WEBVTT Kind: captions Language: en 00:00:01.500 --> 00:00:04.680 [ Silence ] 00:00:05.390 --> 00:00:10.760 Okay, thanks for coming back. A couple of announcements. 00:00:10.760 --> 00:00:15.379 So next week we are back on track on the normal day and time, 00:00:15.379 --> 00:00:19.520 so Wednesday at 10:30, the speaker will be Simon Klemperer. 00:00:19.520 --> 00:00:22.950 The title is not finalized, but he will be talking about 00:00:22.950 --> 00:00:26.620 ambient noise tomography in southern California to identify 00:00:26.620 --> 00:00:30.949 mafic lower crust, partial melt, and San Andreas Fault dip. 00:00:30.949 --> 00:00:34.829 Today our speaker is Emmanuel Gaucher, 00:00:34.829 --> 00:00:37.469 and he will be introduced by Martin Schoenball. 00:00:38.700 --> 00:00:41.579 - Yeah, it’s my pleasure to introduce Emmanuel. 00:00:41.579 --> 00:00:46.949 He earned his Ph.D. from IPGP in Paris, where he worked on induced seismicity 00:00:46.949 --> 00:00:51.100 at the pilot enhanced geothermal system in Soultz. 00:00:51.100 --> 00:00:53.760 Then he joined industry. He was working for two years for 00:00:53.760 --> 00:00:56.960 CGG-Veritas and 10 years 00:00:56.960 --> 00:01:00.879 for Magnitude, where he provided monitoring services 00:01:00.879 --> 00:01:03.649 for hydraulic fracturing operations. 00:01:03.649 --> 00:01:08.500 And in 2010, he joined KIT, the Karlsruhe Institute of Technology, 00:01:08.500 --> 00:01:15.189 to support the group in developing better methods for reservoir imaging 00:01:15.189 --> 00:01:20.009 and reservoir monitoring. And we are excited for your talk. 00:01:21.740 --> 00:01:24.080 - Thank you, Martin. 00:01:24.090 --> 00:01:25.869 So good afternoon, ladies and gentleman. 00:01:25.869 --> 00:01:27.939 Thank you very much for coming. 00:01:27.939 --> 00:01:32.670 I’m very, very pleased and honored to have a talk here. 00:01:32.670 --> 00:01:35.170 It’s -- and to be here today. And I would like thank again 00:01:35.170 --> 00:01:37.880 Martin for -- I mean, 00:01:37.880 --> 00:01:42.140 is in this -- the opportunity to give this talk here and also the 00:01:42.140 --> 00:01:47.850 whole team -- the support team for these ESC seminars. 00:01:47.850 --> 00:01:50.689 So what I’m going to talk about today is 00:01:50.689 --> 00:01:54.200 about some works I’ve done quite recently. 00:01:54.200 --> 00:01:56.479 And I will -- I’m going to focus actually on the 00:01:56.479 --> 00:01:59.710 uncertainties and inaccuracies of earthquakes. 00:01:59.710 --> 00:02:02.819 And especially the hypocenter absolute locations. 00:02:02.819 --> 00:02:05.439 So what is very important here is absolute locations. 00:02:05.439 --> 00:02:10.259 So I will not talk about [inaudible] -- different type of locations. 00:02:10.259 --> 00:02:13.340 So will talk about standard, old-fashioned, 00:02:13.340 --> 00:02:16.580 if we could say sometimes, location techniques. 00:02:16.580 --> 00:02:19.580 And I tried to develop two directions. 00:02:19.580 --> 00:02:23.910 I would like to show you an example in a geothermal application. 00:02:23.910 --> 00:02:28.170 So actually I was attending this workshop in Stanford this week 00:02:28.170 --> 00:02:32.720 the three previous days, and we were talking a lot about induced seismicity 00:02:32.730 --> 00:02:34.600 in geothermal fields. 00:02:34.600 --> 00:02:38.720 And so I think it’s something we can -- I can explain. 00:02:38.720 --> 00:02:41.070 So there is a lot of things I presented there. 00:02:41.070 --> 00:02:45.220 And I would like also to present you a theoretical development 00:02:45.220 --> 00:02:51.060 I was thinking about, very simply. 00:02:52.500 --> 00:02:57.070 So the motivation behind this, actually, is that when we really think about 00:02:57.070 --> 00:03:00.900 that the hypocenters of the earthquakes are basically the primary attributes 00:03:00.900 --> 00:03:02.820 from which we are going to derive 00:03:02.820 --> 00:03:05.780 a lot of other attributes from the earthquakes. 00:03:05.780 --> 00:03:09.820 And for example, it’s a lot used for characterizing the seismic source 00:03:09.820 --> 00:03:13.730 or to have a focal mechanism, we need to have first the location 00:03:13.730 --> 00:03:18.150 of the earthquakes. Also, to compute the magnitude of 00:03:18.150 --> 00:03:20.750 the seismic moment of the earthquakes, we also need to have the location. 00:03:20.750 --> 00:03:24.350 So it’s very important to have this information. 00:03:24.350 --> 00:03:29.090 And when we look at the description of the underground of the subsurface, 00:03:29.090 --> 00:03:32.650 actually a lot of people are using the location of these earthquakes 00:03:32.650 --> 00:03:36.380 to try to delineate fractures and faults in the underground. 00:03:36.380 --> 00:03:39.820 So it’s also very important. 00:03:39.820 --> 00:03:43.980 Another thing I will not really discuss here in this talk is the fact that, 00:03:43.980 --> 00:03:47.140 when you are building catalogs -- because then it means that we are 00:03:47.140 --> 00:03:50.450 putting together the locations and the time of the occurrence 00:03:50.450 --> 00:03:55.480 of the earthquakes, it’s a lot used for the dynamic investigations 00:03:55.480 --> 00:03:59.380 of the earthquakes and the dynamic of the earthquakes in time and space, 00:03:59.380 --> 00:04:03.890 which has some interest in, of course hazard mitigation. 00:04:03.890 --> 00:04:07.730 But of course, all these results actually are linked to the reliability 00:04:07.730 --> 00:04:10.070 we can also have on the location of the earthquakes. 00:04:10.070 --> 00:04:13.980 And so here you have a few pictures which are showing 00:04:13.980 --> 00:04:19.030 in what we were doing with the location of the earthquakes and trying always 00:04:19.030 --> 00:04:25.100 to fit fractures of faults or to give kind of [inaudible] fracture network. 00:04:25.100 --> 00:04:29.980 And actually I’m going to mainly focus on this part here. 00:04:31.060 --> 00:04:35.150 So maybe just to follow up this, I would like to -- probably known, 00:04:35.150 --> 00:04:40.140 but just to be clear on the terminology I’m going to use here, 00:04:40.140 --> 00:04:44.880 I consider the error in the location as the superposition of two things. 00:04:44.880 --> 00:04:49.460 The first one is, it’s the inaccuracy, and the second one is the imprecision. 00:04:49.460 --> 00:04:53.190 So if you have a target, and you know that the 00:04:53.190 --> 00:04:57.370 earthquakes should be located here, so you expect the earthquakes 00:04:57.370 --> 00:05:01.660 located here actually, but after your location process, it’s there. 00:05:01.660 --> 00:05:06.139 I mean, your location is not accurate, okay? 00:05:06.139 --> 00:05:10.800 Because it doesn’t spot really on the target you should expect. 00:05:10.800 --> 00:05:15.830 But it’s rather precise because the uncertainty domain is more, okay? 00:05:15.830 --> 00:05:19.720 And usually these inaccuracies are coming from the discrepancies 00:05:19.720 --> 00:05:22.380 you have between a model and the reality. 00:05:22.380 --> 00:05:26.190 And these discrepancies are not taken into account in the process 00:05:26.190 --> 00:05:30.110 of the location itself, so in the inverse problem of the location. 00:05:30.110 --> 00:05:34.020 So typically -- I will give a counter-example later, but typically, 00:05:34.020 --> 00:05:37.960 for example, wrong velocity models -- or using wrong velocity models 00:05:37.960 --> 00:05:43.450 to locate earthquakes, will lead to bias. I mean, or to these inaccuracies. 00:05:43.450 --> 00:05:47.200 On the other side, you can have a very accurate location, 00:05:47.200 --> 00:05:50.700 but which is really, really un-precise, okay? 00:05:50.700 --> 00:05:54.210 So I don’t know which one you prefer, but actually 00:05:54.210 --> 00:05:57.970 I would rather prefer this one. I will explain that later. 00:05:57.970 --> 00:06:01.350 And actually, this imprecision here, I will speak most of the time 00:06:01.350 --> 00:06:04.139 about uncertainty. So I will mix the two things. 00:06:04.139 --> 00:06:08.700 So, to me, imprecision and uncertainties in this talk will be similar. 00:06:08.700 --> 00:06:11.639 These are coming also from the uncertainties we can 00:06:11.639 --> 00:06:14.880 take into account inside the inverse problem of the location. 00:06:14.880 --> 00:06:17.919 So typically the -- picking uncertainties. 00:06:17.919 --> 00:06:20.300 So this could be included in the inverse problem, and then this 00:06:20.300 --> 00:06:24.110 could be actually mapped back in the domain of the location, 00:06:24.110 --> 00:06:26.940 which gives these ellipsoids of locations. 00:06:26.940 --> 00:06:30.470 Of course, everybody wants something which is accurate and precise, 00:06:30.470 --> 00:06:32.130 which is not always the case. 00:06:32.130 --> 00:06:34.590 And we have to be very careful of this case. 00:06:34.590 --> 00:06:37.470 Because when you see maps of earthquakes which are 00:06:37.470 --> 00:06:42.200 showing you uncertainties in location -- okay, here you have -- you will have 00:06:42.200 --> 00:06:44.720 a point with -- I don’t know, sometimes you have segments 00:06:44.720 --> 00:06:46.180 or you have ellipsoids sometimes. 00:06:46.180 --> 00:06:49.620 But it doesn’t mean that the earthquake was in this zone. 00:06:49.620 --> 00:06:51.090 Actually, the earthquake should be there. 00:06:51.090 --> 00:06:52.900 So it’s really misleading results. 00:06:52.900 --> 00:06:55.410 So we have always to remember that you have -- 00:06:55.410 --> 00:06:57.940 you may have inaccuracies in your location. 00:06:57.940 --> 00:07:03.669 So that’s kind of terminology I’m going to use in the rest. 00:07:03.669 --> 00:07:07.620 So my outline. I want to discuss two things I said. 00:07:07.620 --> 00:07:13.300 So maybe I want to show you a case -- a field case in the geothermal field, 00:07:13.300 --> 00:07:15.710 which is intended to model the propagation of the 00:07:15.710 --> 00:07:20.150 velocity model errors into the location of the earthquakes. 00:07:20.150 --> 00:07:24.480 And I will do this in the field, which is the Rittershoffen geothermal field. 00:07:24.480 --> 00:07:28.560 And later I will speak about the theoretical development. 00:07:29.960 --> 00:07:34.710 So in this topic, actually we will see two or four different things. 00:07:34.710 --> 00:07:37.449 We will see actually what’s the effect of the picking uncertainties 00:07:37.449 --> 00:07:41.900 we may have or we may expect in this field in the location. 00:07:41.900 --> 00:07:47.010 We are going to have a look on some velocity models’ uncertainties, okay. 00:07:47.010 --> 00:07:49.669 And we are going also to make some local perturbation of the 00:07:49.669 --> 00:07:55.210 velocity model and include a more complex model -- a 3D velocity model. 00:07:55.210 --> 00:07:58.870 So this work was not -- I did not carry out this work alone. 