November 1991 Mw 7.2 Colombia, and 4 August 1998 Mw 7.2 Ecuador) each produced only
1 or 2 aftershocks of M ≥ 5 within 30 days after the main shock. This pattern supports the finding of Singh and
Suárez [1988] using a nonoverlapping set of main shock events, suggesting that this is a robust behavior.
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Figure 3. Aftershock number Naft versus main shock magnitude color-coded by the main shock (a) apparent stress; (b)
scaled radiated energy, ER/M0; (c) static stress drop; and (d) radiation efficiency. The blue and red dots indicate relatively
low or high (respectively) values of each source-parameter with respect to the median of each group. The unfilled symbols
with down pointing arrows mark main shocks with zero aftershock count. The solid black lines indicate the power law fit for
a slope of 1 above Mcrt, and the solid blue and red lines represent the power law fit for each group of low or high sourceparameters (respectively) from the bootstrap method, and the dashed lines represent the fit for the whole magnitude
range. The thin dashed black outer lines represent the 20% and 95% confidence intervals. Histograms on the far right of
each panel show the distribution of bootstrap realizations generating given values of the prefactor K (equation (1)) for each
group (red and blue) calculated using all magnitudes and above Mcrt. The dashed lines represent the 5% and 95% confidence levels, and the solid black lines indicate the mean of each group. The source parameter distributions are shown in
Figure S1.
We calculate M0-M1 for our data set, again comparing the western and eastern circum-Pacific events. A general decrease of aftershock productivity with increase of M0-M1 is found (Figure S5a). We infer an overall
higher level of aftershock productivity as inferred from lower M0-M1 for the western circum-Pacific. We also
find that background activity levels are systematically higher in the western circum-Pacific than in the eastern
circum-Pacific (Figure S6a) along with higher (12%) mean b-value of eastern Pacific, compared to western
Pacific zones (Table S2), as shown in previous studies [Tsapanos, 1990b; Nishikawa and Ide, 2014].
Aftershock productivity is not strongly correlated with the regional background activity level in western
and eastern regions separately despite sharing the regional baseline shift (Figure S6b).
4.2. Main Shock Source Parameters and Aftershock Productivity
Aftershock productivity is plotted as a function of main shock magnitude (Mw) in Figure 3, color-coded by
relative values of source parameters: (a) apparent stress, σ a; (b) moment-scaled radiated energy, ER/M0; (c) static stress-drop, Δσ s; and (d) radiation efficiency η. To simplify the display we bin source parameters with
respect to the median. For main shock source parameters that are strongly dependent on the rupture velocity
(static stress drop and radiation efficiency) we evaluate the range of estimates from the three rupture velocities considered by Ye et al. [2016] (Group 2, Table S1). Relatively high (red) or low (blue) value of the source
parameter is designated based on all three estimates being consistently more or less than 10% from the median in each set; otherwise, we label the value as neutral (white). For ER/M0 , apparent stress and when stress
drop was calculated based on a predefined single rupture velocity (Group 1, Table S1) we establish relative
high or low values from 10% above or below the median of each parameter in each group. We find that
for static stress-drop and apparent stress there are relatively clear separations in aftershock productivity
between the events with low or high relative source parameter values (Figures 3a and 3c).
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To obtain a statistically meaningful distribution of the two groups of high (red) and low (blue) parameters, we
resample the data with 1000 bootstrap samples to estimate K (equation (1)), assuming a constant power law
(α = 1). We consider events distributed between 10% to 95% intervals from the power law fit (dashed black
lines, Figures 2a and 3). Both apparent stress (Figure 3a2) and stress drop (Figure 3c2) show some separation
between the two groups which become more pronounced when excluding magnitudes below Mcrt
(Figures 3a3 and 3c3). The most compelling main shock influence is that relatively high static stress drop tends
to associate with lower aftershock productivity, as this has the largest separation between the medians of the
two groups. Description of some outliers from this trend is presented in Text S3.
