WEBVTT Kind: captions Language: en 00:00:00.729 --> 00:00:03.500 - Good morning, everyone. Thank you for coming out. 00:00:03.500 --> 00:00:07.430 Now, to mess with everyone’s heads, our next two seminars 00:00:07.430 --> 00:00:09.570 are going to be on Tuesday instead of Wednesday. 00:00:09.570 --> 00:00:13.139 So please come back Tuesday, November 3rd, at 10:30 a.m., 00:00:13.139 --> 00:00:16.070 where Paul Segall will be discussing new thoughts 00:00:16.070 --> 00:00:18.410 about injection-induced seismicity. 00:00:18.410 --> 00:00:22.199 Today we have Marine Denolle speaking about 00:00:22.199 --> 00:00:23.939 radiated energy of shallow earthquakes. 00:00:23.939 --> 00:00:26.919 She will be joining the Harvard faculty in January. 00:00:26.919 --> 00:00:31.800 Currently she is a Green fellow at IGPP- Scripps working with Peter Shearer. 00:00:31.800 --> 00:00:36.020 In 2014, she received her Ph.D. from Stanford working with Greg Beroza. 00:00:36.020 --> 00:00:39.059 Before that, she got her master’s from IPGP. 00:00:39.059 --> 00:00:42.480 And before that, she was at Ecole Normale Supérieure. 00:00:42.480 --> 00:00:46.030 And she would like you to know that she likes earthquakes. 00:00:49.020 --> 00:00:52.060 - Thank you, Sarah. 00:00:52.060 --> 00:00:54.680 Yeah, when you start counting the years of study in school, 00:00:54.690 --> 00:00:57.550 it’s getting a bit long for what we do. 00:00:57.550 --> 00:01:00.570 So I was here actually a couple years ago, 00:01:00.570 --> 00:01:04.830 and I presented work on virtual earthquakes with [inaudible]. 00:01:04.830 --> 00:01:09.480 But during my post-doc, I’ve -- now, from ground motion, 00:01:09.480 --> 00:01:12.980 I’m turning to source processes. 00:01:12.980 --> 00:01:16.220 And I’ve been really interested in looking at and redefining 00:01:16.230 --> 00:01:19.470 what radiated energy means. 00:01:19.470 --> 00:01:21.410 And I’m working with Peter at Scripps for that, 00:01:21.410 --> 00:01:28.310 and as you can tell, we’re looking at global seismicity as any Shearer study. 00:01:28.310 --> 00:01:32.900 So I just want to go back to really the reason why I was -- 00:01:32.900 --> 00:01:35.320 I’m targeting the radiated energies. 00:01:35.320 --> 00:01:42.200 I actually want to re-understand what gets into the earthquake energy budget. 00:01:42.200 --> 00:01:47.070 There’s ways that we could get maybe from -- to fracture energy. 00:01:47.070 --> 00:01:50.010 So that’s the energy that spent to propagate the rupture. 00:01:50.010 --> 00:01:54.070 There’s energy that is spent by radiating seismic waves. 00:01:54.070 --> 00:01:56.790 I’ll show you that in a little bit. 00:01:56.790 --> 00:02:01.460 And there’s friction, or heat loss, that is spent during, you know, 00:02:01.460 --> 00:02:04.210 friction of the two surfaces. 00:02:04.210 --> 00:02:07.710 So the friction part, we cannot get to it by -- with seismic waves, 00:02:07.710 --> 00:02:11.230 but we can probably get to the other ones with seismic waves. 00:02:11.230 --> 00:02:15.959 So the radiated energy is the kinetic energy carried by seismic waves. 00:02:15.959 --> 00:02:17.760 And I really want to emphasize this because 00:02:17.760 --> 00:02:22.590 this is the definition of what radiated energy should be. 00:02:22.590 --> 00:02:25.510 And what we can -- from the seismic waves, 00:02:25.510 --> 00:02:30.109 we can get to it by saying that this is the density, 00:02:30.109 --> 00:02:34.730 this is phase velocity or wave speed, this is mechanical impedance. 00:02:34.730 --> 00:02:37.409 And when you have -- after this is the velocity squared. 00:02:37.409 --> 00:02:39.230 And so this is the kinetic energy. 00:02:39.230 --> 00:02:44.209 And we have to integrate this over all the time -- the duration of the shaking. 00:02:44.209 --> 00:02:48.549 And we are capturing this over a finite, closed surface 00:02:48.549 --> 00:02:53.689 to capture all the flux of the energy out. 00:02:53.689 --> 00:02:58.469 So in seismology, we really like to think in terms of frequency and content. 00:02:58.469 --> 00:03:03.299 So we use Parseval theorem very often to go from the seismogram that you 00:03:03.299 --> 00:03:10.730 measure to the spectrum that we can estimate with Fourier transforms. 00:03:10.730 --> 00:03:15.969 Interestingly, all -- most of the energy is carried by high-frequency seismic 00:03:15.969 --> 00:03:20.639 waves, which means that all the -- long- period part that tends to estimate the 00:03:20.639 --> 00:03:27.819 static part of the earthquake, like seismic moment, does not contain that energy. 00:03:27.819 --> 00:03:32.329 And really something that we tend to forget is that 00:03:32.329 --> 00:03:38.359 that surface that we integrate on is usually for a body wave -- a sphere. 00:03:38.359 --> 00:03:43.709 And we also make approximations that we are in the far-field of the source. 00:03:43.709 --> 00:03:46.650 And all those assumptions are also made using a whole space. 00:03:46.650 --> 00:03:49.279 And I just want to emphasize that we tend to forget 00:03:49.279 --> 00:03:53.120 mentioning these assumptions that are key actually to defining 00:03:53.120 --> 00:03:58.139 what we do with the data and how we process the data. 00:03:58.139 --> 00:04:02.510 And all of this -- when we record seismograms, we really need to be 00:04:02.510 --> 00:04:05.959 in the far-field from the source and have this homogeneous whole space, 00:04:05.959 --> 00:04:09.499 so we need to remove all the 3D path effects from the waveform 00:04:09.499 --> 00:04:11.900 to really satisfy this assumption. 00:04:11.900 --> 00:04:15.569 Okay, so from the global point of view, 00:04:15.569 --> 00:04:20.730 we want to estimate what the seismogram can tell us about the source. 00:04:20.730 --> 00:04:26.800 And to get that S-zero that was showing earlier, we need to define that focal 00:04:26.800 --> 00:04:32.310 sphere around the source and capture all the [inaudible] that leave the source. 00:04:32.310 --> 00:04:35.370 And for this, we need to sample all the seismic waves 00:04:35.370 --> 00:04:37.190 that leave the source on that sphere. 00:04:37.190 --> 00:04:40.870 On we -- I’m going to define this as a takeoff angle, but we do need 00:04:40.870 --> 00:04:49.160 to retrieve those in -- oops, sorry -- in wave propagation in the real Earth. 00:04:49.160 --> 00:04:52.920 To capture all those different takeoff angles, we actually look at -- 00:04:52.920 --> 00:04:58.230 we receive the waveforms at different angular distances from the source. 00:04:58.230 --> 00:05:00.020 Because of ray bending in the Earth. 00:05:00.020 --> 00:05:04.250 And by looking at global phases -- this is the angular distance 00:05:04.250 --> 00:05:09.700 from zero to 180 -- the waveform that we get is rather complicated. 00:05:09.700 --> 00:05:17.850 We have the P rightly followed by the PP and all those other, like -- 00:05:17.850 --> 00:05:25.950 I would call that a really distinct coda wave of the P wave here. 00:05:25.950 --> 00:05:31.090 What I want to emphasize is to look at the -- oops -- the big earthquakes -- 00:05:31.090 --> 00:05:36.560 I’m interested in the large earthquakes -- 100 seconds, which should be the 00:05:36.560 --> 00:05:40.870 pulse width of your seismogram -- 100 seconds actually -- 00:05:40.870 --> 00:05:45.810 and we start to capture a lot of those global phases. 00:05:45.810 --> 00:05:47.550 But if we look at even larger earthquakes -- 00:05:49.600 --> 00:05:55.400 whoops, sorry, old Mac -- larger earthquakes, we are -- 00:05:55.430 --> 00:05:58.390 we now need to incorporate all those different phases. 00:05:58.390 --> 00:06:01.000 And so to really just get the P, we’re going to have to 00:06:01.000 --> 00:06:04.430 deconvolve information of all those global phases. 00:06:04.430 --> 00:06:08.710 And for that -- for that, we need really to understand why the 3D Green’s function 00:06:08.710 --> 00:06:13.460 is to really capture all those -- the pulse wave for those big ones. 00:06:13.460 --> 00:06:18.780 Okay, so there are three ways to get to the Green’s functions. 00:06:18.780 --> 00:06:21.890 And I want to go through all of them individually. 00:06:21.890 --> 00:06:24.110 The first one will be -- let’s say we know exactly 00:06:24.110 --> 00:06:28.050 what the velocity model is in the Earth, and we’re going to propagate 00:06:28.050 --> 00:06:32.580 numerically all the seismic waves and at high frequencies. 00:06:32.580 --> 00:06:37.960 So this will be ideal because we would capture all the -- we can capture all the 00:06:37.960 --> 00:06:43.140 wave fields in the 3D Earth, and all the receivers can be used for this. 00:06:43.140 --> 00:06:50.810 But the downside of this is that it is computationally very intensive 00:06:50.810 --> 00:06:52.720 and that we actually need to know what the 00:06:52.720 --> 00:06:56.940 global velocity models are at very high resolution. 