WEBVTT 00:00:00.000 --> 00:00:03.000 Alright, sar i'm hitting record now. 00:00:03.000 --> 00:00:12.000 Ok welcome back. So we have one last exciting session for everyone, and then we are. 00:00:12.000 --> 00:00:15.000 Done for the day, so let us start by bringing up. 00:00:15.000 --> 00:00:21.000 Killian and morgan page, whoa. 00:00:21.000 --> 00:00:24.000 I'll kick. I'll kick it off. So christy asked. 00:00:24.000 --> 00:00:32.000 Wouldn't it be great to have a lot of paleo seismic data? And our 1st talk today by michael oskin is gonna. 00:00:32.000 --> 00:00:38.000 Hopefully demonstrate the cool stuff that we can do with alios seismic data. So with that. 00:00:38.000 --> 00:00:41.000 Take it away. 00:00:41.000 --> 00:00:46.000 Hello, and thank you for attending my presentation. Let's get started. 00:00:46.000 --> 00:00:52.000 Seismic data are currently under utilized for understanding time, dependent earthquake hazard. 00:00:52.000 --> 00:00:58.000 Here i am, showing 2 paleo seismic sites from california for faults that slip at about a centimeter per year. 00:00:58.000 --> 00:01:04.000 With similar average earthquake recurrence. Currently these 2 sites are treated the same for time to visit hazard. 00:01:04.000 --> 00:01:08.000 But, as you can see from these time series, and from the coefficient of variation. 00:01:08.000 --> 00:01:17.000 They are quite different. The san yucinto fault. Exhibits a much less regular earthquake return time than the hayward fault. 00:01:17.000 --> 00:01:23.000 When we look more broadly at paleo seismic time series, we find that they are in general not very periodic. 00:01:23.000 --> 00:01:28.000 This is a compilation of cov. From paleo-size records ordered by fault, slipgrate. 00:01:28.000 --> 00:01:36.000 You want it all? In 2018. And most sites fall within a range of point 4 to point 8, which means that the standard deviation of recurrence. 00:01:36.000 --> 00:01:44.000 Is a significant fraction of the mean. Now pentheism time series are quite noisy because. 00:01:44.000 --> 00:01:47.000 It's difficult to date. The events often from bracketings. 00:01:47.000 --> 00:01:53.000 Stratagraphic layers. But that's not a reason to dismiss the data. 00:01:53.000 --> 00:01:57.000 我们addition to the ages of events，there is the ordering of events。 00:01:57.000 --> 00:02:03.000 And that irregularity up. Persist through multiple events in the time series. 00:02:03.000 --> 00:02:09.000 So what i'm showing here. Is the hog lake, paleo-sizebook site on the san yucinto fault. 00:02:09.000 --> 00:02:18.000 And the individual peaks there correspond to events, and the color corresponds to the length of the previous intersismic interval. 00:02:18.000 --> 00:02:23.000 With orange colors, meaning short relative to the mean and purple colors, meaning long relative to the mean. 00:02:23.000 --> 00:02:30.000 And the intensity of the color corresponds to the standard deviation of that interval relative to the mean. 00:02:30.000 --> 00:02:36.000 And we can see here. There are some quite high confidence intervals that are short as well as long. 00:02:36.000 --> 00:02:39.000 And explaining. This is an important part of the problem. 00:02:39.000 --> 00:02:44.000 Of understanding, time, dependent, hazard. 00:02:44.000 --> 00:02:53.000 Now i will be comparing in this talk. 2 probability distributions, 4 time dependent earthquake, hazard. 00:02:53.000 --> 00:02:59.000 Brownie, and passes time and the wibal distribution. The difference between these distributions is important. 00:02:59.000 --> 00:03:06.000 Both for predicting the time, dependence of. The likelihood of the next earthquake, and for understanding earthquake physics. 00:03:06.000 --> 00:03:09.000 And what i'm going to show is that the viable distribution. 00:03:09.000 --> 00:03:19.000 Fits better, and is a plausible outcome of spatially controlled time, dependent hazard along a fault. 00:03:19.000 --> 00:03:24.000 Let's start by looking at this classic figure from shimazakhi and nakeda in 1980. 00:03:24.000 --> 00:03:34.000 Strictly periodic bavior would be predicted. If the fault always climbs from a lower threshold, stress tau 2 to an upper threshold, stress tau, one. 00:03:34.000 --> 00:03:39.000 At a constant rate of loading, and then the earthquake returns us back to the lower threshold. 00:03:39.000 --> 00:03:44.000 Time, predictable baviour. Would occur if. 00:03:44.000 --> 00:03:48.000 The size of the earthquake predicted. The time the wait to the next one. 00:03:48.000 --> 00:03:53.000 Where smaller events would have a shorter time to wait till the next event. 00:03:53.000 --> 00:04:00.000 Slip. Predictable model is the opposite. Where the longer we wait the larger, the next event will be. 00:04:00.000 --> 00:04:04.000 In a paleo seismic study of the rightwood site of the san andreas. Fault. 00:04:04.000 --> 00:04:08.000 Where weldon at all in 2,004 were able to get timing and. 00:04:08.000 --> 00:04:12.000 Slip. They showed that none of these models fit very well. 00:04:12.000 --> 00:04:17.000 The time principal model. So a slight hint that the largest events. 00:04:17.000 --> 00:04:22.000 In the upper right of that plot. Were followed by the longest wait times, so. 00:04:22.000 --> 00:04:30.000 A weak dependence, and the select predictable model was essentially anti-correlated. 00:04:30.000 --> 00:04:37.000 Most paleo seismic sites don't give us slip per event, and therefore we can't do the kind of tests that weldon at all showed. 00:04:37.000 --> 00:04:42.000 Instead, all we have is earthquake, timing. And that's what we're going to be using here. 00:04:42.000 --> 00:04:48.000 Showing here the example in this slide of. A site on the altitog in china. 00:04:48.000 --> 00:04:55.000 Where there are 9 earthquake events. and the event timing is shown by the inset plot at lower right. 00:04:55.000 --> 00:05:02.000 I'm gonna be taking those event ages differences by sampling who the time series to produce intervent times. 00:05:02.000 --> 00:05:06.000 And then looking at the distribution of inter-event times. 00:05:06.000 --> 00:05:10.000 Plotted in rank order in acculative probability plot, as shown here. 00:05:10.000 --> 00:05:16.000 And then fitting distribution, functions. To those plots. 00:05:16.000 --> 00:05:22.000 Now we're going to be comparing the brownian pest time model to the wibble model. So let's look more closely at each of these. 00:05:22.000 --> 00:05:27.000 Brownian passage time model is an evolution of the characteristic earthquake model. 00:05:27.000 --> 00:05:32.000 Is defined by both. A ground state. And an upper straight, where the earthquake occurs. 00:05:32.000 --> 00:05:38.000 And then the variation in timing. Is caused by perturbations in the loading path. 00:05:38.000 --> 00:05:42.000 The greater the size and frequency of perturbations. The. 00:05:42.000 --> 00:05:48.000 More irregular. The time series becomes. This model is the model now presently used in the. 00:05:48.000 --> 00:05:58.000 Time dependent national seismic hazard model. The viable distribution is a model that's widely applied in survival analysis. 00:05:58.000 --> 00:06:02.000 It is best to think about it. In my view in terms of its hazard function. 00:06:02.000 --> 00:06:09.000 A hazard function. The probability of an event happening given that it hasn't happened yet. 00:06:09.000 --> 00:06:17.000 The probability of an earthquake on the san andreas fault in northern california, given that it hasn't happened in in 120 years. 00:06:17.000 --> 00:06:22.000 The viable distribution defined by a hazard function. That's a power law of time. 00:06:22.000 --> 00:06:26.000 TV raised to a power k. If k is 0. 00:06:26.000 --> 00:06:29.000 Then the hazardous time independent. It's the same every year. 00:06:29.000 --> 00:06:35.000 If it's 1, then it's increasing linearly. Say. In proportion to steady loading of the fault. 00:06:35.000 --> 00:06:41.000 If it's much greater than one, we start to approach periodic bavior. 00:06:41.000 --> 00:06:44.000 This is the pdf. And cdf of the viable distribution. 00:06:44.000 --> 00:06:49.000 And if we derive from that the hazard function we find that is indeed. 