The inverse trend of stress drop with aftershock productivity is stronger than the difference of stress drop
between the eastern and western circum-Pacific. The difference between the median stress drop of the
low- and high-productivity groups is 2 MPa, whereas the difference between the median stress drop of the
regions is only 0.2 MPa. The inverse trend of stress drop with productivity accompanied by lack of separation
between the eastern and western circum-Pacific regions is also demonstrated by a subtle increase in static
stress drop with M0-M1 (Figure S5b), with a lack of high values of static stress drop for low M0-M1.
5. Interpretation
5.1. Regional Variations of Aftershock Productivity
Western Pacific zones tend to have overall higher aftershock productivity (Figure 2c), and this is not strongly
correlated with stress drop variation (Figure S1). For example, consider two events in the same region
(Mindanao). The event of 5 March 2002 Mw 7.5 has four aftershocks (seven expected from the overall average
trend) and a relatively high stress drop estimate of 6.2 MPa (median is 3.4 MPa, for VR 2.5 km/s), whereas the
21 January 2007 Mw 7.5 has 28 aftershocks and a relatively low stress drop of 2.2 MPa. In addition, if the two
trends were coupled, the depressed productivity of the eastern circum-Pacific should result in a difference
between regional medians of static stress drop, which is not found to be the case (Figures S5b and S1c).
Singh and Suárez [1988], and Tajima and Kanamori [1985a, 1985b] suggested that regional variations in aftershock productivity and aftershock zone expansion between the two sides of the circum-Pacific are a product
of different distributions of asperity sizes, and this may correlate with seismic coupling [Scholz and Campos,
1995; Scholz and Campos, 2012]. The regional pattern is also correlated with oceanic versus continental subduction, which may influence the upper plate susceptibility to aftershocks. In general, Central and South
America subduction zones involve younger and hotter underthrusting lithosphere [Syracuse et al., 2010],
which may contribute to depressed aftershock productivity of the eastern circum-Pacific.
In order to evaluate these factors, we investigate the productivity relative to seafloor age (Figure S7a), convergence rate (Figure S7b), estimated temperature of the slab at 30 km depth, T30 km (Figure S7c), and thermal
parameter ϕ (Figure S7d), where ϕ = A v sin(δ), A is the age of the subducted plate, v is the convergence
rate, and δ is the dip angle of the slab [Kirby et al., 1991]. Using the parameters from Syracuse et al. [2010],
we observe a general increase of productivity for colder and older subducted plates (Figures S7a, S7c, and
S7d). The greater volume of material available for brittle failure in cold lithosphere may provide higher susceptibility around the source regions.
5.2. Main Shock Source Parameters and Aftershock Productivity
The trend of increasing productivity with lower main shock static stress drop is a somewhat surprising finding. Studies of aftershock productivity have documented that variations in the state of stress after an earthquake control the aftershock behavior on a variety of scales, with an increase of aftershocks associated with
increased Coulomb stress change for individual events [King et al., 1994; Baer et al., 2008; Hauksson et al., 2008;
Kroll et al., 2013; Wetzler et al., 2014, and many others]. The relative increase of M0-M1 reported by Tsapanos
[1990a, 1990b] for intraplate versus interplate earthquakes is compatible with our results, since intraplate
earthquakes tend to have relatively high static stress drop [Ye et al., 2012]. However, our observation for interplate main shocks contradicts the study of Yamanaka and Shimazaki [1990], which included intraplate events.
Returning to equation (1), we can connect to the well-established relationship between earthquake magnitude and rupture area [Kanamori and Anderson, 1975]. For a fixed stress drop and large magnitude the area
of rupture scales as ~10M, so aftershock numbers should tend to scale with the area of the rupture. This
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Figure 4. Aftershock number Naft versus main shock rupture area color-coded by the main shock (a) apparent stress; (b)
scaled radiated energy, ER/M0; (c) static stress drop; and (d) radiation efficiency. The blue and red dots indicate relatively
low or high (respectively) values of each source-parameter with respect to the median of each group. The unfilled symbols
represent main shocks with zero aftershock count. The solid black lines indicate the power law fit for a slope of 1; the
2
As
4
As
dashed black lines represent constant trends of 2 × 10 10 and 2 × 10 10 . The solid blue and red lines represent the
power law fit for each group of low or high source-parameters (respectively) from the bootstrap method. Histograms on the
far right of each panel show the distribution of the deviations from the trends for number of realizations for each group (red
and blue). The dashed lines represent the 5% and 95% confidence levels, and the solid black lines indicate the mean of each
group. The source parameter distributions are shown in Figure S1.