00:06:56.940 --> 00:06:59.420 But, you know, an upside of this is we can actually 00:06:59.420 --> 00:07:02.840 characterize uncertainty, which we cannot in other methods. 00:07:02.840 --> 00:07:06.730 The second method is to use empirical Green’s functions. 00:07:06.730 --> 00:07:10.500 And those are usually small earthquakes that are 00:07:10.500 --> 00:07:12.560 nearby the main event of interest. 00:07:12.560 --> 00:07:15.120 They capture the full 3D path. 00:07:15.120 --> 00:07:18.890 This is the grand truth of the wave propagation. 00:07:18.890 --> 00:07:23.220 But one of the downsides is that the small events 00:07:23.220 --> 00:07:25.510 tend to have lower signal-to-noise ratio. 00:07:25.510 --> 00:07:30.820 So we can only look at those in some finite frequency bandwidth. 00:07:30.820 --> 00:07:33.140 And we actually need to know information 00:07:33.140 --> 00:07:36.740 about this event to recalibrate the path. 00:07:36.740 --> 00:07:40.210 So we need to know what the source spectrum of that event is 00:07:40.210 --> 00:07:45.310 to really remove the path effects from using those Green’s functions. 00:07:45.310 --> 00:07:49.450 And lastly, we can use a more simplified view of the Earth 00:07:49.450 --> 00:07:54.320 using a simple Earth model that are 3D but only radially symmetric. 00:07:54.320 --> 00:07:58.960 And we can do retracing and simple Q attenuation 00:07:58.960 --> 00:08:03.000 to model what the attenuation and geometrical spreading should be. 00:08:03.000 --> 00:08:06.270 This is computationally not -- it’s totally inexpensive. 00:08:06.270 --> 00:08:12.870 It’s a fairly good approximation at long period if we capture -- if we think that -- 00:08:12.870 --> 00:08:19.810 most of the lateral variations are smooth over large wavelength. 00:08:19.810 --> 00:08:21.250 But that has a lot of downside. 00:08:21.250 --> 00:08:27.600 Of course, it’s only valid to capture the direct speed within a certain angular 00:08:27.600 --> 00:08:33.969 distance between 30 and 90 degrees to remove all the [inaudible] effect. 00:08:33.969 --> 00:08:39.959 And it does not include all the lateral path effects, as I just mentioned. 00:08:39.959 --> 00:08:42.939 But in all in those, there’s something that we 00:08:42.939 --> 00:08:48.920 forget to mention is that the free surface really affects the body wave. 00:08:48.920 --> 00:08:50.209 And I’m interested in the shallow earthquakes, 00:08:50.209 --> 00:08:54.079 so I want to show you why the free surface is important. 00:08:54.079 --> 00:08:57.379 For shallow events -- by that I mean every event that is 00:08:57.379 --> 00:09:02.889 above 60, 70 kilometers and magnitude 5 and above, 00:09:02.889 --> 00:09:05.829 the seismogram that we get is actually composed of 00:09:05.829 --> 00:09:11.769 the direct peak and rightly followed the pP and the sP. 00:09:11.769 --> 00:09:15.410 And for most of those, the thrust events -- the thrust events, 00:09:15.410 --> 00:09:21.040 for instance, have such a mechanism that the sP and pP tend to arrive 00:09:21.040 --> 00:09:26.560 with opposite polarity than the direct P. So this is quite interesting. 00:09:26.560 --> 00:09:29.230 What it does in terms of the amplitude spectrum -- let’s say 00:09:29.230 --> 00:09:34.639 you have a simple stick seismogram with two delta functions 00:09:34.639 --> 00:09:36.660 that are normalized and with opposite polarity. 00:09:36.660 --> 00:09:42.240 If you take the amplitude spectrum of this seismogram, you actually get -- 00:09:42.240 --> 00:09:48.249 sorry, this nicely shaped spectrum that has all those troughs. 00:09:48.249 --> 00:09:55.849 And the dt -- sorry, there’s some interesting -- all right -- oops. 00:09:58.560 --> 00:10:01.300 All right. Sorry. 00:10:01.310 --> 00:10:04.009 The dt -- this difference in frequency that you can see here -- 00:10:04.009 --> 00:10:04.949 there’s some kind of harmonics. 00:10:04.949 --> 00:10:10.620 It really depends on the dt -- the difference in the pulse arrival. 00:10:10.620 --> 00:10:13.649 And so if you imagine that now we are convolving this 00:10:13.649 --> 00:10:18.660 with a finite source that has a pulse width -- a finite width here, 00:10:18.660 --> 00:10:21.819 sometimes they actually may overlap and destructively interfere. 00:10:21.819 --> 00:10:26.540 And if you convolve a Brune model to the spectrum I showed you earlier, 00:10:26.540 --> 00:10:30.220 you should get, you know, this high-frequency fall-off rate 00:10:30.220 --> 00:10:36.910 and also a downgoing spectrum here that is combining the source spectrum 00:10:36.910 --> 00:10:39.879 and the Green’s function spectrum to be somewhat biased. 00:10:39.879 --> 00:10:43.649 What I really want to say is this brings some higher apparent corner 00:10:43.649 --> 00:10:48.610 frequency that should not be confused with the source corner frequency. 00:10:48.610 --> 00:10:51.029 And so the key parameters that we’re looking at is 00:10:51.029 --> 00:10:58.689 this difference in arrival time is actually very dependent on the source depth. 00:10:58.689 --> 00:11:02.319 And the degrees of separation between those two pulses really depends on 00:11:02.319 --> 00:11:05.360 the pulse width, which relates to the earthquake size. 00:11:05.360 --> 00:11:07.110 And I’m just going to call that A. 00:11:07.110 --> 00:11:10.910 And so there’s some parameter we can say, you know, the source depth 00:11:10.910 --> 00:11:16.649 versus the source size, and look at that ratio to now dimensionalize this. 00:11:16.649 --> 00:11:19.170 So I’m showing this ratio here. 00:11:19.170 --> 00:11:23.920 I’m using the relation that relates earthquake size with earthquake corner 00:11:23.920 --> 00:11:29.050 frequency depending on beta, shear wave speed, and this k parameter. 00:11:29.050 --> 00:11:33.689 And I’m showing this varying from very low numbers to very large numbers. 00:11:33.689 --> 00:11:40.379 What it means is that -- I’m just showing when this ratio is less than 1, 00:11:40.379 --> 00:11:43.269 we have the source size that is greater than the source depth. 00:11:43.269 --> 00:11:49.800 And when this ratio is greater than 1, the earthquake is deeper than its source size. 00:11:49.800 --> 00:11:52.649 So what I’m showing here is the apparent corner frequency 00:11:52.649 --> 00:11:57.490 you would get if you just assumed this is the source corner frequency 00:11:57.490 --> 00:12:02.350 over the true corner frequency that I predicted. 00:12:02.350 --> 00:12:06.579 This red curve is the mean of all the scenario I ran 00:12:06.579 --> 00:12:09.470 with different focal mechanism. 00:12:09.470 --> 00:12:13.730 And what I’m showing here -- and the 1 is basically saying 00:12:13.730 --> 00:12:16.920 that we retrieved the right corner frequency. 00:12:16.920 --> 00:12:21.649 Above 1, which is what we see, we retrieve a corner frequency that 00:12:21.649 --> 00:12:28.020 would be about two times or higher than what the source corner frequency is. 00:12:28.020 --> 00:12:31.100 So it really affects -- those depth phases really affect 00:12:31.100 --> 00:12:35.059 the spectrum that we get from P waves. 00:12:35.059 --> 00:12:40.949 Okay, so the way I fit the displacement spectra is not by directly fitting what 00:12:40.949 --> 00:12:48.879 we call the Brune model, which is just a flat low-frequency and fall-off of 2. 00:12:48.879 --> 00:12:51.939 What I do is I build a Green’s function using a very simple homogeneous 00:12:51.939 --> 00:12:57.889 [inaudible] space medium with a stick seismogram, and then I convolve that -- 00:12:57.889 --> 00:13:00.389 which I solve with the source depth and the radiation pattern -- 00:13:00.389 --> 00:13:04.589 I convolve that with the source spectrum, so Brune model or others. 00:13:04.589 --> 00:13:06.779 And this is what I fit to the data. 00:13:06.779 --> 00:13:14.279 So what it looks like, if it works, is this is my source spectrum here that falls 00:13:14.279 --> 00:13:20.399 with a high-frequency fall-off rate of 2. This is my synthetic in dashed lines. 00:13:20.399 --> 00:13:22.319 And the data is shown with thicker lines here. 00:13:22.319 --> 00:13:27.850 This is an example of magnitude 7.3 Nepal earthquake. 00:13:27.850 --> 00:13:29.899 So I stacked over all the stations for that example. 00:13:29.899 --> 00:13:33.420 But what I wanted to see is that fall-off here should 00:13:33.420 --> 00:13:37.819 really not be confused with the fall-off of the source spectrum. 