WEBVTT Kind: captions Language: en-US 00:00:02.625 --> 00:00:06.554 [silence] 00:00:06.578 --> 00:00:09.460 Hi, everyone. Welcome to the Earthquake Science Center 00:00:09.460 --> 00:00:14.207 seminar series for January 27th, 2021. 00:00:14.207 --> 00:00:18.886 As a reminder, please turn off your cameras and mute your microphones. 00:00:18.886 --> 00:00:21.849 All of the functions are available through the menu bar that pops up 00:00:21.849 --> 00:00:24.619 when you hover over the bottom of your Teams window, or, at this point, 00:00:24.619 --> 00:00:27.652 everyone’s probably updated, and it’s up at the top. 00:00:27.652 --> 00:00:31.509 Live captioning is also available. Click the three-dot More button, 00:00:31.509 --> 00:00:34.769 and choose “turn on live captions.” 00:00:34.769 --> 00:00:36.760 Today’s speaker is Andy Michael. 00:00:36.760 --> 00:00:39.847 But first, we have a few announcements. 00:00:39.847 --> 00:00:42.808 Next week’s seminar will be by Leah Langer from the USGS, 00:00:42.808 --> 00:00:45.930 giving a talk entitled, Impact of 3D Structure 00:00:45.930 --> 00:00:50.440 on Static Green’s Functions for Slip Inversion. 00:00:50.440 --> 00:00:52.540 If you have recommendations for future seminar speakers 00:00:52.540 --> 00:00:55.080 this season – and remember, our pool of possible speakers 00:00:55.080 --> 00:00:59.332 has been greatly increased by the new virtual world that we live in. 00:00:59.332 --> 00:01:06.066 Feel free to email myself and/or Tamara Jeppson to nominate speakers. 00:01:06.066 --> 00:01:08.300 The next all-hands meeting for the Earthquake Science Center 00:01:08.333 --> 00:01:10.820 is on February 12th. Those involved will have gotten 00:01:10.820 --> 00:01:15.600 a calendar invite for that. The big news is that next week, 00:01:15.600 --> 00:01:18.220 the Earthquake Science Center is hosting the Northern California 00:01:18.220 --> 00:01:21.792 Earthquake Hazards Workshop. It will take place from Tuesday through 00:01:21.792 --> 00:01:25.722 Thursday, February 2nd through 4th. This will take the place of next week’s 00:01:25.722 --> 00:01:29.830 seminar. Registration for that is still open until Friday this week. 00:01:29.830 --> 00:01:33.930 And I think Susan or one of us may insert a link 00:01:33.930 --> 00:01:36.785 to the registration in the chat. 00:01:36.785 --> 00:01:41.190 Okay. So today’s speaker is Andy Michael from the 00:01:41.190 --> 00:01:44.229 Earthquake Science Center. If you have questions for Andy, 00:01:44.229 --> 00:01:48.180 you can either type them into the chat, and Tamara and I will field them 00:01:48.180 --> 00:01:51.330 and decide whether they’re appropriate to interrupt the speaker. 00:01:51.330 --> 00:01:55.200 Or you can raise your hand using the function in Teams. 00:01:55.200 --> 00:01:58.300 We will be monitoring the chat and reading out the questions, either, 00:01:58.300 --> 00:02:01.855 if they’re urgent, at the time, or we’ll save them for the end. 00:02:01.855 --> 00:02:08.149 When we read the questions at the end, feel free to ask the question yourself. 00:02:08.149 --> 00:02:10.100 You can either raise your hand or unmute yourself and 00:02:10.100 --> 00:02:15.030 turn on video to chime in. We all like seeing faces these days. 00:02:15.030 --> 00:02:18.370 With that, I will hand it over to Jeanne Hardebeck, 00:02:18.370 --> 00:02:22.400 who will be introducing Andy. - Hi. Thank you. 00:02:22.400 --> 00:02:25.920 It’s my pleasure to introduce Andy Michael to a crowd that 00:02:25.920 --> 00:02:32.310 probably mostly knows him already, but – so Andy did his undergrad at MIT 00:02:32.310 --> 00:02:35.950 and his Ph.D. at Stanford. And he came over to the Survey 00:02:35.950 --> 00:02:41.175 right after Stanford and has been with the Survey ever since. 00:02:41.175 --> 00:02:47.430 And, as a Ph.D. student, Andy developed a method for inverting 00:02:47.430 --> 00:02:52.160 earthquake focal mechanisms for stress, which is now a standard and widely 00:02:52.160 --> 00:02:58.990 used method for inverting for stress. And he’s also applied that method to 00:02:58.990 --> 00:03:02.580 a number of important problems, such as understanding how a large 00:03:02.580 --> 00:03:08.558 earthquake can change the stress around the area where it occurred. 00:03:08.558 --> 00:03:13.488 After that, he’s turned his attentions more towards earthquake forecasting, 00:03:13.488 --> 00:03:19.250 testing earthquake forecasting and predictions, and working on PSHA – 00:03:19.250 --> 00:03:23.569 probabilistic seismic hazard assessment. He and I are currently leading the 00:03:23.569 --> 00:03:27.849 development of the USGS Operational Aftershock Forecast product – a product 00:03:27.849 --> 00:03:32.910 that’s been live on the USGS website for a couple of years now, where we 00:03:32.910 --> 00:03:37.220 issue aftershock forecasts following magnitude 5 events in the U.S. 00:03:37.220 --> 00:03:42.319 On the more research-y side, he’s been working recently with Andrea Llenos 00:03:42.319 --> 00:03:48.957 on how to do forecasting and PSHA in areas of induced seismicity in swarms. 00:03:48.957 --> 00:03:53.879 And that’s the sort of work he’s going to be talking about today. 00:03:53.879 --> 00:03:57.670 Andy also serves on NEPEC, the National Earthquake Prediction 00:03:57.670 --> 00:04:02.030 Evaluation Council, which advises the USGS director on kind of 00:04:02.030 --> 00:04:06.769 all matters related to earthquake forecasts and earthquake predictions. 00:04:06.802 --> 00:04:10.379 And he’s had a number of service roles in – important roles in 00:04:10.379 --> 00:04:14.170 Seismological Society of America, including being the editor in chief 00:04:14.170 --> 00:04:17.910 of BSSA for many years, serving on the SSA board of directors 00:04:17.910 --> 00:04:21.246 and publication committee. 00:04:21.246 --> 00:04:26.900 One of Andy’s other interests is music, and he’s actually found ways to 00:04:26.900 --> 00:04:31.500 combine those interests in music and seismology and put together 00:04:31.500 --> 00:04:36.980 and gave a widely enjoyed talk called The Music of Earthquakes, 00:04:36.980 --> 00:04:41.621 that hopefully some of you have had the chance to see at some point. 00:04:41.621 --> 00:04:47.060 So today he’s going to be talking about his work on probabilistic seismic hazard 00:04:47.060 --> 00:04:53.020 assessment, and particularly a new method that he’s developed for dealing 00:04:53.020 --> 00:04:56.710 with situations where earthquakes are very clustered, which breaks down 00:04:56.710 --> 00:05:00.220 some of the usual assumptions that go into PSHA. 00:05:00.220 --> 00:05:02.957 So I will turn it over to Andy. 00:05:02.957 --> 00:05:06.527 - Okay. Thank you, Jeanne. Appreciate the very kind introduction. 00:05:06.527 --> 00:05:11.740 And I also want to thank Susan Garcia, Tamara Jeppson, and Austin Elliott 00:05:11.740 --> 00:05:16.160 for their work to lead the seminar and organize all of this. 00:05:16.160 --> 00:05:23.590 So, with that, I’ll share my screen and admit that I’m a little bit nervous about 00:05:23.590 --> 00:05:26.800 giving this talk because I think the audience is a combination of people 00:05:26.800 --> 00:05:30.669 who know far more about volcanoes, and particularly Kilauea, than I do 00:05:30.669 --> 00:05:35.050 and people who know far more about PSHA than I do. 00:05:35.050 --> 00:05:40.190 But I think this talk is an example of how we can start with a, you know, 00:05:40.190 --> 00:05:45.670 applied problem, which was developing the update to the National Seismic 00:05:45.670 --> 00:05:50.440 Hazard Model for Hawaii and come across some really interesting 00:05:50.440 --> 00:05:55.000 science to do in it. And so my pleasure – while I’m giving the talk, 00:05:55.000 --> 00:05:57.910 this is really a collaboration – very equal collaboration between 00:05:57.910 --> 00:06:02.449 myself and Andrea Llenos and is actually the subject of two papers – 00:06:02.449 --> 00:06:08.539 one on forecasting just the – really the – focused on the collapse 00:06:08.539 --> 00:06:11.880 of Kilauea, which you can see in the background of this slide. 00:06:11.880 --> 00:06:20.417 This is the post – a post-collapse picture of the central part of Kilauea caldera. 00:06:20.417 --> 00:06:25.919 And that paper, which is Llenos and Michael, is already in review in GRL. 00:06:25.919 --> 00:06:29.919 And another paper on the methodology, which I’m supposed to be writing, 00:06:29.919 --> 00:06:35.020 is still in preparation. So Andrea is ahead of me. 00:06:35.020 --> 00:06:37.610 We have a lot of acknowledgements to give. 00:06:37.610 --> 00:06:41.472 From HVO, people like Jefferson Chang in seismology, 00:06:41.472 --> 00:06:44.380 and Tina Neal, who is leading as their head, and Paul Okubo, 00:06:44.380 --> 00:06:49.160 who is now at University of Hawaii. Brian Shiro really gave us a lot of 00:06:49.160 --> 00:06:52.066 help understanding the volcano. And I put an et al. there because, 00:06:52.066 --> 00:06:57.199 for instance, pictures like this, which are looking from over the collapse, 00:06:57.199 --> 00:07:00.880 which is sort of a little bit behind the camera, back at HVO, which is actually 00:07:00.880 --> 00:07:05.964 under the word “Acknowledgments” here, were taken by many, many people 00:07:05.964 --> 00:07:10.520 working on the 2018 eruption and the volcano before and afterwards. 00:07:10.520 --> 00:07:13.210 I also want to point out that, while HVO is here, and you can see 00:07:13.210 --> 00:07:15.850 its sort of parking lot here, we’re going to be looking at data 00:07:15.850 --> 00:07:19.530 from a seismometer that’s in this sort of open area here. 00:07:19.530 --> 00:07:25.180 So a little bit – not quite at HVO, a little further away, but just 00:07:25.180 --> 00:07:29.110 by a couple hundred meters. From the Volcano Science Center, 00:07:29.110 --> 00:07:32.558 gotten a lot of help from Kyle Anderson, Ed Brown, 00:07:32.558 --> 00:07:35.792 Alicia Hotovec-Ellis, and Emily Montgomery-Brown. 00:07:35.792 --> 00:07:40.363 And I think one of the things I really miss about being out of the office is 00:07:40.363 --> 00:07:46.582 not being across the hall [chuckles] from Kyle, Alicia, and Emily. 00:07:46.582 --> 00:07:51.729 I see a lot of my closer colleagues on Teams a lot, 00:07:51.729 --> 00:07:54.560 but I haven’t seen you guys for a while. 00:07:54.560 --> 00:07:57.410 The Geologic Hazards Science Center – basically, a long list of people from 00:07:57.410 --> 00:08:05.675 the National Seismic Hazard Model. So Ned, Nico, Dan McNamara, 00:08:05.675 --> 00:08:09.121 who is now a consultant, Morgan Moschetti, Chuck Mueller, 00:08:09.121 --> 00:08:13.750 Mark Petersen, Peter Powers, and Allison Shumway have been key. 00:08:13.750 --> 00:08:17.830 We decided to put Fred Klein and Tom Wright on a line by themselves 00:08:17.830 --> 00:08:23.240 because their truly voluminous and exhaustive works on Kilauea were 00:08:23.240 --> 00:08:27.847 critical to our starting to understand the volcano at all. 00:08:27.847 --> 00:08:30.770 And I’m really glad – so I noticed that Tom is on here. 00:08:30.770 --> 00:08:36.909 And finally, Jack Baker at Stanford, who has put some great notes online 00:08:36.909 --> 00:08:39.996 to help me really understand how PSHA actually works. 00:08:39.996 --> 00:08:43.039 And also lent me some chapters from his upcoming textbook 00:08:43.039 --> 00:08:47.125 that also helped me along the way. 00:08:48.558 --> 00:08:51.939 So let’s just locate ourselves in the 2018 eruptions. 00:08:51.939 --> 00:08:56.879 This is from a Tina Neal et al. Science paper on the overall eruption. 