00:07:58.870 --> 00:08:01.979 So there are co-authors or colleagues who helped me. 00:08:01.979 --> 00:08:04.790 Xavier Kinnaert, Ulrich Achauer, and Thomas Kohl from the KIT 00:08:04.790 --> 00:08:06.729 or the University of Strasbourg. 00:08:06.729 --> 00:08:12.749 And this work was funded partly by all these entities. 00:08:15.120 --> 00:08:18.139 So how we are going to do it, because it’s always a bit difficult 00:08:18.139 --> 00:08:23.169 to actually compute the bias, so you really have to model it, I mean, 00:08:23.169 --> 00:08:26.620 because you have to know where are the earthquakes at the beginning. 00:08:26.620 --> 00:08:29.560 So what we are going to do is that we are going to put 00:08:29.560 --> 00:08:33.060 synthetic event locations into a reservoir. 00:08:33.060 --> 00:08:36.360 Okay, in this case, this is our geothermal reservoir. 00:08:36.370 --> 00:08:38.939 And what we are going to do is that we are going -- within a 00:08:38.939 --> 00:08:42.529 given velocity model, we are going to propagate the seismic waves, 00:08:42.529 --> 00:08:45.160 or the body waves, the P and the S waves. 00:08:45.160 --> 00:08:50.129 And this is going to give us a set, or a data set of observed arrival times. 00:08:50.129 --> 00:08:53.309 So P and S wave arrival times on a given network. 00:08:53.309 --> 00:08:56.670 So we are controlling the network. We are controlling the source location, 00:08:56.670 --> 00:08:59.519 and we are also controlling the velocity model. 00:08:59.519 --> 00:09:02.850 So this is the first step. That’s the modeling step. 00:09:02.850 --> 00:09:06.769 The second step, we take this data set, 00:09:06.769 --> 00:09:10.970 and we are going to change the hypothesis compared to before. 00:09:10.970 --> 00:09:12.689 So what we are going to do is that we are going to 00:09:12.689 --> 00:09:17.579 change the velocity model, which should reflect some kind of reality. 00:09:17.579 --> 00:09:21.610 And we are also starting to include uncertainties in the pickings. 00:09:21.610 --> 00:09:24.589 So I will explain this a little bit. 00:09:24.589 --> 00:09:29.100 And we are going to locate these synthetic earthquakes as we do usually. 00:09:29.100 --> 00:09:33.629 And here I’m going to use a non-linear location technique, 00:09:33.629 --> 00:09:39.339 which is using the software developed by Lomax and his colleagues, 00:09:39.339 --> 00:09:44.069 which is called NonLinLoc, and which is working with 3D velocity models. 00:09:44.069 --> 00:09:46.490 And within -- or behind this location software, 00:09:46.490 --> 00:09:51.470 there is also the same array tracers as during the modeling step. 00:09:51.470 --> 00:09:54.759 So we end up with the relocated sources. 00:09:54.759 --> 00:09:56.309 Of course, there will be some mismatch 00:09:56.309 --> 00:09:59.189 because we changed the hypothesis, potentially. 00:09:59.189 --> 00:10:02.680 So when we compare, we will get the inaccuracies. 00:10:02.680 --> 00:10:06.490 So the comparison directly, or the direct comparison between the 00:10:06.490 --> 00:10:11.179 original location and the final locations will give us the bias or the inaccuracies. 00:10:11.179 --> 00:10:13.240 And actually, the probability density function 00:10:13.240 --> 00:10:16.760 function for the location will give us the uncertainties. 00:10:18.790 --> 00:10:21.949 So a little bit of background about Rittershoffen geothermal field. 00:10:21.949 --> 00:10:25.019 So it’s located in the Upper Rhine Graben in Europe. 00:10:25.019 --> 00:10:26.600 And it’s located in France. 00:10:26.600 --> 00:10:30.269 It’s very close to Soultz-sous-Forêts, which is another geothermal field. 00:10:30.269 --> 00:10:34.209 And this Upper Rhine Graben is in a zone where you can have a lot of, 00:10:34.209 --> 00:10:38.559 potentially, geothermal fields because there is a huge geothermal -- 00:10:38.559 --> 00:10:42.610 unusual high geothermal gradient in the area. 00:10:42.610 --> 00:10:46.220 And you can see on this map on the left that location 00:10:46.220 --> 00:10:49.579 of existing geothermal fields, which are all -- most of them -- 00:10:49.579 --> 00:10:53.029 I mean, these four fields are enhanced geothermal systems, 00:10:53.029 --> 00:10:57.230 and this system -- this field is a hydrothermal system. 00:10:57.230 --> 00:11:02.889 And there are other fields which are actually under development in this area. 00:11:02.889 --> 00:11:05.420 And exploration is also going on. 00:11:05.420 --> 00:11:09.220 So this Rittershoffen geothermal field consists of doublets, 00:11:09.220 --> 00:11:14.480 or two ways, we are drilled down to 2.5 kilometers depth 00:11:14.480 --> 00:11:18.149 into the Triassic sandstone and the Paleozoic granite. 00:11:18.149 --> 00:11:22.749 So you can see here on this section -- structural section, 00:11:22.749 --> 00:11:26.749 actually where is sitting the granite, and you have all the sedimentary 00:11:26.749 --> 00:11:29.889 formation cover on the top of it. 00:11:29.889 --> 00:11:32.540 You can see that’s it’s the graben, so it’s fairly complicated. 00:11:32.540 --> 00:11:34.679 You have normal faults. 00:11:34.679 --> 00:11:39.019 And these two wells actually are targeting the fault, 00:11:39.019 --> 00:11:42.220 which is just about here. 00:11:42.220 --> 00:11:46.929 So these two formations -- so around these depths, actually, 00:11:46.929 --> 00:11:50.240 so the sandstone and the granite will constitute the reservoir 00:11:50.240 --> 00:11:54.679 where we can get this hot waterfall producing heat. 00:11:54.679 --> 00:11:58.459 And this process heat, which is expected to be -- to deliver 00:11:58.459 --> 00:12:03.179 24 megawatt thermal at a flow rate of 70 liters per second 00:12:03.179 --> 00:12:09.170 in 170 degrees C is going to be used by a factory which is 15 kilometers away. 00:12:09.170 --> 00:12:13.309 So in December 2012, the first wells were drilled. 00:12:13.309 --> 00:12:20.019 In June 2013, this well was stimulated by hydraulic stimulation. 00:12:20.019 --> 00:12:23.239 Then the second well was drilled in 2014. 00:12:23.239 --> 00:12:25.999 And this well was giving expectation regarding the productivity, 00:12:25.999 --> 00:12:31.480 so it was not stimulated. Because the field was 00:12:31.480 --> 00:12:34.910 under development, there was seismic monitoring going on. 00:12:34.910 --> 00:12:41.029 And here you can have -- you can see a map of the location of the stations 00:12:41.029 --> 00:12:44.809 which were working before the stimulation of the first well. 00:12:44.809 --> 00:12:48.509 So this stimulation induced seismicity. 00:12:48.509 --> 00:12:51.179 And this is the whole idea or the whole reason 00:12:51.179 --> 00:12:54.309 why we are also doing this study in this field. 00:12:54.309 --> 00:12:58.449 So where is the mouse -- so here is the location of the well head. 00:12:58.449 --> 00:13:02.920 And you can see that we have actually 17 stations which are 00:13:02.920 --> 00:13:07.860 distributed in the north -- northern part and northwestern part, I should say. 00:13:07.860 --> 00:13:10.739 So around this area is the Soultz-sous-Forêts geothermal fields. 00:13:10.739 --> 00:13:13.239 So this explains the location of these stations. 00:13:13.239 --> 00:13:18.089 And these stations were more focused on the Rittershoffen geothermal field. 00:13:18.089 --> 00:13:22.949 So we have a mix between three- component sensors and vertical sensors, 00:13:22.949 --> 00:13:26.660 which means that we can use P and S waves for the three-component sensors. 00:13:26.660 --> 00:13:29.189 We are going to use only P wave for location 00:13:29.189 --> 00:13:32.469 when we have only vertical sensors. 00:13:33.639 --> 00:13:37.800 This network was developed over time. So actually it was [inaudible]. 00:13:37.800 --> 00:13:42.639 So this network of 15 usable stations became, before the drilling, 00:13:42.639 --> 00:13:48.019 a network of 16 stations, so with one station put in the forest. 00:13:48.019 --> 00:13:52.860 So this could not be deployed before the stimulation due to permitting issues. 00:13:52.860 --> 00:13:58.089 But then we were able, then, to develop -- or to put this sensor here. 00:13:58.089 --> 00:14:04.529 And later on, so before the drilling, we could actually add up a huge network of, 00:14:04.529 --> 00:14:09.610 in total, 41 stations located all around this drilling pad. 00:14:09.610 --> 00:14:12.759 So what we are going to look at is actually -- 00:14:12.759 --> 00:14:14.239 we are going to vary in the network. 00:14:14.239 --> 00:14:16.420 We have to also see the impact this could have 00:14:16.420 --> 00:14:18.209 on the location of the earthquakes afterwards. 00:14:18.209 --> 00:14:22.290 So I will very often talk about this network with 15 stations, 00:14:22.290 --> 00:14:25.390 16 stations, or 41 stations. 00:14:26.709 --> 00:14:29.199 So when we want to locate earthquakes, of course, 00:14:29.199 --> 00:14:33.059 we need a 1D -- we need a velocity model -- sorry. 00:14:33.059 --> 00:14:37.429 And here we actually built what we called a reference 1D velocity model. 00:14:37.429 --> 00:14:41.779 So this reference model was built from a zero-offset VSP, 00:14:41.779 --> 00:14:45.799 which was shot at the well -- the first well which was drilled. 00:14:45.799 --> 00:14:50.480 And actually, from the geological log and the different -- at the 00:14:50.480 --> 00:14:58.929 main stratigraphic layers, we actually decided to put constant velocities. 00:14:58.929 --> 00:15:06.179 So we made a combination of this zero-offset VSP and of the sonic log -- 00:15:06.179 --> 00:15:11.189 of the sonic log for the -- to compute the S wave velocities. 00:15:11.189 --> 00:15:14.410 And we were able, then, to obtain the profile of the -- 00:15:14.410 --> 00:15:17.559 of the velocity of the P waves, which is here in red, 00:15:17.559 --> 00:15:21.350 and of the S waves, which are -- which is here in green. 00:15:21.350 --> 00:15:23.299 So you can see here that we have actually 00:15:23.299 --> 00:15:25.980 two large contrasts -- velocity contrasts. 00:15:25.980 --> 00:15:29.449 One is at the top of the Lias in the sedimentary zone, 00:15:29.449 --> 00:15:32.819 around 1,500 meters depth. 00:15:32.819 --> 00:15:40.730 And one at the top of the granite here, which is around 2,200 meters depth. 00:15:40.730 --> 00:15:47.420 So this model will be actually used always to relocate our synthetic sources. 00:15:47.420 --> 00:15:49.920 And the reason is because most of the time, 00:15:49.920 --> 00:15:52.029 we are still using 1D velocity model. 00:15:52.029 --> 00:15:55.809 And especially, for example, when we are using real-time picking, 00:15:55.809 --> 00:15:59.049 or automatic picking procedures, we are still -- I mean, 00:15:59.049 --> 00:16:02.049 seismologists are still using 1D model. 00:16:02.049 --> 00:16:04.619 And so this is actually what we used in the fields 00:16:04.619 --> 00:16:07.889 when we -- when we were monitoring real-time. 00:16:07.889 --> 00:16:12.569 So we just want to see what’s the effect of using this type of model. 