WEBVTT Kind: captions Language: en-US 00:00:00.820 --> 00:00:05.440 [inaudible background conversations] 00:00:05.940 --> 00:00:11.220 Okay, everyone. I guess we’ll get started. 00:00:11.220 --> 00:00:15.860 Before we get started with today’s seminar, a couple of announcements. 00:00:15.860 --> 00:00:21.240 Please remember that this coming Monday at 2:00 p.m. is the memorial 00:00:21.240 --> 00:00:27.240 celebration for Dave Hill, and it’ll be here in this room at 2:00 p.m. 00:00:27.240 --> 00:00:31.510 For next week for seminar, we’re going to have Kathryn Materna 00:00:31.510 --> 00:00:34.060 from UC-Berkeley will come to talk to us. 00:00:34.060 --> 00:00:40.120 And I think that’s it for announcements. And so then it’s my pleasure to 00:00:40.120 --> 00:00:47.350 introduce today’s speaker, Kris Pankow. She got her Ph.D. at UC-Santa Cruz 00:00:47.350 --> 00:00:52.270 working on deep subduction zone stuff and then took a – kind of a big career 00:00:52.270 --> 00:00:56.550 change to go to University of Utah and start working on more – 00:00:56.550 --> 00:01:01.590 much more crustal-related problems. So at University of Utah, 00:01:01.590 --> 00:01:05.100 she’s the assistant director – is it assistant director or associate … 00:01:05.100 --> 00:01:06.171 - The associate … 00:01:06.171 --> 00:01:10.080 - Sorry. Associate director of the seismographic stations, 00:01:10.080 --> 00:01:14.250 and she’s also research faculty there. And she does research on a number 00:01:14.250 --> 00:01:18.360 of interesting topics including things like mine-induced earthquakes. 00:01:18.360 --> 00:01:23.760 And today, she’s going to be talking about dynamic triggering. Thanks. 00:01:27.680 --> 00:01:32.260 - Let’s see if this works. Okay. All right. Thanks, Jeanne. 00:01:32.260 --> 00:01:35.180 And thanks for everyone – for coming today. 00:01:36.060 --> 00:01:41.200 I’m going to talk about – oh, I have to be tall. Okay. 00:01:41.200 --> 00:01:43.540 Talk about some work that I’ve been doing for a while on 00:01:43.540 --> 00:01:47.520 dynamic earthquake triggering. And these are more sort of 00:01:47.520 --> 00:01:52.760 thoughts that I’ve had, and I hope that this spawns some discussion. 00:01:54.920 --> 00:01:58.020 So that we’re all on the same page, when I’m talking about remote 00:01:58.020 --> 00:02:03.399 dynamic triggering, I’m talking about, when an earthquake occurs someplace 00:02:03.400 --> 00:02:10.380 in the world, and at a distant location, we start seeing small earthquakes. 00:02:10.380 --> 00:02:13.080 And this is a little cartoon version of this. 00:02:13.090 --> 00:02:17.930 The surface waves come by, and you start to see earthquakes occurring here. 00:02:17.930 --> 00:02:21.230 Maybe it’s body waves. So this is what I’m talking about 00:02:21.230 --> 00:02:24.239 when I’m talking about dynamic earthquake triggering. 00:02:24.239 --> 00:02:28.930 And this has been studied for a long time now. 00:02:28.930 --> 00:02:30.709 And there’s a lot of big-picture questions. 00:02:30.709 --> 00:02:37.329 We’re really trying to get at, you know, what is the state of stress in the crust? 00:02:37.329 --> 00:02:41.110 And can these dynamic earthquakes tell us something about that? 00:02:41.110 --> 00:02:47.609 And even sort of more specific questions – why do some seismic waves 00:02:47.609 --> 00:02:52.590 trigger earthquakes and others don’t? Is it a function of the seismic waves? 00:02:52.590 --> 00:02:56.629 Is it a function of the peak dynamic stress, the frequency, 00:02:56.629 --> 00:02:59.739 the orientation, or, say, the particle motions? 00:03:00.500 --> 00:03:05.680 Or is it something specific to the location of the fault 00:03:05.690 --> 00:03:08.719 that’s being triggered? Is it the orientation of that fault? 00:03:08.719 --> 00:03:13.519 Is it the crustal stress in that fault? Are there fluids involved? 00:03:13.519 --> 00:03:18.879 What – so what I’m hoping in terms of my looking at this research is, what can 00:03:18.879 --> 00:03:24.120 we learn about the earthquake process by, in a sense, these controlled 00:03:24.120 --> 00:03:26.620 experiments that aren’t so well-controlled, right? 00:03:26.620 --> 00:03:30.340 They don’t happen all the time, but I think there’s really good 00:03:30.340 --> 00:03:34.740 information that we can learn about the process by studying these earthquakes. 00:03:37.709 --> 00:03:41.300 So I didn’t realize you were having a memorial for Dave, so this is some of 00:03:41.300 --> 00:03:49.600 Dave’s pioneering work following the 1992 magnitude 7.3 Landers earthquake. 00:03:50.880 --> 00:03:54.480 It was found – if this is the epicenter of the earthquake, where we’d expect 00:03:54.490 --> 00:03:58.430 the aftershocks to be is sort of in this red circle here. 00:03:58.430 --> 00:04:02.400 And in the first paper published on dynamic earthquake triggering by Hill 00:04:02.400 --> 00:04:07.940 and others, what was found was that, following this earthquake, there were 00:04:07.940 --> 00:04:12.639 earthquakes in the western U.S. So not located in that area where 00:04:12.639 --> 00:04:17.620 we’d typically see aftershocks. And I would say that probably at 00:04:17.620 --> 00:04:20.769 this time, if you would have asked anyone if this could happen, they 00:04:20.769 --> 00:04:26.550 probably would have said no. Okay? So here we are with this empirical 00:04:26.550 --> 00:04:30.939 evidence that this is what’s going on – the first paper. 00:04:30.939 --> 00:04:35.770 I got pulled into this topic in 2002 following the Denali Fault 00:04:35.770 --> 00:04:40.419 earthquake in Alaska. It was a right-lateral strike-slip fault 00:04:40.419 --> 00:04:46.370 with very strong directivity to the southeast. And, in fact, if you follow the 00:04:46.370 --> 00:04:49.970 propagation here, it goes right through Yellowstone National Park in Utah – 00:04:49.970 --> 00:04:55.120 sort of the areas of peak dynamic stress. This is from work of Velasco and et al. 00:04:55.120 --> 00:04:58.110 where we actually went through and measured the peak dynamic stress 00:04:58.110 --> 00:05:01.599 in the western U.S. following this earthquake. 00:05:01.600 --> 00:05:07.480 And, at the time, Stephan Husen was a postdoc working on Yellowstone. 00:05:07.480 --> 00:05:09.940 And he came in, and he said, Yellowstone’s going crazy. 00:05:09.949 --> 00:05:13.770 I think we have dynamic triggering. If – you know the old helicorders, 00:05:13.770 --> 00:05:16.889 the drum records? Sometimes they were really nice 00:05:16.889 --> 00:05:19.349 because you could look at the drum, and you could just see earthquakes 00:05:19.349 --> 00:05:25.919 going on all the time. And even more so, the water features 00:05:25.919 --> 00:05:29.700 in Yellowstone were starting to bubble, and there was just a lot of activity 00:05:29.700 --> 00:05:34.640 in Yellowstone. And that made me look at the data in Utah. 00:05:34.640 --> 00:05:41.200 And so this is the timing of the arrival of the surface waves – the body waves 00:05:41.219 --> 00:05:43.580 and the surface waves of the Denali Fault earthquake, and you can 00:05:43.580 --> 00:05:47.539 see this longer-period energy being from the main shock. 00:05:47.539 --> 00:05:51.710 And then, all of the sudden, each one of these red spikes in the spectrogram 00:05:51.710 --> 00:05:57.699 is a small local earthquake. This is a station in northern Utah. 00:05:57.699 --> 00:06:02.550 This is – this is pretty atypical for Utah. This would be more than we’d see in 00:06:02.550 --> 00:06:06.680 a typical aftershock sequence, okay? So we had a lot of activity going on 00:06:06.680 --> 00:06:13.930 in Utah as well that led me into this study to start looking at this question – 00:06:13.930 --> 00:06:16.200 or these multiple questions. 00:06:17.440 --> 00:06:23.540 And so there’s been a lot of work done on this, and there’s been many review 00:06:23.550 --> 00:06:26.610 studies at this time, but there’s a couple of really nice figures 00:06:26.610 --> 00:06:30.419 from some Hill and Prejean work. And, in this first one, which was 00:06:30.419 --> 00:06:35.470 published in 2007 – so sort of early – I would say early in the study of 00:06:35.470 --> 00:06:41.800 dynamic earthquake triggering, you can see – let’s see. Where did my mouse go? 00:06:41.800 --> 00:06:44.900 There it is. It’s very touchy. 