by Ross S. Stein, Ph.D., Temblor
The authors claim they found dynamic triggering of tiny aftershocks up to 275 km (150 mi)
from an M=7.2 mainshock in 2010, but they have not proved their case.
Citation: Stein, R.S., (2019), Ten times more earthquakes now detected in Southern California, Temblor, http://doi.org/10.32858/temblor.020
What did they do?
In a study published this month in Science, Zachary Ross and Egill Hauksson (both from Caltech), Daniel Trugman (Los Alamos National Laboratory) and Peter Shearer (Scripps Institution of Oceanography) were able to increase the number of recorded southern California earthquakes during 2010-2017 from 180,000 to 1.8 million. They did this by recovering all the quakes that stuck down to a magnitude of 0.29, whereas in the original catalog, only quakes larger than magnitude 1.7 had been reliably recovered. The relationship between earthquake size and frequency obeys a ‘power-law distribution,’ which means that when you drop down one magnitude unit, you get 10 times more quakes.
How did they do it?
They employed a method called ‘template matching’. Template matching takes advantage of the similar waveforms recorded at seismometers for quakes located very close together. Each quake was compared to 248,000 template earthquakes, making this is an enormously computer-intensive process. So, they harnessed an array of 200 NVIDIA graphic processing units. NVIDIA’s are designed for video gaming and for self-driving cars, so this is a special kind of scientific dividend. Then, they more precisely located all the earthquakes using a method called ‘double-difference relocation.’ Both methods have been used for a decade or so, but never on so large a data set. The new catalog is now freely available to all researchers (scedc.caltech.edu), a great gift to seismologists around the world.
Here is an example of the dazzling detail of the relocated seismicity (colored by depth) in the new catalog, which I annotated. Because most of the seismicity at depth lies to the northeast of the fault at the ground surface, the faults must be inclined 8-9° to the northeast, consistent with earlier studies (Fattaruso et al, 2014).
Did they discover remote aftershocks of an M=7.2 mainshock up to 300 km (180 mi) away?
In the panel on the right below, sites where the quake rate is higher in the week after the 2010 M=7.2 El Mayor-Cucapah (Baja California) earthquake are red, while sites where the rate is lower are white. The authors declare these are aftershocks, but in fact, their job is to prove it. This would not be unprecedented, as remote triggering following other large shocks has been widely reported (Hill et al., 1993; Brodsky et al., 2000; Prejean et al., 2004; Velasco et al., 2008; Pollitz et al., 2012). But the difference is that the new study bases its findings exclusively on very small (Magnitude<1.0) quakes.
The ‘Noise’ plot was kindly provided by the authors; the ‘Signal’ plot comes from their paper, with the blue aftershock zone boundary added here. Sites with no reliable rate change are grey.
On the left panel above is another ‘week after vs. week before’ comparison provided by Zachry Ross, but not centered in the earthquake, so presumably this is just random quake rate variability. I’ve inscribed a blue line around the apparent (mostly red) aftershock zone, which extends twice as far from the mainshock as had been visible before their new catalog was created. Aftershocks promoted by the permanent stress changes in the earth should extend to about 100-135 km, and so the authors ascribe the more distant shocks to dynamic triggering carried by the seismic waves, which reach 300 km away within about 2 minutes from the time the quake begins; within about an hour, those waves will have encircled the globe and will have dissipated, if not disappeared, in southern California.
Here, below, is another figure in their paper that I have annotated, showing the quake rate relative to the preceding year collapsed on to a line with distance from the epicenter. The quakes within about 135 km or twice the fault length, are consistent with static stress triggering. But for the next 100 km, the quake rate does not decay, which is not what one would expect if they were caused by the seismic wave propagation, which diminishes in amplitude as it propagates away from the rupture, just as ripples diminish in amplitude and spread out as they expand after one throws a stone into a pond. If there is a decay, it is obscured by noise.
The aftershocks the authors attribute to remote dynamically triggered events exhibit a rate 2-4 times higher in the week after the mainshock than in the preceding year.
In the next figure below, I compare the authors’ aftershock plot with their plot of seismicity density for the entire catalog period, 2008-2017. If the red quakes are indeed aftershocks, then they should not be correlated with the event density. That’s because aftershock locations should be most influenced by the epicenter and fault rupture. But here, instead, the aftershocks locate just where the long-term seismic rate is highest. It’s almost as if the location of the mainshock doesn’t matter. How could that be so?