00:16:14.410 --> 00:16:18.029 So the first thing we are going to look at is just 00:16:18.029 --> 00:16:22.639 looking at the effect of the picking uncertainties in the location. 00:16:22.639 --> 00:16:26.259 So what we are going to do is that we are going to assign 00:16:26.259 --> 00:16:28.989 picking uncertainties on the P wave and the S waves, 00:16:28.989 --> 00:16:32.889 coming from the seismicity, which was induced in the field. 00:16:32.889 --> 00:16:34.839 So from the seismicity induced in the field, 00:16:34.839 --> 00:16:37.600 what we’ve found is that, when we were manually processing 00:16:37.600 --> 00:16:41.809 the data, we were setting plus or minus 20 milliseconds 00:16:41.809 --> 00:16:44.429 uncertainty in the P and the S wave pickings. 00:16:44.429 --> 00:16:47.579 So this is what we are going to put for all the stations 00:16:47.579 --> 00:16:52.699 which are 4 kilometers around the drill pad. 00:16:52.699 --> 00:16:56.470 And then, for all the stations which are away from this 4 kilometers radius, 00:16:56.470 --> 00:16:58.389 we will put plus or minus 50 milliseconds. 00:16:58.389 --> 00:17:02.679 So these numbers are really coming from the seismicity we recorded there. 00:17:02.679 --> 00:17:06.309 And then what we will do is that we will put sources, or synthetic sources, 00:17:06.309 --> 00:17:14.220 of earthquakes in the underground in 3D in a 200 meters mesh -- meters mesh. 00:17:14.220 --> 00:17:19.370 What I’m going to call the uncertainty afterwards is actually the length -- 00:17:19.370 --> 00:17:25.260 or plus or minus the length of the largest -- of the lengths of the largest 00:17:25.260 --> 00:17:31.309 eigenvector, which is corresponding to 68.3% location confidence ellipsoid. 00:17:31.309 --> 00:17:35.000 So which is the standard measurement that we say. 00:17:35.000 --> 00:17:39.429 So I’m not -- I have to summarize, if you want, the result of this patatoide, 00:17:39.429 --> 00:17:42.700 or this ellipsoid, of the location uncertainties. 00:17:42.700 --> 00:17:48.399 And so I take only the largest half-lengths of this ellipsoid. 00:17:48.399 --> 00:17:49.789 And this is what we obtained here. 00:17:49.789 --> 00:17:53.100 So you can see, for the network with 15 stations -- so this network 00:17:53.100 --> 00:17:57.059 is located mainly on the northwest part of the well pad. 00:17:57.059 --> 00:18:02.350 So you can see, on the right-hand side, different sections. 00:18:02.350 --> 00:18:05.630 So here you have the well, which is in the middle of the cube. 00:18:05.630 --> 00:18:09.610 And you have the north, which is there. The east, which is there. 00:18:09.610 --> 00:18:11.760 And of course, the south and the west. 00:18:11.760 --> 00:18:14.720 And the depths, which is along this axis. 00:18:14.720 --> 00:18:18.610 What you can see is that the location uncertainty -- so we are 00:18:18.610 --> 00:18:21.389 only talking here about picking uncertainties -- 00:18:21.389 --> 00:18:24.480 what’s the result in the location uncertainties is about -- 00:18:24.480 --> 00:18:29.899 can range between plus or minus 30 meters up to plus or minus 245 meters. 00:18:29.899 --> 00:18:34.850 And this is only by assigning these picking uncertainties. 00:18:34.850 --> 00:18:39.139 So you can see that this 245 meters, for example, this is already one-tenth 00:18:39.139 --> 00:18:45.840 of the depth, which is quite -- this is not negligible, I would say. 00:18:45.840 --> 00:18:50.260 The other thing we can see here with the color plot, which is really easy to see, 00:18:50.260 --> 00:18:52.730 that actually these uncertainties are increasing 00:18:52.730 --> 00:18:55.389 when we are going to southeast. 00:18:55.389 --> 00:18:58.830 And this a direct effect we can see of the network coverage, 00:18:58.830 --> 00:19:02.809 which is everything is located in the northwestern part. 00:19:02.809 --> 00:19:06.620 The other thing that we can notice that there is obviously a depth variation. 00:19:06.620 --> 00:19:10.440 So the deeper we go, usually the larger will be the uncertainty in the location. 00:19:10.440 --> 00:19:12.389 I mean, we know that very well. 00:19:12.389 --> 00:19:15.210 And this is actually following the velocity model. 00:19:15.210 --> 00:19:18.620 But within one formation, what we find that it’s pretty constant 00:19:18.620 --> 00:19:21.360 within one formation. 00:19:21.360 --> 00:19:25.179 And we have an increase until the granite, so which is, I would say, 00:19:25.179 --> 00:19:29.159 the limit, which is about plus or minus 175 meters. 00:19:30.520 --> 00:19:32.900 What’s the effect of adding one station? 00:19:32.909 --> 00:19:34.919 So when we add this station, which is in the forest -- 00:19:34.919 --> 00:19:38.409 so the station is located a little bit in the southeast. 00:19:38.409 --> 00:19:44.299 We are decreasing a little bit the range of the location uncertainties -- not so much. 00:19:44.299 --> 00:19:47.480 But maybe what is more important in this case is that what we are seeing 00:19:47.480 --> 00:19:49.750 is that we are actually attenuating this effect 00:19:49.750 --> 00:19:54.779 of having different uncertainties for given depths. 00:19:54.779 --> 00:19:57.529 You know, so it’s more homogeneous for given depths. 00:19:57.529 --> 00:20:02.690 So we are starting to attenuate this effect, especially in the southeast part. 00:20:02.690 --> 00:20:05.740 And this is due just by using one station. 00:20:05.740 --> 00:20:08.299 But with [inaudible], of course, this depth [inaudible]. 00:20:08.299 --> 00:20:13.090 When we go to 41 stations, what we see are two effects. 00:20:13.090 --> 00:20:14.840 The first thing is that, for given depths, 00:20:14.840 --> 00:20:19.049 now the uncertainties are constant, which is quite interesting and 00:20:19.049 --> 00:20:22.360 quite important, actually, which means that we are looking the same way. 00:20:22.360 --> 00:20:25.590 I mean, it’s not biased anymore when we are looking for 00:20:25.590 --> 00:20:28.330 given depths in the location. 00:20:28.330 --> 00:20:30.580 And also we are decreasing a lot the range. 00:20:30.580 --> 00:20:33.159 So we are now having the largest uncertainty, 00:20:33.159 --> 00:20:37.570 which is about plus or minus 115 meters. 00:20:37.570 --> 00:20:42.909 So we divided about by 2 the uncertainties in the location. 00:20:42.909 --> 00:20:48.610 So there is clearly an effect when we increase the number of stations, 00:20:48.610 --> 00:20:51.460 we are decreasing the uncertainty amplitudes. 00:20:51.460 --> 00:20:54.519 And because we increased the coverage of our network, we also 00:20:54.519 --> 00:21:02.830 decreased the variation spatially, so the radial variation of this uncertainty. 00:21:04.920 --> 00:21:10.980 This second thing we are looking at is -- okay, we have 1D velocity model, 00:21:10.990 --> 00:21:14.159 which was built for [inaudible] or for zero-offset VSP 00:21:14.159 --> 00:21:17.909 and then a [inaudible], so we combined things. 00:21:17.909 --> 00:21:20.779 But we are not -- you know, not very sure. 00:21:20.779 --> 00:21:22.740 I mean, when we are looking at the [inaudible], 00:21:22.740 --> 00:21:25.870 we are not very sure of the velocity we put there. 00:21:25.870 --> 00:21:29.750 So what we are going to do here, we are going to make a Monte Carlo sampling. 00:21:29.750 --> 00:21:34.059 And we are going to draw randomly velocity models. 00:21:34.059 --> 00:21:38.539 And how we do that, actually, is that we are taking 150 models 00:21:38.539 --> 00:21:42.240 for the P and S wave, which will be independently chosen, 00:21:42.240 --> 00:21:46.330 and we are going to perturb each layer by plus or minus 5% -- 00:21:46.330 --> 00:21:50.909 and uncertainty of plus or minus 5%. 00:21:50.909 --> 00:21:54.419 Which is not very much, when you’re thinking about it. 00:21:54.419 --> 00:21:58.710 So this gives -- so again, we have the blue line here, 00:21:58.710 --> 00:22:03.070 which is the reference 1D velocity model, and the red lines gives you here 00:22:03.070 --> 00:22:07.990 the possible models we could get with this perturbation of 5%. 00:22:07.990 --> 00:22:11.330 And we do the same independently for the S waves, which means that 00:22:11.330 --> 00:22:18.179 somehow we are also allowing changes of the EPS ratio for each layer. 00:22:18.179 --> 00:22:20.070 And so for each model, we are calculating the -- 00:22:20.070 --> 00:22:24.309 just the probability density function for the location of the earthquakes. 00:22:24.309 --> 00:22:30.389 And when we sum up these probability density functions over all the models, 00:22:30.389 --> 00:22:33.690 what we will get is the final probability density function of the location of the 00:22:33.690 --> 00:22:38.590 earthquakes, which takes into account this variation of the velocity model. 00:22:38.590 --> 00:22:42.490 So this is one way of integrating velocity model uncertainties 00:22:42.490 --> 00:22:45.150 into the location uncertainties. 00:22:48.059 --> 00:22:50.419 When we are using the network of 15 stations -- 00:22:50.419 --> 00:22:52.909 so here it’s a bit more time-consuming. 00:22:52.909 --> 00:22:58.970 So I put two planes of sources -- 9-by-9 sources separated by 300 meters. 00:22:58.970 --> 00:23:03.230 And so you see a north-south section -- vertical section here. 00:23:03.230 --> 00:23:06.000 And an east-west section, which is here. 00:23:06.000 --> 00:23:09.380 And actually, what you are seeing here are the ellipsoids, 00:23:09.380 --> 00:23:15.210 so the contour with one standard deviation around the location. 00:23:15.210 --> 00:23:21.399 So what you are seeing here is that the deeper we go, the larger is this ellipsoid. 00:23:21.399 --> 00:23:25.840 We knew that already somehow, but this is enhanced in this case. 00:23:25.840 --> 00:23:28.950 And also what we clearly see here, we could not see that before, 00:23:28.950 --> 00:23:32.820 is the shape, if you want, of the uncertainty in the location. 00:23:32.820 --> 00:23:36.440 And the shape is varying in space, clearly. 00:23:36.440 --> 00:23:41.250 So depending if you are in the north or if you are in the south. 00:23:41.250 --> 00:23:45.409 So these a posteriori location uncertainties actually are ranging 00:23:45.409 --> 00:23:49.899 between plus or minus 100 meters and plus or minus 500 meters now. 00:23:49.899 --> 00:23:52.460 Because we changed the velocity model. 00:23:52.460 --> 00:23:56.500 Okay, and the location uncertainties are larger than 00:23:56.500 --> 00:23:58.340 plus or minus 300 meters in the granite. 00:23:58.340 --> 00:24:04.730 So we doubled the result -- almost doubled the result we had before. 00:24:04.730 --> 00:24:07.850 What we also -- here it’s maybe not very clear on this -- on this plot, 00:24:07.850 --> 00:24:11.620 but what we -- what we still see is that we have larger uncertainties 00:24:11.620 --> 00:24:14.840 on the east and south, again, due to the network coverage. 