00:08:56.879 --> 00:09:01.730 So the island of Hawaii is here. And we’re going to look – this larger 00:09:01.730 --> 00:09:07.277 inset is what is sometimes called sort of the south – well, the south flank is here. 00:09:07.309 --> 00:09:12.360 But this – we’re looking at this part of the island. Kilauea Caldera is here, 00:09:12.360 --> 00:09:14.999 and the lava comes up, and it then travels down through – 00:09:14.999 --> 00:09:19.269 underground through the Upper, Middle, and East Rift Zones. 00:09:19.269 --> 00:09:23.379 And then most of the great photographs you saw of lava spewing out of the 00:09:23.379 --> 00:09:27.574 ground and fountaining come from the lower East Rift Zone here, 00:09:27.574 --> 00:09:36.949 so fairly far away from Kilauea Caldera. And there’s a map of the eruptions here. 00:09:36.949 --> 00:09:40.139 What what we’re going to look at are actually the explosive earthquakes 00:09:40.139 --> 00:09:46.347 and the collapse of Kilauea Caldera, or at least part of the caldera, 00:09:46.347 --> 00:09:50.980 and the damage it caused. 00:09:50.980 --> 00:09:53.699 So the next thing is going to be a time lapse. 00:09:53.699 --> 00:09:55.925 We’re looking from HVO. 00:09:55.962 --> 00:10:00.660 This is in April – this is April 14th, 2018. 00:10:00.660 --> 00:10:04.600 So this is the inner caldera, or Halemaʻumaʻu. 00:10:04.600 --> 00:10:07.639 The full caldera is much larger than this. 00:10:07.639 --> 00:10:11.399 And you can see, there was already lava and some steaming going on. 00:10:11.399 --> 00:10:13.339 This had been going on for quite a while. 00:10:13.339 --> 00:10:15.139 And we’re now going to do a time lapse in 23 seconds. 00:10:15.139 --> 00:10:19.970 It’s going to take us through August 20th, and you’ll see this area 00:10:19.970 --> 00:10:25.449 start dropping down and, on some of these scarps out here, a very large 00:10:25.480 --> 00:10:30.259 amount of displacement. The total down-dropping is 500 meters 00:10:30.259 --> 00:10:34.559 in a few months. Actually, it mostly takes place in a month. 00:10:36.613 --> 00:10:39.420 So now we’re getting to the beginning of May when things are going to 00:10:39.420 --> 00:10:42.259 start really happening. There’s explosions. 00:10:42.259 --> 00:10:43.839 Ash hiding things a lot. 00:10:43.839 --> 00:10:46.941 And you can start seeing [laughs] – stuff is starting to drop out. 00:10:46.941 --> 00:10:52.199 If you keep your eye over here, you’ll see this huge white scarp open up. 00:10:53.378 --> 00:10:59.410 And, by the end – so now we’re at August 20th, the scenery has changed 00:10:59.410 --> 00:11:03.410 a lot, and, as Andrea likes to say, you can’t watch this often enough. 00:11:03.410 --> 00:11:06.250 So let’s do it one more time. 00:11:08.917 --> 00:11:16.871 [silence] 00:11:16.871 --> 00:11:22.000 So we’re in June now when the collapse accelerates. 00:11:22.949 --> 00:11:28.899 And the end of July. And it’s basically over by a few days into July. 00:11:29.847 --> 00:11:33.363 Whoops. [laughs] We didn’t mean to play it a third time, 00:11:33.363 --> 00:11:37.449 but sometimes control of PowerPoint gets beyond me. 00:11:37.449 --> 00:11:41.420 Okay, so let’s talk about the overall caldera and the collapse again. 00:11:41.420 --> 00:11:45.800 So this is a Lidar image taken out of Tina Neal’s paper again. 00:11:45.800 --> 00:11:50.369 HVO is here. The seismometer I mentioned, UWE, is here. 00:11:50.369 --> 00:11:52.850 And you can see the outline, in this Lidar image, 00:11:52.850 --> 00:11:55.808 of the overall caldera of Kilauea. 00:11:55.808 --> 00:12:00.579 This caldera actually formed about 500 years ago in a very large collapse 00:12:00.579 --> 00:12:05.109 and then largely has filled in. And then here is the – sort of the 00:12:05.109 --> 00:12:09.683 inner caldera. And this is a really interesting place to me. 00:12:09.683 --> 00:12:13.660 Several years back, Stephanie and I – a lot of you know my wife, 00:12:13.660 --> 00:12:16.332 Stephanie Ross, in the marine program – works on tsunamis. 00:12:16.332 --> 00:12:20.902 So we were – we did a large hike around and across Kilauea Caldera. 00:12:20.902 --> 00:12:25.569 And we came out of Kilauea Iki – another caldera that’s right here – 00:12:25.569 --> 00:12:28.959 sort of an offshoot. And you can come down, and there’s a trail that 00:12:28.959 --> 00:12:33.519 starts about here and goes sort of north of this blue transect line. 00:12:33.551 --> 00:12:39.179 And this is a very long, desolate hike that goes slightly uphill when we did it. 00:12:39.179 --> 00:12:42.230 And we got up to, eventually, here. Hiked around – there’s another trail 00:12:42.230 --> 00:12:44.910 that will take you around to this sort of public overlook. 00:12:44.910 --> 00:12:48.183 This is actually a parking lot. 00:12:48.183 --> 00:12:51.559 And then, you know, finished the transect across and then went back 00:12:51.559 --> 00:12:55.675 to hiking around the outside of the – so here’s what it looked like – 00:12:55.675 --> 00:13:00.239 that’s a 2009 Lidar image. Here it is at the end of the collapse. 00:13:00.239 --> 00:13:02.259 And it’s dramatically different. 00:13:02.259 --> 00:13:05.430 Our hike would now take us down a – at this point – 00:13:05.430 --> 00:13:10.670 let me add the cross-sections. So, as our hike – we got to this point, 00:13:10.670 --> 00:13:14.089 you go down about an 85- to 100-meter scarp. 00:13:14.089 --> 00:13:18.316 Now, instead of going uphill, you’re going downhill. 00:13:18.316 --> 00:13:21.832 I’m sorry. I suppose I should turn on the laser pointer. 00:13:21.832 --> 00:13:24.220 Okay, now you should be able to see my pointer better. 00:13:24.220 --> 00:13:27.850 You’re now going downhill, and our hike would have taken us 00:13:27.850 --> 00:13:30.519 to about this point, at which point, you just drop down another 00:13:30.519 --> 00:13:35.459 100 or 200 meters, and hopefully not more, before the old hike would 00:13:35.459 --> 00:13:40.350 have taken us around in a circle. The parking lot and the overlook 00:13:40.350 --> 00:13:44.259 from Halemaʻumaʻu is down – also dropped down into the collapse, 00:13:44.259 --> 00:13:46.980 which took place on these ring faults. 00:13:46.980 --> 00:13:55.691 So the – this is a collapse of – total volume of about 0.83 cubic kilometers. 00:13:55.691 --> 00:13:59.100 So, while there’s a lot of the caldera that you can see is still undisturbed – 00:13:59.100 --> 00:14:03.470 it’s not as big as the collapse 500 years ago – it’s a pretty big event 00:14:03.470 --> 00:14:07.527 and probably the largest collapse in the last 200 years. 00:14:08.519 --> 00:14:15.059 But, of course, I’m not, you know, professionally interested in the change 00:14:15.059 --> 00:14:18.660 in the topography as the earthquakes interest me. 00:14:18.660 --> 00:14:22.369 And I remember that there was a really great video of the earthquakes that was 00:14:22.369 --> 00:14:27.589 done by Jefferson Chang from HVO, and he first showed it at SSA. 00:14:27.589 --> 00:14:30.808 At least, the first time I saw it was at SSA in 2019. 00:14:30.808 --> 00:14:34.290 And I borrowed it from him. He was very gracious to let me 00:14:34.290 --> 00:14:37.105 use it for this video. And not only are we going to see 00:14:37.105 --> 00:14:41.889 map animation of the earthquakes at Kilauea Caldera and down the entire 00:14:41.889 --> 00:14:46.619 East Rift Zone, and there’s a magnitude 6.9 that will happen here that was 00:14:46.619 --> 00:14:51.441 part of this eruptive sequence – that’s this earthquake here, 00:14:51.441 --> 00:14:55.029 but he also sonofied the seismogram – a continuous seismogram from this 00:14:55.029 --> 00:15:00.239 station, RIMD. And so we’ll be hearing the earthquakes. 00:15:00.239 --> 00:15:02.600 And one thing I really want you to listen for as we start playing 00:15:02.600 --> 00:15:06.429 through it – as this red line moves through – is these two earthquakes here, 00:15:06.429 --> 00:15:11.669 which is a magnitude 5.4 foreshock to the 6.9, and the 6.9 are extremely sharp, 00:15:11.669 --> 00:15:14.429 impulsive earthquakes. And, when we get to these caldera 00:15:14.429 --> 00:15:18.019 collapse events, of which there are many, listen to the fact that they’re 00:15:18.019 --> 00:15:21.339 not as impulsive, even though they’re very close to the station. 00:15:21.339 --> 00:15:23.824 You don’t get all the high-frequency content. 00:15:23.850 --> 00:15:27.035 And that’s a very interesting part of these earthquakes. 00:15:27.035 --> 00:15:32.277 Now, to show you this, I’m going to have to jump out of the PowerPoint 00:15:32.277 --> 00:15:39.000 and go to QuickTime because this video does not play well in … 00:15:44.363 --> 00:15:48.079 So you should be able to hear it, and I will also be talking over it. 00:15:48.079 --> 00:15:50.779 And I’m going to fast-forward at times because it’s a three-minute video, 00:15:50.779 --> 00:15:52.990 and we don’t need to watch all of it today. 00:15:52.990 --> 00:15:56.429 But particularly remember to listen for these very sharp earthquakes 00:15:56.429 --> 00:16:01.105 and the difference in the caldera collapse magnitude 5 events. 00:16:01.105 --> 00:16:07.722 [static sounds] 00:16:07.756 --> 00:16:12.832 [explosions] 00:16:12.864 --> 00:16:16.439 All right, so you can get that sort of sound in your head – 00:16:16.439 --> 00:16:18.799 those very sharp events. And we will come up here 00:16:18.799 --> 00:16:21.375 on the first of the caldera collapse events. 00:16:21.375 --> 00:16:24.066 [periodic explosion sounds] 00:16:24.066 --> 00:16:26.750 Around May 17. 00:16:26.750 --> 00:16:31.254 [static and periodic explosion sounds] 00:16:31.254 --> 00:16:41.691 [more frequent explosion sounds] 00:16:41.691 --> 00:16:46.799 So a lot of magnitude 5 events happening. 00:16:46.799 --> 00:16:49.027 As we start looking at these, notice the seismicity, which is 00:16:49.027 --> 00:16:51.709 showing – total number of earthquakes in shown in light blue – 00:16:51.709 --> 00:16:54.809 ramps up to magnitude 5 and then ends. 00:16:54.809 --> 00:16:58.589 [explosion sounds] 00:16:58.589 --> 00:17:02.535 So, unlike aftershocks, there’s a pause after the biggest earthquakes 00:17:02.535 --> 00:17:06.250 in this sequence within the caldera. 00:17:06.250 --> 00:17:14.332 [explosion sounds] 00:17:14.332 --> 00:17:17.058 And they start happening basically daily now. 00:17:17.058 --> 00:17:20.316 [explosion sounds] 00:17:20.316 --> 00:17:25.750 And I’m actually going to speed ahead because there’s many, many of these. 00:17:25.750 --> 00:17:27.740 So you lose the sound for a while. 00:17:27.740 --> 00:17:32.292 Just imagine being a few kilometers from these sort of magnitude 5 00:17:32.292 --> 00:17:37.559 explosive earthquakes on a daily basis. Let’s listen to a few more of them. 00:17:37.559 --> 00:17:38.753 [explosion sounds] 00:17:38.753 --> 00:17:41.000 They haven’t changed. 00:17:41.000 --> 00:17:44.801 [explosion sounds] 00:17:44.801 --> 00:17:49.113 [inaudible] pattern of seismicity leading up these events. 00:17:49.113 --> 00:17:52.440 And then finally, early in August, we’re going to have the last two of these. 00:17:52.440 --> 00:17:58.285 [explosion sounds] 00:17:58.285 --> 00:18:01.988 And then the sequence dies away at this point. 00:18:01.988 --> 00:18:05.503 [quieter explosion sounds] 00:18:05.503 --> 00:18:07.917 [video stops] And notice that there was a total of 00:18:07.917 --> 00:18:12.220 [chuckles] 58,000 earthquakes in this animation over a few months. 