00:06:49.000 --> 00:06:59.000 Proportional to a power law of time. Now let's look at the rightwood site on the san andreas fault. Using these 2 distributions. 00:06:59.000 --> 00:07:03.000 This is a plot of the inter event. Times in rank order. 00:07:03.000 --> 00:07:10.000 And you can see that they range from a few decades to over 200 years. So quite a bit of variation. 00:07:10.000 --> 00:07:17.000 For each individual time series that i've sampled from the paleo seismic data. I fit a brownian passage, time, distribution. 00:07:17.000 --> 00:07:23.000 Shown here with the orange lines. Any viable distribution shown that the blue lines. 00:07:23.000 --> 00:07:28.000 And you can see visually the libel distribution fits the distribution of inter event times. 00:07:28.000 --> 00:07:33.000 Much better than the brownian passage. Time. We can show this more quantitatively. 00:07:33.000 --> 00:07:40.000 By taking each individual distribution, fit. And differences, their log likelihood. 00:07:40.000 --> 00:07:48.000 How well they fit. The individual data points. And then i can show that on the histogram here to see the aggregate of all the sampling through the. 00:07:48.000 --> 00:07:59.000 Repeated, sampling through the time series. And what you see is that most of those samplings are better fit by the wabble distribution than the brownian passes. Time, distribution. 00:07:59.000 --> 00:08:08.000 Now i've extended it here in this figure to the 8 longest paleo seismic sites that are available from the san andreas fault and san dieucinto fault in california. 00:08:08.000 --> 00:08:14.000 And from the alpine fault in new zealand. And there are 2 things that jp out right away. One. 00:08:14.000 --> 00:08:22.000 You can see a lot of blue on those histograms, so for most of these sites the viable distribution fits better than brownie, and passage. Time. 00:08:22.000 --> 00:08:27.000 in one example. At the mystic lake site, the. 00:08:27.000 --> 00:08:34.000 Distribution tends to fit equally well and the same thing for lake purringa site on the alpine fold. 00:08:34.000 --> 00:08:38.000 The second thing that jps out is the hazard exponents are quite different. 00:08:38.000 --> 00:08:48.000 The shape of these distributions also shows that. The san andreas fault and sanjinto fault in california tend to have hazard exponents that are equal to one or less. 00:08:48.000 --> 00:08:55.000 Whereas the alpine fault has hazard exploits that are greater than 2. 00:08:55.000 --> 00:09:00.000 So now let's look at this in terms of hazard functions. So this is a plot of hazard function. 00:09:00.000 --> 00:09:06.000 Hazard on the vertical axis. And the elapsed time from the prior event on the horizontal axis. 00:09:06.000 --> 00:09:13.000 And the black lines are the mean, hazard function, and the green and other colored lines represent individual sample fits. 00:09:13.000 --> 00:09:21.000 To the paleo-sizebook time series. And you can see here that the alpine fault with the green lines. 00:09:21.000 --> 00:09:28.000 Has this very nonlinear hazard function? Early on for the 100 to 150 years. The hazard is very low. 00:09:28.000 --> 00:09:33.000 And then it accelerates and become an increase is nonlinearly. 00:09:33.000 --> 00:09:35.000 That's kind of what we expect faults to do. 00:09:35.000 --> 00:09:41.000 They have this early time, period, where lasted rebound means the probability of another event is low. 00:09:41.000 --> 00:09:46.000 And then the likelihood takes off as we wait longer. 00:09:46.000 --> 00:09:52.000 The san andreas and san juiceento fault, though don't show that kind of bavior. Their hazard functions are either linear. 00:09:52.000 --> 00:10:00.000 Or have exponents less than one. They're all climbing. So the hazard is all increasing at these sites. 00:10:00.000 --> 00:10:06.000 But the hazard is either. Is increased as quickly. Early on. 00:10:06.000 --> 00:10:10.000 And so there's a much higher likelihood of short return times on these faults. 00:10:10.000 --> 00:10:12.000 认为没有point fault。 00:10:12.000 --> 00:10:15.000 Another way. To look at this data is to compare it. 00:10:15.000 --> 00:10:19.000 By multiplying the inter event, time by the slip rate. 00:10:19.000 --> 00:10:23.000 And then comparing that to. Independent measurements of slipper, event. 00:10:23.000 --> 00:10:33.000 Now there's really sparse data for this, for the alpine fault, but with data does exist, indicates that the events on the alpine fault are large, with between 6 and 8 meters of slip. 00:10:33.000 --> 00:10:38.000 Per earthquake, earthquake. The san andreas and the san juinto fault average. 00:10:38.000 --> 00:10:48.000 2 to 4 meters of slip per event. The events are more frequent, and they are smaller. 00:10:48.000 --> 00:10:56.000 This point is really brought home by looking at reconstructions of the paleo earthquake record from multiple paleo seismic sites. 00:10:56.000 --> 00:11:01.000 Here's a figure for the central part of the alpine fault from hoorthodol, 2021. 00:11:01.000 --> 00:11:04.000 And most of the events can be correlated across the fault. 00:11:04.000 --> 00:11:14.000 The earthquakes are infrequent, but they are large. And the time interval on average, for between events on the fault is long. 00:11:14.000 --> 00:11:21.000 The san andreas fault baves quite differently. This is the maxim rupture model reconstructed by sharer and yule. 00:11:21.000 --> 00:11:23.000 And what you see is that most events. 00:11:23.000 --> 00:11:29.000 Are short, partial ruptures. The frequency of events. Overall in the fault is much higher. 00:11:29.000 --> 00:11:35.000 And events that are system spanning, rupturing, say, more than two-thirds of the fault. 00:11:35.000 --> 00:11:45.000 Are very, very uncoon. So. How do we put this contrasting fault bavior into a single self-consistent model. 00:11:45.000 --> 00:11:49.000 I believe it has to do with the spatial contribution of a fault. 00:11:49.000 --> 00:11:58.000 To the hazard at a particular observation site. So imagine a fault loading at time. T. 1 to t. 5, shown in the left here. 00:11:58.000 --> 00:12:01.000 And then our paleo seismic site in the middle of the fault. 00:12:01.000 --> 00:12:05.000 The likelihood that an earthquake will rupture through that site. 00:12:05.000 --> 00:12:10.000 Is an integral of the hazard along nearby part of the fault, with more distant areas. 00:12:10.000 --> 00:12:17.000 Contributing less likelihood than earthquakes, that rupture. Or initiate close to our site. 00:12:17.000 --> 00:12:22.000 For the case of the alpine fault, it exhibits a system spanning rupture, mode. 00:12:22.000 --> 00:12:32.000 The raptures tend to be large rupture through all the paleo-size, and they probably reset the fault below a minim level of loading to nucleate the next earthquake. 00:12:32.000 --> 00:12:39.000 And so we have an elastic rebound type process, and there's a wait time until we start to have enough loading to nucleate an event. 00:12:39.000 --> 00:12:42.000 And then we rapidly connect all those areas together. 00:12:42.000 --> 00:12:47.000 Into a probability. Of the next earthquake occurring. 00:12:47.000 --> 00:12:52.000 是的。 00:12:52.000 --> 00:12:56.000 The san andreas and sanus sptuffault. Exhibit a partial rupture, mode. 00:12:56.000 --> 00:13:05.000 In general, the level of hazard is higher. And the previous earthquakes may not be large enough to reset the fault below that ground, stating. 00:13:05.000 --> 00:13:22.000 Therefore elastic rebound doesn't necessarily apply. Subsequent events may be shorter. Partial ruptures that don't break through our paleo-sismic site, but they do contribute to reducing the hazard at that site, because they lower the hazard contribution from those adjacent parts of the fault. 00:13:22.000 --> 00:13:26.000 And this gives rise to something i call the survivor effect. 00:13:26.000 --> 00:13:31.000 You have a patch of fault between other parts of the fault that it ruptured. 