00:24:14.840 --> 00:24:18.260 But we still have the same effect. 00:24:19.950 --> 00:24:23.139 We also have location inaccuracies in this case. 00:24:23.139 --> 00:24:26.659 We can compute them, but they are relatively small, I would say, 00:24:26.659 --> 00:24:30.590 compared to the mesh we used for the velocity model, which was 20 meters. 00:24:30.590 --> 00:24:34.639 So they are around the same order -- around the same order within 00:24:34.639 --> 00:24:38.710 the sediments between 10 meters and 30 meters and a bit larger 00:24:38.710 --> 00:24:41.130 in the granite, in this case. 00:24:43.580 --> 00:24:47.470 When we add one station -- so the station number 16 -- sorry, 00:24:47.470 --> 00:24:53.279 so what I wanted to say is that this increase of 5% velocity uncertainties 00:24:53.279 --> 00:24:58.740 lead to a 200% increase in the uncertainty of the locations. 00:24:58.740 --> 00:25:03.220 So here it’s clear evidence that it’s a non-linear problem. 00:25:05.059 --> 00:25:08.519 When we are adding the stations which is in the southeast 00:25:08.519 --> 00:25:11.539 compared to the rest of the stations, what we see here -- 00:25:11.539 --> 00:25:12.889 so the two same planes -- 00:25:12.889 --> 00:25:16.429 is that the shape of the ellipsoid is very different. 00:25:16.429 --> 00:25:19.340 And now it’s no more -- the ellipsoid is a lot more vertical 00:25:19.340 --> 00:25:24.090 compared to before where they were pointing to the southeast. 00:25:24.090 --> 00:25:26.370 And this is just because we added this new station. 00:25:26.370 --> 00:25:32.350 So we are completely changing the shape of this location uncertainty. 00:25:32.350 --> 00:25:37.059 We are also decreasing these uncertainties now, 00:25:37.059 --> 00:25:41.639 and in the granite, we reach plus or minus 220 meters. 00:25:41.639 --> 00:25:47.399 But it’s still a bit larger to the south and to the east. 00:25:47.399 --> 00:25:50.580 So in this case, with this 5% velocity uncertainty, 00:25:50.580 --> 00:25:55.779 we go up to 150% location uncertainty increase. 00:25:55.779 --> 00:25:59.240 So it’s very clear that we have now a decrease, again, 00:25:59.240 --> 00:26:02.250 of the uncertainties with the increasing number of stations. 00:26:02.250 --> 00:26:05.669 But also taking into account the fact that we had uncertainties 00:26:05.669 --> 00:26:09.210 in the velocity model. 00:26:09.210 --> 00:26:16.480 Another test we did is that we tried to perturb the model in 3D. 00:26:16.480 --> 00:26:18.659 Because we know that we stimulated this field, 00:26:18.659 --> 00:26:22.070 so we wanted to see, what’s the effect if, for example, 00:26:22.070 --> 00:26:24.919 the injection of the water when we are stimulating 00:26:24.919 --> 00:26:29.409 the underground actually is changing the velocity there. 00:26:29.409 --> 00:26:34.600 So what we’ve done is that we are -- we perturbed the velocity by 10%, 00:26:34.600 --> 00:26:37.990 so we decreased the velocity by 10% in the cylinder, 00:26:37.990 --> 00:26:42.669 which corresponds to the injection zone in this well. 00:26:42.669 --> 00:26:47.350 And the Vs by 5%. So a decrease of Vs by 5%, 00:26:47.350 --> 00:26:51.399 which corresponds to a decrease of Vp over Vs by 5%, about. 00:26:51.399 --> 00:26:53.980 And then, again, we put sources every 40 meters 00:26:53.980 --> 00:26:57.220 on the east-west and north-south planes. 00:26:57.220 --> 00:26:58.879 And this is what you can see here. 00:26:58.879 --> 00:27:04.159 So on the top, you have this east and depth section. 00:27:04.159 --> 00:27:06.980 And here you have the north and depth section. 00:27:06.980 --> 00:27:13.960 So this grayish area is the area where we have perturbed the velocity model. 00:27:13.960 --> 00:27:15.470 And here again. So it’s a cylinder. 00:27:15.470 --> 00:27:18.129 So it’s really 3D. 00:27:18.129 --> 00:27:21.940 And we can really -- what we -- what we see is actually these 00:27:21.940 --> 00:27:24.360 location inaccuracies are X-, Y-, and Z-dependent. 00:27:24.360 --> 00:27:27.539 So are not the same everywhere. 00:27:27.539 --> 00:27:31.700 So they are not the same in amplitude, and they are not the same in directions. 00:27:31.700 --> 00:27:37.549 We can also see that we have some uncertainties or some -- sorry, 00:27:37.549 --> 00:27:41.490 inaccuracies, which are both the perturbed zone, okay -- 00:27:41.490 --> 00:27:43.159 this is just due to the array pass. 00:27:43.159 --> 00:27:48.159 I mean, this is -- these are zones which are seen by the array pass when we are 00:27:48.159 --> 00:27:54.919 locating the earthquakes, so which are still going through this perturbed area. 00:27:54.919 --> 00:27:58.850 Just -- it’s not there on this picture, but I’ll just remind you that behind this, 00:27:58.850 --> 00:28:02.509 we have different velocities, of course. 00:28:02.509 --> 00:28:06.269 Because we have the different layers. 00:28:06.269 --> 00:28:11.600 And so these inaccuracies are of the order of 5 meters 00:28:11.600 --> 00:28:15.669 to 30 meters and a maximum of 55 meters. 00:28:15.669 --> 00:28:19.720 So they are actually very, very small. Okay? 00:28:19.720 --> 00:28:23.779 And the time residuals associated to these inaccuracies or to these 00:28:23.779 --> 00:28:27.580 relocations are of the order of plus or minus 2 milliseconds 00:28:27.580 --> 00:28:31.570 plus or minus 3 milliseconds, which is 10 times smaller 00:28:31.570 --> 00:28:35.580 than the uncertainties we have in our pickings. 00:28:35.580 --> 00:28:38.610 So what it means is that actually it’s very difficult with an 00:28:38.610 --> 00:28:41.850 absolute location technique to see such effects at such scale. 00:28:41.850 --> 00:28:47.600 So 300 meters around the well, more or less, at 2.5 kilometers depth. 00:28:47.600 --> 00:28:50.830 So it would be really, really difficult to identify such variation 00:28:50.830 --> 00:28:54.230 with this absolute location technique. 00:28:56.420 --> 00:29:02.760 Okay, maybe more interestingly is -- I said at the beginning, I mean, 00:29:02.769 --> 00:29:07.289 this is always a time, actually, when we are developing geothermal fields. 00:29:07.289 --> 00:29:10.809 People are -- the operators are looking for faults and fractures. 00:29:10.809 --> 00:29:14.149 Because this is where you are expecting to have the highest permeabilities 00:29:14.149 --> 00:29:19.129 and the possibility to actually produce a large amount of water. 00:29:19.129 --> 00:29:21.789 So of course, the wells are targeting faults. 00:29:21.789 --> 00:29:25.129 And when they are targeting faults, I mean, in this case, you might also 00:29:25.129 --> 00:29:28.370 find these normal faults, so we also have some movement -- 00:29:28.370 --> 00:29:30.340 we had some movement on these faults. 00:29:30.340 --> 00:29:35.509 And actually this means that the model is not 1D, but should be 3D. 00:29:35.509 --> 00:29:39.600 So what we’ve done is that we integrated a default, which was targeted 00:29:39.600 --> 00:29:44.679 by the well, which is more or less north-south and dipping 60 degrees west. 00:29:44.679 --> 00:29:49.629 And we shifted. So this fault accounts for a shift of 200 meters vertically. 00:29:49.629 --> 00:29:53.570 And so what we did is that we put the reference 1D model 00:29:53.570 --> 00:29:55.570 on the -- on the western block. 00:29:55.570 --> 00:29:58.690 And on the eastern block, we just shifted this model by 200 meters. 00:29:58.690 --> 00:30:02.240 Okay, so now we end up with a 3D model which integrates 00:30:02.240 --> 00:30:04.799 the fault and the movement on this fault. 00:30:04.799 --> 00:30:07.440 And this model is the model with which we are going to 00:30:07.440 --> 00:30:10.399 generate our synthetic arrivals. 00:30:10.399 --> 00:30:16.129 But we are still going to relocate with the 1D velocity model. 00:30:16.129 --> 00:30:20.149 So I will show you a succession of results with synthetic sources 00:30:20.149 --> 00:30:22.720 positioned on different planes. 00:30:22.720 --> 00:30:26.049 So you will have -- we will have fault planes, which are plus or 00:30:26.049 --> 00:30:31.399 minus 1,200 meters around the middle of the open-hole section. 00:30:31.399 --> 00:30:32.870 So the well is there. 00:30:32.870 --> 00:30:35.179 The section -- the open-hole section is there. 00:30:35.179 --> 00:30:38.029 So we have one horizontal plane of sources. 00:30:38.029 --> 00:30:42.600 We have the sources positioned exactly on the faults. 00:30:42.600 --> 00:30:45.669 And we have also sources on the north-south plane 00:30:45.669 --> 00:30:50.190 and sources on an east-west plane. 00:30:50.190 --> 00:30:54.519 And so what’s happening when we are relocating these sources 00:30:54.519 --> 00:30:59.480 with the network of 15 stations? So this is the result. 00:30:59.480 --> 00:31:01.620 So in gray, again, that’s the original locations. 00:31:01.620 --> 00:31:05.960 And the color [inaudible] corresponds to the new location of the earthquakes. 00:31:05.960 --> 00:31:10.070 And the color code is related to the uncertainty of the location. 00:31:10.070 --> 00:31:12.240 So here with these plots, we see both things. 00:31:12.240 --> 00:31:15.029 We see both the bias in the location and the -- 00:31:15.029 --> 00:31:18.999 and the uncertainties in the location with the color scale. 00:31:18.999 --> 00:31:23.889 So if we look on the location inaccuracies, actually, 00:31:23.889 --> 00:31:28.679 what we see that -- globally, and we have to look in more details, 00:31:28.679 --> 00:31:32.379 but globally, we have an eastern median shift of about plus -- 00:31:32.379 --> 00:31:34.929 of about 360 meters in the east. 00:31:34.929 --> 00:31:41.019 So all the earthquakes are shifted by 360 meters in the east, about. 00:31:41.019 --> 00:31:44.379 The other thing, if we look at, especially this horizontal plane, 00:31:44.379 --> 00:31:48.179 what we can see that all the S waves which are located in the northwest part 00:31:48.179 --> 00:31:51.840 and upper corner, so these points, 00:31:51.840 --> 00:31:56.649 actually put deeper and down to the south of the network. 00:31:56.649 --> 00:32:00.710 But if we take this point, which is located [inaudible] on this plane, 00:32:00.710 --> 00:32:05.190 this point is going to be moved shallower and to the north. 00:32:05.190 --> 00:32:06.669 So it’s not only a shift. 00:32:06.669 --> 00:32:12.639 You know, we are actually distorting the surface and bending the surface. 00:32:12.639 --> 00:32:18.450 So we are really changing the original surface of the earthquakes. 00:32:18.450 --> 00:32:21.309 If we look on the other side on the location uncertainties, I mean, 00:32:21.309 --> 00:32:25.539 they are very similar to what we’ve seen already with the 1D velocity model. 00:32:25.539 --> 00:32:28.100 And in this case, of the order of what 00:32:28.100 --> 00:32:35.649 we’ve seen before, which is plus or minus 150 meters inside the granite. 