00:18:12.220 --> 00:18:17.830 It’s really an impressive sequence and also an impressive job of data analysis 00:18:17.830 --> 00:18:24.246 by the seismologists such as Jefferson and Brian Shiro at HVO. 00:18:25.449 --> 00:18:27.894 All right. So back to the PowerPoint. 00:18:27.894 --> 00:18:31.750 Let’s see if I can do all these things smoothly. 00:18:32.762 --> 00:18:36.699 And we’re on the laser pointer. Yeah. 00:18:38.082 --> 00:18:40.730 Okay, so what happened at HVO? 00:18:40.730 --> 00:18:43.610 So here’s HVO. Here’s the observation tower 00:18:43.610 --> 00:18:49.886 where the previous video was taken from – the time lapse. 00:18:49.886 --> 00:18:52.929 And you – and coming to work in the morning, and you have explosive 00:18:52.929 --> 00:18:58.110 eruptions going on not far away. So that gives you – actually this makes 00:18:58.110 --> 00:19:01.950 it looks almost like HVO was even closer than it – than it might be 00:19:01.950 --> 00:19:05.309 if you look at it from above. But this is pretty menacing looking. 00:19:05.309 --> 00:19:09.220 There was damage at HVO from the magnitude 6.9 earthquake, 00:19:09.220 --> 00:19:13.059 which was further away. But looking at photos that 00:19:13.059 --> 00:19:16.824 Ed Brown from the Volcano Science Center lent me, 00:19:16.824 --> 00:19:21.610 clearly there’s progressive damage and additional damage from 00:19:21.610 --> 00:19:24.210 the sequence of magnitude 5s. So some of the damage 00:19:24.210 --> 00:19:29.240 were these very large floor offsets and tilts. 00:19:29.240 --> 00:19:31.419 This is a photo that – there was apparently some cracking in these 00:19:31.419 --> 00:19:35.753 columns from the 6.9, but it got worse. So this is a support column. 00:19:35.753 --> 00:19:39.460 You can see it’s spalling away. 00:19:39.460 --> 00:19:43.090 A table here that collapsed. Some of the things that were on it 00:19:43.090 --> 00:19:47.660 and attached to it in one of the labs. And things thrown off the shelves. 00:19:47.660 --> 00:19:50.549 And this is their library. There’s a lot of discussion – 00:19:50.549 --> 00:19:53.360 and these earthquakes did not have the highest frequencies in them, 00:19:53.360 --> 00:19:56.870 but let’s be clear that they had – they still produced strong shaking 00:19:56.870 --> 00:20:01.679 that threw stuff around at HVO. I think it’s a little hard for me to know 00:20:01.679 --> 00:20:05.100 fully exactly what happened in the 6.9 and what happened later, 00:20:05.100 --> 00:20:08.970 but for instance, this picture of the library, there are other pictures where 00:20:08.970 --> 00:20:11.929 stuff hadn’t been thrown away and – thrown off, and I saw pictures 00:20:11.929 --> 00:20:14.710 from sometime in June. I like to point out that BSSA 00:20:14.710 --> 00:20:17.699 seems to largely still be on the shelf. 00:20:18.878 --> 00:20:21.860 All right. So earthquakes like this at caldera collapses are not unique. 00:20:21.860 --> 00:20:24.919 One of the really famous collapses is in the Galapagos, 00:20:24.919 --> 00:20:31.070 island of Fernandina, in 1968. There were 75 magnitude 4.5 events, 00:20:31.070 --> 00:20:38.210 and, in a paper that John Filson led in JGR 1973 – so here’s the earthquakes. 00:20:38.210 --> 00:20:40.409 Magnitudes up to 5 – well, I think a little above that, 00:20:40.409 --> 00:20:45.839 but this is the magnitude 5 line. This is for a week in June 1968 00:20:45.839 --> 00:20:49.279 showing essentially the same thing. A lot of little earthquakes leading up 00:20:49.279 --> 00:20:53.889 to 5s. And he suggested that there was some sort of tidal periodicity going on. 00:20:53.889 --> 00:20:58.750 These are both water and Earth tides. 00:20:59.840 --> 00:21:03.230 Nearby – I don’t know if that really holds up or not. 00:21:03.230 --> 00:21:05.310 The problem with studying this sequence is that the 00:21:05.310 --> 00:21:10.510 closest seismometer was on South America and – 00:21:10.510 --> 00:21:15.269 I believe in Ecuador, and so you don’t have any close-in records. 00:21:15.269 --> 00:21:20.074 Here’s another collapse more recently from Iceland. 00:21:20.074 --> 00:21:25.285 And it had 77 magnitude greater than 5 events from this paper 00:21:25.285 --> 00:21:32.330 by Gudmundsson in Science. And here is a plot of M-w 00:21:32.330 --> 00:21:36.560 versus time for several months. And we can see that there’s 00:21:36.560 --> 00:21:39.580 a lot of magnitude 5 events. The blue and the red symbols 00:21:39.580 --> 00:21:42.871 have to do with the locations around the caldera. 00:21:42.871 --> 00:21:47.649 And they also had caldera subsidence measured by GPS. 00:21:47.649 --> 00:21:50.480 So you can see that some of the subsidence events – now we can 00:21:50.480 --> 00:21:52.840 see they happen with the earthquakes happen. 00:21:52.840 --> 00:21:55.250 The view of this isn’t as good as the view at Kilauea. 00:21:55.250 --> 00:21:59.309 Because here is an aerial photo of the volcano. 00:21:59.309 --> 00:22:03.080 The caldera is shown here, and it’s ice-filled. 00:22:03.080 --> 00:22:06.950 So [chuckles] we’re having to put the GPS station on top of the ice in 00:22:06.950 --> 00:22:11.519 the middle of the caldera. We can’t just see exactly what was happening. 00:22:11.519 --> 00:22:17.240 So the Kilauea collapse is really unique in terms of the quality of the data. 00:22:17.240 --> 00:22:20.169 So we want to assess the hazard from these collapse earthquakes 00:22:20.169 --> 00:22:24.580 for the 2021 NSHM update. Our first goal was to try to build 00:22:24.580 --> 00:22:28.000 a physical model of these events. And we spent a lot of time looking at 00:22:28.000 --> 00:22:33.110 the data that went into, for instance, this figure from the Neal et al. paper, 00:22:33.110 --> 00:22:38.500 such as a GPS record of the collapse from a station that’s very close to it, 00:22:38.500 --> 00:22:44.799 and actually was then lost once the collapse enveloped it, and then 00:22:44.799 --> 00:22:48.910 another station that was further out. There’s also tilt meters that you can see 00:22:48.910 --> 00:22:53.179 the individual collapse events each day. And the earthquake counts. 00:22:53.179 --> 00:22:56.610 The problem we ran into is, while you might want to tie these earthquakes to, 00:22:56.610 --> 00:23:00.389 say, the slip on the ring faults that actually brought the caldera down, 00:23:00.389 --> 00:23:05.605 that’s not what was happening here. These earthquakes are negative 00:23:05.605 --> 00:23:09.720 implosions, or negative vector – comes in with linear vector dipoles. 00:23:09.720 --> 00:23:12.840 They’re essentially the trigger at the beginning of the collapse. 00:23:12.840 --> 00:23:16.700 Most of the slip on the ring faults seems to be aseismic. 00:23:16.700 --> 00:23:21.090 And so this would be like trying to do a physical model of magnitude, you 00:23:21.090 --> 00:23:26.947 know, 7 or 8 or 9 earthquakes with only the first few seconds of that earthquake. 00:23:26.972 --> 00:23:32.100 And so we spent a long time trying to reprocess the data in varied ways to 00:23:32.100 --> 00:23:34.410 see if we could tie, for instance, the size of the daily collapse, 00:23:34.410 --> 00:23:38.730 the size of the earthquake, and there’s really no good relationship there. 00:23:38.730 --> 00:23:43.316 And so we had to move on to trying to build a statistical model. 00:23:43.316 --> 00:23:45.539 And so I want to go over how we did that and then 00:23:45.539 --> 00:23:48.042 how we applied it to PSHA. 00:23:48.925 --> 00:23:55.289 So HVO, nicely, puts on a updated table of Kilauea historical activity. 00:23:55.289 --> 00:23:59.878 They updated it – last time we looked at it was in June. 00:23:59.878 --> 00:24:04.590 And this takes into account a lot of previous work, including, you know, 00:24:04.590 --> 00:24:08.722 compilations by Fred Klein and Tom Wright. 00:24:08.722 --> 00:24:13.630 And so we went through this table and we – you can’t read it here, I’m sure, 00:24:13.630 --> 00:24:17.250 but what we did was we looked for summit subsidence events. 00:24:17.250 --> 00:24:19.240 There’s a lot of language in this table. 00:24:19.240 --> 00:24:22.009 There are occasionally things called “caldera collapses.” 00:24:22.009 --> 00:24:25.386 Those are usually also called “summit subsidence events.” 00:24:25.386 --> 00:24:29.470 But a lot of subsidence events are not called collapses. 00:24:29.470 --> 00:24:32.799 So what we decided was we were going to call something a collapse 00:24:32.799 --> 00:24:37.919 if it was a summit subsidence event that had non-elastic deformation 00:24:37.919 --> 00:24:40.230 as shown by the existence of collapse earthquakes, 00:24:40.230 --> 00:24:44.777 or at least earthquakes in the caldera during the collapse. 00:24:44.777 --> 00:24:48.429 From 1906 onwards, from when we really have good sort of continuous 00:24:48.429 --> 00:24:55.639 observations of Kilauea, there were 16 summit subsidence events in that table. 00:24:55.639 --> 00:25:00.429 And we have an earthquake catalog that’s been compiled, both by people 00:25:00.429 --> 00:25:06.070 at HVO and then also was re-processed to try to make it as consistent as possible 00:25:06.070 --> 00:25:10.600 by Chuck Mueller for the NSHM. And, in 114 years, there were 00:25:10.600 --> 00:25:20.253 six seismogenic collapses – in 1924, ’55, ’60, ’69, ’77, and 2018 – 00:25:20.286 --> 00:25:23.090 that occurred with seismicity that was likely to be in the caldera. 00:25:23.090 --> 00:25:25.149 Obviously, if we go back further in time, some of the 00:25:25.149 --> 00:25:30.199 locations are less certain. For instance, here is, for the 1924 00:25:30.199 --> 00:25:36.580 collapse, a magnitude time plot – magnitude here and time across here. 00:25:36.580 --> 00:25:42.249 And we see that these inner dotted lines are the actual time of the collapse, 00:25:42.249 --> 00:25:47.039 and there were a lot of earthquakes occurring up to – not up to – 00:25:47.039 --> 00:25:50.100 almost up to magnitude 5. But all these earthquakes were 00:25:50.100 --> 00:25:54.240 given the same location here on sort of the rim of the caldera. 00:25:54.240 --> 00:25:57.830 So we don’t necessarily have good locations, but still, it seems consistent 00:25:57.830 --> 00:26:00.940 this was some sort of collapse. And, actually, this one is definitely 00:26:00.940 --> 00:26:04.840 called a collapse in everyone’s writing about it. 00:26:04.840 --> 00:26:09.030 So what we can do is we can model the six collapses as a Poisson rate – 00:26:09.030 --> 00:26:13.999 a Poisson distribution of 2.6 collapses every 50 years. 00:26:13.999 --> 00:26:16.789 And we have tested the sequence of six collapses, 00:26:16.789 --> 00:26:19.110 and we cannot reject the Poisson model for them. 00:26:19.110 --> 00:26:23.144 So they may be random, independent collapses. 00:26:23.144 --> 00:26:25.389 The next thing we need to know – because what we really want are the 00:26:25.389 --> 00:26:28.669 number of earthquakes due to collapses, is we need to know the – you know, 00:26:28.669 --> 00:26:31.289 the forecasted number of earthquakes per collapse. 00:26:31.289 --> 00:26:36.590 So how many magnitude 4 or 5 earthquakes occur per collapse? 00:26:36.590 --> 00:26:39.970 So often, we would try to infer this from extending things out 00:26:39.970 --> 00:26:43.580 on a magnitude-frequency plot, such as we have here, where we 00:26:43.580 --> 00:26:47.970 have the number of earthquakes. And this is in the 2018 collapse 00:26:47.970 --> 00:26:51.791 versus magnitude. And this does not fit the sort of nice, 00:26:51.791 --> 00:26:57.625 straight line we like to see usually on Gutenberg-Richter plots for PSHA. 00:26:58.863 --> 00:27:02.799 So it’s hard to extrapolate. What we really have here is a lot of 00:27:02.799 --> 00:27:07.550 earthquakes just over magnitude 5 – around magnitude 5.3. 