00:13:37.819 --> 00:13:41.600 So this brings you an interesting apparent seismic moment 00:13:41.600 --> 00:13:45.749 that is much lower than the true seismic moment. 00:13:45.749 --> 00:13:48.999 It also captures this, you know, fall-off here. 00:13:48.999 --> 00:13:51.869 We can see that in the data very clearly. 00:13:51.869 --> 00:13:56.490 So this is how I basically get to the source spectra. 00:13:56.490 --> 00:13:58.029 So this is an example of that same earthquake. 00:13:58.029 --> 00:13:59.629 I’m showing purely data. 00:13:59.629 --> 00:14:02.949 This is the red curve here. This is the spectrum. 00:14:02.949 --> 00:14:07.149 This is the data. And my model stick seismogram. 00:14:07.149 --> 00:14:11.470 You can see clearly the P and the sP coming after. 00:14:11.470 --> 00:14:15.709 And we can fit that with my -- with the synthetics, and you can 00:14:15.709 --> 00:14:19.329 see it can retrieve those notches fairly well. 00:14:19.329 --> 00:14:23.249 So this worked out pretty well. 00:14:23.249 --> 00:14:27.179 Another interesting aspect to, you know, having the spectral shape 00:14:27.179 --> 00:14:29.819 is to get to the radiated energy. 00:14:29.819 --> 00:14:35.110 And so it has been proposed that you get the radiated energy above, 00:14:35.110 --> 00:14:38.869 you know, the P, the sP, and the pP, we can say we can sum the energies, 00:14:38.869 --> 00:14:41.910 and that should be equal to the total energy. 00:14:41.910 --> 00:14:46.149 And this is a fairly good approximation if we look at deep earthquakes. 00:14:46.149 --> 00:14:48.420 But if we look at shallow earthquakes, 00:14:48.420 --> 00:14:51.970 what I’m showing here is a lower focal sphere. 00:14:51.970 --> 00:14:56.129 And I’m showing the ratio of this left-hand term with the right-hand term. 00:14:56.129 --> 00:14:58.800 And saying what is the actual energy measured -- 00:14:58.800 --> 00:15:01.499 the flux of energy of the P with [inaudible], 00:15:01.499 --> 00:15:04.800 and what would be the sum of those energies. 00:15:04.800 --> 00:15:09.369 So red colors show that it’s positive, which actually indicates -- sorry, 00:15:09.369 --> 00:15:15.029 so above 1 -- it indicates this is a measure of constructive interference. 00:15:15.029 --> 00:15:19.769 So the total actually energy you measure is greater than the sum of the energies. 00:15:19.769 --> 00:15:22.300 So there’s some effect of interference. 00:15:22.300 --> 00:15:26.429 And the blue colors below 1 shows that the actual energy flux 00:15:26.429 --> 00:15:28.269 is less than the sum of the energies, 00:15:28.269 --> 00:15:33.259 which indicates a destructive interference of the -- of the depth phases. 00:15:33.259 --> 00:15:36.350 What I’m showing in those little dots here in 3D 00:15:36.350 --> 00:15:41.410 is the zone we are actually sampling with global phases. 00:15:41.410 --> 00:15:43.819 So it’s really interesting to think about it. 00:15:43.819 --> 00:15:48.790 As we grab this full focal sphere, the only slim part of 00:15:48.790 --> 00:15:52.610 the lower focal sphere is sampled by the P waves that we use. 00:15:52.610 --> 00:15:56.410 So we only see a very small part of the 00:15:56.410 --> 00:16:00.769 full wave field radiating out of the source. 00:16:00.769 --> 00:16:08.179 Okay, so there are two main approaches to estimating radiated energy. 00:16:08.179 --> 00:16:12.439 And I’m going to [chuckles] call the first one the Boatwright approach. 00:16:12.439 --> 00:16:18.309 This estimate of radiated energy is some term with -- 00:16:18.309 --> 00:16:24.470 proportionality to the -- sorry, the integral of the spectrum. 00:16:24.470 --> 00:16:29.100 This is to respect Parseval theorem, so capturing the proportionality. 00:16:29.100 --> 00:16:32.139 We have mechanical impedance here again that I indicated 00:16:32.139 --> 00:16:35.439 earlier for P waves. 00:16:35.439 --> 00:16:43.699 And -- sorry -- we have the integral of the velocity squared 00:16:43.699 --> 00:16:47.730 of the waveform in the frequency domain. 00:16:47.730 --> 00:16:54.550 So what’s good about this approach? It’s the true measure of energy flux. 00:16:54.550 --> 00:16:56.699 There is a lot of downside, though. There are downsides to this, 00:16:56.699 --> 00:17:00.499 is that every individual measurements, it’s sensitive to the radiation pattern. 00:17:00.499 --> 00:17:03.230 So we need to know the focal mechanism 00:17:03.230 --> 00:17:05.779 and the takeoff angle for this. 00:17:05.779 --> 00:17:09.919 We need also the knowledge on the geometrical spreading. 00:17:09.919 --> 00:17:14.260 And we need -- this requires that we have a well-distributed and 00:17:14.260 --> 00:17:19.189 dense network of receivers to capture the full -- the full focal sphere. 00:17:19.189 --> 00:17:23.760 And interestingly, this approach has often been done by using what I call 00:17:23.760 --> 00:17:28.610 the 1D Green’s function, which is just the exponential decay with the Q model, 00:17:28.610 --> 00:17:33.190 which is the third -- it was my third column for the Green’s function. 00:17:33.190 --> 00:17:35.850 And this has often been done like this. 00:17:35.850 --> 00:17:39.120 And there’s -- the paper from Boatwright showing -- ’86 -- 00:17:39.130 --> 00:17:42.100 show that we can actually correct this measure of energy 00:17:42.100 --> 00:17:44.769 to account for depth phases using the ratio of the energies. 00:17:44.769 --> 00:17:53.640 Okay, so the other approach we call single-station approach is -- relies on 00:17:53.640 --> 00:17:58.450 normalizing the spectrum here, which is the same as this one, but normalized. 00:17:58.450 --> 00:18:01.460 And on an independent knowledge of the seismic moments -- 00:18:01.460 --> 00:18:07.669 let’s say with surface waves. And on the average radiation pattern 00:18:07.669 --> 00:18:11.179 of the P waves squared -- an average over the focal sphere. 00:18:11.179 --> 00:18:14.320 And you have the mechanical impedance on the denominator. 00:18:14.320 --> 00:18:19.299 So plus sides on this approach -- it only relies on the spectral shape. 00:18:19.299 --> 00:18:23.529 So we abstract from -- away from all the [inaudible] 00:18:23.529 --> 00:18:27.990 information, and we only look at the spectral shape here. 00:18:27.990 --> 00:18:34.640 And if everything is good, only one station is sufficient to get the full energy. 00:18:34.640 --> 00:18:38.519 So downsides of that is that spectral shape is never constant 00:18:38.519 --> 00:18:40.769 at all azimuth and takeoff angles. 00:18:40.769 --> 00:18:44.809 Any directivity effect will alter the spectral shape. 00:18:44.809 --> 00:18:48.200 And so that -- every single station is actually 00:18:48.200 --> 00:18:49.850 going to have a different answer. 00:18:49.850 --> 00:18:52.809 The other downside is that a normalization to low frequency, 00:18:52.809 --> 00:18:56.149 as I just showed you earlier, is really -- depends strongly 00:18:56.149 --> 00:18:58.429 on the low-frequency end of the spectrum. 00:18:58.429 --> 00:19:01.960 So if you have this downgoing low-frequency [inaudible], 00:19:01.960 --> 00:19:06.899 then you should be careful with how this is being normalized. 00:19:06.899 --> 00:19:12.490 The other assumptions that gets into this is it really relies on the whole space -- 00:19:12.490 --> 00:19:15.860 homogeneous whole space assumption around the source. 00:19:15.860 --> 00:19:20.380 Which, as soon as you reach the free surface, 00:19:20.380 --> 00:19:24.649 that assumption is, of course, not valid. 00:19:24.649 --> 00:19:28.360 And interestingly, this has -- this approach tends to be 00:19:28.360 --> 00:19:30.110 along with empirical Green’s function. 00:19:30.110 --> 00:19:35.049 And those two methods -- there are two ways to get radiated energy. 00:19:35.049 --> 00:19:39.419 There are two ways to remove path effect that’s commonly done. 00:19:39.419 --> 00:19:44.529 And they tend to never -- they tend to decouple in this way. 00:19:44.529 --> 00:19:46.350 Which I think I want to promote that. 00:19:46.350 --> 00:19:48.320 We should probably use empirical Green’s function 00:19:48.320 --> 00:19:54.059 but using this true approach as a more grand truth answer. 00:19:54.059 --> 00:20:01.190 To summarize on -- voila -- to summarize on the plus and minuses 00:20:01.190 --> 00:20:05.929 from these two approach, this -- the Boatwright work, energy tends to 00:20:05.929 --> 00:20:11.649 be an underestimate of the true energy because of the destructive interferences. 00:20:11.649 --> 00:20:14.230 And the single-station energy tend to overestimate 00:20:14.230 --> 00:20:17.850 because of this higher apparent corner frequencies. 00:20:17.850 --> 00:20:22.320 And so both need corrections to account for depth phases 00:20:22.320 --> 00:20:26.159 if we were to use the 1D Green’s function that I mentioned. 