00:13:31.000 --> 00:13:38.000 It may exhibit this decelerating hazard over time, because of that loss of the contribution from the nearby parts of the fall. 00:13:38.000 --> 00:13:44.000 And so this gives rise to the 2 contrasting hazard functions that we observed from the paleo-size data. 00:13:44.000 --> 00:13:49.000 And it is consistent with a slipper event data. We also observe. 00:13:49.000 --> 00:13:54.000 Do we live in an unusual times. Well, yes and no. 00:13:54.000 --> 00:14:02.000 Looking at the distribution of inter-event times. None of the open intervals we see for the southern zend andreas fallop. 00:14:02.000 --> 00:14:07.000 Or northern san andrea's fault lie outside the range of intervent times that are observed. Paleo seismically. 00:14:07.000 --> 00:14:15.000 So not that unusual. But we do live in a time that followed 2 very large events on the san andreas fall. 00:14:15.000 --> 00:14:17.000 1,857. 00:14:17.000 --> 00:14:21.000 We're both unusually long, large events, with a lot of slip. 00:14:21.000 --> 00:14:24.000 And so, if there's any time when this system's going to have. 00:14:24.000 --> 00:14:30.000 Longer intervent time. Time pitcherable bavior. It would be now. 00:14:30.000 --> 00:14:37.000 In the perhaps the coincidence of large events of both the northern and southern part of the falls is unusual. 00:14:37.000 --> 00:14:45.000 What about other faults? Well, there's not a lot of records to go on, but a sampling of them indicates that the partial rupture mode is the norm. 00:14:45.000 --> 00:14:49.000 Here are 2 sites on the dead seafall, where the records are shorter, but the. 00:14:49.000 --> 00:14:57.000 The historic constraints are really good, and they both indicate hazard exponents less than one. 00:14:57.000 --> 00:15:01.000 Here's the turbid record from the cascadia subduction zone. 00:15:01.000 --> 00:15:07.000 And both central cascade and southern cascadia show hazard exponents near unity or less. 00:15:07.000 --> 00:15:12.000 So not the strongly periodic bavior we see for the alpine vault which. 00:15:12.000 --> 00:15:20.000 Appears to be unusual. Hideous hazard records from california and new zealand show contrasting time, dependent recurrence bavior. 00:15:20.000 --> 00:15:28.000 Both well fit by the viable distribution. The alpine fault exhibits a system-spanning rapture mode with hazard that increases nonlinearly. 00:15:28.000 --> 00:15:35.000 San andreas and san yussinto faults exhibit a partial rupture mode with chaotic, variably sized, and more frequent events. 00:15:35.000 --> 00:15:41.000 The partial rupture mode appears to be coon. More frequent events and rapid post event, hazard increase. 00:15:41.000 --> 00:15:44.000 Thank you. 00:15:44.000 --> 00:15:55.000 Alright. Thank you very much, mike. We're gonna have time for oral questions at the end of the session, after all, 3 speakers. But you can continue to use the chat, to make coents and ask questions. 00:15:55.000 --> 00:15:59.000 next up. We have le saltage from guy carpet, carpenter. 00:15:59.000 --> 00:16:06.000 Who's going to be talking about modeling, long term fault, memory. 00:16:06.000 --> 00:16:13.000 Hello, my name is le saltich, and today i'm going to be discussing modeling, long-term fault, memory. 00:16:13.000 --> 00:16:22.000 And i'd like to give. my thanks to all of my colleagues and co-authors on this talk. 00:16:22.000 --> 00:16:27.000 And now we'll go ead and get started. So 1st we'll discuss. 00:16:27.000 --> 00:16:33.000 Earthquake cycles, and then move up to this concept of earthquake supercycles. 00:16:33.000 --> 00:16:44.000 So since the 19 6, san francisco, earthquake. Dominant paradigm has been the earthquake cycle in which a strain acculates between large earthquakes. 00:16:44.000 --> 00:16:56.000 And is released by fault slip when an earthquake occurs over time. This should cause quasiperiodic earthquakes, and a steady acculation of culative displacement. 00:16:56.000 --> 00:17:07.000 However, long earthquake records often show more complex bavior. Supercycles appear as patterns longer than individual earthquake cycles. 00:17:07.000 --> 00:17:13.000 In the often clustered earthquake. History, culative displacement, and culative strain records. 00:17:13.000 --> 00:17:24.000 Such long term variability is often difficult to reconcile with coonly used models of earthquake recurrence. 00:17:24.000 --> 00:17:31.000 Super cycles have been observed in many tectonic environments at many timescales. 00:17:31.000 --> 00:17:36.000 here. We're showing a selection of some of these places where. 00:17:36.000 --> 00:17:46.000 Super cycles have been proposed. The best data come from plate boundaries, because rapid plate motion gets shorter, and hence easier to observe cycles. 00:17:46.000 --> 00:17:55.000 Super cycles have also been identified in plate, boundary zones, and in continental interiors. 00:17:55.000 --> 00:18:04.000 So this leads to the following questions. How do we characterize or identify super cycles or clusters in earthquake records. 00:18:04.000 --> 00:18:09.000 What causes, super cycles. How do they arise from steady plate, motion. 00:18:09.000 --> 00:18:16.000 And how do they affect our ability to assess earthquake hazards. 00:18:16.000 --> 00:18:26.000 To the 1st question. Earthquake sequences are often characterized by their aperiodicity, which is the extent that they differ from perfectly periodic. 00:18:26.000 --> 00:18:29.000 This is also termed the coefficient of variation. 00:18:29.000 --> 00:18:37.000 就是finds alpha equals sigma over mu，where mu and sigma are the mean and standard deviation of the recurrence intervals。 00:18:37.000 --> 00:18:42.000 Alpha equals 0 is a perfectly periodic sequence, because. 00:18:42.000 --> 00:18:51.000 Standard deviation is 0. Alpha equals, one could correspond to a sequence produced by an ideal poisson process, because sigma is equal to mu. 00:18:51.000 --> 00:18:55.000 But it can also arise from other stochastic processes. 00:18:55.000 --> 00:19:07.000 Although sequences with alpha greater than one, are often termed, clustered. We prefer to use the term bursty, because sequences with alpha. Less than one can also be quite clustered. 00:19:07.000 --> 00:19:12.000 Sequences from the previous slide, which have all been proposed to have supercycles and clusters. 00:19:12.000 --> 00:19:24.000 Follow along the entire range of this aperiodicity spectr from 0 all the way to greater, much greater than one. 00:19:24.000 --> 00:19:29.000 周四，a little bit deeper at these aperiodicity issues。 00:19:29.000 --> 00:19:34.000 and in specifically in using them to characterize sequences. 00:19:34.000 --> 00:19:38.000 Sequences with the same aperiodicity can be quite different. 00:19:38.000 --> 00:19:44.000 Because the aperiodicity depends only on the mean and standard deviation of the intervent times. 00:19:44.000 --> 00:19:47.000 It does not depend on the order of events. 00:19:47.000 --> 00:19:57.000 So here we have an example of 2 earthquake sequences, with the same aperiodicity where the top looks clustered. 00:19:57.000 --> 00:20:08.000 The bottom. Looks like it's changing from a longer recurrence time in the past to more recent shorter recurrence times, and they have the exact same aperiodicity. 00:20:08.000 --> 00:20:15.000 So let's look at another. Issue in aperiodicity to characterize sequences. 00:20:15.000 --> 00:20:22.000 Sequences with nominally quasiperiodic aperiodicity. So adds alpha, less than one. 00:20:22.000 --> 00:20:31.000 Can be quite clustered here. We show how the aperiodic changes by increasing the length of the gaps between clusters. 00:20:31.000 --> 00:20:38.000 Although all look clustered to the eye. Sequences, with. 00:20:38.000 --> 00:20:43.000 An alpha about equal to one which often appear, need not be. 00:20:43.000 --> 00:20:51.000 Interpreted as resulting from a poisson process. 00:20:51.000 --> 00:21:00.000 Which leads us to probability, models. Neither of the coon models for large earthquake recurrence include super cycles. 00:21:00.000 --> 00:21:02.000 So啊。 00:21:02.000 --> 00:21:05.000 One coon model is the poisson model. 00:21:05.000 --> 00:21:11.000 我们的probability of large earthquakes is constant with time。 