00:06:44.900 --> 00:06:49.039 Sort of a collection of four earthquakes where we were pretty sure we had 00:06:49.039 --> 00:06:53.449 dynamic earthquakes triggering. So following Landers, you can see 00:06:53.449 --> 00:06:58.139 the green triangles here showing that Landers triggered earthquakes 00:06:58.139 --> 00:07:02.539 in the western U.S. Hector Mine – the magnitude 7.2 00:07:02.540 --> 00:07:06.300 in southern California – triggered events primarily in California. 00:07:06.300 --> 00:07:12.460 Primarily in these geothermal systems. The Denali earthquake triggered events, 00:07:12.460 --> 00:07:15.840 again, through much of western United States. 00:07:15.840 --> 00:07:19.249 And then the Sumatra earthquake – it was shown that the – it triggered 00:07:19.249 --> 00:07:22.699 events at Mount Wrangell. And these events were found in the 00:07:22.699 --> 00:07:28.159 surface waves, and they were in phase with the peak dynamic stress. Okay? 00:07:28.159 --> 00:07:31.219 So a couple of observations that I want to come back to later. 00:07:31.220 --> 00:07:35.140 So some of these first cases of dynamic earthquake triggering. 00:07:35.140 --> 00:07:38.169 These aren’t small, localized areas of triggering. 00:07:38.169 --> 00:07:41.090 These were triggering large areas. We were triggering much of the 00:07:41.090 --> 00:07:48.370 western United States with these studies. So, in the next review study, or – 00:07:48.370 --> 00:07:52.780 from Hill and Prejean 2015, there’s another summary figure. Okay, so from 00:07:52.780 --> 00:07:57.180 2007 to 2017, now all the symbols on these plots are places where 00:07:57.180 --> 00:08:02.150 there is dynamic triggering documented. 00:08:02.150 --> 00:08:06.520 If they’re big circles, they were larger events – 5-1/2 and larger. 00:08:06.520 --> 00:08:11.830 If they’re orange, people went back and looked at the pre-instrumental catalog. 00:08:11.830 --> 00:08:16.479 The smaller circles are smaller earthquakes, and with instrumental data, 00:08:16.479 --> 00:08:23.650 we start to see triggered tremor. And people – in some work, 00:08:23.650 --> 00:08:26.580 we started enhancing catalogs, and that was done in this work with 00:08:26.580 --> 00:08:30.059 Velasco where we had blue. So we weren’t just looking at catalog data. 00:08:30.059 --> 00:08:32.539 We were starting to enhance the catalogs. 00:08:32.539 --> 00:08:38.430 Okay, so all this work has been done. Why am I still looking at this, okay? 00:08:38.430 --> 00:08:41.860 Is there something that still needs to be done? 00:08:42.990 --> 00:08:46.200 So – and I failed to say this at the beginning. 00:08:46.209 --> 00:08:50.269 This is work that I’m doing with Debi Kilb from Scripps. 00:08:50.269 --> 00:08:57.079 And the questions we’re going after is – and motivating this particular study is 00:08:57.079 --> 00:09:01.670 we – from that previous figure, we see all these documented cases. 00:09:01.670 --> 00:09:06.250 And if you actually go and look in the literature, we’re calling dynamic 00:09:06.250 --> 00:09:11.900 triggering different things depending on different statistics and different criteria. 00:09:11.900 --> 00:09:16.760 And so one of the things that I would like to look at is, 00:09:16.760 --> 00:09:20.540 what are the indicators of dynamic triggering? 00:09:20.540 --> 00:09:25.100 From those first studies from Landers and Denali, it seemed to be this wide, 00:09:25.100 --> 00:09:31.070 spatial extent of increased rates. Okay? And then, if you look at those dots 00:09:31.070 --> 00:09:35.980 from 2015, maybe it’s not so wide. Maybe you can get localized triggering. 00:09:35.980 --> 00:09:39.550 But, as a community, I think we need to decide, what are really 00:09:39.550 --> 00:09:45.320 the indicators of this? Is it enough to have events coincident 00:09:45.320 --> 00:09:49.130 with the passage of the surface waves? Or do they have to be in phase? 00:09:49.130 --> 00:09:53.130 Do we have to have a rate increase? What’s the spatial extent? 00:09:53.130 --> 00:09:56.610 And so this is one of the questions motivating this study. 00:09:56.610 --> 00:10:00.220 But if we’re going to talk about rate increases being an indicator of dynamic 00:10:00.220 --> 00:10:04.949 triggering, what are we going to say about rates? 00:10:04.949 --> 00:10:08.470 How are we going to measure rates, and how are we going to measure 00:10:08.470 --> 00:10:12.950 a statistically significant rate change? Okay? 00:10:12.950 --> 00:10:16.440 And this is what I’m going to spend much of my time talking about in this – 00:10:16.440 --> 00:10:22.910 in this talk. And it’s one thing that we have a curated catalog to 00:10:22.910 --> 00:10:26.800 talk about statistical significance. But a lot of the work being done 00:10:26.800 --> 00:10:30.230 in dynamic earthquake triggering now is using enhanced catalogs with 00:10:30.230 --> 00:10:33.920 really short time windows. So I’ve been thinking about this 00:10:33.920 --> 00:10:37.680 for a while, and I think it’s a timely time for us, 00:10:37.680 --> 00:10:42.509 as geophysicists and seismologists, to be thinking about this. 00:10:42.509 --> 00:10:47.840 This is from a couple weeks ago – March 20, 2019, in Nature. 00:10:48.630 --> 00:10:53.540 The statisticians – or a group of statisticians want to get rid of this 00:10:53.540 --> 00:10:58.610 concept of statistical significance. Okay, this particular comment 00:10:58.610 --> 00:11:06.269 has 800 signatories, okay? And this was on the 20th. 00:11:06.269 --> 00:11:09.050 By the 27th, there were at least three letters saying that 00:11:09.050 --> 00:11:11.820 we can’t get rid of statistical significance. Okay? 00:11:11.820 --> 00:11:17.970 So this is something that’s happening in the statistical community, where 00:11:17.970 --> 00:11:20.839 they’re really having this discussion. And what these people want to do is, 00:11:20.839 --> 00:11:25.699 they want to take the idea of statistical significance and put it in the closet with 00:11:25.699 --> 00:11:29.360 things like the ether and the cyclops. And so that’s what this cartoon 00:11:29.360 --> 00:11:33.370 is showing us, is that maybe it has served its purpose and has 00:11:33.370 --> 00:11:36.630 brought us as far as we can get with this particular idea. 00:11:36.630 --> 00:11:39.640 And let’s just put it in the closet for now. 00:11:41.320 --> 00:11:45.610 So a few quotes from this paper that I think are important for our discussion 00:11:45.610 --> 00:11:52.560 on dynamic earthquake triggering and how we use statistics is, unfortunately, 00:11:52.560 --> 00:11:55.910 the false belief that crossing the threshold of statistical significance is 00:11:55.910 --> 00:11:59.680 enough to show that a result is real. Okay? 00:11:59.680 --> 00:12:02.160 Just because we say it’s statistically significant, based on 00:12:02.160 --> 00:12:07.839 whatever statistics we decide to use, we then decide that it’s real. 00:12:07.840 --> 00:12:10.640 And I think we need to think about that more. 00:12:11.870 --> 00:12:17.060 Like the 0.05 threshold – and this is talking about a P value – from which it 00:12:17.079 --> 00:12:23.220 came the default 95% used to compute intervals is an arbitrary convention. 00:12:23.220 --> 00:12:27.290 It is based on the false idea that there is a 95% chance that the computed 00:12:27.290 --> 00:12:31.670 interval itself contains the true value. So when we talk about statistical 00:12:31.670 --> 00:12:36.089 significance, we are somewhat picking these arbitrary values 00:12:36.089 --> 00:12:39.100 for which to measure things across. 00:12:40.610 --> 00:12:44.720 And then what they’re trying to get at is these – they want to 00:12:44.720 --> 00:12:49.440 talk about compatibility versus statistical significance. 00:12:49.440 --> 00:12:55.720 And this hinges on the correctness of the statistical assumptions. 