00:27:07.550 --> 00:27:09.740 And, of course, the magnitudes of the earlier earthquakes 00:27:09.740 --> 00:27:12.919 are much more uncertain. So what we did was, we just tabulated 00:27:12.919 --> 00:27:16.580 the number of earthquakes produced in each of the seismic collapses, 00:27:16.580 --> 00:27:21.100 and then we modeled that with a negative binominal distribution. 00:27:21.100 --> 00:27:24.917 We like it – use this distribution. First of all, it’s a discrete distribution. 00:27:24.917 --> 00:27:31.019 It models – it gives us probabilities of the numbers of integers from 00:27:31.019 --> 00:27:35.285 zero and greater, which is the same thing the Poisson distribution does. 00:27:35.285 --> 00:27:38.259 And it’s often used to model earthquake clustering because it provides more 00:27:38.259 --> 00:27:43.503 variability – a wider range of outcomes than you get from a Poisson model. 00:27:43.503 --> 00:27:47.129 So in 1924 – we already showed this magnitude-time plot. 00:27:47.129 --> 00:27:49.269 Notice that all the earthquakes were fixed, 00:27:49.269 --> 00:27:53.207 except for one or two, to a zero depth 00:27:53.243 --> 00:27:57.831 in fixed locations. There were 24 magnitude 4 and aboves. Two of them 00:27:57.831 --> 00:28:04.535 were greater than magnitude 4.5, and none were above magnitude 5. 00:28:04.568 --> 00:28:10.417 In 2018, we have much more exact locations in terms of depths, 00:28:10.458 --> 00:28:16.605 and locations, but there were 85 4s and greater, 54 5s and greaters. 00:28:16.605 --> 00:28:19.221 And I’m just going to tell you – not show all the maps – that, in all the 00:28:19.221 --> 00:28:23.699 other seismic collapses, there were no magnitude 4 or greater earthquakes. 00:28:23.699 --> 00:28:26.839 They were magnitude 2s and 3s. 00:28:27.503 --> 00:28:31.200 So now, to get the probability of the number of events per collapse, 00:28:31.200 --> 00:28:35.889 we tabulate the number of events – and so, for magnitude 4s, 00:28:35.889 --> 00:28:40.179 we have 24, four zeroes, and 85. And, for magnitude 5, 00:28:40.179 --> 00:28:44.191 we have five zeroes and 54. And we use the negative 00:28:44.191 --> 00:28:47.887 binomial distribution. And so, in each of these plots, starting here 00:28:47.887 --> 00:28:51.830 with magnitude 4, we can see the number of magnitude 4 events 00:28:51.830 --> 00:28:55.167 in a collapse versus the cumulative probability. 00:28:55.167 --> 00:29:00.029 So four of the six times, or two-thirds, there were zero. 00:29:00.029 --> 00:29:02.753 And then we have the one time with 24. 00:29:02.753 --> 00:29:06.902 And then the one time with 85. And then the model – the negative 00:29:06.902 --> 00:29:11.220 binomial model, you know, comes close to this and smooths it out 00:29:11.220 --> 00:29:14.600 so that we could have the possibility of having all the intervening numbers, 00:29:14.600 --> 00:29:17.425 or even more earthquakes. 00:29:17.425 --> 00:29:20.100 Obviously, we don’t have a lot of data, so this is uncertain, but we do 00:29:20.100 --> 00:29:27.816 carry through that uncertainty in the distributions to our results. 00:29:27.816 --> 00:29:32.332 And here is the fit for the magnitude 5 and greater earthquakes. 00:29:34.605 --> 00:29:37.649 So, as I said, we have the possibility of more earthquakes, but we wanted to 00:29:37.649 --> 00:29:42.470 put some maximum number on here. And what we did was we looked at, 00:29:42.470 --> 00:29:45.649 what was the biggest collapse that could happen if the magma body 00:29:45.649 --> 00:29:49.740 under Kilauea doesn’t radically change. 00:29:49.740 --> 00:29:52.690 So basically, the idea of these collapses is, you have a 00:29:52.690 --> 00:29:59.019 magma body here. This is depth. And this is distance across. 00:29:59.019 --> 00:30:01.320 And the collapse is – you know, there’s some sort of withdrawal 00:30:01.320 --> 00:30:04.749 of magma here – you know, the eruption that was taking place – 00:30:04.749 --> 00:30:07.527 and basically is a piston that this drops down. 00:30:07.527 --> 00:30:10.610 And so the maximum collapse that can take place is essentially the volume 00:30:10.610 --> 00:30:14.988 that’s above the magma chamber, which we estimated at being 00:30:14.988 --> 00:30:23.183 about 2.2 cubic kilometers. The 2018 collapse was about 0.825 – 00:30:23.183 --> 00:30:27.669 that’s a pretty exact number. There’s certainly uncertainty in that. 00:30:27.669 --> 00:30:31.519 And so, if we just do a ratio of the number of earthquakes to the number – 00:30:31.519 --> 00:30:36.240 the volume of possible collapses, and then round up a bit, we concluded 00:30:36.240 --> 00:30:39.700 that we would allow up to 300 magnitude 4-plus events 00:30:39.700 --> 00:30:47.839 happen in any single collapse. This is an extremely uncertain number. 00:30:47.839 --> 00:30:50.824 It’s a back-of-the-envelope sort of calculation. 00:30:50.824 --> 00:30:53.639 But we have looked at the sensitivity of our results to this number, 00:30:53.639 --> 00:30:57.419 and they’re not very sensitive to it all. It is a parameter that has the 00:30:57.419 --> 00:31:01.169 least control over the hazard. And so we’re not too worried 00:31:01.169 --> 00:31:03.289 about it, but we do think it’s a good idea not just to let there 00:31:03.289 --> 00:31:06.750 be an infinite number of events. 00:31:07.644 --> 00:31:10.000 Okay, so we have a input collapse rate. 00:31:10.000 --> 00:31:12.909 That was the Poisson model at 2.6 for 50 years. 00:31:12.909 --> 00:31:16.722 And we have these negative binomial distributions for the event rates. 00:31:16.722 --> 00:31:19.129 So we have the Poisson distribution of collapses. 00:31:19.129 --> 00:31:24.490 That’s going to be the probably, sub u, of u. And the reason I use u is it’s for 00:31:24.490 --> 00:31:29.105 the probability of underlying processes. That’s what’s driving the system. 00:31:29.105 --> 00:31:33.570 So the p-sub-u is that probability. We’re using a Poisson model in this 00:31:33.570 --> 00:31:37.850 case – it doesn’t always have to be Poissonian – with a rate, lambda. 00:31:37.850 --> 00:31:41.700 And then we need to have the probability of the number of 00:31:41.700 --> 00:31:44.529 earthquakes – and this is the probability of the response to the underlying 00:31:44.529 --> 00:31:48.669 process, p-sub-r for response. The number of earthquakes 00:31:48.669 --> 00:31:51.850 due to one collapse. And that’s the negative binomials 00:31:51.850 --> 00:31:55.769 that we saw in the previous slides. And the parameters are r and p, 00:31:55.769 --> 00:31:59.410 which are shape parameters for the negative binomial distribution. 00:31:59.410 --> 00:32:03.159 And then, Nmax, which we went over as a cap that fortunately 00:32:03.159 --> 00:32:07.289 doesn’t matter too much. So we have to combine these two 00:32:07.289 --> 00:32:10.989 to get an overall model. Because what we want 00:32:10.989 --> 00:32:14.919 is the combined probability. The probability combined that this 00:32:14.919 --> 00:32:18.957 gives us a probability of e earthquakes occurring during the time period 00:32:18.957 --> 00:32:23.490 of interest – say, the next 50 years. We have those two input distributions – 00:32:23.490 --> 00:32:26.433 just here so you can look at them if you need them. 00:32:26.433 --> 00:32:31.470 And then the combined probability would just be a sum over the sum – 00:32:31.470 --> 00:32:35.074 up to some total number of collapses. We just go up to some number that’s, 00:32:35.074 --> 00:32:39.670 like, very unlikely to happen. So anything we’re leaving out 00:32:39.670 --> 00:32:44.610 is negligible. And we have the probability of the number of collapses 00:32:44.610 --> 00:32:50.559 happening times the probability of earthquakes given that number 00:32:50.559 --> 00:32:54.149 of collapses. So the problem is, we don’t actually have this. 00:32:54.149 --> 00:32:58.628 What we have is the probability of earthquakes due to one collapse. 00:32:58.628 --> 00:33:02.559 But we can take basically, kind of with a recursive process, 00:33:02.559 --> 00:33:09.167 over the number of collapses, where we can get this p-r, e, comma, u. 00:33:09.167 --> 00:33:14.029 And so, basically, we can always – if we have u minus 1 – 00:33:14.029 --> 00:33:17.003 so here’s p-r of u minus 1. 00:33:17.003 --> 00:33:21.460 And we have p-r of 1 – of k, comma, 1 – so we are using 00:33:21.460 --> 00:33:25.259 a k here because we have sums going on. That’s the summation here. 00:33:25.259 --> 00:33:28.950 We can always get the next one. So, if we have one, we can put 00:33:28.950 --> 00:33:37.355 p-r-k-1 here and p-r-j-1 here. We can get p-r-e, comma, 2. 00:33:37.355 --> 00:33:42.869 And we can just add, then, build 3, 4, 5, and 6 with a special case 00:33:42.869 --> 00:33:45.920 for the zero, where it’s basically just that the probability – if there’s 00:33:45.920 --> 00:33:51.496 no collapses, that the probability of collapse earthquakes is zero. 00:33:51.496 --> 00:33:55.629 So, basically, this recursive process allows us to analytically 00:33:55.629 --> 00:33:59.950 derive this combined distribution that forecasts the number of earthquakes 00:33:59.950 --> 00:34:03.582 in the next 50 years due to collapses. 00:34:03.619 --> 00:34:08.520 Okay, so here’s what the overall thing – overall distribution looks like. 00:34:08.520 --> 00:34:11.675 So here we have magnitude 4s – the number of magnitude 4 00:34:11.675 --> 00:34:14.909 earthquakes in 50 years. And then, in the right-hand plot, 00:34:14.909 --> 00:34:18.450 we have magnitude 5 earthquakes in 50 years. 00:34:18.450 --> 00:34:22.230 And the vertical axes are the cumulative probability. 00:34:22.230 --> 00:34:28.020 And the black lines show what happened in the 2018 eruption. 00:34:28.020 --> 00:34:34.625 So 85 here, and I think this is about 54 events here. 00:34:35.378 --> 00:34:38.675 Our preferred model using the best-fitting parameters for the 00:34:38.675 --> 00:34:44.011 Poisson distribution and the negative binomial is this blue line. 00:34:44.011 --> 00:34:46.503 And so, for instance, here, we can see that, if we get to 00:34:46.531 --> 00:34:49.909 the observed number of earthquakes in 2018, there’s 00:34:49.909 --> 00:34:53.988 an 85% chance that we’d have a lower number in the next 50 years 00:34:53.988 --> 00:34:57.270 and about a 15% chance that we’d have a higher number. 00:34:57.270 --> 00:34:59.780 So this is a somewhat unlikely outcome, what happened 00:34:59.780 --> 00:35:04.917 in 2018, on a 50-year basis. But that was the largest collapse in at least 00:35:04.943 --> 00:35:09.430 200 years. So it doesn’t surprise us that we get a result like this. 00:35:09.430 --> 00:35:14.510 The green lines – dashed lines show the range of uncertainties derived 00:35:14.510 --> 00:35:19.316 from these gray distributions are from sampling the range of 00:35:19.316 --> 00:35:22.290 uncertainty in all of our parameters. 00:35:22.290 --> 00:35:26.847 So this is plus or minus one sigma – the dashed green lines. 00:35:26.847 --> 00:35:30.920 Here’s the Poisson model in red. So the Poisson model in red, 00:35:30.920 --> 00:35:33.359 if we go out to the observed number of earthquakes, basically says that 00:35:33.359 --> 00:35:38.431 it was certain, or virtually certain – it’s 99.999-something – that we would 00:35:38.431 --> 00:35:42.650 have fewer earthquakes and a very small probability that we would 00:35:42.650 --> 00:35:47.150 have more than what we observed. So the Poisson model essentially rules 00:35:47.150 --> 00:35:51.740 out the possibility of what we observed in 2018, or says, at least, 00:35:51.740 --> 00:35:56.347 that it was uncertain on the scale of many millennia. 