00:32:35.649 --> 00:32:37.059 Now we add the new station. 00:32:37.059 --> 00:32:40.720 So we have this station, which is in the forest in the southeast. 00:32:40.720 --> 00:32:44.619 What we see that actually the inaccuracies are increasing. 00:32:44.619 --> 00:32:50.070 And so the location of the earthquakes are even more east than before. 00:32:50.070 --> 00:32:54.659 But the location uncertainties on the other side are decreasing. 00:32:54.659 --> 00:32:57.409 Because we have added a new station. 00:32:57.409 --> 00:33:00.570 So it’s the same thing as before because we added a new station 00:33:00.570 --> 00:33:02.560 while decreasing the uncertainties. 00:33:02.560 --> 00:33:06.540 And we still have this effect that the points which are 00:33:06.549 --> 00:33:10.110 in the northwest are going to be moved deeper into the southeast. 00:33:10.110 --> 00:33:12.619 And the point which are in the southeast are going to 00:33:12.619 --> 00:33:17.330 move up and a little bit also east, but more north. 00:33:17.330 --> 00:33:21.850 What’s going to happen with 41 stations? 00:33:23.450 --> 00:33:25.950 So this will be even worse. 00:33:25.950 --> 00:33:32.419 Okay, and we are going to increase again the median shift by -- I mean, yeah, 00:33:32.419 --> 00:33:38.980 we are going now to have 430 meters away from the original locations. Sorry. 00:33:38.980 --> 00:33:43.429 Okay? But the location uncertainties are decreasing. 00:33:43.429 --> 00:33:47.929 Okay, so now we are reaching also the plus or minus 100 meters 00:33:47.929 --> 00:33:51.059 inside the granite, like before. 00:33:51.059 --> 00:33:53.940 So there is a completely different behavior between 00:33:53.940 --> 00:33:55.669 the inaccuracies and the uncertainties. 00:33:55.669 --> 00:33:59.690 This is what we see with these absolute location techniques. 00:33:59.690 --> 00:34:05.190 The only thing which was brought by this really large coverage network 00:34:05.190 --> 00:34:09.860 of 41 stations is that we actually don’t have so much movement -- 00:34:09.860 --> 00:34:13.790 north-south movement of the sources now anymore. 00:34:13.790 --> 00:34:17.840 Because, if you wish, all the stations -- I mean, 00:34:17.840 --> 00:34:20.300 there is a good north-south coverage now. 00:34:20.300 --> 00:34:25.580 And so the earthquakes are going to stay at the same latitude. 00:34:26.980 --> 00:34:31.060 Okay, and we have also a symmetry with this north-south fault, 00:34:31.070 --> 00:34:36.679 and this is also explaining why the north-south movement disappears. 00:34:36.679 --> 00:34:40.490 But we still have this huge, you know, movement. 00:34:40.490 --> 00:34:44.580 And the planes -- okay, there are a bit more planes, I would say. 00:34:44.580 --> 00:34:50.940 They are not bending a little bit less than before. But they are still distorted. 00:34:52.610 --> 00:34:57.420 So if we try to summarize what we’ve seen with this original 3D fault model, 00:34:57.420 --> 00:35:01.630 so this is what we thought is the reality, but we are locating in this 1D model. 00:35:01.630 --> 00:35:06.140 Okay, by increasing the network, actually, we moved -- we increase 00:35:06.140 --> 00:35:12.400 also the inaccuracies for 360 meters to about 430 meters. 00:35:12.400 --> 00:35:16.350 But this north-south displacement decreased with the coverage. 00:35:16.350 --> 00:35:20.200 But this eastern shift is permanent. And also the depth shift we’ve seen 00:35:20.200 --> 00:35:26.820 on the different planes is also still there. And it’s quite large, actually. 00:35:26.820 --> 00:35:29.980 On the contrary, what we’ve seen is that the uncertainties were decreasing. 00:35:29.980 --> 00:35:33.800 Okay, so we moved from plus or minus 150 meters 00:35:33.800 --> 00:35:37.820 in the granite down to 100 meters in the granite. 00:35:37.820 --> 00:35:41.180 So again, I want really to stress this. This is very, very important. 00:35:41.180 --> 00:35:46.200 The behavior is completely different between inaccuracies and uncertainties. 00:35:46.200 --> 00:35:51.630 Okay, and it’s just because they are very different things, which are not taken 00:35:51.630 --> 00:35:55.620 and not processed the same way when you are locating the earthquakes. 00:35:55.620 --> 00:36:00.000 Okay, and in this case, the inaccuracies were a lot larger than the uncertainties. 00:36:00.000 --> 00:36:04.130 So we are exactly in the case where I put -- you know, 00:36:04.130 --> 00:36:07.550 in my first slide, the really, really bad case where we have to be 00:36:07.550 --> 00:36:10.800 very careful when we want to interpret the earthquake’s location -- 00:36:10.800 --> 00:36:12.450 this absolute earthquake location. 00:36:12.450 --> 00:36:15.970 I mean, when we want to -- when we want to delineate 00:36:15.970 --> 00:36:19.680 or try to identify faults and fractures in the underground, 00:36:19.680 --> 00:36:25.210 what it means is that actually what we see is a distortion of the reality. 00:36:25.210 --> 00:36:29.880 Okay, so these planes -- these original planes are no more planes anymore. 00:36:29.880 --> 00:36:31.590 They are bended, what we’ve seen. 00:36:31.590 --> 00:36:34.850 They are -- they can be rotated, bended, distorted completely. 00:36:34.850 --> 00:36:37.070 So we have to be very careful, then, when we say, okay, 00:36:37.070 --> 00:36:39.490 with the earthquakes, we see a fault which is 00:36:39.490 --> 00:36:42.170 going 25 degrees north and so on. 00:36:42.170 --> 00:36:47.140 What we’re seeing is a distortion of the reality. 00:36:47.140 --> 00:36:53.110 So the question is, what would be the effect of calibration shots in the well? 00:36:53.110 --> 00:36:59.980 Okay, so what it means is that we are going to actually put 00:36:59.980 --> 00:37:02.650 an active source somewhere where we know the location 00:37:02.650 --> 00:37:08.910 and we try to use this information to see if we can correct from these effects. 00:37:08.910 --> 00:37:12.410 And actually what we will see that it’s correcting quite a lot. 00:37:12.410 --> 00:37:15.230 So what we’ve done is that we assume that we add a calibration shot 00:37:15.230 --> 00:37:19.140 in the middle of the open-hole section of this well. 00:37:19.140 --> 00:37:22.810 And we are just going to apply standard station corrections. 00:37:22.810 --> 00:37:29.340 Okay, so what we do is, at the time observed in this 3D fault model, okay, 00:37:29.340 --> 00:37:33.640 coming from this shot -- this perforation shot or this 00:37:33.640 --> 00:37:38.870 explosive shot or something else -- I mean, it could be a reverse process -- 00:37:38.870 --> 00:37:41.370 minus the time calculated when we are locating, 00:37:41.370 --> 00:37:43.320 this would be used as a station correction. 00:37:43.320 --> 00:37:45.900 So for each station, we will get a correction. 00:37:45.900 --> 00:37:50.430 And so we are just going to apply this correction now to our times. 00:37:50.430 --> 00:37:51.930 And this is what we get. 00:37:51.930 --> 00:37:54.860 So with this network of 15 stations, what we see is that we are -- 00:37:54.860 --> 00:37:59.190 almost all the eastern shift is removed. 00:37:59.190 --> 00:38:01.570 And for the uncertainties, it’s like as usual. 00:38:01.570 --> 00:38:03.880 Okay, so the same amount of uncertainties. 00:38:03.880 --> 00:38:09.000 Now the displacement -- horizontal displacement is only by about 30 meters. 00:38:09.000 --> 00:38:12.130 And the vertical displacement by about 40 meters. 00:38:12.130 --> 00:38:18.120 And it’s shallower for the horizontal plane, in average. 00:38:18.120 --> 00:38:23.440 When you have 16 stations, you can see that the horizontal shift 00:38:23.440 --> 00:38:27.930 is about 30 meters again. The vertical shift can be a bit higher. 00:38:27.930 --> 00:38:33.100 And so we can see that we have some kind of bending of the faults -- 00:38:33.100 --> 00:38:36.990 of the original planes of sources here. 00:38:36.990 --> 00:38:39.980 So which is a bit worse than the previous case. 00:38:39.980 --> 00:38:43.720 And with 41 stations, this will be even worse. 00:38:43.720 --> 00:38:47.360 So we also have a bit more of this bending. 00:38:47.360 --> 00:38:49.970 So it means that, what it's going to do is that 00:38:49.970 --> 00:38:53.440 everything is accommodated by the depths of the earthquakes, more or less. 00:38:53.440 --> 00:38:56.540 So we are changing, actually, the dipping of the planes 00:38:56.540 --> 00:38:59.960 of the earthquake’s location. 00:39:02.230 --> 00:39:05.080 What is important to remember is that this -- the effect of this 00:39:05.080 --> 00:39:08.760 very simple calibration shot, in this case, decreased by 00:39:08.760 --> 00:39:12.150 one order of magnitude the bias we had before. 00:39:12.150 --> 00:39:16.250 Okay, just one shot -- one location. And now the inaccuracies are 00:39:16.250 --> 00:39:19.490 smaller than the uncertainties. I mean, in this specific case. 00:39:19.490 --> 00:39:27.040 And then, okay, so it means that it would be easier to interpret our data. 00:39:27.040 --> 00:39:30.100 And what is also very important when we are going to interpret 00:39:30.100 --> 00:39:32.950 this delineation of earthquakes is that now the distribution 00:39:32.950 --> 00:39:36.740 of the earthquakes is more representative of the reality. 00:39:36.740 --> 00:39:40.440 Despite the depth shift still exists. 00:39:42.990 --> 00:39:47.740 So to conclude on this work, I think the main message -- 00:39:47.740 --> 00:39:52.670 I mean, what I -- the take-out message really 00:39:52.670 --> 00:39:57.330 is uncertainties and inaccuracies are behaving really differently. 00:39:57.330 --> 00:40:01.990 And this is something which is maybe not so obvious at the beginning. 00:40:01.990 --> 00:40:04.820 Okay, it’s not because we are adding more stations that we are 00:40:04.820 --> 00:40:08.290 going to improve both the uncertainties and the inaccuracies. 00:40:08.290 --> 00:40:12.030 Okay, we’ve seen that this actually is the contrary. 00:40:12.030 --> 00:40:16.400 Because we are bringing more inconsistency with the model. 00:40:16.400 --> 00:40:19.840 And this is why the inaccuracies are increasing. 00:40:19.840 --> 00:40:21.270 The spatial distribution of the earthquakes 00:40:21.270 --> 00:40:23.160 may be a distortion of the reality. 00:40:23.160 --> 00:40:26.470 It’s very clear we have to keep this in mind. 00:40:26.470 --> 00:40:29.400 But it’s worth carrying out calibration shot-type operation. 00:40:29.400 --> 00:40:32.420 I mean, this is also very important. 00:40:32.420 --> 00:40:35.260 And if we can try to do -- I mean, especially this 00:40:35.260 --> 00:40:37.000 local monitoring -- reservoir monitorings, 00:40:37.000 --> 00:40:42.310 if they can try to have these kind of shots or other ways to do it, you know, 00:40:42.310 --> 00:40:45.110 with sources on the surface and the [inaudible] in the well, 00:40:45.110 --> 00:40:50.370 which would be the same, I mean, this is really, really worth doing it. 00:40:50.370 --> 00:40:52.160 This methodology could be used to characterize 00:40:52.160 --> 00:40:56.630 the location capabilities of an existing or future seismic network. 