00:12:55.730 --> 00:12:59.019 I would also say it depends on whether or not you are using – 00:12:59.019 --> 00:13:02.870 following the assumptions in the statistics that you’re using. 00:13:02.870 --> 00:13:06.569 So they want to get rid of statistical significance and talk about confidence 00:13:06.569 --> 00:13:10.279 intervals as compatibility intervals. So I just want to throw this out there 00:13:10.279 --> 00:13:14.000 because we often use statistics in seismology and geophysics. 00:13:14.000 --> 00:13:17.319 And I think this is a discussion – a broader discussion that’s 00:13:17.320 --> 00:13:20.020 happening that maybe we should be paying attention to. 00:13:21.020 --> 00:13:23.699 So back to dynamic earthquake triggering. 00:13:23.699 --> 00:13:30.410 And some of the statistics we’ve used. And the first one, and probably the 00:13:30.410 --> 00:13:34.220 one that’s most widely cited, in the beta statistic. 00:13:34.220 --> 00:13:38.269 This was developed by Matthews and Reasenberg in 1988. 00:13:38.269 --> 00:13:41.210 And it measures the difference in seismicity rate between the number of 00:13:41.210 --> 00:13:47.500 earthquakes – and sorry, this is a typo – in a post-interval time. 00:13:47.500 --> 00:13:50.529 And you subtract the number of earthquakes you’d predict for that 00:13:50.529 --> 00:13:55.300 time using a pre-interval time. And then you normalize by the 00:13:55.300 --> 00:14:02.569 standard deviation. You must have an earthquake in the time that you’re 00:14:02.569 --> 00:14:07.730 using to establish the rate. Okay, there must be at least one earthquake. 00:14:07.730 --> 00:14:11.290 So I don’t know how many of you have read Matthews and Reasenberg. 00:14:11.290 --> 00:14:16.019 It’s a pretty dense paper with lots of mathematical notation. 00:14:16.019 --> 00:14:21.440 And this is how they define the beta statistic in terms of a moment 00:14:21.440 --> 00:14:25.150 and some probabilities. If we put it into something that 00:14:25.150 --> 00:14:30.120 we can actually plug some numbers into in terms of earthquakes, it’s really 00:14:30.120 --> 00:14:33.500 the number of earthquakes and what I’m calling the after window. 00:14:33.500 --> 00:14:37.770 So that’s what A is standing for. You subtract the number that 00:14:37.770 --> 00:14:41.680 you’d predict by measuring the rate – so the number before divided by 00:14:41.680 --> 00:14:45.260 the time before, multiplying by the time. 00:14:45.260 --> 00:14:50.250 And then you multiply by the variance in this prediction. Okay? 00:14:50.250 --> 00:14:53.560 So it’s pretty clear to see here, if the number of earthquakes in 00:14:53.560 --> 00:14:58.500 your before window is zero, your computer is not going to like it when 00:14:58.500 --> 00:15:01.440 you try and calculate this equation, okay? 00:15:01.440 --> 00:15:04.920 You get lots of things like undefineds and such. 00:15:04.920 --> 00:15:08.120 Okay, so that’s a big – a big clue here is, 00:15:08.120 --> 00:15:12.790 you have to have a long enough time window to have this value. 00:15:12.790 --> 00:15:15.449 If you go through and you read the paper, it actually assumes 00:15:15.449 --> 00:15:18.319 a declustered catalog and a Poisson catalog. 00:15:18.319 --> 00:15:22.319 So it’s assuming earthquakes happen at a constant rate and are independent. 00:15:22.320 --> 00:15:25.540 So you’ve done some type of declustering. 00:15:25.540 --> 00:15:28.569 I actually think we need to have a discussion here because the 00:15:28.569 --> 00:15:32.850 statistic is also really trying to tell us when the earthquake 00:15:32.850 --> 00:15:38.040 is varying from an independent catalog. 00:15:38.040 --> 00:15:42.160 Importantly here, in this paper, they say significant anomalies 00:15:42.170 --> 00:15:47.410 located by this test in very short intervals should be treated suspiciously. 00:15:47.410 --> 00:15:50.100 So if you’re using the really small windows and you get 00:15:50.100 --> 00:15:56.340 significant values, it should be a suspicious result. 00:15:56.340 --> 00:16:01.540 Significance is found by looking at a distribution of beta over an interval. 00:16:01.540 --> 00:16:06.000 [inaudible] talk about this being an asymmetric function. 00:16:06.000 --> 00:16:10.940 You’re only normalizing by the variance of the before window. 00:16:10.949 --> 00:16:15.420 So this isn’t going to collapse to a nice Gaussian, even with lots of n. 00:16:15.420 --> 00:16:21.290 So it’s not clear that you can just say beta greater than 2 is significant. 00:16:21.290 --> 00:16:24.260 And, in this original paper, Matthews and Reasenberg, 00:16:24.260 --> 00:16:26.800 they suggest contouring the values of beta to look at 00:16:26.800 --> 00:16:31.639 where you really have peaks or applying other statistical values. 00:16:31.639 --> 00:16:36.190 And to show this, in a recent paper by Prejean and Hill, where they 00:16:36.190 --> 00:16:39.639 were looking at volcanic systems, where they are sure they aren’t 00:16:39.639 --> 00:16:44.939 looking at Poissonian-type distributions, to get around this, they re-sampled their 00:16:44.939 --> 00:16:49.050 catalog multiple times and then used the distribution of beta 00:16:49.050 --> 00:16:53.639 to find when it was significant. And they found that, 00:16:53.639 --> 00:16:58.600 for 95% of the time, in each volcanic center, your beta range 00:16:58.600 --> 00:17:03.700 at the significance level could be 2.7 or it could be 16. 00:17:05.220 --> 00:17:08.940 And to further illustrate this, in a paper – and there’s lots of examples. 00:17:08.940 --> 00:17:13.260 This was just a nice figure. This is by Johnson and Bürgman from 2015. 00:17:13.260 --> 00:17:18.440 They were looking at the Indian Ocean earthquake on the Blanco Fault Zone. 00:17:18.450 --> 00:17:22.770 And you can see their distribution of beta values here at the start 00:17:22.770 --> 00:17:26.470 of the surface waves coming in – or, at the start of their study window – 00:17:26.470 --> 00:17:32.010 sorry – at this red curve is around 5. And then it jumps up to 9. 00:17:32.010 --> 00:17:35.200 So this goes to the question of, what do we mean by statistical 00:17:35.200 --> 00:17:39.800 significance, and how are we using our statistics to get there? 00:17:41.720 --> 00:17:45.680 A second statistic – the Z statistic – I actually wasn’t familiar with this 00:17:45.680 --> 00:17:49.400 statistic, and still I read the Prejean and Hill paper, and they actually required 00:17:49.400 --> 00:17:56.070 that their triggering passed both the beta statistic and the Z statistic. 00:17:56.070 --> 00:17:59.260 And so I went and looked at this more, and this is really a symmetrical 00:17:59.260 --> 00:18:04.540 version of the beta statistic. It’s depending on a rate before and after. 00:18:05.760 --> 00:18:11.380 And so here’s a formulization of it from the Aron and Hardebeck paper. 00:18:11.380 --> 00:18:15.820 And the Z statistic is the difference in the means between two time intervals, 00:18:15.820 --> 00:18:18.520 normalized by their variances. 00:18:18.530 --> 00:18:23.270 So the sum – the square root of the variances there. 00:18:23.270 --> 00:18:27.030 And so just, again, if you want to plug some numbers in, and we use the same 00:18:27.030 --> 00:18:33.340 terminology, you can look at the number of events after and times before, 00:18:33.340 --> 00:18:37.770 it’s some algebra to go from here to here, but it’s pretty straightforward. 00:18:37.770 --> 00:18:43.510 And so key here is that this – you’re looking at the variance over 00:18:43.510 --> 00:18:47.210 two different time windows surrounding the time that you’re looking at. 00:18:47.210 --> 00:18:52.570 Okay, so this is a symmetric function. So if you’re looking at the limits here, 00:18:52.570 --> 00:18:58.040 you can actually – if you have large n, probably 30 or larger, this will collapse 00:18:58.040 --> 00:19:00.800 to a Gaussian, and you can talk about significance in sort of 00:19:00.800 --> 00:19:06.070 our standard way of talking about significance at 1.96 and 2.57 00:19:06.070 --> 00:19:10.360 for 95 and 99 – these arbitrary values. 