00:20:26.159 --> 00:20:30.500 But on the other hand, they can also -- we can also characterize uncertainties 00:20:30.500 --> 00:20:32.559 if we are to use empirical Green’s functions, 00:20:32.559 --> 00:20:34.010 which will be in the following work. 00:20:34.010 --> 00:20:37.100 So I want to show you two example of this work. 00:20:37.100 --> 00:20:41.539 The first is, I was working for the Nepal earthquake. 00:20:41.539 --> 00:20:44.000 There was a sequence of earthquakes with the 00:20:44.000 --> 00:20:50.679 main shock starting on this part of the main [inaudible] thrust. 00:20:50.679 --> 00:20:56.380 This is the western part of the entire fault that ruptured during that earthquake. 00:20:56.380 --> 00:21:02.649 And so it was in April, magnitude 7.8. 00:21:02.649 --> 00:21:07.179 The actual -- most of the slip occurred underneath Kathmandu. 00:21:07.179 --> 00:21:10.980 And it had two aftershocks that were not buried within the coda of the 00:21:10.980 --> 00:21:15.320 main events that we can distinctly get the P waves -- P waves from. 00:21:15.320 --> 00:21:19.370 There were magnitude 7.3 and 6.8. 00:21:19.370 --> 00:21:24.820 The waveform from this sequence of earthquakes are really, really interesting. 00:21:24.820 --> 00:21:29.850 I’m showing here the 7.8, the 7.3, and the 6.8. 00:21:29.850 --> 00:21:34.090 This is azimuth. And I’m using all the stations 00:21:34.090 --> 00:21:40.120 that are within 30 to 90 degrees of azimuth -- of takeoff angles. 00:21:40.120 --> 00:21:44.130 We have time going from zero to 100 seconds. 00:21:44.130 --> 00:21:49.330 I color-coded them such that they are always of positive polarity for the P. 00:21:49.330 --> 00:21:53.669 But what you can see on all of -- the first -- all the waveforms, 00:21:53.669 --> 00:21:58.639 the distinct -- whoops -- P -- sP phase that arrives, 00:21:58.639 --> 00:22:02.019 which is of opposite sign of the main P. 00:22:02.019 --> 00:22:05.190 And this interacts with the main pulse 00:22:05.190 --> 00:22:09.409 and yields all those destructive interferences. 00:22:09.409 --> 00:22:14.610 So looking at their [inaudible] spectrum, what I’m showing here is just the P -- 00:22:14.610 --> 00:22:18.380 that waveform P and PD spectrum, and I just removed 00:22:18.380 --> 00:22:21.950 the path effect with the [inaudible] as I mentioned earlier. 00:22:21.950 --> 00:22:25.019 So see those very clear first downgoing part here 00:22:25.019 --> 00:22:27.059 and those troughs that are really distinct. 00:22:27.059 --> 00:22:29.779 They are not noise. We don’t need to smooth the spectra. 00:22:29.779 --> 00:22:32.309 They have structure in them that are really interesting. 00:22:32.309 --> 00:22:37.620 Those troughs are useful to constrain for depth and for -- and for mechanisms. 00:22:37.620 --> 00:22:43.480 So what I’m showing is, with azimuth, for all the three different earthquakes, 00:22:43.480 --> 00:22:48.130 I’m showing the stack spectrum here, and I’m showing the best-fit 00:22:48.130 --> 00:22:51.750 source spectrum that we found using our approach. 00:22:51.750 --> 00:22:53.669 So as you can see, I’m not going to 00:22:53.669 --> 00:22:57.200 interpret this part as the source seismic moment. 00:22:57.200 --> 00:23:00.820 Rather have the source spectrum going a bit above and respecting, 00:23:00.820 --> 00:23:04.130 therefore, the actual seismic moment. 00:23:04.130 --> 00:23:07.269 So if we were to pick -- on all those waveforms, we could pick -- 00:23:07.269 --> 00:23:10.740 we could fit a Brune model and get the corner frequency. 00:23:10.740 --> 00:23:15.419 What we would get with different azimuth is this form 00:23:15.419 --> 00:23:17.880 I’m showing here in logspace. 00:23:17.880 --> 00:23:22.929 The yellow -- the gray are per station. 00:23:22.929 --> 00:23:26.340 The yellow are if the average of spectra over azimuth bin. 00:23:26.340 --> 00:23:29.970 So you can see very nicely that there is very interesting 00:23:29.970 --> 00:23:34.289 directivity effects that we can see in those corner frequencies. 00:23:34.289 --> 00:23:38.059 Some directions seems to have higher corner frequency than others. 00:23:38.059 --> 00:23:42.389 And that can be due to a -- just being explained by a simple moving source. 00:23:42.389 --> 00:23:50.580 So those are just measurements we make from our rho spectra. 00:23:50.580 --> 00:23:58.009 If we were to calculate a stress drop from corner frequency estimate 00:23:58.009 --> 00:24:02.200 where we can measure -- we can estimate the static stress drop 00:24:02.200 --> 00:24:06.750 with the corner frequency -- and I’m using the Madariaga ’76 relation. 00:24:06.750 --> 00:24:12.470 With that correction, we get a stress drop of 140 MPa for that main event. 00:24:12.470 --> 00:24:17.659 So obviously, this is very high. And with a correction -- go back here -- 00:24:17.659 --> 00:24:21.000 we get -- accounting for the depth phases, you know, 00:24:21.000 --> 00:24:25.220 we actually get lower, more realistic stress drop for that one event. 00:24:25.220 --> 00:24:28.570 Now, I know that this is a higher estimate on others’ study. 00:24:28.570 --> 00:24:34.909 And I will show you that this method seems to 00:24:34.909 --> 00:24:37.419 provide higher estimates in general. 00:24:37.419 --> 00:24:42.169 So these are the spectral shape again for those three events. 00:24:42.169 --> 00:24:45.240 I also fit the high-frequency fall-off rate. 00:24:45.240 --> 00:24:52.120 I found the stress drop from corner frequency of about 20 megapascal. 00:24:52.120 --> 00:24:56.159 For the first aftershock, I got about 20 megapascal, too. 00:24:56.159 --> 00:25:02.320 And for one of the small one, I actually got a 40 megapascal stress drop. 00:25:02.320 --> 00:25:05.909 So those are interesting shape because we really capture 00:25:05.909 --> 00:25:09.870 the structure due to that Green’s function. 00:25:09.870 --> 00:25:13.639 Also note that, for this min one, I know a question will rise, 00:25:13.639 --> 00:25:17.000 how can we fit the corner frequency way up there when we 00:25:17.000 --> 00:25:20.380 actually don’t have data for that? 00:25:20.380 --> 00:25:25.309 A lot of the misfit function that I choose have a global minimum to that. 00:25:25.309 --> 00:25:30.179 And I’m trying to look at corner frequencies that range between -- for that 00:25:30.179 --> 00:25:35.230 magnitude size between 0.1 megapascal to 200 megapascal or something. 00:25:35.230 --> 00:25:36.850 And I do a [inaudible] search. 00:25:36.850 --> 00:25:39.639 There’s a global minimum to that misfit function. 00:25:39.639 --> 00:25:43.470 And I attempt to have a pretty good estimate of that corner frequency, 00:25:43.470 --> 00:25:46.740 even though we don’t have the data for it. 00:25:46.740 --> 00:25:50.080 Now, to measure radiated energy, we need to apply a correction 00:25:50.090 --> 00:25:54.740 to the depth phase -- to the spectrum again. 00:25:54.740 --> 00:25:57.110 What I do is I measure first the apparent energy. 00:25:57.110 --> 00:26:00.480 I’m calling that apparent because it’s within two frequency bands. 00:26:00.480 --> 00:26:04.720 So usually between let’s say 100 seconds and 2 hertz, 00:26:04.720 --> 00:26:07.720 this is a limited bandwidth of measure. 00:26:07.720 --> 00:26:13.730 A measure for each of those station -- I measure this energy 00:26:13.730 --> 00:26:15.440 between the frequency bin. 00:26:15.440 --> 00:26:19.919 Now, I know, since I fit the source depth and focal mechanism, 00:26:19.919 --> 00:26:23.980 I can build synthetic. I can predict what the energy would be 00:26:23.980 --> 00:26:27.840 given the fact that I have the source spectrum and the Green’s function. 00:26:27.840 --> 00:26:31.500 And so this synthetic energy I can calculate it between 00:26:31.500 --> 00:26:35.720 [inaudible] and infinite frequencies. 00:26:35.720 --> 00:26:38.740 And by doing the ratio of those two, I know what is the bias 00:26:38.740 --> 00:26:42.000 in radiated energy if we don’t account for depth phases. 00:26:42.000 --> 00:26:43.870 And I can create a correction based on this. 00:26:43.870 --> 00:26:47.470 So it’s very simple, and I want to show that -- 00:26:47.470 --> 00:26:50.110 you know, I presented two ways to measure energy. 00:26:50.110 --> 00:26:53.299 If we don’t correct for depth phases, the two ways are shown here 00:26:53.299 --> 00:26:55.389 where I have, in yellow, the Boatwright energy, 00:26:55.389 --> 00:27:01.259 and in red, the station energy -- single-station energy with azimuth. 00:27:01.259 --> 00:27:04.120 After correction, we actually better fit those two together. 