00:21:11.000 --> 00:21:21.000 So the fault has no memory, because timing of previous earthquakes has no bearing on when the next will occur. So clusters arise purely by chance. 00:21:21.000 --> 00:21:27.000 As record length increases, the standard deviation of recurrence intervals approaches the mean. 00:21:27.000 --> 00:21:33.000 This model is non-physical, but it's coonly used in hazard mapping. 00:21:33.000 --> 00:21:43.000 We also have the earthquake cycle or renewal. Model, where the probability of large earthquakes increased with time, until one occurs. 00:21:43.000 --> 00:21:55.000 At which point the probability drops to 0. The fault has only short-term memory, because the probability of a large earthquake depends only on the time since the previous one. 00:21:55.000 --> 00:22:00.000 Recurrence is quasipperiodic. As record length increases. 00:22:00.000 --> 00:22:09.000 The standard deviation becomes less than the mean, and this is increasingly used in hazard mapping. 00:22:09.000 --> 00:22:15.000 We present an alternative. The what we call the long term fault, memory model. 00:22:15.000 --> 00:22:22.000 们reflects acculated strain via a simple model with two parameters。 00:22:22.000 --> 00:22:28.000 The probability grows with time at rate a indicating a steady strain. Acculation. 00:22:28.000 --> 00:22:32.000 And the probability drops after an earthquake by r. 00:22:32.000 --> 00:22:41.000 But not necessarily to 0, indicating a partial strain release. So a controvers the long-term seismicity rate. 00:22:41.000 --> 00:22:47.000 R controls the cluster length. And a small ratio of r. To a. 00:22:47.000 --> 00:22:52.000 The probability can stay high, yielding super cycles and clusters and long-term memory. 00:22:52.000 --> 00:22:58.000 A large ratio of r to a. Gives the usual earthquake cycle model, with only short-term memory. 00:22:58.000 --> 00:23:06.000 So a and r. Control. Overall sequence properties. But when an earthquake occurs is random. 00:23:06.000 --> 00:23:15.000 So the quick probability can depend on many. Asked earthquakes in this model. Not just the most recent one. 00:23:15.000 --> 00:23:17.000 And here's a so. 00:23:17.000 --> 00:23:19.000 锅子technology to help。 00:23:19.000 --> 00:23:29.000 help your understanding of this. So. Faults can have hot streaks like earthquake clusters, where many occur close in time. 00:23:29.000 --> 00:23:34.000 And subs like earthquake gaps, where no earthquakes occur. 00:23:34.000 --> 00:23:40.000 And so we would not predict the performance of a sports team based only on their previous game. 00:23:40.000 --> 00:23:44.000 The rest of the season is likely to be much more useful. 00:23:44.000 --> 00:23:56.000 And similarly, earthquake probabilities depend on the history of many past earthquakes, not just the most recent one. 00:23:56.000 --> 00:24:06.000 So let's look at an example. Where we use the long-term vault memory model to. 00:24:06.000 --> 00:24:14.000 Recreate the palate creek. Paleocyismic sequence in california. So ltfm. 00:24:14.000 --> 00:24:27.000 Parameters can be chosen to match aspects of an earthquake. History such as clustering bavior, although event dates differ between the simulation and observed record due to the model stochastic nature. 00:24:27.000 --> 00:24:42.000 And, as you can see, longer intervals between earthquakes begin at times of low probability, which is consistent with the pattern noted for culative strain by weldon. 00:24:42.000 --> 00:24:47.000 And finally, what is the implication for hazard, estimation? 00:24:47.000 --> 00:24:52.000 So to investigate this we created a 50,000 year simulation. 00:24:52.000 --> 00:24:58.000 And we sampled it for typical paleo seismic record lengths. In this case it's the pallet creek record length. 00:24:58.000 --> 00:25:02.000 And we find that some parts of the look record. Look. 00:25:02.000 --> 00:25:12.000 Strongly periodic. Where alpha is less than point 5, implying a seismic cycle, while others look weekly, periodic, poissonian or birthday. 00:25:12.000 --> 00:25:25.000 And the takeaway here is at a given paleo seismic or instrental window may give a biased view of the long-term seismicity. 00:25:25.000 --> 00:25:30.000 And here is a final example of why clustering is. 00:25:30.000 --> 00:25:39.000 Crucial for infurring earthquake probabilities, using an example of the cascadia subduction zone, where in 2,012. 00:25:39.000 --> 00:25:42.000 你。 00:25:42.000 --> 00:25:49.000 Looked. Clustered, and then in 2,017 it looked a little bit less clustered as a new event was found. 00:25:49.000 --> 00:25:54.000 And i'm. So, whether we asse we are. 00:25:54.000 --> 00:26:00.000 In the most recent cluster matters, much more than the probability density function assed. 00:26:00.000 --> 00:26:10.000 Because within a cluster. Inter event. Times has smaller, mean, and standard deviation, making the next earthquake appear more likely sooner. 00:26:10.000 --> 00:26:16.000 们large even as the paleo seismic record evolves。 00:26:16.000 --> 00:26:27.000 And so assessments of probabilities, including whether a large earthquake is overdue, should specify the assptions made. 00:26:27.000 --> 00:26:32.000 So in smary super cycles and clusters have been observed in many tectonic environments. 00:26:32.000 --> 00:26:42.000 We we propose a simple model, incorporating, long-term fault memory into the seismic cycle which simulates the observed supercycle bavior. 00:26:42.000 --> 00:26:47.000 In ltfm earthquake probability depends on many previous earthquakes. Not just the past. One. 00:26:47.000 --> 00:26:49.000 For a given fault. 00:26:49.000 --> 00:26:55.000 们intervals can look quasiperiodic，implying a seismic cycle。 00:26:55.000 --> 00:27:02.000 They can look poissonian or clustered so short records can give a biased view of long term seismicity. 00:27:02.000 --> 00:27:07.000 And finally, where clusters occur, whether the cluster is assed ongoing can dramatically affect. 00:27:07.000 --> 00:27:15.000 Inferred earthquake probabilities. And this effect can be significantly larger than that of the assed probability. Density, function. 00:27:15.000 --> 00:27:27.000 Or recurrence times. Thank you very much. 00:27:27.000 --> 00:27:34.000 Alright. Thank you for that talk. Le now we find out whether luca. 00:27:34.000 --> 00:27:43.000 Made it to our session. Yes, who's luva here. 00:27:43.000 --> 00:27:45.000 Yes, i am. 00:27:45.000 --> 00:27:53.000 Fantastic. I think everyone needs to applaud luca before he even starts, because he's in singapore and. 00:27:53.000 --> 00:27:58.000 giving us a talk at an ungodly hour of the day. So. 00:27:58.000 --> 00:28:05.000 Thank you for that, and i'll stop talking and let you present. 00:28:05.000 --> 00:28:12.000 Hello, everyone. My name is lucavalio. I am based at the autop, servatorio singapore and the asian school of the environment at. 00:28:12.000 --> 00:28:22.000 Neat technological university. Today i'll be talking about the rapture propagation across full stepovers, and what physics-based models can tell us about seismic hazard. 00:28:22.000 --> 00:28:31.000 Before i begin. I want to acknowledge that this work is the result of collaborative work with a nber of colleagues this, that below. 00:28:31.000 --> 00:28:35.000 The central question of this talk is a simple but important. 00:28:35.000 --> 00:28:47.000 Under what physical conditions can earthquake, rapture, jp. Fault discontinuities, and produce larger events than expected from single-fold models. 00:28:47.000 --> 00:28:51.000 Let me start by setting the context on the left side of. 00:28:51.000 --> 00:29:06.000 Your screen you can see the rapture button from the 2,016 minus 7.8 kikiuda earthquake in new zealand, and on the right side we have the 1,992 min, 7.3 lander's earthquake in california. 00:29:06.000 --> 00:29:10.000 What is striking about these events is the complexities. 00:29:10.000 --> 00:29:19.000 Folds are frequently not isolated. Structures and earthquakes occurring on fault networks can extend across multiple fault segments. 00:29:19.000 --> 00:29:23.000 The kakura earthquake, in particular, is considered the most. 00:29:23.000 --> 00:29:31.000 Complex rapture event i recorded. As it rupture at least a 21 segments. 