00:19:10.360 --> 00:19:14.620 Okay. There’s a second equation in the Aron and Hardebeck paper 00:19:14.620 --> 00:19:18.700 for the beta statistic. And I wanted to talk about this a little bit. 00:19:18.700 --> 00:19:22.540 This is what they used in the Prejean and Hill paper to calculate beta. 00:19:22.540 --> 00:19:28.280 And it’s really nice because it gets rid of this singularity, right? 00:19:28.280 --> 00:19:31.500 We aren’t counting the events just in a before window. 00:19:31.500 --> 00:19:35.460 You’re looking at the windows over the full time, okay? 00:19:35.460 --> 00:19:40.210 So if N is the number of events in the full time window you’re looking at, 00:19:40.210 --> 00:19:44.180 and T is the full time window, you’re still looking at the number of 00:19:44.180 --> 00:19:49.620 events in an after window and subtracting the expected value. 00:19:49.620 --> 00:19:56.600 But you’re actually normalizing by essentially a variance in both windows. 00:19:56.600 --> 00:20:03.620 So I’m not sure this is strictly follows the beta statistic that we saw in 00:20:03.620 --> 00:20:08.520 Matthews and Reasenberg, but it does a really nice job of dealing with 00:20:08.520 --> 00:20:13.520 this singularity issue. And I just wanted to point out that, 00:20:13.520 --> 00:20:18.910 if you actually have a symmetric window – so your time before and 00:20:18.910 --> 00:20:24.600 your time after are equal, okay, and you – and here I’m just 00:20:24.600 --> 00:20:31.010 substituting in N equals N-A plus N-B, and T equals T-A plus T-B. 00:20:31.010 --> 00:20:35.610 This beta version reduces, and if your time windows are equal, 00:20:35.610 --> 00:20:40.870 it’s equivalent to the Z statistic. Okay? There’s nothing to say you have to 00:20:40.870 --> 00:20:45.580 use symmetric windows. You can have different time windows. 00:20:45.580 --> 00:20:50.640 But, again, I think – this isn’t a strict beta statistic. 00:20:50.640 --> 00:20:57.520 It might actually work a little bit better, and I’ll show you that going forward. 00:20:57.520 --> 00:21:01.140 Mainly because we don’t have that singularity. 00:21:01.140 --> 00:21:04.720 I do want to point out that, in the original formulations of the 00:21:04.720 --> 00:21:12.120 Z statistic by Haberman in the 1980s, these were also assuming a Poisson 00:21:12.120 --> 00:21:17.220 catalog and an independent catalog, so looking at declustered catalogs. 00:21:19.160 --> 00:21:23.570 So a third statistic that I’ll just briefly talk about is, if we just simply assume 00:21:23.570 --> 00:21:27.420 a Poisson distribution, which means that we have a constant rate, and we grab 00:21:27.420 --> 00:21:32.140 any window, and we measure the mean in that window, we can compare 00:21:32.140 --> 00:21:39.210 windows by looking at how far away it is in terms of standard deviation. 00:21:39.210 --> 00:21:42.540 And this is what I’ve used in a number of studies. 00:21:42.540 --> 00:21:46.760 I probably won’t be using it again, but that was the basis. 00:21:46.760 --> 00:21:50.680 So you’re really just looking at the difference in the means. 00:21:50.680 --> 00:21:52.090 Okay. 00:21:52.090 --> 00:21:58.040 So what we set out to do was we wanted to find a new way to do this without 00:21:58.040 --> 00:22:00.650 fewer assumptions. And that’s what I was going to come talk to you about. 00:22:00.650 --> 00:22:03.090 But then I found out there’s lots of good things out there. 00:22:03.090 --> 00:22:06.030 And so it – sort of the nature of what I’ve been doing has been 00:22:06.030 --> 00:22:10.860 changing some. But this statistic looks at an empirical distribution. 00:22:10.860 --> 00:22:16.740 So we take long windows of time to establish rates. 00:22:16.740 --> 00:22:20.821 By looking at long windows, we aren’t – the assumption is, we don’t have to 00:22:20.821 --> 00:22:27.820 decluster because the dependent times are going to show up on the tail. 00:22:27.820 --> 00:22:30.970 And what we’re really going to see in terms of the primary distribution, 00:22:30.970 --> 00:22:33.510 or where most of the events are, is the independent part, and that 00:22:33.510 --> 00:22:37.640 will allow us to define what’s happening in the catalogs. 00:22:37.640 --> 00:22:43.390 The one thing we do require is that we have a magnitude of completeness. 00:22:43.390 --> 00:22:47.270 And similar magnitudes. And then we take this distribution, 00:22:47.270 --> 00:22:49.680 and we explore ways to measure the significance. 00:22:49.680 --> 00:22:53.450 We use the Chebyshev Inequality Theorem, which is five times the 00:22:53.450 --> 00:22:59.230 standard deviation. Should give you at least 96% – another arbitrary value. 00:22:59.230 --> 00:23:02.800 We looked at the percentiles within the distribution. 00:23:02.800 --> 00:23:06.800 And advantages here is we have few assumptions. 00:23:06.800 --> 00:23:10.460 I’m going to show you it doesn’t matter what the length of our windows are 00:23:10.460 --> 00:23:14.220 because we’re looking at the catalog, and we’re defining the character of the 00:23:14.220 --> 00:23:21.580 catalog. And then we also aren’t limited, as in many dynamic earthquakes studies, 00:23:21.580 --> 00:23:24.620 of just looking around the time windows of teleseismic arrivals. 00:23:24.620 --> 00:23:28.160 We’re looking across the entire catalog. 00:23:28.160 --> 00:23:32.760 So first thing we do is we look at magnitude of completeness. 00:23:32.760 --> 00:23:36.720 And we’re just approximating this – the maximum curvature. 00:23:37.440 --> 00:23:43.840 I can show you later that I don’t think this is critical to our work, but it does 00:23:43.840 --> 00:23:48.820 get rid of some of the small events that might bias our distributions. 00:23:49.630 --> 00:23:53.200 And then what we do is, for our time window – and we settled on three-year 00:23:53.210 --> 00:23:57.070 windows because that gave us somewhat constant magnitude of completeness – 00:23:57.070 --> 00:23:59.500 we start at the beginning of the three-year window, 00:23:59.500 --> 00:24:04.070 and we pick a time interval. Five hours, 12 hours, a day, five days – 00:24:04.070 --> 00:24:08.490 whatever you want it to be, and you just start counting. 00:24:08.490 --> 00:24:13.240 So if you’re using a five-hour window, you count all the earthquakes from 00:24:13.240 --> 00:24:16.720 zero-zero to zero-five. And then you slide your 00:24:16.720 --> 00:24:19.590 window by an hour, and you count again. 00:24:19.590 --> 00:24:22.960 This gives us 26,000 data points. 00:24:23.260 --> 00:24:29.420 And then we put this on a distribution histogram here. 00:24:29.420 --> 00:24:34.080 And what should surprise no one in this room is that, for most catalogs, 00:24:34.090 --> 00:24:38.790 at a five-hour time window, what you mostly count is zero. Okay? 00:24:38.790 --> 00:24:43.030 We don’t typically see that many earthquakes happening. 00:24:43.030 --> 00:24:48.570 But you get earthquakes – you can get going out to 5, 6, 7. 00:24:48.570 --> 00:24:51.680 This is just using the Utah catalog as an example. 00:24:51.680 --> 00:24:55.780 And then we can look at sort of what the character of these distributions are. 00:24:55.780 --> 00:24:59.020 We can find the mean. We could get the standard deviation. 00:24:59.020 --> 00:25:02.100 We can find five times the standard deviation and get the 00:25:02.100 --> 00:25:05.840 threshold that the Chebyshev Inequality Theorem tells us. 00:25:05.840 --> 00:25:10.220 We can look at the distribution of itself and find out where 95% of the data 00:25:10.220 --> 00:25:15.670 is in the solid red or 99% of the data is in the dashed red. 00:25:15.670 --> 00:25:18.420 And we can start looking at the full character of this and 00:25:18.420 --> 00:25:22.630 start defining thresholds based on these characters. 00:25:22.630 --> 00:25:26.160 And it’s going to change if you have different windows. 00:25:26.980 --> 00:25:33.340 So using that and these thresholds, we define thresholds where the 00:25:33.340 --> 00:25:41.220 catalog is anomalous at our arbitrary significance levels of 95 and 99%. 00:25:41.220 --> 00:25:44.020 And so every dot on here is one of our windows. 