Annotated versions of the figures in Ross et al. (2019). The seismicity density (the number of quakes in each 2 km x km cell) is on the left, and the elevated quake rate after the 2010 mainshock is on the right.
Here are two possible explanations for this conundrum:
• Since the event density plot contains the 2010 aftershocks, the two plots are not independent. An event density plot with the first week, or year, after the M=7.2 shock removed would make them nearly independent. I asked the authors if they could provide it, but they chose not to. Irrespective, the highest aftershock density will be near the (yellow) fault rupture, from the U.S.-Mexico border to the south. But the correlation extends ~200 km northwest of that, so I suspect the correlation will remain regardless.
• If the correlation between longterm event density and aftershocks is real, it would mean that the places which preferentially respond to dynamic triggering are those with very high local seismicity rates, not those with a particular fault geometry or distance from the epicenter. The amplitude and character of the seismic waves would be less important than the sensitivity of certain fault locations to shaking. This would be new and exciting new.
So, are the remote aftershocks a discovery or a mirage?
Here is what the authors, or any researchers, would need to do to prove that these events are aftershocks: At least some aftershocks should be triggered as the seismic waves move past those locations in the first few minutes, and no aftershocks at all can strike until the surface waves arrive. Further, the one attribute that distinguishes aftershocks from all other shocks is that their occurrence rate decreases with time in a very particular way: the quake rate decays with 1/time (e.g., 10 hr after the mainshock, the quake rate is 1/10th of its rate in the first hour, 100 hr after the mainshock, the quake rate is 1/100th of its rate in the first hour, etc.). This is called Omori decay in honor of its discovery in 1894 by the Japanese seismologist, Fusakichi Omori, who also came to San Francisco to study the great 1906 earthquake. If the red quakes do not exhibit Omori decay, they are not aftershocks. Another case of tiny, dynamically triggered earthquakes was falsified by these tests (Felzer and Brodsky, 2006; Richards-Dinger et al., 2010). So, do these shocks exhibit Omori decay?
If these really are aftershocks, and if they really are correlated with the background seismicity rate, we are going to learn something new and important about how the Earth works.
Emily E. Brodsky, Vassilis Karakostas, and Hiroo Kanamori, A New Observation of Dynamically Triggered Regional Seismicity: Earthquakes in Greece Following the August, 1999 Izmit, Turkey Earthquake, Geophys. Res. Let., 27, 2741-2744.
Laura A. Fattaruso, Michele L. Cooke, and Rebecca J. Dorsey (2014), Sensitivity of uplift patterns to dip of the San Andreas fault in the Coachella Valley, California, Geosphere, 10, 1235–1246, doi:10.1130/GES01050.1
Karen R. Felzer & E. E. Brodsky (2006), Decay of aftershock density with distance indicates triggering by dynamic stress, Nature, 441, 735–738, doi:10.1038/nature04799
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Stephanie K. Prejean, Hill, D. P., Brodsky, E. E., Hough, S. E., Johnston, M. J. S., Malone, S. D., Oppenheimer, D. H., Pitt, A. M., and Richards-Dinger, K. B. (2004), Remotely triggered seismicity on the United States west coast following the Mw 7.9 Denali Fault earthquake, Bull. Seism. Soc. Am., 94, S348-S359.
Keith Richards-Dinger, R.S. Stein, R.S., and S. Toda (2010), Decay of aftershock density with distance does not indicate triggering by dynamic stress, Nature, 467, 583-586, doi:10.1038/nature0940
Zachary E. Ross, Daniel T. Trugman, Egill Hauksson, and Peter M. Shearer (2019), Searching for hidden earthquakes in southern California, Science 10.1126/science.aaw6888.
Velasco, Aron A., Hernandez, S., Parsons, T., and Pankow, K. (2008). Global ubiquity of dynamic earthquake triggering, Nature Geoscience, 1, 375-379.
Fred F. Pollitz, R. S. Stein, V. Sevilgen, and R. Bürgmann (2012). The 11 April 2012 East Indian Ocean earthquake triggered large aftershocks worldwide, Nature, 490, 250-253.