00:35:56.347 --> 00:35:58.880 It’s extremely unlikely. And we get the same thing – 00:35:58.880 --> 00:36:02.613 patterns if we looked at the magnitude 5 earthquakes. 00:36:02.613 --> 00:36:07.750 Again, the Poisson model basically cannot explain those earthquakes. 00:36:11.410 --> 00:36:15.680 Okay. So we have a model of the number of earthquakes. 00:36:15.680 --> 00:36:17.940 And we now want to compute the hazard due to those earthquakes – 00:36:17.940 --> 00:36:22.211 the ground shaking hazard. And we go back to the 1968 paper 00:36:22.211 --> 00:36:25.220 by Allin Cornell on engineering seismic risk analysis – 00:36:25.220 --> 00:36:31.150 a seminal paper for PSHA. And, near the end, he says the 00:36:31.150 --> 00:36:34.940 assumption that the occurrences of earthquakes follow the behavior 00:36:34.940 --> 00:36:39.550 of the Poisson process model can only be removed at a great penalty. 00:36:39.550 --> 00:36:42.980 And what he meant by that was that it would make the solutions 00:36:42.980 --> 00:36:47.670 very inefficient or not analytic. And he wanted efficient, 00:36:47.670 --> 00:36:50.819 analytic solutions so that you could explore parameter choices. 00:36:50.819 --> 00:36:54.769 And that’s critical. And that’s what we do with logic trees in PSHA. 00:36:54.769 --> 00:36:59.020 And so, I mean, he was using the Poisson model, not because he thought 00:36:59.020 --> 00:37:02.339 it explained everything – he was specific that it didn’t explain elastic 00:37:02.339 --> 00:37:06.020 rebound and it didn’t explain aftershocks – but because it got to 00:37:06.020 --> 00:37:09.790 a tool that was very useful. But a lot of the rest of the paper, 00:37:09.790 --> 00:37:15.990 I’ll point out, was actually about developing ground motions at a site 00:37:15.990 --> 00:37:19.910 due to earthquakes, say, in some uniform area or due to 00:37:19.910 --> 00:37:22.319 uniform earthquakes happening along some fault. 00:37:22.319 --> 00:37:27.600 There’s a lot of development of other parts of PSHA that are incredibly 00:37:27.600 --> 00:37:31.400 important in this paper. It’s really a very, you know, broad and 00:37:31.400 --> 00:37:37.152 beautiful paper. But, when we have distributions of events that can’t 00:37:37.152 --> 00:37:39.750 be modeled by the Poisson process, we have the urge to see if we 00:37:39.750 --> 00:37:43.319 need to try something else. So there are some existing 00:37:43.319 --> 00:37:48.050 approaches for non-Poissonian PSHA. 00:37:48.087 --> 00:37:51.316 You can do simulations. So, for instance, the UCERF3-ETAS 00:37:51.316 --> 00:37:55.770 model that Ned Field led and many of us participated in, 00:37:55.770 --> 00:38:00.140 is a simulation model. However, Boyd’s 2012 paper included 00:38:00.140 --> 00:38:03.690 some simulation approaches. And simulations are great. 00:38:03.690 --> 00:38:05.940 They allow for a very wide range of effects. 00:38:05.940 --> 00:38:08.030 I would almost say they were great enough to be considered 00:38:08.030 --> 00:38:10.996 the best possible method. 00:38:10.996 --> 00:38:14.707 But they can be extremely computationally expensive. 00:38:14.707 --> 00:38:20.480 And so they may not be usable for very, very large problems. 00:38:20.480 --> 00:38:26.140 And so here is an example of aftershock hazard from a HayWired hypothetical 00:38:26.140 --> 00:38:33.378 earthquake on the Hayward Fault that was published in 2018 in SRL. 00:38:33.378 --> 00:38:37.042 So that’s a simulation model. 00:38:37.042 --> 00:38:39.820 Another approach are these deterministic combinations. 00:38:39.820 --> 00:38:42.902 This is Memphis. There are the New Madrid 00:38:42.902 --> 00:38:48.830 earthquakes, so that’s 1, 2, and 3. And both Oliver and then, before him, 00:38:48.830 --> 00:38:54.140 Toro and Silva in the Technical Report, looked at the ground motions due to, 00:38:54.140 --> 00:38:58.140 say, the union of all of these events. And this allows for correlations 00:38:58.140 --> 00:39:01.250 between sources – like, these three events will always happen 00:39:01.250 --> 00:39:04.000 when one of them happens. But it tends to be a very specific 00:39:04.000 --> 00:39:07.660 approach and doesn’t really allow us to model a range of behaviors 00:39:07.660 --> 00:39:12.621 such as we want to see in Kilauea Caldera. 00:39:12.621 --> 00:39:15.650 I’m going to do a quick review of Poisson PSHA so you know 00:39:15.650 --> 00:39:19.625 how it works. I had to learn a lot of this recently. 00:39:20.589 --> 00:39:23.957 So the first thing we need is a ground motion prediction equation. 00:39:23.996 --> 00:39:27.761 I’m going to use one from Allin Cornell in 1979. 00:39:27.761 --> 00:39:31.849 And what we have in these equations are – this one’s very simple. 00:39:31.849 --> 00:39:37.710 Just a function of magnitude and distance, R. 00:39:37.710 --> 00:39:42.549 We get a mean ground motion due to some earthquake, and we can plug in a 00:39:42.549 --> 00:39:47.619 magnitude 6, for instance, 10 kilometers away from our site of interest. 00:39:47.619 --> 00:39:52.250 And we also have some sort of sigma. And basically, we get a log normal 00:39:52.250 --> 00:39:54.830 distribution of ground motions due to one earthquake. 00:39:54.830 --> 00:39:58.290 So, if one earthquake happens, then our distribution of 00:39:58.290 --> 00:40:00.690 ground motions looks like this. 00:40:00.690 --> 00:40:06.799 We have ground motion as a PGA on this scale plotted in log form. 00:40:06.799 --> 00:40:10.580 And then the probability of exceedance. So we can, say, read off, you know, 00:40:10.580 --> 00:40:15.510 here there’s a 10% chance that the ground motions will exceed something 00:40:15.510 --> 00:40:24.430 like 0.6 g, if that earthquake happens. And that’s sort of our basic ingredient, 00:40:24.430 --> 00:40:28.363 and we’re used to plotting it in this way. 00:40:29.222 --> 00:40:32.329 These probability of exceedance given one earthquake can include 00:40:32.329 --> 00:40:38.449 variations in magnitude, distance – like, a lot of what was in Allin’s paper – 00:40:38.449 --> 00:40:40.829 focal mechanisms, stress drop – anything you want. 00:40:40.829 --> 00:40:45.250 So here is our one-earthquake curve. Here are a suite of curves 00:40:45.250 --> 00:40:49.230 from magnitude 5 to 7.5. And then the red line is the 00:40:49.230 --> 00:40:52.799 combination of those using the probability distribution of 00:40:52.799 --> 00:40:55.970 a Gutenberg-Richter distribution with a b value of 1. 00:40:55.970 --> 00:41:00.740 So I could use just this one curve to represent the possibility that our 00:41:00.740 --> 00:41:05.652 next earthquake comes from a range of possible earthquakes. 00:41:05.652 --> 00:41:08.450 I’m not actually going to do that. I’m going to use this magnitude 6 curve, 00:41:08.450 --> 00:41:12.059 but it really doesn’t matter. The brilliance of this is that we 00:41:12.059 --> 00:41:14.821 can use – this curve can contain a lot of information about the 00:41:14.821 --> 00:41:19.605 earthquake source, and we can just carry it along as a single distribution. 00:41:20.519 --> 00:41:23.566 If we want to factor in the Poisson rate of earthquakes, 00:41:23.566 --> 00:41:27.050 so we start with that exceedance curve – probability of ground motion greater 00:41:27.050 --> 00:41:31.722 than x, given one earthquake and a Poisson rate of earthquakes. 00:41:31.722 --> 00:41:35.300 And the rate of exceedance given that is simply the rate of ground 00:41:35.300 --> 00:41:38.000 motion greater than x, given – instead of one earthquake, given 00:41:38.000 --> 00:41:43.707 a Poisson distribution, is just lambda times the original distribution. 00:41:43.707 --> 00:41:46.520 So, on this graph here, we see the original distribution 00:41:46.520 --> 00:41:50.369 here given one earthquake. And, if the rate if 0.5, 00:41:50.369 --> 00:41:55.144 it just drops down by a factor of 2. The dashed line is then the rate curve. 00:41:55.144 --> 00:41:58.810 And, to be honest, a lot of PSHA just stops here. This stops, 00:41:58.810 --> 00:42:02.449 not with probability of exceedance, but with rate of exceedance. 00:42:02.449 --> 00:42:07.829 For instance, pulling out of the NSHM model for 2014 for Building 19 at 00:42:07.829 --> 00:42:14.060 Moffett Field, we see that what they plot up is actual annual frequency – 00:42:14.060 --> 00:42:18.000 or, which is another term for rate – annual frequency exceedance. 00:42:18.000 --> 00:42:21.082 This is not a probability plot. 00:42:21.082 --> 00:42:25.894 And this is – the black line, for instance, is the PGA curve, 00:42:25.894 --> 00:42:28.472 and then we have a couple spectral levels. 00:42:28.472 --> 00:42:34.609 And then the line through here is the time horizon of 475 years or 10%. 00:42:34.609 --> 00:42:39.670 The rate that – it implies 10% in 50 years, as we talk about. 00:42:39.670 --> 00:42:41.829 This is extremely convenient to work in rates. 00:42:41.829 --> 00:42:46.750 Rates are linear. So if we have, say, two source zones at a site, and we have 00:42:46.750 --> 00:42:50.329 exceedance rate curves for both of them, we can just add them together. 00:42:50.329 --> 00:42:55.886 If we want to go from annual frequency to 50 years, we can just multiply by 50. 00:42:55.886 --> 00:42:58.299 So, I mean, we don’t want to give up on Poisson because 00:42:58.299 --> 00:43:01.625 it does a lot, but it doesn’t do everything. 00:43:02.441 --> 00:43:04.730 We want to – by the way, compute probability of exceedance 00:43:04.730 --> 00:43:08.319 of Poisson rate – go another step. So we want to get the rate. 00:43:08.319 --> 00:43:10.960 We start with the rate. And we want to say, you know, 00:43:10.960 --> 00:43:14.520 the number of times – k is number of exceedances, so we want to know 00:43:14.520 --> 00:43:17.800 the probability of getting more than one ground motion. 00:43:17.800 --> 00:43:21.589 We can take 1 minus the probability of getting zero ground motions, 00:43:21.589 --> 00:43:27.030 and that just drops out very nicely in Poisson statistics for – 00:43:27.030 --> 00:43:30.359 to be 1 minus e to the minus rate. 00:43:30.359 --> 00:43:33.950 And so, on this plot here, the black dashed line is the rate, and then 00:43:33.950 --> 00:43:38.119 the red dashed line is the probability. And notice that they become 00:43:38.119 --> 00:43:43.250 very similar – almost equal for small probabilities, where we’re often 00:43:43.250 --> 00:43:47.480 working for engineering applications. So, again, you can get away with 00:43:47.480 --> 00:43:50.250 working in rate because, for small probabilities, 00:43:50.250 --> 00:43:52.625 they’re essentially the same. 00:43:53.910 --> 00:43:57.070 I want to note one thing I do do here that’s not usually done. 00:43:57.070 --> 00:44:00.760 I’m showing the probability of no ground motion to basically 00:44:00.760 --> 00:44:04.269 be the probability of no event in the class we’re studying. 00:44:04.269 --> 00:44:06.050 Of course, this is a log-log plot. 00:44:06.050 --> 00:44:12.059 I just artificially stick it down here with a zero. 00:44:12.059 --> 00:44:15.700 This may bother you to see zero on a log scale, but, for some of 00:44:15.700 --> 00:44:19.150 what I’ll discuss, I want you to note that I’m doing it because there is a 00:44:19.150 --> 00:44:24.121 probability of no caldera collapse earthquakes in the next 50 years. 00:44:24.121 --> 00:44:26.470 Okay, so that’s how we do Poisson. 00:44:26.470 --> 00:44:30.910 But what about the caldera collapses – the probability of a number of caldera 00:44:30.910 --> 00:44:34.230 collapses of – collapse earthquakes in 50 years? 