00:25:44.030 --> 00:25:47.190 If it’s red, it was above the threshold value. 00:25:47.190 --> 00:25:50.090 If it’s green, it’s below the threshold value. 00:25:50.090 --> 00:25:53.830 And then we compare that to the timing of teleseismic waves, 00:25:53.830 --> 00:25:58.110 which are the green lines. And for this window – 00:25:58.110 --> 00:26:01.380 I picked this window because, if we didn’t see Denali in Utah 00:26:01.380 --> 00:26:04.150 as significant, we had a problem. 00:26:04.150 --> 00:26:09.020 But we also found two other events. We found the Kuril event, 00:26:09.020 --> 00:26:13.220 which I’m going to talk about in just a couple minutes, actually happened 00:26:13.230 --> 00:26:17.520 within the window that we originally said we had increased seismicity 00:26:17.520 --> 00:26:20.860 from the Denali earthquake. So, in our original study, 00:26:20.860 --> 00:26:23.990 we didn’t discriminate between these two main shocks. 00:26:23.990 --> 00:26:26.330 And then we also found this Molucca Sea event, 00:26:26.330 --> 00:26:29.370 which I will come back to at the end of the talk. 00:26:29.370 --> 00:26:31.780 The other thing about this method that I’ll just put a plug in 00:26:31.780 --> 00:26:35.260 for right now is it also finds other time periods in the catalog 00:26:35.260 --> 00:26:37.490 where there’s significant changes. 00:26:37.490 --> 00:26:41.060 These are probably related to main shock/aftershock sequences. 00:26:41.060 --> 00:26:45.000 I had a high school statistics teacher working for me this summer on 00:26:45.000 --> 00:26:48.430 a research project, and she took and applied this technique to 00:26:48.430 --> 00:26:51.541 the Yellowstone data, just looking for subtle changes, so maybe 00:26:51.541 --> 00:26:56.050 small swarm-type events. And that’s work we’re still looking at. 00:26:56.050 --> 00:27:00.380 But I think there’s other applications than dynamic earthquake triggering. 00:27:01.420 --> 00:27:06.330 So here’s that Kuril event I talked about. The Denali Fault earthquake. 00:27:06.330 --> 00:27:10.300 The primary – the original one that we said we had dynamic 00:27:10.300 --> 00:27:14.400 earthquake triggering came in here on the 3rd of November. 00:27:14.400 --> 00:27:18.710 We had a magnitude 3 and some aftershocks spiking things here. 00:27:18.710 --> 00:27:26.840 It looks like it was starting to roll over, and then energy from the 7.3 event, 00:27:26.840 --> 00:27:33.650 which we partly discarded because it’s – this is a deep event – 459 kilometers. 00:27:33.650 --> 00:27:38.000 But, you know, this comes to the question of, what do we mean by 00:27:38.000 --> 00:27:41.190 statistical significance, and what are the indicators of dynamic triggering? 00:27:41.190 --> 00:27:45.880 And if we’re just going to use rates, then is this dynamic earthquake triggering? 00:27:45.880 --> 00:27:53.740 Did this event further the excitation in Utah, or was it just by chance? 00:27:55.300 --> 00:27:59.900 So that’s the method. We applied it to four catalogs in the western U.S. 00:27:59.900 --> 00:28:05.950 We looked at 500 main shocks from the world – 11 sort of more regional events. 00:28:05.950 --> 00:28:08.770 The catalogs we looked at – we chose catalogs that we had 00:28:08.770 --> 00:28:12.660 some experience with, which is always kind of 00:28:12.660 --> 00:28:16.010 a good idea if you want to blindly dig into catalogs, we have the 00:28:16.010 --> 00:28:21.640 ANZA catalog, Utah catalog, Yellowstone, and Montana. 00:28:22.420 --> 00:28:25.040 Reasons why you might want some experience with the catalog is, 00:28:25.040 --> 00:28:28.650 we know, in Utah, to get rid of the mining seismicity. 00:28:28.650 --> 00:28:34.200 So this polygon here of white is where we have coal mines in Utah. 00:28:34.200 --> 00:28:37.390 And while there might be dynamic earthquake triggering going on in the 00:28:37.390 --> 00:28:43.480 coal mines, decoupling the production history and the things that generate 00:28:43.480 --> 00:28:49.480 mining seismicity from incoming waves was more than we wanted in this study. 00:28:51.170 --> 00:28:53.780 We then calculate the magnitude of completeness for these 00:28:53.780 --> 00:28:58.880 33-year-long catalogs in three-year windows. 00:28:58.880 --> 00:29:02.920 Pink and red are Utah and Montana, respectively. 00:29:02.920 --> 00:29:07.220 And they’re relatively consistent across the board. 00:29:07.880 --> 00:29:13.000 ANZA is in green, and in 2004 here, there was 00:29:13.010 --> 00:29:15.920 a large drop in the magnitude of completeness. 00:29:15.920 --> 00:29:20.360 This plays into the threshold values. So if you start seeing – if there’s – 00:29:20.360 --> 00:29:23.400 if the magnitude of completeness drops, your threshold’s going to go up 00:29:23.400 --> 00:29:26.550 because there’s more earthquakes. And then, in Yellowstone, 00:29:26.550 --> 00:29:33.480 it’s a little bit more scattered, but there’s also a drop here in about 1996. 00:29:34.840 --> 00:29:40.800 Just a reminder, we count the events in five- or 12-hour windows. 00:29:40.800 --> 00:29:47.700 And then we look – I’m going to show the results in the – from either the 99% 00:29:47.700 --> 00:29:53.240 threshold primarily. Will also be some results from the 95% threshold. 00:29:54.920 --> 00:30:02.680 So if we just look at thresholds for the 33-year catalogs for the four different 00:30:02.680 --> 00:30:08.780 regions, not surprising, the magnitude of completeness was pretty stable 00:30:08.780 --> 00:30:13.220 for Utah and Montana, and the threshold values are pretty stable. 00:30:13.860 --> 00:30:18.860 ANZA had that drop in the magnitude of completeness, and you can see 00:30:18.860 --> 00:30:27.920 this bimodal change in the threshold values that accompany that. 00:30:27.920 --> 00:30:35.940 Yellowstone is all over the board. And so one question we had was, 00:30:35.940 --> 00:30:42.440 well, maybe our assumption that, with 26,000 windows, 00:30:42.440 --> 00:30:45.820 we could not really worry about the independent versus dependent events 00:30:45.820 --> 00:30:50.400 when we look at rates is not valid here because of the swarms 00:30:50.400 --> 00:30:54.280 and other activity going on. So we actually took two windows – 00:30:54.280 --> 00:31:01.040 Before ’96 and after ’96 – and calculated magnitude of completenesses and did – 00:31:01.040 --> 00:31:03.790 ran through the rest of the analysis with those values. 00:31:03.790 --> 00:31:07.501 I don’t have time to go into that too much, other than to say 00:31:07.501 --> 00:31:13.220 we get almost the same results when we’re looking for significant increases. 00:31:13.220 --> 00:31:15.580 There’s just a couple changes. 00:31:18.760 --> 00:31:23.200 For those of you who don’t want to count 33 years’ worth of data, 00:31:23.200 --> 00:31:27.160 and you’re doing enhanced studies, we also went through and said, 00:31:27.160 --> 00:31:31.550 well, we have 500 earthquakes, and we’re looking at pre-event windows 00:31:31.550 --> 00:31:36.580 as well, so let’s count the number of earthquakes in the pre-event windows 00:31:36.580 --> 00:31:40.730 and look at the distributions just from the 500 earthquakes we looked at. 00:31:40.730 --> 00:31:44.280 And that’s what you see here for the four different catalogs. 00:31:44.280 --> 00:31:48.060 When I’m comparing the statistics against our results, I don’t do any 00:31:48.071 --> 00:31:52.120 magnitude of completeness correction because, in a lot of the dynamic 00:31:52.120 --> 00:31:55.180 earthquake triggerings, especially – studies, especially if you’re looking at 00:31:55.180 --> 00:32:01.990 enhanced studies, they don’t have enough of a catalog to get a magnitude 00:32:01.990 --> 00:32:04.870 of completeness, so they just count all the events they see. 00:32:04.870 --> 00:32:07.150 So that’s what we’re going to compare our statistics here – 00:32:07.150 --> 00:32:11.240 sort of the curated catalog versus an enhanced-type catalog. 