00:29:31.000 --> 00:29:44.000 Of distinct faults. These rays of fundamental question for say kazarda's assessment, and in particular tried to understand the ability of multiple false segments to rupture within a single earthquake event. 00:29:44.000 --> 00:29:48.000 And this is particularly crucial for assessing the potential of a. 00:29:48.000 --> 00:29:55.000 Upper limits for the earthquake magnitudes in any given region. 00:29:55.000 --> 00:30:03.000 Now, when we think about the rapture propagation, we typically focus on what happens along the fold itself. 00:30:03.000 --> 00:30:10.000 But there is another critical process of killing of fault, and this is the power, elastic response. 00:30:10.000 --> 00:30:15.000 As you can see from this figure when sleep occur on a fault, it creates a distinct. 00:30:15.000 --> 00:30:26.000 Button in the surrounding rocks. On the side of one side of the fault that we observe a pluralistic compaction which increases poor pressure. 00:30:26.000 --> 00:30:32.000 And on the other side we see dilation which decreases poor fluid pressure. 00:30:32.000 --> 00:30:37.000 These instantaneous response in the sleep driven porfly pressure. 00:30:37.000 --> 00:30:48.000 Resulting from pouralastic compaction, ventilation. Can influence capture, propagation across these continues like, fault, step overs. 00:30:48.000 --> 00:30:57.000 So we try to focus on this. Project by running through the seismic cycle simulations. 00:30:57.000 --> 00:31:03.000 In particular to investigate this, so we perform a two-dimensional sequence simulations. 00:31:03.000 --> 00:31:10.000 And what you can see. Here are the snapshots from our models, showing the different stages of a rapture evolution. 00:31:10.000 --> 00:31:14.000 The color scalar represent the slip rate on default. 00:31:14.000 --> 00:31:25.000 With the warmer colors, indicating faster sleep. The key feature to notice is how the rapture interacts with the step. Over the gap between the 2 fold segments. 00:31:25.000 --> 00:31:30.000 The one and folder tube. What our simulation reveal is that. 00:31:30.000 --> 00:31:35.000 Then i make a variation in the effect. Enormous stress, even by these polarastic effects. 00:31:35.000 --> 00:31:42.000 Strongly affect weather, rupture can propagate across the full september, or whether it gets arrested at the step. 00:31:42.000 --> 00:31:48.000 Over the boundary. The physical mechanism is straightforward and. 00:31:48.000 --> 00:31:54.000 的use by sleep on the fourth segment。I can modify。 00:31:54.000 --> 00:31:59.000 The stress data, and in particular, the effect enormous stress on the second fold segment. 00:31:59.000 --> 00:32:08.000 Making it easier and or harder for the rapture to jp the gap. 00:32:08.000 --> 00:32:14.000 Now the strength of these poural elastic coupling depends critically on a material properties. The. 00:32:14.000 --> 00:32:19.000 So-called scantung coefficient, which we call it. Ye with the term b. 00:32:19.000 --> 00:32:32.000 So the scampton coefficient quantifies. How. Much poorly pressure increases in response to a change in mean stress, under andraine conditions, and essentially tell us how effectively stress changes. 00:32:32.000 --> 00:32:36.000 的。 00:32:36.000 --> 00:32:40.000 On the left side you can see 2 simulations. 00:32:40.000 --> 00:32:47.000 With a scamptone coefficient of point 4, with a relatively weak and pluralistic coupling, and another model with. 00:32:47.000 --> 00:32:54.000 point 8. And with meaning that we have a stronger poro, elastic, coupling. 00:32:54.000 --> 00:33:00.000 On the right side. You can see the same models in particular, the slip of evolution for both. 00:33:00.000 --> 00:33:05.000 Holds. The results shows that with higher scampton coefficient we observe a much. 00:33:05.000 --> 00:33:16.000 Better synchronization between the 2 fold. That, i'm sure. On the second fault, initiates much earlier, and propagate the. 00:33:16.000 --> 00:33:19.000 Straight. From the 1st event. And so, in other words. 00:33:19.000 --> 00:33:25.000 A higher scamptone, coefficient promotes 40 interaction, and increases like the likelihood. 00:33:25.000 --> 00:33:32.000 Of rapture propagating across across the step, over. 00:33:32.000 --> 00:33:36.000 的。 00:33:36.000 --> 00:33:40.000 Could not rely on just one or 2 events. 00:33:40.000 --> 00:33:46.000 的baviour has inherited in the viability we wanted to。 00:33:46.000 --> 00:33:50.000 们。 00:33:50.000 --> 00:33:58.000 So what you can see here is the result of analysing nerous seismic cycles in our simulation, where we track how. 00:33:58.000 --> 00:34:05.000 The probability of RAM rapture. Jping. Change over time and across different parameters value. 00:34:05.000 --> 00:34:09.000 In particular for different values of this canton coefficients. 00:34:09.000 --> 00:34:15.000 By examining over 120 setic cycles we were able to achieve. 00:34:15.000 --> 00:34:23.000 more stable, statistically robust estimate of rapture, jping. Of the probability of rapture jping across the step over. 00:34:23.000 --> 00:34:26.000 And this allowed us to move. Beyond the. 00:34:26.000 --> 00:34:37.000 我们observations and establish quantitative relationship between the material properties in particular，the scantung coefficient，and the rupture bavior。 00:34:37.000 --> 00:34:41.000 We then tried to connect our model results to. 00:34:41.000 --> 00:34:47.000 Practical seismic assessment displought, shows the critical step over with them. 00:34:47.000 --> 00:34:56.000 Meaning the maxim gap distance. The rupture can. Jp as a function of the scantung coefficient. 00:34:56.000 --> 00:35:05.000 We determine the stopover weed that gives at least a 50% chance likelihood of rapture jping. 00:35:05.000 --> 00:35:12.000 For values as canton coefficients. And then we compare these results with the previous studies. Previous neric studies. 00:35:12.000 --> 00:35:18.000 是shown by different colors here with different markers and the key findings。 00:35:18.000 --> 00:35:23.000 His highlighted in the area with the green green area. 00:35:23.000 --> 00:35:29.000 These represent the critical step over a weeds for a typical scandal coefficient of a point 5 to. 00:35:29.000 --> 00:35:34.000 Point 9, which is what we expect usually for the earth crust. 00:35:34.000 --> 00:35:42.000 我的significant here is that the physics based model，predict larger，critical step over the width。 00:35:42.000 --> 00:35:53.000 And simpler static stress calculation would suggest because we are capturing the dynamic power, elastic effect, that enhance rapture, propagation. 00:35:53.000 --> 00:36:09.000 Now, with these estimates. The question is whether the model predictions match what we observe in nature. This plot shows observations of stepover wheat from historical strikesleep earthquakes. Sir. 00:36:09.000 --> 00:36:16.000 And each point represents an actual earthquake. Where we know whether the rapture jped. 00:36:16.000 --> 00:36:26.000 The step over or was arrested them. So the green box again indicate the critical step over with for our model with a 50% chance of a. 00:36:26.000 --> 00:36:34.000 Rapture, jping or arresting. Corresponding to a range of scantung coefficients from point 5 to point 9. 00:36:34.000 --> 00:36:42.000 And the agreement is quite good. Our physical space model, which explicitly include this pluralistic effects. 00:36:42.000 --> 00:36:47.000 Appeared to capture the range of observed bavior in natural. 00:36:47.000 --> 00:37:00.000 Earthquakes. Now for this second part of the presentation, i want to briefly introduce a new computational tool that allow us to migrate from 2D. To a full 3D. Domain. 00:37:00.000 --> 00:37:08.000 Discord. Pi quake 3D. Is an open source, python-based simulator, which we recently published and released. 00:37:08.000 --> 00:37:23.000 Bike, wake implements, quasi, dynamic earthquake cycle modeling, using the boundary element method, and it supports realistic three-dimensional vol geometry, and the hierarchical servers. 