00:27:04.120 --> 00:27:07.509 So it’s kind of a interesting validation of this approach 00:27:07.509 --> 00:27:12.269 is that both independent estimate match better in [inaudible] azimuth. 00:27:12.269 --> 00:27:16.940 So I did this also for the other earthquakes. 00:27:16.940 --> 00:27:23.690 I could find interesting directivity effects to this. 00:27:23.690 --> 00:27:27.830 Now, what I wanted to say, roughly, from this short study is 00:27:27.830 --> 00:27:31.580 any magnitude 6 and above within upper 35 kilometers 00:27:31.580 --> 00:27:35.490 is going to have this effect, and very strongly. 00:27:35.490 --> 00:27:38.450 The interferences really bias the corner frequency 00:27:38.450 --> 00:27:41.120 and the low-frequency asymptote. 00:27:41.120 --> 00:27:44.779 And so we need to correct for this bias in radiated energy. 00:27:44.779 --> 00:27:48.100 We can do that by this -- understanding the source depth, 00:27:48.100 --> 00:27:52.210 or calculating the source depth and the -- using the source size. 00:27:52.210 --> 00:27:55.490 Now I want to show you a second example 00:27:55.490 --> 00:27:58.769 in which I’m now looking globally. 00:27:58.769 --> 00:28:02.649 I’m focusing primarily on subduction earthquakes that are 00:28:02.649 --> 00:28:06.389 thrust-driven because they have the same radiation pattern, roughly, 00:28:06.389 --> 00:28:11.379 as what the Nepal earthquake had. So here is my database. 00:28:11.379 --> 00:28:18.950 I have about 2,600 thrust earthquake that have a magnitude 5-1/2 and above. 00:28:18.950 --> 00:28:23.140 Since 1990 until this summer in 2015. 00:28:23.140 --> 00:28:25.040 And I intentionally picked the earthquake 00:28:25.049 --> 00:28:30.210 that were shallower than 50, though some were 60 kilometers. 00:28:30.210 --> 00:28:34.789 And what I’m showing here is a -- usually I center it around Europe, but 00:28:34.789 --> 00:28:38.169 this time really, the thrust earthquakes, we got to center around the Pacific. 00:28:38.169 --> 00:28:41.320 We’re just going to look at all the events that are 00:28:41.320 --> 00:28:50.220 along the subduction zone, and then we have some diffuse seismicity in Tibet. 00:28:50.220 --> 00:28:56.040 So first, we best fit the focal depth. And I’m showing here a very simple 00:28:56.049 --> 00:29:02.610 histogram of that fit that we did globally for all those earthquakes. 00:29:02.610 --> 00:29:07.159 The PDE estimate range from, you know, the surface down to 00:29:07.159 --> 00:29:11.500 about 60, 80 kilometers for my -- the catalog I chose. 00:29:11.500 --> 00:29:17.409 Interestingly, the CMT estimate seems to only go after 10 kilometers’ depth. 00:29:17.409 --> 00:29:19.580 And I am not exactly sure why. 00:29:19.580 --> 00:29:25.730 And that the distribution of those depth is of course greatly at the 10 kilometers. 00:29:25.730 --> 00:29:31.370 And with our estimate, what we tend to have is more Gaussian-like 00:29:31.370 --> 00:29:37.090 looking depth estimate with a center around, like, 25 kilometers. 00:29:37.090 --> 00:29:40.789 So I’m not going to use -- I used the CMT depth 00:29:40.789 --> 00:29:43.019 for the magnitude N and above. 00:29:43.019 --> 00:29:47.250 Because what does a depth mean when you have such a large earthquake? 00:29:47.250 --> 00:29:50.399 And I’d rather trust the CMT solutions for that 00:29:50.399 --> 00:29:53.409 than our estimate that rely on point sources. 00:29:53.409 --> 00:29:57.899 But we do distribute roughly the focal depths. 00:29:57.899 --> 00:30:03.940 Now I want to show you an example of a cluster that I found in Taiwan. 00:30:03.940 --> 00:30:06.639 Maybe to go back into this, what I’m really interested in 00:30:06.639 --> 00:30:10.340 is looking at radiated energy with all the different earthquakes. 00:30:10.340 --> 00:30:15.519 But by having this 1D Green’s function, I’m only going to look at clusters, 00:30:15.519 --> 00:30:19.590 in which case, those clusters will have the same -- roughly the same 00:30:19.590 --> 00:30:23.559 Green’s function, just to make sure I’m not biasing the estimates 00:30:23.559 --> 00:30:27.649 by having a wrong Green’s functions to it comparing the same objects. 00:30:27.649 --> 00:30:32.889 So I’m showing here example of a few earthquakes that I -- 00:30:32.889 --> 00:30:37.730 that came out of that clustering. And I’m recording this in Australia. 00:30:37.730 --> 00:30:41.710 I’m showing here, color-coded with different magnitude -- 00:30:41.710 --> 00:30:45.620 this is a magnitude 5.9 -- very well-recorded. 00:30:45.620 --> 00:30:50.289 6.1, then we have a bunch of -- 6.3, 6.5, and then we have 00:30:50.289 --> 00:30:53.059 Chi-Chi coming up here. So they have opposite polarity, 00:30:53.059 --> 00:30:57.529 which probably indicates some kind of nodal plane location. 00:30:57.529 --> 00:31:01.840 I captured the energy -- the seismic wave with a running -- with a window 00:31:01.840 --> 00:31:06.610 that varies in length because I do want to capture not much noise 00:31:06.610 --> 00:31:09.830 in the small earthquakes and only capture the pulse width. 00:31:09.830 --> 00:31:15.879 But I also want to be able to capture the full pulse width for the big ones. 00:31:15.879 --> 00:31:20.669 What I show here to the right is the -- just like actually for Nepal -- 00:31:20.669 --> 00:31:26.909 the data is shown with those rough spectra, color-coded for the same thing. 00:31:26.909 --> 00:31:31.090 We have these nice troughs, again, that we see in the spectra. 00:31:31.090 --> 00:31:34.690 The dashed are the synthetics for that given station. 00:31:34.690 --> 00:31:40.649 As we see, we fit best the troughs and the downgoing low-frequency end. 00:31:40.649 --> 00:31:44.180 And then the thinner lines are going to be the source spectra 00:31:44.180 --> 00:31:49.900 with the right -- with the seismic moment imposed by the CMT solution. 00:31:49.909 --> 00:31:54.110 So you can see that, even though we have a finite bandwidth, you know, 00:31:54.110 --> 00:31:59.029 between -- I think it is 75 seconds to 2 hertz, we can actually understand 00:31:59.029 --> 00:32:04.159 the full spectra shape by the -- by using the depth phases. 00:32:04.159 --> 00:32:11.070 What I want to show here is those gray dots are the corner frequency 00:32:11.070 --> 00:32:15.710 that would appear if the earthquake had a 1 MPa stress drop. 00:32:15.710 --> 00:32:19.649 So I’m showing here where that corner frequency should be. 00:32:19.649 --> 00:32:25.279 And the colored one are the ones that I show that best fit our spectra. 00:32:28.260 --> 00:32:32.400 Okay, so now I’m going to try to convince you that we sometimes 00:32:32.400 --> 00:32:36.800 see earthquakes scaling with seismic moment. 00:32:36.800 --> 00:32:38.679 What I’m showing on the top is going to be 00:32:38.679 --> 00:32:41.659 all the corner frequency that we best fit. 00:32:41.659 --> 00:32:45.840 The circles are going to be average with -- for each event -- 00:32:45.840 --> 00:32:47.970 averages for each station in each event. 00:32:47.970 --> 00:32:51.779 The blue dots are going to be for each different station, just to see 00:32:51.779 --> 00:32:55.840 there is a spread -- within one event, stations have a different bias. 00:32:55.840 --> 00:32:59.720 All the lines shown to the top represent the -- 00:32:59.720 --> 00:33:04.980 a constant stress drop of 0.1 MPa, 1 MPa, 10 MPa, 100 MPa. 00:33:04.980 --> 00:33:07.350 And then the X axis is going to be seismic moment 00:33:07.350 --> 00:33:11.019 retrieved from the CMT solutions. 00:33:11.019 --> 00:33:13.929 And I’m just showing basically what the spread is like. 00:33:13.929 --> 00:33:18.220 We have a pretty good -- not much variation 00:33:18.220 --> 00:33:21.169 in the corner frequency estimate for each event. 00:33:21.169 --> 00:33:27.180 We do carefully select the data to do so. 00:33:27.180 --> 00:33:33.320 And interestingly, we see that there is some trends in this scaling. 00:33:33.320 --> 00:33:35.090 This is pretty [inaudible], right? 00:33:35.090 --> 00:33:37.779 We said there would be a higher apparent corner frequency, 00:33:37.779 --> 00:33:41.649 and that appears to be so. This is the stress drop using 00:33:41.649 --> 00:33:45.259 the Madariaga ‘76 relation, and the [inaudible] ‘57. 00:33:45.259 --> 00:33:51.309 For the same seismic moment, we can fit -- again, circles are per event, 00:33:51.309 --> 00:33:54.470 blue circles are for each station -- each event. 00:33:54.470 --> 00:33:58.080 We can fit -- I do a L1 fit with bootstrapping on the sampling 00:33:58.080 --> 00:34:03.970 of the data to look at the trends. And we find a slope of 0.33 00:34:03.970 --> 00:34:08.929 with a standard deviation of 5% for this stress drop. 00:34:08.929 --> 00:34:12.950 For the scaled radiated energy, which I do not correct for the phases yet, 00:34:12.950 --> 00:34:17.599 I also get a slightly smaller slope, but yet still positive, 00:34:17.599 --> 00:34:22.280 of 0.27 and a standard deviation of 4%. 