00:32:11.240 --> 00:32:13.590 And so, if you just – if you’ve looked at 500 events, 00:32:13.590 --> 00:32:18.300 you can form the distribution. And, while the 99% thresholds 00:32:18.300 --> 00:32:22.810 here shown in these purple curves are not exactly what we saw in the 00:32:22.810 --> 00:32:27.580 previous slide, they’re pretty close. So it’s saying that maybe you could do some 00:32:27.580 --> 00:32:32.620 random sampling of your catalog with a lot of numbers, where you could actually get the 00:32:32.620 --> 00:32:38.380 distribution, and you could form the rates in this way. Okay. 00:32:39.030 --> 00:32:42.900 So some results. So this is results if we just assume 00:32:42.900 --> 00:32:48.320 a Poisson process and look at the – essentially the difference in the means. 00:32:48.320 --> 00:32:52.080 The results with our new approach are the green stars. 00:32:52.080 --> 00:32:57.570 So we don’t get that many cases of what we’d call statistical rate changes. 00:32:57.570 --> 00:33:02.540 In comparison to when we use – just looking at a mean and looking at 00:33:02.540 --> 00:33:06.050 the standard deviations from the mean. Okay. 00:33:06.860 --> 00:33:11.200 We do see a decrease at the 99% level, so telling us things are working. 00:33:11.210 --> 00:33:19.380 And the main reason for this is, to use the statistic properly for Poisson, 00:33:19.380 --> 00:33:24.410 we have to assume we have large n, and oftentimes, we don’t have large n. 00:33:24.410 --> 00:33:27.790 We have quite small n. So there’s two scales here. 00:33:27.790 --> 00:33:33.260 On the left is for the gray bars, and on the right is for the orange bars. 00:33:33.260 --> 00:33:37.990 The gray bars would be the number of events for the black stars in the previous 00:33:37.990 --> 00:33:40.980 slide where there was some statistical significance looking at 00:33:40.980 --> 00:33:45.310 the number of pre-events and the number of post-events. 00:33:45.310 --> 00:33:49.440 And then, for our new approach, we’re using this empirical distribution. 00:33:49.440 --> 00:33:55.250 And what you can see is, many of the events from the difference in the mean 00:33:55.250 --> 00:33:58.240 that showed up as stars that we didn’t find with our rate changes 00:33:58.240 --> 00:34:02.390 are because there’s really just a few events. 00:34:02.390 --> 00:34:05.930 And it’s probably not really significant because we really 00:34:05.930 --> 00:34:10.220 didn’t properly account for the assumptions in the statistics. 00:34:11.320 --> 00:34:14.899 But for our new rate change, you can see that, at 95%, 00:34:14.899 --> 00:34:22.040 you can start to get significant changes at 3 and 4. At 99%, you really have to 00:34:22.040 --> 00:34:26.100 see about six events in the post window for it to be significant. 00:34:28.049 --> 00:34:31.760 So then I compared this with the Z statistic. 00:34:31.760 --> 00:34:34.920 The green symbols, again, are using our empirical rates. 00:34:34.920 --> 00:34:42.460 Stars are at 99%. Crosses are at 95%. Comparing those to a Z statistic, looking 00:34:42.470 --> 00:34:48.609 at just five hours plus and minus when the teleseismic energy came through. 00:34:48.609 --> 00:34:53.259 Stars, again, are at 99%. Crosses are at 95%. 00:34:53.260 --> 00:34:56.520 And we largely get the same answer. 00:34:57.740 --> 00:35:04.019 There are some differences. In some cases, the Z statistic finds 00:35:04.019 --> 00:35:07.880 what would be considered significant triggering that we don’t identify. 00:35:07.880 --> 00:35:11.130 And, in all of those cases, that’s a function of the magnitude 00:35:11.130 --> 00:35:16.529 of completeness correction. So, in our analysis, we look at – 00:35:16.529 --> 00:35:20.259 we remove many of the smallest events with the magnitude of completeness, 00:35:20.259 --> 00:35:22.470 but those are counted when we do the Z statistic. 00:35:22.470 --> 00:35:25.310 So that’s one difference there. 00:35:25.310 --> 00:35:31.410 In the cases where we see triggering – or, we have a statistical rate increase 00:35:31.410 --> 00:35:36.430 that are not found by the Z statistic is where there’s a subtle change in rates, 00:35:36.430 --> 00:35:39.170 like what we saw with the Kuril event in Utah. 00:35:39.170 --> 00:35:41.250 And I’ll show a few more examples of this. 00:35:41.250 --> 00:35:46.180 So the Z statistic is not picking up what might be a subtle rate change 00:35:46.180 --> 00:35:51.200 where the actual number of events is larger than you’d expect to see. 00:35:51.910 --> 00:35:56.120 So just going through some examples and coming back to, what are the 00:35:56.120 --> 00:36:00.759 indicators of dynamic earthquake triggering, and what do we mean 00:36:00.759 --> 00:36:09.289 by statistical significance, if we start with the three events that are 00:36:09.289 --> 00:36:12.330 well-documented as triggering, and we look at the character 00:36:12.330 --> 00:36:16.650 of the cumulative earthquake plots – so this is the cumulative number 00:36:16.650 --> 00:36:20.210 of earthquakes with time. Where the red bars are, 00:36:20.210 --> 00:36:23.519 that’s – those are our five-hour windows. 00:36:23.520 --> 00:36:28.820 You can see, for Landers, Denali in Utah, and Denali in Yellowstone, 00:36:28.820 --> 00:36:32.900 you had pretty constant rates. Then these huge changes. 00:36:32.900 --> 00:36:36.680 And, in each of these catalogs, you can see that we had events 00:36:36.680 --> 00:36:41.559 widespread throughout the region – maybe not quite as much in Utah 00:36:41.559 --> 00:36:46.030 for Landers, but there were a couple locations that were triggered here. 00:36:46.030 --> 00:36:50.280 So really clear – nothing, something. 00:36:52.210 --> 00:36:55.760 If we look more closely at some of the results from Yellowstone – and I’m just 00:36:55.779 --> 00:37:01.220 showing a few of the examples here. Excuse me – we see that, at the 00:37:01.220 --> 00:37:07.579 99% confidence level – this arbitrary value again – we see, 00:37:07.580 --> 00:37:12.680 following the 1985 Mexico City event, pretty much nothing. 00:37:12.680 --> 00:37:18.340 A big step. Again, spatially distributed throughout Yellowstone. 00:37:19.100 --> 00:37:23.480 It’s a pretty – the scale over here is quite large because, a few weeks later, 00:37:23.480 --> 00:37:26.740 we had the start of a Yellowstone swarm. Okay? 00:37:26.740 --> 00:37:30.630 But I would argue that this is a pretty distinct step. 00:37:30.630 --> 00:37:36.720 In these two other cases, which were flagged at 95% confidence by both 00:37:36.720 --> 00:37:40.900 our method and the Z statistic, you know, it looks like you have 00:37:40.900 --> 00:37:45.940 a pretty constant rate, and then you do see these bumps in seismicity. 00:37:45.940 --> 00:37:51.700 In these cases, it seems to be isolated regionally within the catalog. 00:37:51.710 --> 00:37:55.280 But then, if we look at this, right, we have an increase here. 00:37:55.280 --> 00:37:57.740 We have something that looks about the same here. 00:37:57.740 --> 00:38:00.059 Something that looks about the same here. 00:38:00.059 --> 00:38:04.360 You can say the same thing down – following this 2003 event, 00:38:04.360 --> 00:38:09.640 where you have sort of these repeating types of increases. 00:38:09.640 --> 00:38:14.000 And so, if we’re talking about an indicator for dynamic earthquake 00:38:14.000 --> 00:38:17.549 triggering, is this dynamic earthquake triggering? 00:38:17.549 --> 00:38:21.730 It doesn’t fit our classical model of the original studies. 00:38:21.730 --> 00:38:25.609 And, in some of the more recent studies, we don’t look at things over a long 00:38:25.609 --> 00:38:28.759 time period, so we just look at these rate changes. 00:38:28.759 --> 00:38:32.730 So what does it mean to be dynamically earthquake triggered, 00:38:32.730 --> 00:38:37.120 and how are we going to separate this? How can we actually get to 00:38:37.120 --> 00:38:41.480 that causative nature versus just looking at a rate change? 00:38:42.970 --> 00:38:47.000 If we look at ANZA, this is following the Baja earthquake. 00:38:47.009 --> 00:38:49.680 95% confidence interval. 