thinking underlies estimating rupture area based on aftershock distribution. However, it is now recognized
that many, if not most, aftershocks occur outside the area of coseismic slip as evidenced by locations and
focal mechanisms [e.g., Asano et al., 2011]. In fact, many aftershock studies have focused on the stress concentrations at the edge of rupture as being aftershock-rich zones [e.g., King et al., 1994].
Combining these lines of reasoning suggests that aftershocks should be most abundant for earthquakes with
large stress changes over large regions [e.g., Dieterich, 1994]. But, in general, we expect high stress drop
events to tend to have smaller rupture dimensions (Figure S8), so that a smaller adjacent region will be perturbed. It is not obvious which effect will dominate the statistics of aftershock productivity. Fortunately, the
finite-fault models provide estimates of coseismic slip area, AS (Table S1), associated with each specific stress
drop determination. Thus, we can partially unpack the stress drop behavior by relating Naft to AS, as shown in
Figure 4. Here we use the AS values found for rupture velocities of 2.5 km/s or for preferred rupture models for
some of the events from Ye et al. [2016].
There is a clear relationship between the number of aftershocks and AS as expected from the magnitude
dependence, but the fluctuations about the general trend are systematically influenced by stress drop,
radiated energy and radiation efficiency, and apparent stress. For a given rupture area, both higher radiated
energy and higher stress drop tend to result in more aftershocks, but the stress drop effect is more pronounced, such that lower radiation efficiency is accompanied by more aftershocks. There is again substantial
scatter in the behavior, and the AS estimates have significant uncertainty, but the bootstrapping of the deviations supports significance of the trends. It is important to note that the behavior is opposite that inferred
from the Mw scaling. For the Mw scaling, large stress drop events had aftershock productivity generally lower
than the trend; for As scaling large stress drop events have high productivity. The patterns found here indicate that the areal fluctuations that inversely contribute to stress drop variations tend to affect aftershock
production somewhat more than stress change directly, with the latter only becoming evident when
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coseismic rupture area is held fixed. Ye et al. [2016] provide estimates of average slip over the areas AS that
give the static stress drops, and we explored systematic of scatter of productivity relative to average slip,
but the behavior is more scattered than when AS is used to scale the population. There are systematic effects
of source rupture properties on aftershock productivity, but the underlying variability of rupture dimensions
obscures the behavior when Mw is used to organize the population.
6. Conclusions
Analysis of 104 megathrust earthquakes located in circum-Pacific subduction zones reveals that variations in
aftershock productivity are affected by two distinctive trends: a regional trend with island arcs in the western
Pacific being more productive than continental arcs in the eastern Pacific and a trend of lower productivity
for higher stress drop main shocks when examined as a function of Mw. The regional behavior may be influenced by western zones having slab thermal parameters that result in a moderate increase of productivity for
colder/older plates. The inverse relationship of stress drop with aftershock productivity is explained when we
consider productivity as a function of coseismic rupture area. For a fixed rupture area the productivity
increases with stress drop, as expected for stress transfer calculations or inferences of dynamic stress triggering. The variation of rupture area dominates slip variability in the stress drop measures, reversing the trend
found when Mw is used to sort the population. These results demonstrate the influence of source physics
on the ensuing aftershock sequence and the value of quantitative source parameter estimation for predicting
aftershock productivity.
Acknowledgments
Aftershocks metadata for this study
were accessed through the Northern
California Earthquake Data Center
(NCEDC), doi:10.7932/NCEDC. This work
was supported by the U.S. NSF grant
EAR1245717 (T.L.) and was funded by
the Geological Survey of Israel, at the
Ministry of Energy and Water Resources,
and the Gordon and Betty Moore
Foundation GBMF3289. We thank an
anonymous reviewer and Satoshi Ide for
improving the manuscript.
WETZLER ET AL.
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