00:40:56.630 --> 00:40:59.220 And what is maybe the most important is with regards 00:40:59.220 --> 00:41:02.150 maybe to the expected variability of a velocity model. 00:41:02.150 --> 00:41:05.470 I think we are never going to develop a field 00:41:05.470 --> 00:41:08.150 where we have no idea of what’s the underground. 00:41:08.150 --> 00:41:11.320 So if we could try to actually quantify these variations, 00:41:11.320 --> 00:41:15.750 we can use that actually to try to model what has been done here 00:41:15.750 --> 00:41:18.260 and try to see what would be the best network or the network 00:41:18.260 --> 00:41:21.380 which would minimize these effects with regard to 00:41:21.380 --> 00:41:25.090 the variability of the velocity model. 00:41:25.090 --> 00:41:28.000 Also something we are doing a lot now is we are 00:41:28.000 --> 00:41:29.940 using relative location approaches. 00:41:29.940 --> 00:41:35.170 So the question is how this would affect the relocation -- 00:41:35.170 --> 00:41:40.420 relative location approaches. So I think it’s not so obvious to answer 00:41:40.420 --> 00:41:44.110 this question because the methodology would be a little bit different. 00:41:44.110 --> 00:41:46.950 Because, of course, these relative location approaches are depending on, 00:41:46.950 --> 00:41:50.920 like a bit, the tomography where you are setting your earthquakes. 00:41:50.920 --> 00:41:52.840 So you have to have a fairly good idea of where you’re 00:41:52.840 --> 00:41:57.700 really willing to put your earthquakes beforehand. 00:42:00.120 --> 00:42:06.340 Okay. I move somewhere else completely different. 00:42:06.350 --> 00:42:09.540 I would like now to present you a new formulation -- 00:42:09.540 --> 00:42:15.050 a new Bayesian formulation which is intended to integrate properly 00:42:15.050 --> 00:42:18.640 the seismic wave polarization when we want to locate earthquakes. 00:42:18.640 --> 00:42:26.430 So we are still going to keep a non-linear earthquake location approach. 00:42:26.430 --> 00:42:30.760 And this work has been performed by colleagues in MINES ParisTech in Paris. 00:42:30.760 --> 00:42:34.200 Alexandrine Gesret, Mark Noble, and Thomas Kohl again. 00:42:34.200 --> 00:42:38.530 And this was sponsored by the ministry in Baden-Württemberg 00:42:38.530 --> 00:42:43.610 and all these different partners. So the earthquake’s location -- 00:42:43.610 --> 00:42:48.420 I mean, so far, for example, as I spoke about location using travel times. 00:42:48.420 --> 00:42:51.080 But we can also use the direction of the P wave arrival. 00:42:51.080 --> 00:42:54.190 Okay, this is not very often used. 00:42:54.190 --> 00:42:58.260 This is especially used when you are doing single-station monitoring. 00:42:58.260 --> 00:43:02.010 This is used when you are doing array monitoring, somehow. 00:43:02.010 --> 00:43:04.420 You are using the direction of the P wave arrival. 00:43:04.420 --> 00:43:06.530 Or when you have single-wave monitoring. 00:43:06.530 --> 00:43:11.400 I mean, typically, when we are under oil and gas -- [inaudible] 00:43:11.400 --> 00:43:17.060 oil and gas recoveries with hydro frac jobs, okay, you have sensors which are 00:43:17.060 --> 00:43:20.770 deployed in one well -- a string of several sensors deployed in one well. 00:43:20.770 --> 00:43:23.550 And you have to locate the earthquakes using this. 00:43:23.550 --> 00:43:27.610 So without polarization information, it’s completely -- you cannot do it. 00:43:27.610 --> 00:43:31.160 You have to use the polarization of the waves to look at the earthquakes, 00:43:31.160 --> 00:43:35.880 which gives you the direction from which is occurring the earthquake. 00:43:35.880 --> 00:43:38.780 So the timing will give you the distance, 00:43:38.780 --> 00:43:41.220 and the polarization will give you the direction. 00:43:43.180 --> 00:43:46.020 There are two ways of computing the direction of the arrival. 00:43:46.030 --> 00:43:48.560 So either you are using the apparent velocity, 00:43:48.560 --> 00:43:52.910 and this is typically used when you have an array monitoring. 00:43:52.910 --> 00:43:55.330 So actually you are using the correlation of 00:43:55.330 --> 00:43:58.200 the arrival on the different stations. 00:43:58.200 --> 00:44:01.150 So you are using the joint information, 00:44:01.150 --> 00:44:04.480 which is carried out by your -- the whole network. 00:44:04.480 --> 00:44:09.110 Another way to do it is to look at the polarization of the seismic wave. 00:44:09.110 --> 00:44:13.130 So here it’s a single three-component sensor approach. 00:44:13.130 --> 00:44:15.900 And what you are looking at is the distribution of the energy 00:44:15.900 --> 00:44:19.640 on your single three-component sensor. 00:44:19.640 --> 00:44:24.080 And so, I mean, it’s -- somehow it’s derivated with a hodogram -- 00:44:24.080 --> 00:44:28.370 sometimes called hodogram analysis -- to compute this polarization. 00:44:28.370 --> 00:44:32.220 I’m going to focus on this -- on this topic. 00:44:32.220 --> 00:44:35.510 So I want to keep a single three-component sensor approach. 00:44:35.510 --> 00:44:40.820 So I don’t want to mix the information coming from a seismic network. 00:44:40.820 --> 00:44:44.210 So I will not work with several stations together. 00:44:44.210 --> 00:44:47.690 I can add up the information from single stations, yes. 00:44:47.690 --> 00:44:49.170 But I don’t want to use the information -- 00:44:49.170 --> 00:44:54.950 or the consistent or coherent information between the stations. 00:44:54.950 --> 00:44:57.590 So as I said, the seismic wave polarization, 00:44:57.590 --> 00:44:59.610 so typically is the body waves. 00:44:59.610 --> 00:45:04.810 It’s just a measure of the energy spatial distribution around this arrival. 00:45:04.810 --> 00:45:07.240 And so when you have the P wave and the S wave, for example, 00:45:07.240 --> 00:45:11.940 here on these three components, you are going to look at the hodograms. 00:45:11.940 --> 00:45:16.840 But you can also compute the covariance matrix around this arrival. 00:45:16.840 --> 00:45:22.230 Okay, so just the [inaudible] correlation of the signal of our window, 00:45:22.230 --> 00:45:25.820 which is corresponding -- is out to the P wave or the S wave. 00:45:25.820 --> 00:45:28.970 Most of the time, it’s done on the P wave. 00:45:28.970 --> 00:45:30.690 And what means this covariance matrix? 00:45:30.690 --> 00:45:36.650 Actually, this covariance matrix means that your signal on each -- 00:45:36.650 --> 00:45:40.470 your three-component signal is following a trivariate 00:45:40.470 --> 00:45:44.220 Gaussian distribution, which is centered on zero. 00:45:44.220 --> 00:45:51.190 What it means is that, actually you could -- 00:45:51.190 --> 00:45:55.460 I’ll go -- it will be easier. [chuckles] 00:45:55.460 --> 00:46:00.710 So the trace of these covariance matrix actually tells you 00:46:00.710 --> 00:46:04.100 the mean energy which is around the seismic wave arrival. 00:46:04.100 --> 00:46:06.980 And when you perform principal component analysis of this 00:46:06.980 --> 00:46:10.990 covariance matrix, actually you are going to obtain eigenvectors 00:46:10.990 --> 00:46:15.210 and eigenvalues, and which are going to give you the main direction -- 00:46:15.210 --> 00:46:19.240 the three main or principal direction of the arrival of the energy. 00:46:19.240 --> 00:46:22.930 Okay, and this is along these three directions that you have 00:46:22.930 --> 00:46:26.100 Gaussian distribution of the signal. 00:46:26.100 --> 00:46:29.160 Okay. And that’s why we use covariance matrix. 00:46:29.170 --> 00:46:32.030 So it means that behind this use of covariance matrix, 00:46:32.030 --> 00:46:36.600 you are already thinking about Gaussian signals. 00:46:37.840 --> 00:46:40.880 Typically, with this principal component analysis, 00:46:40.880 --> 00:46:44.040 you look at the eigenvectors, the eigenvalues. 00:46:44.040 --> 00:46:46.800 And with the eigenvalues, if the eigenvalues have the 00:46:46.800 --> 00:46:50.510 same magnitude, it means that your signal is actually not polarized. 00:46:50.510 --> 00:46:52.520 It’s completely isotropic. 00:46:52.520 --> 00:46:55.950 Because the energy is distributed the same way everywhere in space. 00:46:55.950 --> 00:46:59.110 So it means that you won’t see the P wave arrival. 00:46:59.110 --> 00:47:01.360 I mean, there is no specific direction. 00:47:01.360 --> 00:47:05.420 On the contrary, when one of these eigenvalues is really large 00:47:05.420 --> 00:47:08.780 compared to the other ones, then you have what is often called 00:47:08.780 --> 00:47:15.150 a polarized signal around the associated eigenvectors. 00:47:16.020 --> 00:47:19.040 Okay, this is, as I said, usually applying on the P wave. 00:47:19.050 --> 00:47:22.890 And yes, actually this main eigenvector is giving you 00:47:22.890 --> 00:47:26.170 direction from which is arriving the earthquake. 00:47:26.170 --> 00:47:28.970 And this is what you’re going to use when you are locating. 00:47:28.970 --> 00:47:32.820 So there are techniques which are already existing 00:47:32.820 --> 00:47:36.950 and Bayesian non-linear formulation for this. 00:47:36.950 --> 00:47:38.500 And so what the people are doing is that 00:47:38.500 --> 00:47:41.220 they are using this principal eigenvector direction. 00:47:41.220 --> 00:47:47.160 So they are computing the azimuth and the inclination of this vector 00:47:47.160 --> 00:47:50.740 to obtain the direction or to characterize the direction of the arrival. 00:47:50.740 --> 00:47:53.130 These second thing is that they are going to estimate 00:47:53.130 --> 00:47:55.850 the uncertainties on these parameters. 00:47:55.850 --> 00:48:00.880 And then it becomes a bit tricky. They are going to use sometimes 00:48:00.880 --> 00:48:04.280 the degree of the polarization of the signal or the signal linearity, 00:48:04.280 --> 00:48:07.660 which is actually working on the ratios between these 00:48:07.660 --> 00:48:13.830 eigenvalues to see how much energy is distributed and how. 00:48:13.830 --> 00:48:15.670 But there is not really a standard thing. 00:48:15.670 --> 00:48:18.570 I mean, some people -- and I will use that later on 00:48:18.570 --> 00:48:22.810 to compare with, is using the ratios between these eigenvalues 00:48:22.810 --> 00:48:25.240 projecting back into the geographical system. 00:48:25.240 --> 00:48:27.950 Because if you speak about azimuths and inclination, you have to 00:48:27.950 --> 00:48:31.950 go back into this geographical system, which is not necessarily 00:48:31.950 --> 00:48:38.530 the system of this eigensystem -- okay, of the polarization itself. 