00:34:22.280 --> 00:34:27.369 Now, what I’m showing here is I only measured the P energy, 00:34:27.369 --> 00:34:31.309 but I assumed that if P and S share the same corner frequency, 00:34:31.309 --> 00:34:38.230 so I scale the energy to be the true -- the energy of P and S together 00:34:38.230 --> 00:34:40.300 to compare with other studies. 00:34:40.300 --> 00:34:43.230 So this is without correcting for any depth phases. 00:34:43.230 --> 00:34:45.829 If we correct for depth phases, as we predicted, 00:34:45.829 --> 00:34:47.389 we’re going to lower this slope. 00:34:47.389 --> 00:34:52.710 Right? Because we removed this bias from higher upper and corner frequency. 00:34:52.710 --> 00:34:57.359 And what I -- what I would see is we do lower the slope. 00:34:57.359 --> 00:35:02.720 This time we have a [inaudible] with a slope of 0.21 with 7%. 00:35:02.720 --> 00:35:06.359 But there is a residual slope that is still there and sustains 00:35:06.359 --> 00:35:09.859 for a lot of the clusters that I have been looking at. 00:35:09.859 --> 00:35:14.250 Also interesting, we have a difference in slope between scaled energy and 00:35:14.250 --> 00:35:20.780 stress drop, which actually will yield in scaling for fracture energy in the future. 00:35:20.780 --> 00:35:25.950 So also showed the dashed line here as if I used the single station estimate 00:35:25.950 --> 00:35:29.869 rather than the average estimate. So there is some change to it, but the 00:35:29.869 --> 00:35:34.940 errors that we get are fairly consistent -- very small for the slopes we get. 00:35:34.940 --> 00:35:41.270 So we can do that at all clusters -- and this is just ongoing work, 00:35:41.270 --> 00:35:44.300 so I’m just showing -- I’m going to show you a few clusters that I selected 00:35:44.300 --> 00:35:48.000 that have good data and represent what the slope should be. 00:35:48.000 --> 00:35:51.210 I’m not showing the errors, but as you can tell, 00:35:51.210 --> 00:35:52.640 there is some error of some percent. 00:35:52.640 --> 00:35:57.599 And I’m showing -- and green is going to be zero scaling, slope of zero. 00:35:57.599 --> 00:36:03.900 Red is going to be a 0.5 scaling. And blue will be minus-5 scaling. 00:36:03.900 --> 00:36:08.240 So to be fair, this varies a lot on the subduction zone. 00:36:08.240 --> 00:36:15.520 And this is -- in the corals here -- in our oceans, we have negative scaling. 00:36:15.520 --> 00:36:19.530 But we do have strong scaling that I’ve seen very consistent 00:36:19.530 --> 00:36:24.069 in South America and in Sumatra. 00:36:24.069 --> 00:36:29.910 And there is some interestingly smooth pattern to it that I have not yet analyzed. 00:36:29.910 --> 00:36:33.339 So this is for stress drop, and this is for scaled energy. 00:36:33.339 --> 00:36:40.190 They differ a little bit, as I mentioned earlier, but this is quite interesting result. 00:36:40.190 --> 00:36:46.579 Now, I wanted to -- ongoing work is to place those data points on that 00:36:46.579 --> 00:36:53.800 compiled version of scaled energy with seismic moment from Annemarie. 00:36:53.800 --> 00:36:56.900 And I was happy to find that we’re actually going to fill the gap 00:36:56.900 --> 00:37:01.030 between the big ones and the more moderate-sized ones. 00:37:01.030 --> 00:37:04.540 But I also want to emphasize that there is somewhat of a scaling going on here. 00:37:04.540 --> 00:37:06.800 So if I place the numbers I showed you earlier, 00:37:06.800 --> 00:37:10.319 we’re going to be from minus-5 to minus-4. 00:37:10.319 --> 00:37:17.839 So we are going to see some kind of a scaling between those magnitudes here. 00:37:17.839 --> 00:37:21.780 So why would -- should we believe that there is somewhat of a scaling 00:37:21.780 --> 00:37:23.540 between earthquakes and they’re not all self-similar? 00:37:23.540 --> 00:37:28.359 First, the most natural one is that the aspect ratio will change. 00:37:28.359 --> 00:37:31.510 All those magnitudes were switching from 6 to 8. 00:37:31.510 --> 00:37:35.119 We’re going from, you know, circular being good assumption 00:37:35.119 --> 00:37:37.809 to having aspect ratio of really long faults. 00:37:37.809 --> 00:37:41.880 And so that by itself is a break of self-similarity. 00:37:41.880 --> 00:37:46.480 The other thing that I’m really trying to understand is that all those stress drop 00:37:46.480 --> 00:37:53.180 estimates from corner frequencies are based on a circular crack-like rupture. 00:37:53.180 --> 00:37:58.170 But we don’t have the equivalent of such a formulation between 00:37:58.170 --> 00:38:01.579 corner frequency and size for pulse-like ruptures. 00:38:01.579 --> 00:38:07.180 In which case, the -- basically, the pulse-like will have the smaller 00:38:07.180 --> 00:38:10.559 earthquake, but the fault way is actually going to be larger at a given time. 00:38:10.559 --> 00:38:13.770 So it’s going to be a very -- a much different physics, 00:38:13.770 --> 00:38:17.220 I think, to basically look at those terms. 00:38:17.220 --> 00:38:22.210 Other things that are starting to come up is that dynamic weakening mechanism 00:38:22.210 --> 00:38:26.109 for those big ones is becoming important in breaking that scaling. 00:38:26.109 --> 00:38:32.950 And there’s a paper that just came out that showed that thermal pressurization 00:38:32.950 --> 00:38:36.329 in other phenomena for large earthquakes for high slip rate may 00:38:36.329 --> 00:38:40.980 actually break the scaling of earthquakes for a given magnitude. 00:38:40.980 --> 00:38:45.520 And so maybe we should start considering that all those magnitude, 00:38:45.520 --> 00:38:48.079 the physics is slightly different. 00:38:48.079 --> 00:38:51.050 The free surface is going to be different for the shallow earthquakes 00:38:51.050 --> 00:38:54.250 because a small one at 5 kilometers does not fill the free surface, 00:38:54.250 --> 00:38:57.270 but a big one might actually rupture through it. 00:38:57.270 --> 00:39:01.400 And so maybe we should have a variable -- 00:39:01.400 --> 00:39:04.160 different way of thinking from small to big earthquakes. 00:39:04.160 --> 00:39:07.790 Now, I’ve been -- you know, working with Peter, 00:39:07.790 --> 00:39:11.079 you’re very careful with data processing. 00:39:11.079 --> 00:39:14.010 And I think there is -- we really need to emphasize this. 00:39:14.010 --> 00:39:18.970 We found a lot of interesting factor in processing the data and finding this. 00:39:18.970 --> 00:39:23.339 First, we really have to be careful of those depth phases. 00:39:23.339 --> 00:39:25.280 Should not smooth the spectrum. There is structure there. 00:39:25.280 --> 00:39:28.650 We should keep it. We need to capture the 00:39:28.650 --> 00:39:30.380 pulse width -- so fixed window, 00:39:30.380 --> 00:39:33.020 but looking at variable magnitude does not work. 00:39:33.020 --> 00:39:36.280 You really need to remove the noise for the small earthquakes 00:39:36.280 --> 00:39:39.990 by just capturing the pulse width and encompass enough 00:39:39.990 --> 00:39:42.630 to really look at the big ones to capture all the pulse width. 00:39:42.630 --> 00:39:46.829 So I suggest, you know, a variable window length. 00:39:46.829 --> 00:39:53.030 The other thing that we found is, in his study with Bettina Allman in 2009 -- 00:39:53.030 --> 00:39:57.109 and I’ve seen other studies doing this -- imposing a high-frequency fall-off rate 00:39:57.109 --> 00:40:00.660 of 1.6 tends to give you a lower corner frequency 00:40:00.660 --> 00:40:02.710 and therefore a lower stress drop. 00:40:02.710 --> 00:40:05.119 And by the data processing they use, 00:40:05.119 --> 00:40:10.339 we find there is no scaling with this approach, which confirms their study. 00:40:10.339 --> 00:40:15.240 But if we looked at -- by solving for that high-frequency fall-off rate, we found 00:40:15.240 --> 00:40:20.670 that the median was 2, in which case, we do find the scaling when the median is 2. 00:40:20.670 --> 00:40:24.770 And this comes from the fact that there’s a strong tradeoff when you fit spectra 00:40:24.770 --> 00:40:28.190 between the corner frequency and the high-frequency fall-off rate. 00:40:28.190 --> 00:40:32.480 And it’s really hard to fit those two consistently. 00:40:32.480 --> 00:40:36.270 There’s also -- in some of the techniques, 00:40:36.270 --> 00:40:39.660 and some that uses empirical Green’s functions, 00:40:39.660 --> 00:40:44.490 we tend to impose the source spectra, or we tend to impose it to be self-similar. 