00:37:23.000 --> 00:37:32.000 The court supports a multiple execution, backhands gpus accelerated version for parallel evaluation of greens functions. 00:37:32.000 --> 00:37:38.000 And also leverage. Gpu, based linear algebra. 00:37:38.000 --> 00:37:51.000 Libraries to accelerator, dense matrix vector operations. And on the right side. We have also the age metrics plus mpi version which reduce memory, footprint, and computational cost. 00:37:51.000 --> 00:37:59.000 Using. Yourarchical matrix compression. And using a distributed parallelism, he implemented with the mpi. 00:37:59.000 --> 00:38:09.000 It allows us to use also this code for large-scale simulations on high performance, computing platforms. 00:38:09.000 --> 00:38:15.000 Now i want to discuss a specific application of this code. 00:38:15.000 --> 00:38:21.000 20 cent earthquake sequence that exhibit a very interesting fault. Interaction, bavior. 00:38:21.000 --> 00:38:32.000 On october 7, th 2023, among us 6.3. Stuck head out in afghanistan, and this event was called the eq. One. 00:38:32.000 --> 00:38:38.000 What makes this sequence particularly interesting is that less than an hour later. 00:38:38.000 --> 00:38:42.000 的。 00:38:42.000 --> 00:38:49.000 Event. The eq. 2. Followed by a 3rd event of manituda for 5.9. 00:38:49.000 --> 00:39:00.000 These were not just the aftershocks. In the traditional sense they were distinct and main short-level raptures occurring on a separate full structure. 00:39:00.000 --> 00:39:15.000 Within very short time, window, and this sequence raised important question about fold to fault triggering mechanism. And the time scales over which such such interactions can occur. 00:39:15.000 --> 00:39:29.000 To investigate the physical mechanism. Bind these doublet sequence, we set up Model using a bikewig. This work has been leading leading by the phd student brian and research fellow aupe. 00:39:29.000 --> 00:39:41.000 Both at the utop cerebrotty of singapore. The model set up shows 2 faults that are offset by one kilometer from each other, and with one kilometer of overlap. 00:39:41.000 --> 00:39:52.000 Each folt contains velocity, weakening patch, and the area that is capable of selling sleep, surrounded by a velocity strengthening that baves as seismic, lame. 00:39:52.000 --> 00:39:59.000 We then run these seismic. Psychosulations, allowing the model to evolve through many. 00:39:59.000 --> 00:40:12.000 Says mixed sequence, to see. If he could spontaneously reproduce doublet bavior similar to what we observe in the herod sequence. 00:40:12.000 --> 00:40:25.000 Results show that the model does reproduce tablets. Model produces clusters of closely space, large events rather than just isolated the earthquakes and these clusters. 00:40:25.000 --> 00:40:32.000 corresponds to what we call it here, doublet earthquakes, where the rupture is rapidly re-triggered after the first large event. 00:40:32.000 --> 00:40:37.000 And doublets emerge when the stress is not fully released by the inshallah. 00:40:37.000 --> 00:40:41.000 rupture, allowing for fast renucleation on the second fold. 00:40:41.000 --> 00:40:50.000 But now, to look more in detail, we have two videos animations of the first and the second doublet. 00:40:50.000 --> 00:40:55.000 In this first case, you can see that… 00:40:55.000 --> 00:41:03.000 We have a long delay of approximately 7 days between the two ruptures, and the color scale shows the sleep rate on both vaults over time. 00:41:03.000 --> 00:41:05.000 And what you can see here is that, uh, 00:41:05.000 --> 00:41:07.000 one rupture. 00:41:07.000 --> 00:41:12.000 occur on the first fold, and then there is a significant delay of 7 days. 00:41:12.000 --> 00:41:17.000 Before the second rupture occurs on the second fold. And during this delay period, 00:41:17.000 --> 00:41:23.000 The system is undergoing slow stress evolution, in particular a seismic sleep and postseismic stress transfer. 00:41:23.000 --> 00:41:26.000 which are gradually bringing default. 00:41:26.000 --> 00:41:33.000 2, the second fold, close to his failure threshold. 00:41:33.000 --> 00:41:36.000 In contrast, in this second doublet, 00:41:36.000 --> 00:41:40.000 We can see a shorter delay of approximately 00:41:40.000 --> 00:41:46.000 30 minutes, which is much more consistent with what has been observed in the actual Herod earthquake. 00:41:46.000 --> 00:41:52.000 sequence, and again, in this case, we have fault one that ruptures first, but the second 00:41:52.000 --> 00:41:57.000 Rupture follows almost immediately, just with a delay of 30 minutes. 00:41:57.000 --> 00:42:01.000 And this is because the second vault is already very close to failure. 00:42:01.000 --> 00:42:08.000 when Fold 1 ruptures, so only a short transient adjustment is needed before the second rupture 00:42:08.000 --> 00:42:12.000 propagates. This brings us to the conclusion. 00:42:12.000 --> 00:42:15.000 What we have seen from the first part is, uh… 00:42:15.000 --> 00:42:18.000 no fault role of portfolio pressure. 00:42:18.000 --> 00:42:21.000 Poor fleet pressure can play an important role. 00:42:21.000 --> 00:42:24.000 fold, both statically and dynamically. 00:42:24.000 --> 00:42:28.000 And, uh, this can influence the effect, enormous stress, on the… 00:42:28.000 --> 00:42:33.000 Name or fault, and impact rupture propagation in particular across fault stepovers. 00:42:33.000 --> 00:42:40.000 And in the second part of this presentation, we have seen that there is an important fault-fault interaction that can produce 00:42:40.000 --> 00:42:42.000 time-delay doublets. 00:42:42.000 --> 00:42:45.000 not only Centennios triggering, and the delay time is not fixed. 00:42:45.000 --> 00:43:01.000 By running a long-term seismic cycle simulations, we have seen that this can reflect how close the secondary fault is to failure at the time of the interaction. 00:43:01.000 --> 00:43:07.000 That's great, thank you very much, Luca. Um, we now are going to go into a discussion period where you can ask. 00:43:07.000 --> 00:43:17.000 Questions for all the speakers from this session, um, to ask a question, hit the react button and hit raise hand, please. 00:43:17.000 --> 00:43:20.000 Um, Andy. 00:43:20.000 --> 00:43:23.000 Yeah, thanks, Morgan. I guess this is a question for Mike. 00:43:23.000 --> 00:43:27.000 Um, so I think you've done a really great job of showing that… 00:43:27.000 --> 00:43:34.000 rival fits the paleoseismic data at single sites. So if we're doing the hazard for a fault crossing pipeline, 00:43:34.000 --> 00:43:40.000 Seems like a no-brainer. But I like the fact that you were talking about the Weibel resulting from… 00:43:40.000 --> 00:43:45.000 interactions between multiple sources impinging on that one site. 00:43:45.000 --> 00:43:47.000 Because we know that multiple stacked 00:43:47.000 --> 00:43:50.000 log-normal distributions close to BPTs, 00:43:50.000 --> 00:43:52.000 can result in a Weibel distribution. 00:43:52.000 --> 00:43:57.000 So my question is, how do we go from saying, okay, it's… 00:43:57.000 --> 00:44:02.000 Really good distribution for paleo seismic site, for a site on a fall, a point on a fault. 00:44:02.000 --> 00:44:08.000 to what distribution should we be using in seismic hazard assessments when we actually are interested 00:44:08.000 --> 00:44:10.000 in modeling, you know, 00:44:10.000 --> 00:44:16.000 finite ruptures of great length. 00:44:16.000 --> 00:44:24.000 I don't have a simple answer for that. I'm working with what the data shows best, right? Paleo seismology shows timing at a site. 00:44:24.000 --> 00:44:29.000 Um, I think there's more to be done digging into the paleoseismic dataset on the San Andreas Fault. 00:44:29.000 --> 00:44:33.000 And, for example, and a few other faults that have a lot of data. 00:44:33.000 --> 00:44:43.000 Um, to ask the question of what is the range of event sizes? Because what you see from Sharer and Yule's compilation is this Andrea is quite chaotic. 00:44:43.000 --> 00:44:54.000 There's all kinds of event sizes in there. I like to think about the near future when we do have an event on the San Andreas. It'll probably be smaller than most of us expect, and then we're gonna have to ask, what's next? 00:44:54.000 --> 00:44:56.000 Yeah, I guess my sort of point… 00:44:56.000 --> 00:45:00.000 you might be the… you're looking at the repeat of some… of a thing. 