00:44:34.230 --> 00:44:37.750 As we said before, it cannot be explained 00:44:37.750 --> 00:44:43.613 by the Poisson model, so we need something else. 00:44:43.613 --> 00:44:46.530 So we’re going to do non-Poissonian PSHA from order statistics. 00:44:46.530 --> 00:44:49.109 I have not been able to find this in the literature anywhere, 00:44:49.109 --> 00:44:52.940 so I’m hoping we didn’t miss something. Because I think it’s a unique application 00:44:52.940 --> 00:44:56.460 of order statistics. So we have the probability of events – 00:44:56.460 --> 00:44:59.261 the probability of an event in our time period. 00:44:59.261 --> 00:45:01.109 And we have the probability of exceedance for one event. 00:45:01.109 --> 00:45:03.855 Those are the things we’ve developed so far. 00:45:03.855 --> 00:45:08.460 So, if we know the probability of exceedance for not one event, 00:45:08.460 --> 00:45:13.220 but for any n – this is what we don’t know yet – then the probability 00:45:13.220 --> 00:45:17.760 of ground motion exceeding x, given the probability distribution of n, 00:45:17.760 --> 00:45:21.599 would just be the sum over n of the probability of n events times 00:45:21.599 --> 00:45:25.750 the probability of ground motion, given exactly n events. 00:45:25.750 --> 00:45:29.440 And then order statistics are going to give us a way to calculate 00:45:29.440 --> 00:45:33.750 this term here that we don’t know yet. 00:45:34.675 --> 00:45:38.430 So order statistics are basically an approach to say, let’s say, 00:45:38.430 --> 00:45:42.339 instead of taking one sample, we take two samples or three samples, 00:45:42.339 --> 00:45:45.800 and we want to look at, say, the smallest of those samples 00:45:45.800 --> 00:45:49.082 or the largest or the middle – any number within them. 00:45:49.082 --> 00:45:53.210 And an important part of order statistics if that order statistics for 00:45:53.210 --> 00:45:56.170 samples that were taken originally from a uniform distribution. 00:45:56.170 --> 00:46:01.530 So from zero to 1, we have equal probabilities of picking any number. 00:46:01.530 --> 00:46:04.970 And so, if we picked one sample, and we could only look at 00:46:04.970 --> 00:46:07.730 what’s called rank – the level of sample we’re going to look at 00:46:07.730 --> 00:46:10.839 after we sort them – there’s only one to look at. 00:46:10.839 --> 00:46:15.785 So rank 1, sample 1, we get the uniform distribution back. 00:46:15.785 --> 00:46:19.880 Let’s say we look at five samples, and we – each time we do 00:46:19.880 --> 00:46:22.980 a random draw, we take five samples, and we always look at the smallest one. 00:46:22.980 --> 00:46:26.240 That’s rank equals 1. Then obviously, we would 00:46:26.240 --> 00:46:32.099 have a tendency to more likely be picking the smaller values – 00:46:32.099 --> 00:46:35.136 our smallest value of 5 will likely be small. 00:46:35.136 --> 00:46:39.980 And if we pick rank 5, the largest of five samples, 00:46:39.980 --> 00:46:43.000 then we’re likely to pick a large one. And that’s really what we do 00:46:43.000 --> 00:46:45.753 in PSHA is we care about the larger ground motions. 00:46:45.753 --> 00:46:48.930 But, if we pick three samples out of five, we get something 00:46:48.930 --> 00:46:51.710 with a central tendency. 00:46:51.710 --> 00:46:58.770 So the actual math here is that the probability of various values of x 00:46:58.770 --> 00:47:05.369 on the uniform distribution, given picking n samples or r is this equation. 00:47:05.369 --> 00:47:08.527 The equation itself is not particularly important. 00:47:08.527 --> 00:47:13.417 Just want you to know it exists. It’s actually a form of what’s called 00:47:13.417 --> 00:47:18.940 a beta distribution, which is available quickly calculated in packages, 00:47:18.940 --> 00:47:23.000 such as R, which is where I do all my calculations. 00:47:23.714 --> 00:47:28.480 So I want to do some transformations first to make things easier for the 00:47:28.480 --> 00:47:31.450 way I think, at least, and I think the way most statisticians think. 00:47:31.450 --> 00:47:37.230 We’re used to using exceedance curves. But I’m going to reverse this and 00:47:37.230 --> 00:47:39.560 make it a cumulative curve. Instead of the probability of 00:47:39.560 --> 00:47:41.359 ground motion being greater than x, 00:47:41.359 --> 00:47:44.433 it’s now the probability of ground motion less than x. 00:47:44.433 --> 00:47:48.599 And I’m now going to – we usually plot things on a log-log plot. 00:47:48.599 --> 00:47:51.430 I’m now going to plot them on a linear plot. 00:47:51.430 --> 00:47:55.099 So we have cumulative probability here. Linear ground motion here. 00:47:55.099 --> 00:47:59.550 And this actually makes it easy to see that we have a log normal distribution. 00:47:59.550 --> 00:48:03.910 So we’re going to work this way, but it’s just a plotting thing. 00:48:05.152 --> 00:48:07.750 Okay, so what we want to do is we want to find the probability 00:48:07.750 --> 00:48:09.849 for two events as a first step. 00:48:09.849 --> 00:48:14.769 So we have a linear cumulative probability for one event. 00:48:14.769 --> 00:48:18.420 And we have the order statistic for two events 00:48:18.420 --> 00:48:21.394 if we look at the bigger of the two – rank 2. 00:48:21.394 --> 00:48:23.860 And so basically, it shows us that it’s more likely we’re going to 00:48:23.860 --> 00:48:29.160 pick higher numbers. So what is this x that goes from zero to 1? 00:48:29.160 --> 00:48:31.880 What it work – what it works out is the x that goes from zero to 1 00:48:31.880 --> 00:48:35.753 is the cumulative probability distribution here from zero to 1. 00:48:35.753 --> 00:48:39.559 So, if I’m more likely to pick large numbers of cumulative probability, 00:48:39.559 --> 00:48:42.099 that means I’m more likely to pick large ground motions. 00:48:42.099 --> 00:48:45.519 Because this curve monotonically increases. 00:48:45.519 --> 00:48:49.630 So we’re likely to pick stuff out at this end, which corresponds to 00:48:49.630 --> 00:48:53.511 the larger range of ground motions. Here’s how we do that. 00:48:53.550 --> 00:48:57.810 First of all, probability density is not particularly useful in this case. 00:48:57.810 --> 00:49:01.380 I want to do cumulative probability. These are the same curves. 00:49:01.380 --> 00:49:04.690 Except for now, the one on the right is the cumulative sum 00:49:04.690 --> 00:49:07.332 of the one on the left. 00:49:07.332 --> 00:49:08.770 And so just keep that in mind. 00:49:08.770 --> 00:49:13.566 It’s the same curve we showed before, but now it’s a cumulative curve. 00:49:13.566 --> 00:49:17.070 So we have the cumulative probability, and now we’re labeling this first axis – 00:49:17.070 --> 00:49:20.558 this is the cumulative probability of one event. 00:49:20.558 --> 00:49:24.569 And this is the cumulative probability here of two events, 00:49:24.569 --> 00:49:28.785 taking the larger one, so it’s n 2, rank 2. 00:49:28.785 --> 00:49:32.970 And we can use this to transform our probability of ground motion 00:49:32.970 --> 00:49:36.855 for one event to the probability of ground motions for two events. 00:49:36.855 --> 00:49:39.910 Here’s how we do it. We take some input probability 00:49:39.910 --> 00:49:43.390 for one event – say 0.5, which very conveniently goes 00:49:43.390 --> 00:49:47.750 very nicely, for two events, will turn into a probability of 0.25. 00:49:47.750 --> 00:49:50.167 So nice round numbers. 00:49:50.167 --> 00:49:57.190 We first locate the probability of 0.5 on this curve for one event. 00:49:57.190 --> 00:50:02.535 So we get the ground motion here. It’s probably around 0.2 g’s. 00:50:02.566 --> 00:50:06.200 And we drop it down from 0.5 to 0.25. 00:50:06.200 --> 00:50:11.027 So this is – following this blue line here becomes this arrow here. 00:50:11.027 --> 00:50:15.066 And we can then do that for a whole bunch of input probabilities. 00:50:15.066 --> 00:50:19.777 And then, if we connect those arrows, we get a new curve. 00:50:19.777 --> 00:50:22.740 And so this curve here – the dashed line that connects the heads of the 00:50:22.740 --> 00:50:27.309 blue arrows is the probability of ground motion being less than x 00:50:27.309 --> 00:50:30.386 for two events if two events exactly happen. 00:50:30.386 --> 00:50:32.360 And, if you want to look at the math, it’s down here. 00:50:32.360 --> 00:50:36.569 It’s the probability of the ground motion of n events is the – 00:50:36.569 --> 00:50:41.380 is the beta statistic of the probability of ground motion of one event, 00:50:41.380 --> 00:50:45.279 and then given the appropriate rank and [inaudible] parameters based on 00:50:45.279 --> 00:50:48.683 rank and number, which actually are behind 00:50:48.683 --> 00:50:53.500 one of Teams’ little windows for me, so I can’t quite see. 00:50:54.207 --> 00:50:59.433 So we can actually then do this for, say, 1 through 5 events. 00:50:59.433 --> 00:51:01.450 And so here we have the exceedance curves. 00:51:01.450 --> 00:51:04.180 Now I’m back to plotting log-log exceedance. 00:51:04.180 --> 00:51:06.869 So ground motion seismologists feel more comfortable, 00:51:06.869 --> 00:51:09.750 and we’re used to looking at it this way. 00:51:09.750 --> 00:51:11.940 And we see that – you know, here’s the ground motion input 00:51:11.940 --> 00:51:16.261 for one event, and the dashed lines go for 2, 3, 4, and 5 events. 00:51:16.261 --> 00:51:19.400 And so, the more events we have, the higher the ground motions go. 00:51:19.400 --> 00:51:22.849 This curve steps out to the right to higher ground motions. 00:51:22.849 --> 00:51:24.530 And that’s what we would expect. 00:51:24.530 --> 00:51:29.000 More earthquakes, more likely we have some large ground motion. 00:51:31.535 --> 00:51:35.440 Okay. So now we want to compute hazard – compute hazard 00:51:35.440 --> 00:51:39.410 from probability n and the probability of the ground motions 00:51:39.410 --> 00:51:44.441 given different number of events. I can do the simplest possible thing. 00:51:44.441 --> 00:51:47.839 I’m going to say that the probability of a different number of events is a constant. 00:51:47.839 --> 00:51:53.619 And so, from zero to 5 events, it’s 1 over 6. 00:51:53.619 --> 00:51:57.180 So any of these choices – any of these black curves on this plot 00:51:57.180 --> 00:52:01.957 have an equal probability of happening, plus the probability of zero events. 00:52:01.957 --> 00:52:05.760 And then we can just do the sum, from zero to 5. 00:52:05.760 --> 00:52:08.880 The probability, which is a constant, times all these curves. 00:52:08.880 --> 00:52:13.559 So basically, we’re taking some sort of average of these curves plus 00:52:13.559 --> 00:52:16.549 the probability step-down here of no event. 00:52:16.549 --> 00:52:19.894 And we’ve now created a non-Poissonian PSHA. 00:52:19.894 --> 00:52:23.869 And we have a hazard curve that includes non-Poisson statistics. 00:52:23.869 --> 00:52:26.540 And part of my point of putting in a constant probability here is, 00:52:26.540 --> 00:52:28.529 I don’t have to put in a negative binomial. 00:52:28.529 --> 00:52:31.250 I can put in anything I want. I can make even numbers of 00:52:31.250 --> 00:52:36.472 earthquakes possible and odd numbers of earthquakes impossible. 00:52:36.507 --> 00:52:37.950 Doesn’t matter. We can do any – 00:52:37.950 --> 00:52:41.960 we can do any arbitrary earthquake behavior. 00:52:41.960 --> 00:52:46.511 Okay. So remember the caldera? Back to it. 00:52:46.511 --> 00:52:48.359 Do we have all the ingredients we need? 00:52:48.359 --> 00:52:51.120 We have a distribution of the number of events. 