00:40:44.490 --> 00:40:47.040 And by doing so, we actually retrieve self-similarity. 00:40:47.040 --> 00:40:51.299 So there’s some circular thinking that we should be careful of. 00:40:51.299 --> 00:40:54.480 There’s also a lot of problems that we have with the theory 00:40:54.480 --> 00:40:58.170 at this point because of the shallow earthquakes. 00:40:58.170 --> 00:41:00.799 The first is there -- we need to find a similar relation 00:41:00.799 --> 00:41:03.559 between earthquake size and corner frequency, not only 00:41:03.559 --> 00:41:06.760 for crack-like rupture, but we need to think about it for pulse-like rupture. 00:41:06.760 --> 00:41:11.890 And I know Kaneko and Shearer had started working on, you know, 00:41:11.890 --> 00:41:15.260 other aspect ratios for crack-like, but I think we also need to 00:41:15.260 --> 00:41:20.270 start thinking about the much bigger ones. 00:41:20.270 --> 00:41:25.750 You know, so -- all these estimates are showing a 10 MPa average stress drop, 00:41:25.750 --> 00:41:30.180 which is much larger than most other study that use finite source inversion. 00:41:30.180 --> 00:41:35.250 And what is really the stress drop we are sensitive to? 00:41:35.250 --> 00:41:37.109 So we always think -- we’ve made the assumption 00:41:37.109 --> 00:41:38.609 that this is a static stress drop. 00:41:38.609 --> 00:41:44.180 I’m using this plot from Noda and others where you -- X axis you have the slip. 00:41:44.180 --> 00:41:46.220 In the Y axis, you have the strength. 00:41:46.220 --> 00:41:51.770 And it basically describe the -- a strength drop during slip. 00:41:51.770 --> 00:41:58.079 We always assumed that we are sensitive to the static stress drop, 00:41:58.079 --> 00:42:00.990 but the seismic waves are much more sensitive 00:42:00.990 --> 00:42:06.010 to those large variation in stress drop and in rupture speed and all that. 00:42:06.010 --> 00:42:08.250 And so I think that maybe the discrepancy between 00:42:08.250 --> 00:42:14.599 the corner frequency estimate and the finite source estimates 00:42:14.599 --> 00:42:18.790 may come from just talking about a different object. 00:42:18.790 --> 00:42:23.099 And often we found the dynamic stress drop rather bigger 00:42:23.099 --> 00:42:25.359 than static stress drop, so this is important. 00:42:25.359 --> 00:42:31.049 Another thing that I started working on that’s rather -- endeavor is complicated -- 00:42:31.049 --> 00:42:34.580 the radiated energy is always defined in a homogeneous whole space. 00:42:34.580 --> 00:42:37.431 So that gets back to what I said earlier. 00:42:37.440 --> 00:42:39.240 But what happens with the free surface? 00:42:39.240 --> 00:42:44.410 As you go shallower, the rupture itself feels the difference in normal stress. 00:42:44.410 --> 00:42:46.799 And actually, you can see strange behavior 00:42:46.799 --> 00:42:50.819 for earthquakes rupturing through the surface. 00:42:50.819 --> 00:42:53.589 And maybe the earthquake energy budget itself 00:42:53.589 --> 00:42:57.609 is modified by being close to the free surface. 00:42:57.609 --> 00:43:01.069 So you have the source aspect to this. You also have the fact that, for shallow 00:43:01.069 --> 00:43:06.069 earthquakes, you have high-frequency surface waves excited at the source. 00:43:06.069 --> 00:43:06.990 And therefore, they should be 00:43:06.990 --> 00:43:11.930 incorporating it also in the overall radiated energy. 00:43:11.930 --> 00:43:14.849 But this is really ongoing work. 00:43:14.849 --> 00:43:20.609 So I just want to conclude -- you know, short concluding remarks that we -- 00:43:20.609 --> 00:43:25.809 if we do not have ways to properly removed path effects, we can do so, 00:43:25.809 --> 00:43:30.220 but really being careful about the spectral shape from the P waves and 00:43:30.220 --> 00:43:37.089 really looking at the interference between direct and depth phases. 00:43:37.089 --> 00:43:39.460 We can use -- we can use it as a tool 00:43:39.460 --> 00:43:43.319 to constrain for source depth and P spectrum shape. 00:43:43.319 --> 00:43:48.700 And we can correct the radiant energy by doing -- by looking at that fit. 00:43:48.700 --> 00:43:53.349 We applied to this Nepal. I also moved for Nepal into a more finite 00:43:53.349 --> 00:43:58.349 approach view on this earthquake. It’s a really interesting earthquake. 00:43:58.349 --> 00:44:00.900 But also found in this that -- we found a better agreement 00:44:00.900 --> 00:44:03.740 between the two independent estimates. 00:44:03.740 --> 00:44:06.390 And now moving globally, I’m trying to apply this 00:44:06.390 --> 00:44:09.990 to all the global thrust earthquakes. 00:44:09.990 --> 00:44:14.010 And this, by wanting to reduce the scaling, we actually have the residual 00:44:14.010 --> 00:44:20.510 scaling that stays, that varies spatially in both scaling energy and in stress drop. 00:44:20.510 --> 00:44:22.660 And it tends to be positive. 00:44:22.660 --> 00:44:25.760 And, you know, the next step from those would be -- 00:44:25.760 --> 00:44:28.930 from that would be to look at what are the physics that would help 00:44:28.930 --> 00:44:34.240 explain that spatially varying scaling along the megathrusts. 00:44:34.240 --> 00:44:39.329 So looking at oceanic crust, age, convergence rates, 00:44:39.329 --> 00:44:42.190 and trying to see there’s only correlation between the 00:44:42.190 --> 00:44:45.559 geodynamic context and the scaling that we see. 00:44:45.560 --> 00:44:47.300 And that’s it. Thank you. 00:44:47.300 --> 00:44:52.240 [ Applause ] 00:44:53.500 --> 00:44:55.419 - Questions? 00:45:01.680 --> 00:45:03.780 - Yeah, Marine, that was a really nice talk. 00:45:03.790 --> 00:45:07.069 I guess I had a couple of questions. 00:45:07.069 --> 00:45:10.599 Maybe I could use the Taiwan data to illustrate them. 00:45:10.599 --> 00:45:13.140 The apparent scaling you see depends somewhat upon 00:45:13.140 --> 00:45:15.599 what you obtained for the Chi-Chi earthquake. 00:45:15.599 --> 00:45:17.069 So it’s a bit of a leverage point? - Yes. 00:45:17.069 --> 00:45:18.500 - It’s out at the edge. 00:45:18.500 --> 00:45:22.670 And I’m wondering if -- because that earthquake was 00:45:22.670 --> 00:45:27.220 well-recorded by local stations, you can look at the upgoing waves. 00:45:27.220 --> 00:45:29.609 And I’m wondering if you’ve made any comparison between 00:45:29.609 --> 00:45:31.609 the energy estimates you get teleseismically 00:45:31.609 --> 00:45:35.220 with the energy estimates you get from local near data. 00:45:35.220 --> 00:45:37.880 - Yes. So I’ll answer that quickly. 00:45:37.880 --> 00:45:43.630 So this is why we use L1 fit, and we bootstrap on the resampling 00:45:43.630 --> 00:45:46.859 is to make sure that those big ones are not really driving -- 00:45:46.859 --> 00:45:51.230 or reduce the effects of those large one driving the slope. 00:45:51.230 --> 00:45:55.829 - Well, and even with L1, you will always be sensitive to a leverage point. 00:45:55.829 --> 00:45:58.289 - Right. - You don’t -- you don’t escape that. 00:45:58.289 --> 00:46:01.559 - But in the bootstrap, that earthquake sometimes is not used. 00:46:01.559 --> 00:46:07.569 And so the difference in slope is -- the uncertainty actually captures 00:46:07.569 --> 00:46:11.299 whether or not that earthquake is in the data set or not. 00:46:11.299 --> 00:46:14.069 But, I mean, I agree that the big ones are driving up. 00:46:14.069 --> 00:46:19.280 And I honestly think that -- I’m not sure why corner frequency -- 00:46:19.280 --> 00:46:23.579 stress drop from corner frequency would mean for those big ones, 00:46:23.579 --> 00:46:26.809 if they are used as a static stress drop. 00:46:26.809 --> 00:46:32.109 I think they might be actually a different object that we are -- should think about. 00:46:32.109 --> 00:46:36.450 And there -- for the near field -- the near field estimate, it’s a good idea. 00:46:36.450 --> 00:46:42.480 Like, I should actually start looking at any station possible that is close to there. 00:46:42.480 --> 00:46:44.430 - It seemed like it would be a good -- where there’s data available would be 00:46:44.430 --> 00:46:46.090 a good calibration [inaudible]. - Yeah. 00:46:46.090 --> 00:46:50.390 - And so that raises the question about the teleseismic method, that almost 00:46:50.390 --> 00:46:52.770 all the energy is carried in the shear wave, not the P wave. 00:46:52.770 --> 00:46:55.069 So there is a big assumption there about the partitioning. 00:46:55.069 --> 00:46:57.510 - Mm-hmm. - Have you thought about any ways 00:46:57.510 --> 00:47:00.130 that you might begin to look at the teleseismic shear waves 00:47:00.130 --> 00:47:02.730 as a way of trying to get at that? - Yes. 00:47:02.730 --> 00:47:08.450 So attenuation is a bit more complicated for shear waves. 