00:48:38.530 --> 00:48:42.480 And then they are going to assume a Gaussian probability density function 00:48:42.480 --> 00:48:44.750 associated with this observed polarization. 00:48:44.750 --> 00:48:47.320 So what they are going to do when they want to locate is they are 00:48:47.320 --> 00:48:53.540 going to multiply the probability density function carried out by the time with this 00:48:53.540 --> 00:48:57.660 probability density function coming from the polarization of the waves. 00:48:57.660 --> 00:49:03.420 And to compute the likelihood, they are just using least squares, 00:49:03.420 --> 00:49:07.430 working on the differences between the observed angle, so coming from 00:49:07.430 --> 00:49:12.330 this analysis, and computed angles coming from array tracer. 00:49:12.330 --> 00:49:17.740 And they are going to divide by the standard deviation of these angles. 00:49:17.740 --> 00:49:19.840 So this is something which is already used, 00:49:19.840 --> 00:49:22.940 but we see that it’s not quite correct, 00:49:22.940 --> 00:49:25.200 despite it has a lot of similarities 00:49:25.210 --> 00:49:27.280 with what we know from the arrival times. 00:49:27.280 --> 00:49:30.710 Because when you want to compute the probability density function 00:49:30.710 --> 00:49:34.910 with the travel times, actually you have a very similar form with the 00:49:34.910 --> 00:49:39.440 observed times and the calculated times and here the covariance matrix. 00:49:39.440 --> 00:49:44.180 So it’s a very similar-looking equation. 00:49:44.180 --> 00:49:47.960 However, there are several problems with this formulation. 00:49:47.970 --> 00:49:51.420 The first one is we can see that this polarization 00:49:51.420 --> 00:49:53.740 is simplified to a single vector. 00:49:53.740 --> 00:49:59.130 Okay, we had this covariance matrix, which is giving us a lot of information, 00:49:59.130 --> 00:50:03.800 and we are just extracting the principal eigenvector. 00:50:03.800 --> 00:50:06.990 The second thing, it’s quite difficult, as I said, to estimate the uncertainties. 00:50:06.990 --> 00:50:10.690 I mean, how much is it? 5 degrees? 10 degrees? 00:50:10.690 --> 00:50:14.670 How do I do that? How do I compute it? 00:50:14.670 --> 00:50:18.580 And the other thing that we see here that’s the way it’s written 00:50:18.580 --> 00:50:22.290 is actually the -- people are treating independently 00:50:22.290 --> 00:50:24.770 the azimuths and the inclination information. 00:50:24.770 --> 00:50:28.050 So now they are completely independent 00:50:28.050 --> 00:50:34.740 despite originally they were linked to the same eigenvector. Okay? 00:50:36.220 --> 00:50:41.960 The second thing is that this probability density function should not be Gaussian. 00:50:41.960 --> 00:50:45.320 And the reason is that we are -- now what we want to do 00:50:45.320 --> 00:50:50.040 is to compare vectors, and we don’t want to compare scalars. 00:50:50.040 --> 00:50:55.150 Okay? Because we are comparing a direction with another direction 00:50:55.150 --> 00:50:59.730 coming from array tracer, and we are not comparing a time, 00:50:59.730 --> 00:51:03.590 which may vary from minus infinity to plus infinity, for example. 00:51:03.590 --> 00:51:09.170 Okay, so we are -- we want to compare different things. 00:51:11.340 --> 00:51:13.170 So what we propose is something a little bit different. 00:51:13.170 --> 00:51:15.750 I mean, at the end, it doesn’t look so different, 00:51:15.750 --> 00:51:19.400 but it’s based on different -- on directional statistics. 00:51:19.400 --> 00:51:23.530 So what we want to do is actually to -- as I mentioned earlier, 00:51:23.530 --> 00:51:27.640 the covariance matrix actually has all the information about the polarization 00:51:27.640 --> 00:51:30.960 or the energy distribution around the arrivals -- 00:51:30.960 --> 00:51:33.970 the P and the S wave arrivals, for example. 00:51:33.970 --> 00:51:36.780 So why -- you know, putting away a lot of information 00:51:36.780 --> 00:51:40.010 and only taking one eigenvector from it? 00:51:40.010 --> 00:51:43.890 So we keep everything. And this covariance matrix is 00:51:43.890 --> 00:51:47.520 actually representing the distribution of the energy around our arrival. 00:51:47.520 --> 00:51:50.340 Okay, so if there is a P wave, we should see it. 00:51:50.340 --> 00:51:56.420 If there is no P wave, so if it’s noise and isotropic, we should see it as well. 00:51:56.420 --> 00:51:58.490 And we have to use directional statistics. 00:51:58.490 --> 00:52:02.660 And here I don’t invent anything. I’m just speaking up, 00:52:02.660 --> 00:52:10.540 if a 3D variable X -- so here this is our seismogram -- 00:52:10.540 --> 00:52:13.890 follows a trivariate Gaussian distribution centered on zero, 00:52:13.890 --> 00:52:17.950 which is the assumption we made from the beginning when we do 00:52:17.950 --> 00:52:24.370 covariance matrix analysis, with a covariance matrix C, then the 00:52:24.370 --> 00:52:27.960 vector associated to this moment should follow an angular central 00:52:27.960 --> 00:52:31.600 Gaussian distribution on this 3D sphere. 00:52:31.610 --> 00:52:33.000 So it means what? 00:52:33.000 --> 00:52:39.720 It means that it exists a Gaussian distribution associated to vectors. 00:52:39.720 --> 00:52:44.960 Okay? And with this framework, we have -- we can use this 00:52:44.960 --> 00:52:47.760 probability density function. 00:52:47.760 --> 00:52:52.430 And actually doesn’t look so different from what we are used to. 00:52:52.430 --> 00:52:55.060 So what we have here is the covariance matrix we are going to 00:52:55.060 --> 00:52:57.040 measure on our wave. 00:52:57.040 --> 00:53:00.820 Okay, and on the left-hand side, we just have the transpose 00:53:00.820 --> 00:53:05.240 of the polarization vector we are expecting -- so the direction 00:53:05.240 --> 00:53:08.700 of the earthquake we are expecting, or we are calculating with our 00:53:08.700 --> 00:53:13.350 array tracer in here -- the same vector. 00:53:13.350 --> 00:53:17.530 And here we have the gamma function with 3 divided by 2. 00:53:17.530 --> 00:53:23.890 Okay, and this actually scales this probability density function 00:53:23.890 --> 00:53:28.290 correctly in space. This is also very important. 00:53:28.290 --> 00:53:33.800 So this formulation has a property that it is suitable to axial -- 00:53:33.800 --> 00:53:37.590 axial, sorry, and not directional information. 00:53:37.590 --> 00:53:40.000 Because you know when we are measuring the polarization because if -- 00:53:40.000 --> 00:53:43.230 most of the time, we don’t know the focal mechanism of the earthquakes. 00:53:43.230 --> 00:53:47.530 So we don’t know if it’s, you know, going up or going down. 00:53:47.530 --> 00:53:51.220 So have two possibilities -- either this way or this way. 00:53:51.220 --> 00:53:56.250 And so this formulation is taking this into account. 00:53:56.250 --> 00:53:59.900 The second thing is that, because of the normalization factor here, it doesn’t take 00:53:59.900 --> 00:54:05.660 into account the energy -- the amount of energy, but the spatial distribution. 00:54:05.660 --> 00:54:09.020 Okay, so it means that a small earthquake will be 00:54:09.020 --> 00:54:11.370 treated the same way as in a large earthquake. 00:54:11.370 --> 00:54:17.000 It’s only the shape of the covariance matrix which is important. 00:54:17.000 --> 00:54:20.140 And the last thing that it’s correctly normalized over the sphere, 00:54:20.140 --> 00:54:24.090 as I said, with all these coefficient. 00:54:24.090 --> 00:54:29.600 So what I propose is to make a synthetic case to illustrate, actually, 00:54:29.600 --> 00:54:32.940 the two different techniques to show the difference in the location. 00:54:32.940 --> 00:54:37.070 So what we’ve done, we put a downhole network with 00:54:37.070 --> 00:54:43.220 five three-component sensors which are spaced every 50 meters. 00:54:43.220 --> 00:54:47.400 And we put that into a model with three layers -- horizontal layers. 00:54:47.400 --> 00:54:51.550 So we have a 4,500-meter spacing on the top layer. 00:54:51.550 --> 00:54:53.940 Then we have a low-velocity layer here. 00:54:53.940 --> 00:54:58.660 And we have a high-velocity layer again at 5 kilometers per second. 00:54:58.660 --> 00:55:02.690 And we are simulating an hypocenter here. 00:55:02.690 --> 00:55:07.110 The velocity in 1D, and we have one source. 00:55:10.200 --> 00:55:13.270 We are going to locate -- or I’m going to show you 00:55:13.270 --> 00:55:19.140 the location probability even by one station only, okay? 00:55:19.140 --> 00:55:22.300 And what I’ve done -- what I’ve done here is that assumes that I have 00:55:22.300 --> 00:55:28.570 uncertainties in the azimuth of the eigenvector of plus or minus 10 degrees. 00:55:28.570 --> 00:55:30.140 And I don’t know the inclination, 00:55:30.140 --> 00:55:35.610 so I put an uncertainty of plus or minus 90 degrees. 00:55:35.610 --> 00:55:39.240 Okay, and what you see here, so the color plots, 00:55:39.240 --> 00:55:44.750 so you have the elevation, as you can see here, the northing, easting. 00:55:44.750 --> 00:55:50.610 And each surface here corresponds to an iso-probability contour. 00:55:50.610 --> 00:55:55.870 Okay, and it’s the cumulative probability density function. 00:55:55.870 --> 00:55:59.560 So the red contour corresponds to one standard deviation, 00:55:59.560 --> 00:56:02.960 correspond to 68% probability that the earthquake is included -- 00:56:02.960 --> 00:56:08.930 where is the mouse -- is included inside this volume. 00:56:08.930 --> 00:56:14.340 Then the light blue corresponds to 95, or two sigmas, usually understood. 00:56:14.340 --> 00:56:18.410 So it mean that the earthquake has 95% chance to be located 00:56:18.410 --> 00:56:22.700 inside this light blue volume. 00:56:22.700 --> 00:56:23.800 And then you have the dark blue, 00:56:23.800 --> 00:56:28.890 which corresponds to almost 99.7 -- three sigmas. 00:56:28.890 --> 00:56:31.520 So on the left-hand side, you have the existing formulation. 00:56:31.520 --> 00:56:33.200 And on the right-hand side, you have this 00:56:33.200 --> 00:56:37.260 angular central Gaussian formulation. 00:56:37.260 --> 00:56:39.740 What I want you to look at -- so the earthquake is located here 00:56:39.740 --> 00:56:46.690 behind this red plane -- so behind the -- the location of the mouse, more or less. 00:56:46.690 --> 00:56:50.810 And so what we see, that when we take one sigma contour, so the red one, 00:56:50.810 --> 00:56:54.420 it’s going -- it’s going to give us the right direction of the earthquakes. 00:56:54.420 --> 00:56:58.650 So this is -- this is pretty good in both the cases. 