00:38:49.680 --> 00:38:53.359 I would say we had a pretty steady rate. We have a bump in the number 00:38:53.360 --> 00:38:59.500 of events. Widely distributed. I’m not aware of this being documented. 00:38:59.500 --> 00:39:02.660 But – so I think maybe we saw some limited triggering 00:39:02.660 --> 00:39:05.800 in ANZA following the Baja event. 00:39:07.150 --> 00:39:10.920 And then, coming back to the Molucca Sea event that I mentioned earlier, 00:39:10.930 --> 00:39:16.069 and another example from Yellowstone following a Kermadec Islands event, 00:39:16.069 --> 00:39:19.280 if we look at these sequences – these are ones that were not found 00:39:19.280 --> 00:39:24.329 by the Z statistic but did get flagged using our empirical rates. 00:39:24.329 --> 00:39:29.680 We see that a sequence started. In each case, we have some type of 00:39:29.680 --> 00:39:37.119 sequence that began very localized, and then there is this increase in 00:39:37.119 --> 00:39:42.150 this rate. So a significant change that goes with this. 00:39:42.150 --> 00:39:46.820 And, again, is this significant? Is this dynamic earthquake triggering? 00:39:46.820 --> 00:39:52.349 Are these waves further enhancing these sequences, or is this happening by chance? 00:39:52.349 --> 00:39:56.800 So what are the indicators of dynamic earthquake triggering? 00:39:56.800 --> 00:40:01.940 And with that, I’m going to move to the conclusions. 00:40:01.940 --> 00:40:05.759 So what we’ve done is we developed an empirical density distribution 00:40:05.759 --> 00:40:08.710 based on earthquake rates in a tailored time window. 00:40:08.710 --> 00:40:12.600 I showed five-hour windows today because that’s often used in dynamic 00:40:12.600 --> 00:40:16.900 earthquake triggering studies because that’s a pretty long window 00:40:16.900 --> 00:40:19.800 when you’re trying to enhance the catalog. 00:40:19.800 --> 00:40:23.779 We’ve identified past instances of dynamic triggering as well as what 00:40:23.779 --> 00:40:27.650 I think are potentially previously undocumented cases. 00:40:27.650 --> 00:40:31.839 I would argue that looking at these longer catalogs gives us a more robust 00:40:31.840 --> 00:40:37.900 rate to actually form our statistics and look at what we might mean by 00:40:37.900 --> 00:40:44.300 statistically significant rate changes. The Z statistic produces similar 00:40:44.309 --> 00:40:48.410 results to the long-term catalog. I have no idea why. 00:40:48.410 --> 00:40:54.549 Okay, why, if I look at a 10-hour window, with this particular statistic, 00:40:54.549 --> 00:41:00.080 can I reproduce what we get from a long catalog? 00:41:00.080 --> 00:41:03.260 I can’t – I’ve tried to play with some math earlier this week, 00:41:03.260 --> 00:41:06.100 but I don’t have a good answer for that. 00:41:07.060 --> 00:41:10.240 But I would maybe encourage people to move from 00:41:10.240 --> 00:41:13.500 thinking about the beta statistic to the Z statistic. 00:41:14.490 --> 00:41:18.360 And so, if we go back to the questions that I started this with, 00:41:18.360 --> 00:41:22.080 what does it mean to be statistically significant? 00:41:23.040 --> 00:41:28.800 What do these arbitrary values of 95 and 99% mean when we’re talking 00:41:28.810 --> 00:41:32.670 about dynamic earthquake triggering? And should we be using these 00:41:32.670 --> 00:41:41.590 arbitrary values to assert this? I would argue, as was originally argued 00:41:41.590 --> 00:41:44.470 in the Matthews and Reasenberg paper, that we need to sort of further 00:41:44.470 --> 00:41:49.839 investigate this catalog and really look at what’s going on in the background. 00:41:49.839 --> 00:41:54.630 And then, if we’re going to go from these rate changes or earthquakes 00:41:54.630 --> 00:41:59.490 in the surface waves or whatever we’re going to declare as these 00:41:59.490 --> 00:42:04.170 indicators of dynamic triggering, how are we going to define those? 00:42:04.170 --> 00:42:09.760 Is it enough to say we had a subtle increase in an ongoing sequence? 00:42:09.760 --> 00:42:14.640 Do we have to have a large spatial extent of triggering that’s 00:42:14.640 --> 00:42:19.740 triggering all of the western U.S.? Can it be a localized area? 00:42:20.420 --> 00:42:24.480 And maybe all of these are correct, but I think we have to expand 00:42:24.480 --> 00:42:27.240 what we’re thinking about and our definitions as we do this and 00:42:27.240 --> 00:42:31.019 be maybe a little bit more specific when we’re writing our papers 00:42:31.019 --> 00:42:33.990 in terms of what we’re using for statistics and what we’re using 00:42:33.990 --> 00:42:36.640 as indicators for dynamic earthquake triggering. 00:42:36.640 --> 00:42:39.740 So with that, I’ll say thank you and take any questions. 00:42:39.740 --> 00:42:44.900 [Applause] 00:42:44.900 --> 00:42:48.080 - Okay, thank you, Kris. Questions? 00:42:50.700 --> 00:42:54.720 - Okay, as someone who’s actually one of the authors of the Hill et al. paper, 00:42:54.730 --> 00:42:57.950 one of the – one of the joys of that paper was – and being you said, what were we 00:42:57.950 --> 00:43:03.020 thinking beforehand, was that we were completely stunned when it happened. 00:43:03.420 --> 00:43:07.220 And – because it was the largest earthquake we had after we 00:43:07.220 --> 00:43:09.640 had installed, you know, dense seismic networks. 00:43:09.640 --> 00:43:11.540 - Right. - So in the – you know, 00:43:11.540 --> 00:43:14.540 we had a few decades of data and hadn’t seen anything like it. 00:43:14.549 --> 00:43:18.760 Also the statistics are so far off the chart that I think Paul Reasenberg referred to 00:43:18.760 --> 00:43:22.039 it as his mother’s test – the mother test. 00:43:22.039 --> 00:43:24.140 That he showed it to his mother, and she was shocked by it. [laughter] 00:43:24.140 --> 00:43:28.540 You know, so we were sort of saved from a lot of these details. 00:43:30.900 --> 00:43:33.520 One thing that confused me a little bit is that you’re taking an empirical 00:43:33.520 --> 00:43:39.360 distribution, but you’re still computing a mean and a standard deviation. 00:43:40.460 --> 00:43:43.840 And there was one plot in the five-hour things where you had the 95 and the 00:43:43.840 --> 00:43:52.760 99% confidence bounds – the thresholds, in the same integer bin. 00:43:52.760 --> 00:43:56.460 And so I was sort of curious why you’re doing that versus, you know, 00:43:56.460 --> 00:43:59.970 in an empirical distribution, just looking at the point where 00:43:59.970 --> 00:44:06.400 you cross 95 and 99% values. - I’m sorry I was confusing things. 00:44:06.400 --> 00:44:12.780 So first – you’re first comment. Landers, Denali, in our statistics, 00:44:12.780 --> 00:44:14.940 are the mother of all statistics too. - Yeah. 00:44:14.940 --> 00:44:18.999 - I mean, Yellowstone following Denali has – like, we could 00:44:18.999 --> 00:44:23.950 actually get a beta statistic for it. It’s, like, 70 or 80 or something. 00:44:23.950 --> 00:44:25.589 We aren’t talking 2 and 3 anymore, right? 00:44:25.589 --> 00:44:27.359 - Yeah, no. - So, for the cases – 00:44:27.359 --> 00:44:31.460 those well-documented cases, the statistics are all off the chart. 00:44:31.460 --> 00:44:33.380 Regarding this, I’m sorry for the confusion. 00:44:33.380 --> 00:44:40.200 I just put the mean up there to just show where it was. 00:44:40.200 --> 00:44:43.509 The 95 and the 99% are based on the distribution. 00:44:43.509 --> 00:44:45.730 They aren’t based on the standard deviation. 00:44:45.730 --> 00:44:50.930 - Okay. In the inset, why are – my understanding was that the – 00:44:50.930 --> 00:44:53.799 you have two thresholds that are sort of in different places 00:44:53.799 --> 00:44:58.759 within the bin that’s marked 4. - Right. And – yes, the Chebyshev 00:44:58.759 --> 00:45:03.690 Inequality Theorem does use five standard deviations from the mean. 00:45:03.690 --> 00:45:06.930 And we’ve gone away from that, and I didn’t talk about any of the results 00:45:06.930 --> 00:45:09.721 for the exact reason that you talk about. We don’t really have 00:45:09.721 --> 00:45:11.920 a normal distribution. We aren’t really looking at 00:45:11.920 --> 00:45:16.520 something where I’m confident talking about standard deviations. 