00:47:08.450 --> 00:47:13.460 Partitioning, though, depends on the source and not on the wave propagation. 00:47:13.460 --> 00:47:18.000 And so it is true -- so if you have, let’s say, more P energy than S, 00:47:18.000 --> 00:47:21.650 where the partitioning is a -- is a -- is a source of information for 00:47:21.650 --> 00:47:24.539 opening mode and how much of the double couple and 00:47:24.539 --> 00:47:26.980 shear component for opening is important. 00:47:26.980 --> 00:47:30.980 So that by itself is a, I think, fantastic study is to really 00:47:30.980 --> 00:47:34.200 look at diversion between the P energy and the S energy. 00:47:34.200 --> 00:47:37.869 Right now, because we are careful with the wave propagation part -- 00:47:37.869 --> 00:47:40.770 and I actually want to build all those small earthquakes. 00:47:40.770 --> 00:47:42.520 I want them to be my empirical Green’s functions. 00:47:42.520 --> 00:47:47.119 That’s why I had to look into the source spectra. 00:47:47.119 --> 00:47:52.269 I have not yet looked at the S wave. But this is -- this will be done. 00:47:53.540 --> 00:48:02.880 [ Silence ] 00:48:03.560 --> 00:48:05.900 - That was a lovely talk. 00:48:05.900 --> 00:48:14.500 I’m curious if you’ve thought about and even played with the problem 00:48:14.500 --> 00:48:22.299 of differential attenuation between your direct phases and the depth phases. 00:48:22.299 --> 00:48:26.980 This is particularly a problem for subduction zone events 00:48:26.980 --> 00:48:32.760 because the depth phases are basically forced to go through ... 00:48:32.760 --> 00:48:36.360 - Sub-sediments. - ... muck, shall we call it. 00:48:36.360 --> 00:48:40.710 - Yeah, right, right. So I’ve done synthetic tests 00:48:40.710 --> 00:48:44.809 on a different Q for P and Q for S. 00:48:44.809 --> 00:48:47.030 And from what I recall, it was not significant, 00:48:47.030 --> 00:48:54.559 but it’s something I should revisit and that I’m actually looking at the data. 00:48:54.559 --> 00:48:59.450 Also, I’m using the CRUST 1.0 model for the wave speed, 00:48:59.450 --> 00:49:05.030 for variation with that, which may not capture correct the attenuation. 00:49:05.030 --> 00:49:08.440 It’s good [on a] wavelength, but I’m not sure how well it does 00:49:08.440 --> 00:49:12.869 for all those local clusters. Ideally, I would get all the velocity 00:49:12.869 --> 00:49:15.470 model from all those, you know, experiments that have been done 00:49:15.470 --> 00:49:19.870 offshore to get the velocity model and try to get that more robust. 00:49:21.160 --> 00:49:22.620 Yes? 00:49:22.620 --> 00:49:24.100 - Yeah, really nice, clear talk. 00:49:24.100 --> 00:49:27.480 I think I learned several things in various parts. 00:49:27.500 --> 00:49:30.289 Since this plot is still up here, I’ll ask a question about this. 00:49:30.289 --> 00:49:34.789 Have you -- so a naive interpretation would be you could just draw 00:49:34.789 --> 00:49:39.329 a straight line with a slope of zero through those points. 00:49:39.329 --> 00:49:42.920 - Right. - So have you looked at something like 00:49:42.920 --> 00:49:48.990 an AIC -- the Akaike Information Criteria -- to see if adding that additional 00:49:48.990 --> 00:49:53.859 parameter of an adjustable slope improves the fit enough to justify that? 00:49:53.859 --> 00:49:57.890 - You mean two slopes, for instance? Or ... 00:49:57.890 --> 00:50:04.710 - So basically, does allowing a non-zero slope improve the fit 00:50:04.710 --> 00:50:10.359 to the data enough to justify having that as an additional parameter? 00:50:10.359 --> 00:50:15.520 - I [inaudible] this slope from minus-1 to 1. 00:50:15.520 --> 00:50:20.770 - Right. But I guess, does it -- how much does the fit degrade 00:50:20.770 --> 00:50:22.860 if you just assume the slope is zero? 00:50:22.860 --> 00:50:25.779 - Oh, okay. Looking at the misfit function itself? 00:50:25.779 --> 00:50:28.160 - Yeah, basically ... - All right, yeah, right? 00:50:28.160 --> 00:50:31.490 - ... I was thinking, by including a search for slope, you’re allowing 00:50:31.490 --> 00:50:34.289 an additional parameter in there. - Uh-huh. 00:50:34.289 --> 00:50:40.690 - So if you -- does the fit improve enough by, say, including a slope of 0.21 00:50:40.690 --> 00:50:46.540 to justify a distinction from a slope of zero, basically? 00:50:46.540 --> 00:50:49.920 - Right. So what I should show is the misfit function. 00:50:49.920 --> 00:50:53.980 Because if the misfit function -- let’s say the, you know, X axis 00:50:53.980 --> 00:50:58.990 is going to be the slope, Y axis is going to be the residual of the fit, 00:50:58.990 --> 00:51:03.930 if it’s a very sharp global minimum, then it’s very well-constrained. 00:51:03.930 --> 00:51:08.180 If the global minimum is kind of flat, then I can probably allow -- use that 00:51:08.180 --> 00:51:12.760 as a source of uncertainty in the slope. So that’s something 00:51:12.760 --> 00:51:15.120 I should definitely do. - Thanks. 00:51:16.320 --> 00:51:26.440 [ Silence ] 00:51:26.860 --> 00:51:35.540 - I thank David for keeping the [laughs] -- this plot up. 00:51:35.540 --> 00:51:44.440 There’s a clot, shall I call it, of stations -- or not stations, of events ... 00:51:44.440 --> 00:51:45.760 - Events, mm-hmm. 00:51:45.769 --> 00:51:51.530 - ... that appears to be strongly affecting your slope up 00:51:51.530 --> 00:51:56.870 above 10 to the 19th Newton-meters. - Mm-hmm. 00:51:56.870 --> 00:52:02.060 - What moment magnitude is that? I just ... 00:52:02.069 --> 00:52:09.799 - I think that’s -- should be the 7 -- should be either 6.7 or around the 7. 00:52:09.799 --> 00:52:12.900 Because this includes -- that should include more stations, so ... 00:52:12.900 --> 00:52:22.539 - But the -- in fact, and of course, none of this is allowed in -- 00:52:22.539 --> 00:52:27.000 you know, try to fit it for slopes and -- but if you kind of took those out, 00:52:27.000 --> 00:52:33.130 the much larger events don’t seem to be following 00:52:33.130 --> 00:52:36.920 the slope you’re getting. - Right, so ... 00:52:36.920 --> 00:52:37.270 - And ... - Mm-hmm. 00:52:37.270 --> 00:52:42.140 - ... I may be repeating exactly what David was getting at there. 00:52:42.140 --> 00:52:46.069 - No, for sure. So, you know, I’m showing one plot. 00:52:46.069 --> 00:52:48.160 But it’s been two months that I’ve been clustering this 00:52:48.160 --> 00:52:52.109 and finding the scaling residual, and I’m just picking one of them. 00:52:52.109 --> 00:52:58.089 We could remove data to fit the slope, and we could argue that. 00:52:58.089 --> 00:53:01.390 The L1 -- the resampling -- the bootstrap is the reason why we use that. 00:53:01.390 --> 00:53:06.010 It’s the [inaudible] would definitely be biased by those outliers. 00:53:06.010 --> 00:53:09.910 I [inaudible] removing data because I’ve picked those waveforms 00:53:09.910 --> 00:53:13.330 in a really carefully way. And ... 00:53:13.330 --> 00:53:15.859 - [inaudible] - Yeah. No, I mean, I know 00:53:15.859 --> 00:53:19.309 that the slope is going to be affected by scatter around any slope 00:53:19.309 --> 00:53:23.250 that I -- that is fitted here. 00:53:23.250 --> 00:53:29.099 But what would be a suggestion for a consistent way where you don’t remove 00:53:29.099 --> 00:53:33.430 data but resample it such that you find a slope that’s better? 00:53:33.430 --> 00:53:38.670 But another measure of uncertainty should be put there to highlight that. 00:53:40.960 --> 00:53:43.490 You know, I -- I mean, this is a 0.3 slope. 00:53:43.490 --> 00:53:46.710 But there are -- I see 0.5 in some cases. 00:53:46.710 --> 00:53:50.329 And there are, of course, events that will follow in and out, but this 00:53:50.329 --> 00:53:54.579 is scattered around the slope. This is just one example. 00:53:54.579 --> 00:54:00.470 It’s by looking at many of those clusters, many of those events, that -- 00:54:00.470 --> 00:54:06.539 and carefully looking at the data, that it’s reasonable to say that this exists. 00:54:06.540 --> 00:54:10.020 And it spatially varies, so that’s pretty consistent. 00:54:13.420 --> 00:54:17.220 It’s real. [laughter] 00:54:21.040 --> 00:54:24.580 - More questions? 00:54:27.220 --> 00:54:31.580 Okay, well, then let’s meet out front at, let’s say, 00:54:31.589 --> 00:54:35.130 11:45 to walk over to the patio for lunch. 00:54:35.130 --> 00:54:37.260 And let’s thank Marine again. 00:54:37.260 --> 00:54:41.220 [ Applause ] 00:54:45.560 --> 00:54:47.480 - Thanks, Sarah. - Thank you. 00:54:50.340 --> 00:55:05.380 [ Silence ]