00:52:51.120 --> 00:52:53.830 We have the method, yes, but we don’t have a probability 00:52:53.830 --> 00:52:58.083 of exceedance for one event. I’m going to actually just do 00:52:58.083 --> 00:53:00.559 an empirical ground motion curve here. 00:53:00.559 --> 00:53:06.200 We had 40 events studied by Rekoske et al. 00:53:06.200 --> 00:53:11.740 This is spectral acceleration period here versus spectral acceleration in % g. 00:53:11.740 --> 00:53:16.792 And the black lines are each of the 40 events. 00:53:16.792 --> 00:53:20.738 And the red line, by the way, is the magnitude 6.9. 00:53:20.738 --> 00:53:24.738 So you can see it was as strong as the magnitude 5s at short periods, but the 00:53:24.738 --> 00:53:32.105 magnitude 5s were stronger at longer periods at HVO, or station UWE. 00:53:32.105 --> 00:53:36.000 And we see that the peak ground motion was really at half a second. 00:53:36.000 --> 00:53:38.308 So I’m actually going to use that. 00:53:38.351 --> 00:53:43.160 If we plot this up as an exceedance probability, the empirical curves, 00:53:43.160 --> 00:53:45.207 we can then fit log normals to them. 00:53:45.207 --> 00:53:48.510 If I use all the data, I get the dashed lines. 00:53:48.510 --> 00:53:51.510 The black is the observed, and the red is the fit. 00:53:51.510 --> 00:53:54.003 It’s not a good fit to most of the data because there seem to be 00:53:54.003 --> 00:53:59.520 two magnitude 5 earthquakes that are right down here that have extremely 00:53:59.520 --> 00:54:03.490 low ground motions for some reason. So I’m going to rule those out – 00:54:03.490 --> 00:54:06.470 toss them out, and then fit the rest of the data, so I actually 00:54:06.470 --> 00:54:09.003 get a better fit to the bulk of the data. 00:54:09.003 --> 00:54:12.972 And the red line will be my ground motion curve. 00:54:12.972 --> 00:54:15.433 So now we have all the ingredients. 00:54:15.433 --> 00:54:17.630 So we have cumulative probability of the number of events. 00:54:17.630 --> 00:54:21.569 I’m using the magnitude 5 here. 00:54:21.569 --> 00:54:25.470 And we have an exceedance probability curve, which is the solid red line. 00:54:25.470 --> 00:54:29.720 The first thing I want to do is compute the rate of exceedance in 50 years. 00:54:29.720 --> 00:54:33.140 And I do this for a particular reason. I don’t have a method for doing this 00:54:33.140 --> 00:54:36.829 for non-Poisson, so just to be sure, I did 10 million simulations of 00:54:36.829 --> 00:54:41.210 the next 50 years, drawing out of these probability distributions. 00:54:41.210 --> 00:54:45.040 The black line is the theoretical Poisson. 00:54:45.040 --> 00:54:48.597 And the red dashed line is the simulated non-Poisson. 00:54:48.597 --> 00:54:51.988 And they’re exactly identical. 00:54:51.988 --> 00:54:55.410 Basically, if you want to – if you work in rate of exceedance, 00:54:55.410 --> 00:54:57.650 it completely hides non-Poisson effects. 00:54:57.650 --> 00:55:02.125 So, to see non-Poisson effects, we have to work in probability. 00:55:03.144 --> 00:55:08.520 Now we can compute the probability. Both the Poisson models showing here. 00:55:08.520 --> 00:55:10.332 This is now probability of exceedance, 00:55:10.332 --> 00:55:15.371 so different ground motions at half a second. 00:55:15.371 --> 00:55:18.230 Spectral acceleration. 00:55:18.230 --> 00:55:21.920 The black is the Poisson model. And this can be computed either 00:55:21.920 --> 00:55:25.130 as I showed before or with order statistics. 00:55:25.130 --> 00:55:29.050 And then the red line is a non-Poisson model. 00:55:29.050 --> 00:55:34.160 Notice that one big difference is here at zero probability, the Poisson model 00:55:34.160 --> 00:55:37.690 makes it very unlikely that there would be no earthquake in the next 50 years 00:55:37.690 --> 00:55:41.750 in the – a caldera collapse event. Whereas, it’s actually quite likely – 00:55:41.750 --> 00:55:45.690 it’s, I think, about 60% of the time, in the next 50 years, there would be 00:55:45.690 --> 00:55:49.700 no magnitude 5s. And the dotted red lines 00:55:49.700 --> 00:55:54.630 are plus or minus one sigma for the non-Poisson model. 00:55:54.630 --> 00:55:59.780 The uncertainty in the Poisson model is much smaller. 00:55:59.780 --> 00:56:05.332 And then, here we have 2% in 50 years, 10% in 50 years, and 50%. 00:56:05.332 --> 00:56:09.039 And we can see, for one exceedance – the standard things we compute – 00:56:09.039 --> 00:56:13.319 that the Poisson model does a pretty good job at 2%, really quite a good job 00:56:13.319 --> 00:56:18.200 within uncertainties at 10%, but – so, for engineering purposes, 00:56:18.200 --> 00:56:21.449 for building structures, it probably does pretty well, 00:56:21.449 --> 00:56:26.099 even in this highly clustered case. But, for 50%, which is a standard that’s 00:56:26.099 --> 00:56:29.930 close to those used for say, operating standards, keeping things running, 00:56:29.930 --> 00:56:33.799 for infrastructure and tall buildings, there starts to be a very large 00:56:33.799 --> 00:56:40.375 divergence because of the probability of zero events. 00:56:41.433 --> 00:56:43.829 Of course, we can do more – we can do more exceedances. 00:56:43.829 --> 00:56:48.650 And we can do that both with Poisson or with non-Poissonian order statistics. 00:56:48.650 --> 00:56:52.589 So here we have the plot we had before, which was for one exceedance. 00:56:52.589 --> 00:56:56.640 If we model the ground motion we would exceed twice in the 00:56:56.640 --> 00:57:00.800 next 50 years, we can see that the pattern changes a bit. 00:57:00.800 --> 00:57:05.609 Notice that, now, as we go to higher ground motions, the non-Poisson model 00:57:05.609 --> 00:57:10.480 actually exceeds the ground motions from the Poisson model, and that’s 00:57:10.480 --> 00:57:14.089 because it’s more likely to have large numbers of earthquakes. 00:57:14.089 --> 00:57:18.849 We can go to – now here’s 2 again, and now it’s 3. The effect gets larger. 00:57:18.849 --> 00:57:21.816 And we can even be almost silly about this. 00:57:21.816 --> 00:57:24.839 We can go to 10 or 20 exceedances because, you know, we had 00:57:24.839 --> 00:57:28.619 50 earthquakes magnitude 5 and greater in 2018. 00:57:28.619 --> 00:57:32.180 And you can see that this gets – these differences get very large. 00:57:32.180 --> 00:57:34.500 And that’s because, you know, for instance, for 2018, it says 00:57:34.500 --> 00:57:38.319 the Poisson model basically tells us that 20 earthquakes can’t happen. 00:57:38.319 --> 00:57:44.261 Or at least it’s – looks like it’s, you know, well under 1%. 00:57:44.261 --> 00:57:48.183 So, after you compute multiple exceedances, the non-Poisson 00:57:48.183 --> 00:57:51.519 behavior may become more important, and that could be important for 00:57:51.519 --> 00:57:54.750 applications such as in the insurance industry. 00:57:54.750 --> 00:57:57.809 So I want to finish now very quickly with how clustering 00:57:57.809 --> 00:58:01.621 and anti-clustering affects PSHA with some simulations. 00:58:01.651 --> 00:58:07.089 We’re going to measure clustering with the coefficient of variation, which is 00:58:07.089 --> 00:58:11.300 just the mean by the variance of the number of events in the next 50 years. 00:58:11.300 --> 00:58:13.816 These are simulated sequences of events. 00:58:13.848 --> 00:58:16.440 The middle one here is actually a Poisson model. 00:58:16.440 --> 00:58:19.580 So any clustering you see is randomness. 00:58:19.580 --> 00:58:22.960 At the top, we have anti-cluster events. 00:58:22.960 --> 00:58:25.058 This would be maybe due to elastic rebound. 00:58:25.058 --> 00:58:27.170 And, at the bottom, we have highly clustered events – 00:58:27.170 --> 00:58:29.580 may be due to aftershocks. 00:58:30.714 --> 00:58:35.160 I used a negative binomial distribution to produce different 00:58:35.160 --> 00:58:38.029 coefficients of variations. One is the Poisson model – 00:58:38.029 --> 00:58:44.029 2, 5, and 10 are artificial ones. If there’s one earthquake per average 00:58:44.029 --> 00:58:50.859 in 50 years – so a rare earthquake – slightly rare earthquake, we can see 00:58:50.859 --> 00:58:56.160 a fairly large difference as we change coefficient of variation in the hazard. 00:58:56.160 --> 00:59:01.680 If we get to 5 earthquakes – we multiply the underlying rate by 5 – 00:59:01.680 --> 00:59:05.680 this becomes smaller. So lower rates and higher coefficients 00:59:05.680 --> 00:59:12.430 of variability is the line here. The dotted line is 10, 5, and 2. 00:59:12.430 --> 00:59:17.230 So lower rates and higher CV makes non-Poissonian more important. 00:59:17.230 --> 00:59:21.990 And here, we show, for the same rate, rate of 1, we show one exceedance 00:59:21.990 --> 00:59:26.450 and 3 exceedances. And we also see that number of 00:59:26.450 --> 00:59:30.599 exceedances changes the impact. For 1 exceedance, the non-Poissonian 00:59:30.599 --> 00:59:35.579 behavior was actually lower hazard. For 3 exceedances, it’s higher hazard. 00:59:37.175 --> 00:59:42.570 Okay. So, in summary, so earthquake probabilities – we can determine them 00:59:42.570 --> 00:59:45.809 by combining the probability of underlying events and the earthquake 00:59:45.809 --> 00:59:49.644 response to a single underlying event. And that’s what we did at Kilauea. 00:59:49.644 --> 00:59:53.582 Order of statistics gives us an analytic, computationally efficient way to 00:59:53.617 --> 00:59:57.810 compute PSHA with arbitrary earthquake behavior. 00:59:57.810 --> 01:00:03.490 So I think this fulfills Allin Cornell’s goal of having an analytic method. 01:00:03.490 --> 01:00:05.480 Obviously, there’s some penalties, still. 01:00:05.480 --> 01:00:08.619 This isn’t as fast as the Poisson statistics, but it’s so fast, 01:00:08.619 --> 01:00:12.878 even on my laptop, that I can’t notice it running. 01:00:12.878 --> 01:00:17.220 Notice that rate of exceedance, if that’s how we want to present PSHA, 01:00:17.220 --> 01:00:22.210 will hide non-Poissonian behavior and – which increases with lower 01:00:22.210 --> 01:00:27.780 rates and higher variability. Lower rates are equivalent to shorter 01:00:27.780 --> 01:00:32.280 time periods, which are used in re-insurance applications. 01:00:32.280 --> 01:00:34.420 For one exceedance, the Poisson model is actually pretty good. 01:00:34.420 --> 01:00:40.175 So, for a lot of what we do, the Poisson model is fine, and that actually confirms 01:00:40.175 --> 01:00:43.667 work by Marzocchi and Taroni, who basically inferred this 01:00:43.667 --> 01:00:49.619 from a logical argument. But it’s not actually a good model 01:00:49.619 --> 01:00:54.699 for higher probabilities that may be used for some applications. 01:00:54.699 --> 01:00:58.730 For greater numbers of exceedances, the Poisson model is not always 01:00:58.730 --> 01:01:01.730 a good approximation, even at lower probabilities. 01:01:01.730 --> 01:01:04.380 And something we’re going to do in the future is start applying this 01:01:04.380 --> 01:01:08.950 order of statistics approach to extend past work on aftershock PSHA, 01:01:08.950 --> 01:01:14.140 which actually used non-stationary time-dependent Poisson models. 01:01:14.140 --> 01:01:16.058 And we can actually include the true variability we see 01:01:16.094 --> 01:01:18.900 in aftershock sequences. And I think this could give us a way 01:01:18.900 --> 01:01:25.380 to get to a full national operational earthquake forecast in a way that 01:01:25.380 --> 01:01:30.625 we can actually compute in real time. So, thank you. I’ll stop there. 