00:45:16.520 --> 00:45:20.760 I partly left it here because we presented a poster at SSA last year where 00:45:20.770 --> 00:45:25.040 this is the criteria we were using. But the – but these thresholds that 00:45:25.040 --> 00:45:29.910 I talk about, and the results I talk about, are looking at where – the dashed 00:45:29.910 --> 00:45:36.050 red line here is where in the histogram you see 99% of the data. 00:45:36.050 --> 00:45:39.830 And the red solid line is 95. So we actually use the distribution, 00:45:39.830 --> 00:45:43.740 not a mean or a standard deviation. - Okay. Thanks. 00:45:47.860 --> 00:45:50.359 - Thank you. That was an interesting talk. 00:45:50.359 --> 00:45:55.440 So these examples where you sort of discovered possible instances 00:45:55.440 --> 00:46:00.500 of triggered seismicity, and some of them were kind of dispersed, 00:46:00.500 --> 00:46:05.549 and some of them were kind of localized, if you put those localities on, 00:46:05.549 --> 00:46:09.220 say, geologic maps, does anything pop out? 00:46:09.220 --> 00:46:12.670 Do they coincide with faults of particular orientations, 00:46:12.670 --> 00:46:15.420 hydrothermal areas, anything like that? 00:46:16.120 --> 00:46:20.599 - We have not done that. So, in Yellowstone, they’re occurring 00:46:20.599 --> 00:46:24.920 where we have geothermal, hydrothermal systems. 00:46:24.920 --> 00:46:28.549 And, in Utah, probably not so much the case. 00:46:28.549 --> 00:46:30.900 We do have some geothermal systems in central Utah, 00:46:30.900 --> 00:46:33.619 but not in the north where we see these events. 00:46:33.620 --> 00:46:39.120 I’m not as familiar with ANZA as Debi is, so I can’t speak to that. 00:46:41.600 --> 00:46:47.560 [Silence] 00:46:47.560 --> 00:46:49.620 - Hi. Thanks, Kris. So maybe this is naive, 00:46:49.620 --> 00:46:53.480 and I’m not really up on all the dynamic triggering to date, but a lot of times, 00:46:53.490 --> 00:46:56.800 we see these nice waveforms where you can see the surface waves 00:46:56.800 --> 00:46:58.960 or whatever coming through. And then, when you filter at really 00:46:58.960 --> 00:47:02.160 high frequencies, you see the little events popping off, 00:47:02.160 --> 00:47:05.691 exactly timed with those dynamic waves. Can you – 00:47:05.700 --> 00:47:08.220 have you looked at any of that? Or, why or why not? 00:47:08.220 --> 00:47:11.819 Or do you see that? - Yeah. And that was what I showed 00:47:11.819 --> 00:47:16.440 for the first slide from Denali. We filtered the data. 00:47:16.440 --> 00:47:19.349 And I think that’s part of the question that I’m asking. 00:47:19.349 --> 00:47:24.490 Is that enough? Okay? So … - Right. So I – do you see it for some of 00:47:24.490 --> 00:47:28.320 these more – Denali, like you – and you were talking about – pretty clear-cut. 00:47:28.320 --> 00:47:31.680 So what about some of the other more questionable cases or … 00:47:31.689 --> 00:47:32.880 - I haven’t looked … - Because it [inaudible] 00:47:32.880 --> 00:47:35.509 bolster the argument, I guess. - Yeah. And I haven’t looked in detail 00:47:35.509 --> 00:47:41.670 at the waveforms, is the simple answer. For, like, the Mexico event 00:47:41.670 --> 00:47:46.170 in Yellowstone, that – we aren’t going to have data to do that with, right? 00:47:46.170 --> 00:47:49.980 Some of the older events, that data doesn’t exist. 00:47:49.980 --> 00:47:53.650 But for some of the newer events, we could definitely look at the data. 00:47:53.650 --> 00:47:58.880 And for Utah, we don’t filter the data, so the increases in the catalogs 00:47:58.880 --> 00:48:02.240 aren’t including those surface wave windows exactly. 00:48:05.020 --> 00:48:19.660 [Silence] 00:48:20.360 --> 00:48:23.720 - Well, maybe the answer to this question is already included in 00:48:23.720 --> 00:48:30.420 your definitions. [inaudible] statistics that I’m not – pardon me? 00:48:30.420 --> 00:48:33.120 Right to my mouth. Oh, okay. Sorry. Excuse me. 00:48:33.120 --> 00:48:35.040 Maybe the answer to this question is already 00:48:35.040 --> 00:48:40.540 included in some definitions, but when is an event an event? 00:48:40.540 --> 00:48:48.040 I mean, magnitude, orientation? You’re talking about events 00:48:48.040 --> 00:48:54.540 as if all events are equivalent. It seems – that’s what it seems to me. 00:48:54.540 --> 00:48:57.240 Maybe it’s something – as I say, in definitions 00:48:57.240 --> 00:49:00.080 or statistics that I’m not familiar with. 00:49:00.080 --> 00:49:02.280 - Sorry I’m laughing. Walter Arabasz has tried to teach 00:49:02.289 --> 00:49:06.260 me this lesson for the last 20 years. I’m talking about small earthquakes. 00:49:06.260 --> 00:49:09.089 - So that’s it. - So that’s it. So I’m talking about 00:49:09.089 --> 00:49:11.599 small earthquakes, so we have P waves and S waves. 00:49:11.599 --> 00:49:14.930 I mean, other people look for tremor, and I haven’t looked at any of that. 00:49:14.930 --> 00:49:17.710 But what I’m looking at are earthquakes that we’ve 00:49:17.710 --> 00:49:21.300 been located and that are in an earthquake catalog. 00:49:22.460 --> 00:49:26.360 And that’s what we’re counting. So we’re counting everything that’s 00:49:26.369 --> 00:49:30.760 in the catalog, which is a function of the magnitude of completeness. 00:49:30.760 --> 00:49:33.259 Or a detection level, depending on if we’re looking at 00:49:33.260 --> 00:49:36.520 the small time windows or the curated catalog. 00:49:36.520 --> 00:49:38.860 Does that answer the question? 00:49:40.240 --> 00:49:42.240 - Yeah. It answers that question. - Okay. 00:49:42.250 --> 00:49:46.660 - I guess I would ask also, why you do that. 00:49:46.660 --> 00:49:50.180 Is that enough? Is that sufficient? 00:49:51.980 --> 00:49:55.819 - I – well, I guess that’s what I was going after was to find 00:49:55.819 --> 00:50:00.380 dynamically triggered earthquakes. So that’s what I’m counting are the 00:50:00.380 --> 00:50:04.940 earthquakes that could potentially be dynamically triggered. 00:50:04.940 --> 00:50:07.240 And if you wanted to look at other events, you would have to 00:50:07.240 --> 00:50:11.359 process your data separately and define what those events are. 00:50:11.360 --> 00:50:15.140 And so I’ve not included that in this analysis. 00:50:17.940 --> 00:50:20.020 - Thank you. 00:50:21.620 --> 00:50:24.600 [Silence] 00:50:25.100 --> 00:50:30.200 - From what I recall from Landers, up in Mammoth Lakes, the threshold 00:50:30.210 --> 00:50:34.779 was something – calculated something like 1 bar dynamic stress level was – 00:50:34.779 --> 00:50:37.960 seemed to be sort of the magic number – something in that range. 00:50:37.960 --> 00:50:42.430 I just was wondering, have you looked at, for example, tidal triggering and 00:50:42.430 --> 00:50:47.900 how that would compare at much lower dynamic stress levels? 00:50:47.900 --> 00:50:51.279 - I personally have not looked at tidal triggering. 00:50:51.279 --> 00:50:54.170 But what we see from the dynamic earthquake triggering is you’re sort of 00:50:54.170 --> 00:50:59.299 at the same sort of stress level. So, at least from what we saw in 00:50:59.299 --> 00:51:02.839 Denali and Landers – so the same sort of magnitude of change. 00:51:02.840 --> 00:51:07.100 But I haven’t gone and looked for tidal changes, no. 00:51:11.920 --> 00:51:14.680 - Any more questions? 00:51:17.680 --> 00:51:23.080 Okay. Well, I guess we’ll wrap up. If anybody wants to join us for lunch 00:51:23.089 --> 00:51:25.260 with the speaker, please come on up and talk to us. 00:51:25.260 --> 00:51:27.960 I’m not sure that we’re going to go to the café because apparently 00:51:27.960 --> 00:51:31.640 they’re on limited menu right now. So if you want to come to lunch, 00:51:31.640 --> 00:51:34.080 come up and talk to us, and we’ll figure out what to do. 00:51:34.080 --> 00:51:35.880 And please join me in giving Kris another 00:51:35.880 --> 00:51:37.010 round of applause for a great talk. 00:51:37.010 --> 00:51:41.840 [Applause] 00:51:44.160 --> 00:51:50.820 [Silence]