00:45:00.000 --> 00:45:03.000 And what the system does is not repeat itself. 00:45:03.000 --> 00:45:04.000 And so then computing the hazard of the system is a completely different problem, yeah. 00:45:04.000 --> 00:45:09.000 Yes. 00:45:09.000 --> 00:45:10.000 Yes. 00:45:10.000 --> 00:45:17.000 unrelated, but yes, it's a problem of. understanding that chaotic mode, which ultimately we would have to also work from the simulation side. Like, how do we get. 00:45:17.000 --> 00:45:20.000 Yeah. 00:45:20.000 --> 00:45:25.000 multi-cycle simulators that are now… You know, they're quite… they're maturing. 00:45:25.000 --> 00:45:31.000 But they produce very periodic results, right? We don't have the. 00:45:31.000 --> 00:45:32.000 Thanks. 00:45:32.000 --> 00:45:33.000 something that replicates nature very well quite yet. 00:45:33.000 --> 00:45:43.000 I was thinking something really similar, and you see, I didn't know that. You said, um, if you add up BPTs, like, in a non-point way, you get something like Webull. Does that mean National Mass is something like a Webull? Because. 00:45:43.000 --> 00:45:50.000 It uses BPT, but not. on a point-by-point basis, and you can have really short re-ruptures if the ruptures are just, like, slightly overlapping. 00:45:50.000 --> 00:45:52.000 Yeah, this is a point Ned made. 00:45:52.000 --> 00:45:57.000 So, has anyone compared, yeah, the national maps to what… Mike's getting his analysis. 00:45:57.000 --> 00:46:00.000 Yeah, I'm not sure. 00:46:00.000 --> 00:46:08.000 I've… well… Um… I've compared things like the… the simulations that have gone into it. 00:46:08.000 --> 00:46:09.000 Ah. 00:46:09.000 --> 00:46:13.000 And they're much more periodic. But I don't think they depend on that, right? So… the national numbers. 00:46:13.000 --> 00:46:16.000 It was kind of, yeah, the reason they did it that way, but, you know, it's a bit different. 00:46:16.000 --> 00:46:20.000 Yeah. 00:46:20.000 --> 00:46:23.000 Um… next we have, uh, Bin Hao, you have a question? 00:46:23.000 --> 00:46:29.000 Yeah, thank you. Um, I have a question for Luca. Thank you very much, Luca, for the nice presentation. 00:46:29.000 --> 00:46:35.000 Uh, um, I guess also in the chat, there are a few other people who have the same question as me. 00:46:35.000 --> 00:46:38.000 Uh, that is, um, how does… 00:46:38.000 --> 00:46:42.000 Including the wave-mediated stress transfer and also potentially… 00:46:42.000 --> 00:46:48.000 Uh, enhanced dynamic weakening and high velocity affect the probability of, um… 00:46:48.000 --> 00:46:51.000 Crossing that barrier. 00:46:51.000 --> 00:47:10.000 Thank you, thank you for the question. Um, in my simulations, I use, um… quasi-dynamic formulation, so meaning that, as you well know, inertia is not fully resolved, but we include a radiation damping tournament to approximate the energy, the energy loss to wave radiation. 00:47:10.000 --> 00:47:22.000 So, uh, we… I… I captured the stress drop and the rupture propagation reasonably well, I would say, but I do not resolve the full wave-mediated dynamic stress transfer. 00:47:22.000 --> 00:47:29.000 So, if we move to a dynamic model, I think we should expect two main effects. 00:47:29.000 --> 00:47:35.000 Probably the first one would be that dynamic stress pulses will be sharper and be. 00:47:35.000 --> 00:47:44.000 more sparsially concentrated, and that… in that way, we can have a more elevated shear stress across the step-over. 00:47:44.000 --> 00:47:48.000 And potentially increase the… in the probability of, uh. 00:47:48.000 --> 00:48:03.000 of jumping, especially for narrow stepovers. In that sense, I think that fully dynamic rupture can produce maybe a short-lived stress peak that exceeded the quasi-dynamic model prediction. 00:48:03.000 --> 00:48:23.000 perhaps another second point is that we… Include high velocity weakening, flash heating, or dynamic weakening mechanisms that would reduce the effective fracture energy and promote faster rupture acceleration and, um. 00:48:23.000 --> 00:48:31.000 And I'm sure that accelerate that more efficiently is more likely to maintain sufficient energy to overcome the geometrical barrier of. 00:48:31.000 --> 00:48:40.000 of the step over. So, all in all, in our simulations, we were able to take the advantage of the seismic cycle, so get away from the, let's say, the. 00:48:40.000 --> 00:48:53.000 predefined stress. But we didn't include at least, um… Um, we've mediated effects that we have with inertia, so that's definitely something maybe to incorporate in a. 00:48:53.000 --> 00:49:01.000 in seismic cycle simulation in the future. 00:49:01.000 --> 00:49:06.000 Russ, do you want to ask your question? 00:49:06.000 --> 00:49:07.000 You're… you're there. 00:49:07.000 --> 00:49:12.000 Here we go, here we go. I want to come back to Mike Osk, and I thought that was a fantastic talk. I learned a great deal from it. 00:49:12.000 --> 00:49:15.000 And one comment is, 00:49:15.000 --> 00:49:18.000 clearly, as you pointed out, the Alpine Fault 00:49:18.000 --> 00:49:21.000 behaves very differently than just about every other fall. 00:49:21.000 --> 00:49:24.000 So, wouldn't it be great to have an experiment? 00:49:24.000 --> 00:49:31.000 with where Kevin Berryman and the Paleo seismologists on the Alpine Fault go do some San Andreas work. 00:49:31.000 --> 00:49:39.000 And the cage share and the San Andreas people go do some work on the Alpine Fault and know that we get the same results. 00:49:39.000 --> 00:49:42.000 Because this is not the same as a seismometer. 00:49:42.000 --> 00:49:46.000 Whereas magnitude 6 on the San Andreas is identical to a magnitude 6 on the Alpine. 00:49:46.000 --> 00:49:52.000 Okay, let's assume that that's not an issue, and that these are really differences. 00:49:52.000 --> 00:49:59.000 Then, here's my thinking, and I want to hear your thinking. My view is the Alpine Fault is unusually straight and usually isolated. 00:49:59.000 --> 00:50:01.000 It has almost no… 00:50:01.000 --> 00:50:10.000 branch or splay faults, and it has no parallel faults. So, you might expect that it would have more regular behavior, because there's very little stress interaction. 00:50:10.000 --> 00:50:15.000 With all the stuff that's happening in the Bay Area and Southern California. 00:50:15.000 --> 00:50:18.000 Okay, that's… that's one view. 00:50:18.000 --> 00:50:22.000 could be wrong, I'd love to hear your view. 00:50:22.000 --> 00:50:25.000 I think that's a reasonable view. It's not a new one, right? 00:50:25.000 --> 00:50:33.000 was brought up in the paper from. Huckery Creek, that 22… 212 event long record. 00:50:33.000 --> 00:50:41.000 Also, it's just, because it's isolated, it's also quieter, right? There's not as many other faults and aftershock sequences that could. 00:50:41.000 --> 00:50:44.000 lead to some cascade of events that triggers the fall. 00:50:44.000 --> 00:50:49.000 The faults in California relative to slip rate just have much more frequent events. 00:50:49.000 --> 00:51:00.000 And the average event size is smaller. I think we live in a noisier environment, that's my view. 00:51:00.000 --> 00:51:03.000 Gina? 00:51:03.000 --> 00:51:07.000 Um, hi, thanks for the talk. I have a question to you, Mike. 00:51:07.000 --> 00:51:15.000 I just was… I could be a really dumb question, but I was just curious if such, um, more frequent small earthquakes versus more. 00:51:15.000 --> 00:51:23.000 less frequent, like, larger earthquakes thing, is that… been shown in the B value of these regions as well. 00:51:23.000 --> 00:51:25.000 For the current earthquakes? 00:51:25.000 --> 00:51:30.000 I don't have an answer to that. I'm looking at the Paleo data. 00:51:30.000 --> 00:51:38.000 you couldn't even calculate a B value for… well, maybe you could. The Alpine fault sort of has… sometimes it splits into two parts, and sometimes it's end-to-end. 00:51:38.000 --> 00:51:42.000 But there's a lot of end-to-end ruptures in the central part. 00:51:42.000 --> 00:51:48.000 The San Andreas. The mode is about 120 kilometers rupture length. 