01:01:33.180 --> 01:01:35.855 [silence] 01:01:35.855 --> 01:01:42.190 - Thank you, Andy, for that talk. If anyone has questions, please feel free 01:01:42.190 --> 01:01:46.933 to type them in the chat, raise your hand, or you can simply dive in. 01:01:46.933 --> 01:01:49.460 Turn your camera on, and microphone, and ask away. 01:01:49.460 --> 01:01:54.630 [chime sound] So far, there are no questions in the chat. 01:01:54.630 --> 01:02:00.210 So I will – I can kick off with a question going back to how you 01:02:00.210 --> 01:02:06.240 might – how you would – you essentially describe a fairly 01:02:06.240 --> 01:02:12.582 generic model for applying to these pretty complex – or, poorly understood 01:02:12.582 --> 01:02:14.609 sequences of earthquakes around the caldera. 01:02:14.609 --> 01:02:18.390 So how might you change this? Or, can you talk a little bit more about 01:02:18.390 --> 01:02:22.369 the varying mechanisms and rates of the earthquakes themselves 01:02:22.369 --> 01:02:24.701 in these different cases, with the caldera collapses, right – 01:02:24.701 --> 01:02:30.800 some have absolutely none. Some have – the mechanism 01:02:30.800 --> 01:02:33.500 seems to differ for why these are happening. And … 01:02:33.500 --> 01:02:35.260 - Yeah. - … who would – how would you 01:02:35.260 --> 01:02:40.199 actually implement those sorts of different [inaudible] ... 01:02:40.199 --> 01:02:42.933 - Well, I think the – one way we could it is – 01:02:42.933 --> 01:02:44.529 I mean, there seems to be, obviously, 01:02:44.529 --> 01:02:47.730 some relationship between the size of the collapse and the 01:02:47.730 --> 01:02:52.390 number of earthquakes in it. It’s not a simple enough relationship 01:02:52.390 --> 01:02:55.130 for us to implement it at this point. We’ve just considered them 01:02:55.130 --> 01:03:00.109 all one class. So, if we could – if we could get better at, say, 01:03:00.109 --> 01:03:04.019 the size of collapses, that might give us a better forecast of the 01:03:04.019 --> 01:03:10.339 size of future collapses and the number of earthquakes. 01:03:10.339 --> 01:03:14.150 I think the other thing that’s not taken into account here is – that worried 01:03:14.150 --> 01:03:21.457 me a lot – is to what degree did the 2018 eruption reset the system? 01:03:21.457 --> 01:03:24.819 You know, were we – I mean, here we are, all the sudden, 01:03:24.819 --> 01:03:27.949 after 20 years, redoing the Hawaii hazard model. 01:03:27.949 --> 01:03:31.450 And we have this monstrous eruption with all these really interesting 01:03:31.450 --> 01:03:35.450 earthquakes in it. And we have to immediately incorporate them. 01:03:35.450 --> 01:03:38.839 Well, you know, did that collapse just make that – a future collapse 01:03:38.839 --> 01:03:43.070 much less likely in the next 50 years? Or is the system in a situation 01:03:43.070 --> 01:03:48.542 right now where it’s more likely to have another collapse? 01:03:48.542 --> 01:03:52.579 And, you know, over the last month, actually, the bottom 200 meters of the 01:03:52.579 --> 01:03:55.420 caldera – of that collapsed area have now filled in with lava again. 01:03:55.420 --> 01:03:57.430 So it’s already refilling with lava. 01:03:57.430 --> 01:04:01.925 So I really don’t think I can rule out future collapses in the next 50 years. 01:04:01.925 --> 01:04:05.380 And I think an interesting thing is, when the – when the volcanologists 01:04:05.380 --> 01:04:09.529 talk about hazard, they’re often talking about the response – 01:04:09.529 --> 01:04:12.369 the hazard due to an eruption if it happens. 01:04:12.369 --> 01:04:15.319 So very important things like, here’s where the lava would run. 01:04:15.319 --> 01:04:17.560 You know, which you can try to forecast based on 01:04:17.560 --> 01:04:20.480 where the vents are and where they – what the topography is. 01:04:20.480 --> 01:04:23.488 That’s essentially our ground motion prediction equations. 01:04:23.488 --> 01:04:28.099 They get very hesitant about actual probabilistic hazard 01:04:28.099 --> 01:04:32.605 in the way we do it – at least, that’s been my experience talking to them. 01:04:32.605 --> 01:04:35.150 And I think, you know, it’s a very complicated system. 01:04:35.150 --> 01:04:40.839 And it’s probably less constant and time-independent than, say, 01:04:40.839 --> 01:04:44.222 plate motions driving earthquakes on the San Andreas. 01:04:44.222 --> 01:04:48.089 So I think the more we – I think my biggest uncertainty in there is probably 01:04:48.089 --> 01:04:54.996 really – you know, these really big collapses, what happens after them? 01:04:54.996 --> 01:04:56.910 Because I really think we need to think about forecasting 01:04:56.910 --> 01:05:00.750 not just any 50-year period, but the next 50 years. 01:05:02.363 --> 01:05:04.710 - Do you think also – with the earthquakes themselves, I mean you 01:05:04.710 --> 01:05:07.539 showed these plots where you can take the average ground motion, right, but 01:05:07.539 --> 01:05:13.738 the ground motion varies substantially, even within this 2018 sequence. 01:05:13.738 --> 01:05:16.417 You know, the frequency content distribution. 01:05:16.453 --> 01:05:21.809 Do you suspect that that varies between different collapse events? 01:05:21.809 --> 01:05:25.316 And how might that change what you’re … 01:05:25.316 --> 01:05:27.780 - Oh, from one collapse event to another? 01:05:27.780 --> 01:05:29.670 - Yeah. - It’s an interesting question. 01:05:29.670 --> 01:05:32.199 There’s been some questions about, say, resonance in the magma 01:05:32.199 --> 01:05:36.570 chambers and if the magma chamber was very different, and that’s a factor. 01:05:36.570 --> 01:05:43.079 Sure, it could. But I think we have enough sequences where these events 01:05:43.079 --> 01:05:44.902 seem to have similar – I mean, [inaudible] 01:05:44.902 --> 01:05:47.183 and they also think they’re similar mechanisms. 01:05:47.183 --> 01:05:51.910 I don’t actually know about the spectral accelerations there. 01:05:51.910 --> 01:05:54.940 I think there are likely to be, you know, similar sorts of things. 01:05:54.940 --> 01:05:59.910 They’re – you know, in – also the behavior we saw in the Galapagos is – 01:05:59.910 --> 01:06:02.690 seems like these were earthquakes at the beginning of each – 01:06:02.690 --> 01:06:04.980 of a down-dropping, you know, the way they had ramping-up 01:06:04.980 --> 01:06:08.519 earthquakes then a sudden cutoff. 01:06:08.551 --> 01:06:14.119 So I’m guessing the source mechanism is similar and non-tectonic. 01:06:14.119 --> 01:06:17.030 And so maybe the spectral will be similar. 01:06:18.496 --> 01:06:22.869 All right. Brian Shiro asks – he says thanks – thanks for 01:06:22.869 --> 01:06:26.170 an interesting analysis. What do you think of the Butler 2020 01:06:26.170 --> 01:06:31.433 paper on a reverse aftershock description for the collapsed sequences? 01:06:31.433 --> 01:06:33.400 - Yeah. So I have looked at that paper a little bit. 01:06:33.400 --> 01:06:36.550 And there’s also a paper by a student from Davis who 01:06:36.550 --> 01:06:42.074 I think also looked at accelerating release time into them. 01:06:42.074 --> 01:06:45.079 I think what’s fascinating about these earthquakes is that you have 01:06:45.079 --> 01:06:48.970 some sort of failure process that’s accelerating, then the magnitude 5s 01:06:48.970 --> 01:06:53.480 are some sort of release of pressure, and down-dropping, and shutoff. 01:06:53.480 --> 01:06:56.790 I think they’re fascinating. I don’t think they affect the hazard very much. 01:06:56.790 --> 01:06:59.930 Because those small earthquakes aren’t producing that much ground motion. 01:06:59.930 --> 01:07:01.917 We can leave them out. 01:07:01.917 --> 01:07:05.699 It did mean, for instance, that we didn’t try putting an ETAS model on these. 01:07:05.699 --> 01:07:07.029 Because the ETAS model [chuckles] would be 01:07:07.029 --> 01:07:10.847 the magnitude 5 happens, then everything happens after it. 01:07:10.847 --> 01:07:12.280 So I think it’s fascinating. 01:07:12.280 --> 01:07:19.394 I’m not sure it affects what I would do here, how those papers turn out. 01:07:22.299 --> 01:07:26.807 - Thanks for those thoughts. So Morgan Page asks – well, points out 01:07:26.832 --> 01:07:29.789 that she’s also interested in your thoughts on just skipping over 01:07:29.789 --> 01:07:33.920 magnitude entirely and having just a probability distribution for 01:07:33.920 --> 01:07:39.136 ground motion. Is that something we should consider elsewhere also? 01:07:39.136 --> 01:07:42.170 - Well, in essence, we – well, okay. 01:07:42.691 --> 01:07:45.530 Here, we can do it basically – I mean, I still took a – I had to take 01:07:45.530 --> 01:07:48.950 a class of earthquakes 5 and above. I could have taken 4 and above, 01:07:48.950 --> 01:07:52.220 except for, I don’t know that they computed the spectral accelerations 01:07:52.220 --> 01:07:56.299 for all the 4s and above. So, if we have the ground motions 01:07:56.299 --> 01:08:01.519 for a class of earthquakes, yes, we can just use an empirical model. 01:08:01.519 --> 01:08:06.519 You know, the problem is, we have very few recordings of large earthquakes. 01:08:06.519 --> 01:08:10.920 And so we wind up using GMPEs and models so we can, you know, 01:08:10.920 --> 01:08:14.230 extend them around the world. And then this gets to – for instance, 01:08:14.230 --> 01:08:17.670 I think, you know, the paper that Kevin Milner et al. just published 01:08:17.670 --> 01:08:23.190 where they used a earthquake simulator to produce possible earthquakes and 01:08:23.190 --> 01:08:27.253 then computed ground motions due to those earthquakes using CyberShake. 01:08:27.293 --> 01:08:32.420 So, you know, to get a large suite of earthquakes for southern California, 01:08:32.420 --> 01:08:37.600 they had to resort to simulations. That’s one approach to doing that. 01:08:37.600 --> 01:08:42.560 Yeah, it was sort of nice, in this case, that, you know, for this very specific 01:08:42.560 --> 01:08:45.320 case of the station UWE, which is close to HVO, 01:08:45.320 --> 01:08:48.900 I can just use the ground motions. I do need to pick a class of earthquakes, 01:08:48.900 --> 01:08:53.769 in some sense, that my data set of ground motions represents. 01:08:53.769 --> 01:08:57.863 And so here I used magnitude 5 and above. 01:08:57.863 --> 01:09:00.542 - Well, it was nice for you because you didn’t really have a magnitude 01:09:00.573 --> 01:09:02.621 distribution. [laughs] It was well-defined for 01:09:02.652 --> 01:09:04.880 your earthquakes. [laughs] - Well, actually, I mean, 01:09:04.880 --> 01:09:07.850 there is a magnitude – it actually – it’s almost a normal distribution 01:09:07.850 --> 01:09:11.699 centered on magnitude 5.3. I could put that in. 01:09:11.699 --> 01:09:17.300 I mean, the way we combine magnitudes in GMPEs is done 01:09:17.300 --> 01:09:20.832 essentially as an empirical distribution too, so ... 01:09:21.763 --> 01:09:23.073 - Yeah. 01:09:24.128 --> 01:09:27.597 - But, yeah, I liked skipping that step. [laughs] 01:09:29.207 --> 01:09:33.690 - All right. Thanks for this interesting talk and the thoughtful answers, Andy. 01:09:33.690 --> 01:09:37.100 I’ll – we can turn on our microphones and give a brief round of applause 01:09:37.100 --> 01:09:40.850 for Andy, and then we’ll finish the recording here. 01:09:40.850 --> 01:09:44.410 [applause] 01:09:44.410 --> 01:09:45.875 - Thank you. - Thank you. 01:09:45.900 --> 01:09:47.613 - Thanks, Andy. 01:09:47.613 --> 01:09:50.480 - Thanks for the talk. So if anyone wants to stay around, we’ll – 01:09:50.480 --> 01:09:53.781 the meeting will stay open and you can chat a little bit more. 01:09:53.781 --> 01:09:57.710 I’ve got to take off, but thank you all.