00:51:48.000 --> 00:51:56.000 When you look at the Yule and share reconstruction, that's one realization of the data, right? There's other ways to try to schedule the earthquakes through there. 00:51:56.000 --> 00:52:03.000 Um, but… others could speak to seismologic. 00:52:03.000 --> 00:52:04.000 Morgan, do you have some experience to this effect? 00:52:04.000 --> 00:52:05.000 constraints. 00:52:05.000 --> 00:52:07.000 Thank you. 00:52:07.000 --> 00:52:09.000 Huh? 00:52:09.000 --> 00:52:18.000 I actually wanted to, uh… slightly move the conversation. Um, in the chat, we were talking a bit about, um. 00:52:18.000 --> 00:52:23.000 Like, how much of this… we're saying, like, we prefer YBL to BPT, for example. 00:52:23.000 --> 00:52:30.000 And in that case, that's a very, like… I'm wondering how model-dependent that is, like, can we say if the hazard function is always increasing? 00:52:30.000 --> 00:52:34.000 Going back to Leah's talk, she's looking at a whole other class of models, which is very different. 00:52:34.000 --> 00:52:41.000 from BPT and Y will both, where you have, like, this longer-term memory that uses not just the last event, but you can go further back. 00:52:41.000 --> 00:52:47.000 Is there a way we can, from the data itself, outside of the context of the civic model. 00:52:47.000 --> 00:52:52.000 show that that's required. Like, Leia, have you thought about, like. 00:52:52.000 --> 00:53:02.000 A way to, um, quantify the information gain you get by including more than just the last event. 00:53:02.000 --> 00:53:08.000 Um, thanks for the… The question, Morgan. I have not considered. 00:53:08.000 --> 00:53:15.000 in terms of an information gain, but we have… shown that the, you know, if you kind of. 00:53:15.000 --> 00:53:25.000 Um, in our generalized LTF. formulation, which is basically kind of what… we start with a whyble, and then we kind of train it. 00:53:25.000 --> 00:53:35.000 Um, and… and then, uh, compare it. Um, we do see pretty big differences when you get to, like, the conditional probability in terms of. 00:53:35.000 --> 00:53:41.000 Of, uh, the probability differences between those distributions, like BPT, YBOL. 00:53:41.000 --> 00:53:54.000 Um, exponential or log normal, um… So, there's definitely… and big impacts, but in terms of information gain, I'm not quite sure. 00:53:54.000 --> 00:54:07.000 Do you agree with… so Mike was suggesting in the chat that it's sort of like this hazard function is always monotonically increasing. He thinks that, like, the longer you wait, the more dew it is. Do you agree with that, or does it depend if we're in a cluster or not in a cluster? 00:54:07.000 --> 00:54:12.000 Well, that's what we… we were going with that notion, um. 00:54:12.000 --> 00:54:21.000 with LTFM, and that's why we… conceived of this, like, this generalized LTFM model, because we didn't like that the Weibol. 00:54:21.000 --> 00:54:28.000 in the Browning passage time had this… tendency, or not the Bible, but the Browning passage time, to where it eventually… the probability is decreasing once you've waited. 00:54:28.000 --> 00:54:33.000 Yeah. 00:54:33.000 --> 00:54:40.000 you know, a certain amount of time, and so that's what we… that's why we chose the Weibel to base. 00:54:40.000 --> 00:54:49.000 the generalized LTFM model on, because we liked that about it. And… but again, we're, like, we're considering… this is kind of like an abstract, like, single fault. 00:54:49.000 --> 00:54:59.000 You know, with no interactions or anything happening like that, so there's… there's definitely limitations there, and so, you know, whether that's. 00:54:59.000 --> 00:55:08.000 you know, the best assumption, or the best thing to be chasing, I'm not sure, um, but… when we were conceiving this, that is what we were going for. 00:55:08.000 --> 00:55:16.000 But, um, beyond it just being, like, um… in our prior sense, like, we have this intuition, like, in sort of a Bayesian way that should increase. 00:55:16.000 --> 00:55:24.000 Do we often… do we think the data forces it to increase? Mike, do you want to comment on that? Does it have to increase? Independent what exact shape it is. 00:55:24.000 --> 00:55:28.000 Maybe Weibel's better than BPT early on. Long-terms happen. 00:55:28.000 --> 00:55:35.000 I think that the long gaps… Right? You don't have long enough gaps to imply there's a heavy tail or. 00:55:35.000 --> 00:55:36.000 you're plateauing at some constant hazard level. in the records that we have. 00:55:36.000 --> 00:55:41.000 Hmm. 00:55:41.000 --> 00:55:43.000 Okay. 00:55:43.000 --> 00:55:51.000 When you find an unusually long gap, and inevitably in the Pevelios hazard record, you'll find there's a non-conformity. So, like, your information is being lost there. 00:55:51.000 --> 00:55:52.000 It could be a long gap, but there's also a gap in the record. 00:55:52.000 --> 00:55:55.000 So there's no broken buses in… paleo-seismology. 00:55:55.000 --> 00:55:56.000 No. Well, no, there's a lot of broke… the buses are not very well timed, but no, there's no broke down buses. 00:55:56.000 --> 00:55:58.000 Thank you. 00:55:58.000 --> 00:56:01.000 That just, like, it's not coming at all because it just completely broke it. 00:56:01.000 --> 00:56:07.000 In the records that I'm working with, which are on major plate boundary faults. 00:56:07.000 --> 00:56:14.000 Um… but I brought up in the chat the example of the Loma Blanca Fault in New Mexico, which is this 14-event. 00:56:14.000 --> 00:56:24.000 400,000 year long record. And it also fit with a Weibel distribution, with a hazard exponent less than 1. 00:56:24.000 --> 00:56:25.000 What you make of that, I'm not sure, coincidence, but… seems pretty general. 00:56:25.000 --> 00:56:33.000 Yeah, okay. 00:56:33.000 --> 00:56:36.000 And does a much better job of doing… of predicting the short. 00:56:36.000 --> 00:56:52.000 term hazard, whereas. Browning and passage time has got that built-in renewal in it, and the short return times are not well modeled. 00:56:52.000 --> 00:56:53.000 Ross, did you want to jump in? 00:56:53.000 --> 00:56:54.000 Yeah, it has very few short terms, which are in the simulators, and… will appear if you modify it, yeah, but… 00:56:54.000 --> 00:57:02.000 Yeah, I just want to say, I think one thing that could really… a great thing that could come out of this conversation key and off Leah's talk, is that we should agree to banish the term 00:57:02.000 --> 00:57:04.000 overdue. 00:57:04.000 --> 00:57:10.000 Or, at the very least, you get to use it once in your life. 00:57:10.000 --> 00:57:11.000 Because we leave… it just leaves a misimpression. 00:57:11.000 --> 00:57:14.000 Just gets more due. Mm-hmm. 00:57:14.000 --> 00:57:23.000 We just don't have the ability to say that. 00:57:23.000 --> 00:57:24.000 Alright, shall we end the meeting there? 00:57:24.000 --> 00:57:27.000 I agree. 00:57:27.000 --> 00:57:33.000 Um, and then we can have an extra 10 minutes in our day. 00:57:33.000 --> 00:57:36.000 Thank you, everyone, and… 00:57:36.000 --> 00:57:37.000 I don't know if Sarah wants to have closing words. 00:57:37.000 --> 00:57:43.000 I'm just gonna say thank you to our excellent speakers and moderators. That was… 00:57:43.000 --> 00:57:51.000 Fantastic, and amazing, and thank you so much, and we have changed the English language, and we'll never speak of overdue again. 00:57:51.000 --> 00:57:55.000 Although possibly more do, or dual, and… 00:57:55.000 --> 00:57:57.000 Undo. 00:57:57.000 --> 00:58:00.000 Um, so… 00:58:00.000 --> 00:58:01.000 My name's Murray Faison I… 00:58:01.000 --> 00:58:06.000 You have the evening off, come back tomorrow for the last day. We will start again at 9 30 a.m. 00:58:06.000 --> 00:58:12.000 Pacific, unless you want in the fourth session giving a talk, in which case, please come 15 minutes earlier so we can get you set up. 00:58:12.000 --> 00:58:15.000 So, see, almost everyone at 9.30 tomorrow. 00:58:15.000 --> 00:58:17.000 And a few people at 9.15. 00:58:17.000 --> 00:58:21.000 Response.