00:56:58.650 --> 00:57:01.690 What we -- when we look at the other contours, and especially 00:57:01.690 --> 00:57:07.470 this 99.7% chance, we see that there is a huge difference 00:57:07.470 --> 00:57:10.870 between the existing formulation and the new one. 00:57:10.870 --> 00:57:14.560 And what we see is that actually, with this existing formulation, 00:57:14.560 --> 00:57:18.100 the volume which is inside this formulation 00:57:18.100 --> 00:57:23.010 is very small compared to the volume which is inside this one. 00:57:23.010 --> 00:57:27.440 So again, as I said, you have to understand that the volume within 00:57:27.440 --> 00:57:33.990 this 99.7% chance is everything which is internal to this -- to this surface. 00:57:33.990 --> 00:57:36.730 Okay, so it’s including everything. 00:57:36.730 --> 00:57:39.660 Okay, so it’s almost the whole space already. 00:57:39.660 --> 00:57:43.330 Okay, there is only this part which is not included. 00:57:43.330 --> 00:57:49.100 Okay, compared to here, where we are missing all this volume. 00:57:49.100 --> 00:57:52.380 And this is due to the -- actually to the normalizing 00:57:52.380 --> 00:57:57.310 of this probability density function. 00:57:57.310 --> 00:58:01.000 Now if I decrease the uncertainties in the inclination -- okay, so I’m going to 00:58:01.000 --> 00:58:05.840 focus a lot more so I know where -- a lot more where it’s coming from. 00:58:05.840 --> 00:58:08.390 And so you can see that the contour of the one standard deviation 00:58:08.390 --> 00:58:12.250 is really close to the location. 00:58:12.250 --> 00:58:16.640 Then you have two sigmas, and you have three sigmas here. 00:58:16.640 --> 00:58:22.080 Okay, and here with the angular central Gaussian formulation, again, 00:58:22.080 --> 00:58:27.280 you have, again, this red contour, it’s a bit larger than the other one. 00:58:27.280 --> 00:58:30.400 This one is a lot larger, and this one is almost taking the whole space. 00:58:30.400 --> 00:58:33.560 But it’s for the same reason again. 00:58:33.560 --> 00:58:38.880 I mean, with 99.7% chance, you should almost cover the whole space. 00:58:38.880 --> 00:58:43.540 Otherwise, your probability is not well-scaled. 00:58:43.540 --> 00:58:49.410 So when now we are taking all the stations together, so this is what we get. 00:58:49.410 --> 00:58:54.260 So again, the profiles -- one sigma, two sigmas, three sigmas. 00:58:54.260 --> 00:59:01.970 So I did not put a lot of certainty on the angles for the inclination. 00:59:01.970 --> 00:59:05.540 So again, it’s really, like, giving just a plane. 00:59:05.540 --> 00:59:08.170 Okay, and the earthquake is there. 00:59:08.170 --> 00:59:12.160 And if we put plus or minus 10 degrees, okay, for both the azimuth and the 00:59:12.160 --> 00:59:16.070 inclination, then we are really more focusing on the earthquake. 00:59:16.070 --> 00:59:21.220 So here what you see are the contours of the location using only five stations 00:59:21.220 --> 00:59:23.830 and only using the polarization. I did not put time here. 00:59:23.830 --> 00:59:29.550 It’s just to compare the two formulations. 00:59:29.550 --> 00:59:33.180 What it also -- what is actually interesting to see here is that this now, 00:59:33.180 --> 00:59:34.950 when we are mixing all the stations together, 00:59:34.950 --> 00:59:38.560 I mean, this red contour becomes smaller than here. 00:59:38.560 --> 00:59:45.680 So actually, the constraints on the space is better than before. 00:59:45.680 --> 00:59:49.690 So to conclude, this angular central Gaussian -- I mean, 00:59:49.690 --> 00:59:54.440 formulation has the advantage to use the full covariance matrix. 00:59:54.440 --> 00:59:56.070 So we are not going to summarize, 00:59:56.070 --> 00:59:59.320 but just using the covariance matrix straight away in this case. 00:59:59.320 --> 01:00:03.280 Okay, so it’s a kind of all-in-one solution which are going to 01:00:03.280 --> 01:00:06.440 keep the spatial dependencies between the eigenvectors, 01:00:06.440 --> 01:00:08.020 between the azimuth and inclination, and so on. 01:00:08.020 --> 01:00:10.520 We are not going to try separate everything. 01:00:10.520 --> 01:00:12.940 We just keep everything together. 01:00:12.940 --> 01:00:15.440 And so we don’t need to estimate the measurement uncertainties. 01:00:15.440 --> 01:00:16.630 This is already there. 01:00:16.630 --> 01:00:19.360 It’s included in the covariance matrix itself. 01:00:19.360 --> 01:00:23.800 Okay, and so it means that we are not simplifying the single principal vector. 01:00:23.800 --> 01:00:27.460 We are not simplifying things. 01:00:27.460 --> 01:00:29.530 And then the probability density function, I mean, 01:00:29.530 --> 01:00:32.280 we are still within a Gaussian framework. 01:00:32.280 --> 01:00:36.530 So the particle motion for on each traces, okay, 01:00:36.530 --> 01:00:39.960 in the -- are still following Gaussians -- Gaussian movements. 01:00:39.960 --> 01:00:43.340 But because we are comparing angles -- because we are comparing vectors, 01:00:43.340 --> 01:00:46.790 I mean, the formulation of the probability density function is different. 01:00:46.790 --> 01:00:50.730 But behind, it’s still Gaussian assumptions. 01:00:50.730 --> 01:00:54.710 And least-square minimization criterion. 01:00:54.710 --> 01:00:58.560 Because it’s well-normalized, you can directly use it and multiply it 01:00:58.560 --> 01:01:01.980 by the probability density function associated to time, for example. 01:01:01.980 --> 01:01:04.240 So it’s straight away. You don’t need to tune any 01:01:04.240 --> 01:01:09.380 parameters -- [inaudible] parameters if you go for a linear location technique. 01:01:09.380 --> 01:01:11.120 You can just multiply this to things. 01:01:11.120 --> 01:01:15.550 So you don’t need any weighting coefficients. 01:01:15.550 --> 01:01:19.100 So the perspectives for this work -- spatial work. 01:01:19.100 --> 01:01:22.410 There is something I did not discuss which, of course, 01:01:22.410 --> 01:01:27.180 the direction of arrival, when you have a station on the surface, doesn’t really 01:01:27.180 --> 01:01:30.890 point to the direction of the earthquake because you have this surface effect. 01:01:30.890 --> 01:01:34.310 And so we are mixing P and S and reflected S waves on the surface. 01:01:34.310 --> 01:01:37.110 So you have to take this into account when you want to look at with 01:01:37.110 --> 01:01:43.020 surface on the stations -- with -- yeah, stations on the surface. Sorry. 01:01:43.020 --> 01:01:46.010 This could be extended to the S waves. Okay? 01:01:46.010 --> 01:01:49.960 We know that the S waves should be within a plane also [inaudible] 01:01:49.960 --> 01:01:53.640 to the direction of arrival. Okay, so these can be used. 01:01:53.640 --> 01:01:58.260 But this formulation is also interesting to actually orient three-component sensors. 01:01:58.260 --> 01:02:00.710 So you could use it actually to find the best angle 01:02:00.710 --> 01:02:05.330 for computing the sensor orientation. 01:02:07.220 --> 01:02:10.800 And I would like to thank you for your attention. 01:02:10.800 --> 01:02:15.400 [ Applause ] 01:02:16.600 --> 01:02:19.820 - All right. Do we have any questions? 01:02:21.260 --> 01:02:29.480 [ Silence ] 01:02:30.470 --> 01:02:36.120 - So my question is about, you can do synthetic tests forever, 01:02:36.120 --> 01:02:40.340 but if you don’t put in realistic uncertainties, 01:02:40.340 --> 01:02:44.980 then you won’t get -- in your parameters, then you won’t get realistic values out. 01:02:44.980 --> 01:02:50.090 So do you have ideas for strategies to improve our characterization of -- 01:02:50.090 --> 01:02:53.950 I mean, you can pull out a number for picking uncertainties or for 01:02:53.950 --> 01:02:57.020 velocity model uncertainties, but do you have ideas for 01:02:57.020 --> 01:03:00.340 strategies to make those numbers representative of reality? 01:03:00.340 --> 01:03:03.840 - [chuckles] It’s a very, very good question. 01:03:03.840 --> 01:03:09.300 I mean, if we don’t use 3D velocity models, for example, it's because 01:03:09.300 --> 01:03:13.300 we are not able to characterize or to define them originally. 01:03:13.300 --> 01:03:16.890 Because if you would have them in hand, we would use them [inaudible]. 01:03:16.890 --> 01:03:21.080 Okay. So this is actually the difficult part. 01:03:21.080 --> 01:03:25.580 So I think, to me, the best thing would be really to try to have -- 01:03:25.580 --> 01:03:31.160 to be able to construct -- to build a range of possible models 01:03:31.160 --> 01:03:32.560 and then make some kind of -- 01:03:32.560 --> 01:03:37.470 as I showed with Monte Carlo sampling -- these kind of things. 01:03:37.470 --> 01:03:40.050 But my feeling is that, at the end, it will -- 01:03:40.050 --> 01:03:47.000 maybe it’s not going to replace a calibration shot anyway. 01:03:47.000 --> 01:03:52.000 Because this will still be a model. And we are never sure about it. 01:03:52.000 --> 01:03:56.740 And in advance, somehow it’s quite difficult to say, 01:03:56.740 --> 01:04:01.230 will my inaccuracies be -- will be bigger than my uncertainties? 01:04:01.230 --> 01:04:03.440 At the end, I don’t know. 01:04:03.440 --> 01:04:07.250 Because if I don’t know my anagram, you know, it’s quite difficult. 01:04:07.250 --> 01:04:11.460 So, okay, if you put a large range of possible models, 01:04:11.460 --> 01:04:14.570 then you can start to have an idea about this. 01:04:14.570 --> 01:04:18.860 But I think nothing is going really to replace some shots in the field. 01:04:18.860 --> 01:04:22.870 That’s -- and that’s something we have to make clear, for example, 01:04:22.870 --> 01:04:26.170 in -- you know, I mean, geothermal field -- in all applications, 01:04:26.170 --> 01:04:28.540 we shall relate it to reservoir imaging. 01:04:28.540 --> 01:04:32.800 If they want value for this information, they have to 01:04:32.800 --> 01:04:38.160 somehow put money in this -- in this shot or in this operation. 01:04:38.160 --> 01:04:40.309 - Thanks. 01:04:42.240 --> 01:04:47.040 [ Silence ] 01:04:48.190 --> 01:04:52.770 - So I’m just curious if this idea of being able to use the polarization 01:04:52.770 --> 01:04:58.070 to help -- I mean, it -- would you be able to tell if your results 01:04:58.070 --> 01:05:02.860 are affected by a wave having its polarization modified 01:05:02.860 --> 01:05:08.910 by some crustal structure or heterogeneity or a fault, even? 01:05:08.910 --> 01:05:14.670 - So here it’s a little bit different from what I discuss. 01:05:14.670 --> 01:05:19.900 The difference is I discuss how we are going to express 01:05:19.900 --> 01:05:22.170 the probability density function. 01:05:22.170 --> 01:05:24.460 But of course, behind all the tradeoffs, 01:05:24.460 --> 01:05:27.130 all the problems you may have by using the three-component -- 01:05:27.130 --> 01:05:31.470 I mean, the polarization of the wave, this still exists, okay? 01:05:31.470 --> 01:05:33.570 And exactly what you said. 01:05:33.570 --> 01:05:38.230 So I don’t think it’s going to change a lot. 01:05:38.230 --> 01:05:41.560 I mean, that’s something which is still on work, 01:05:41.560 --> 01:05:42.940 so that’s something we want to work with. 01:05:42.940 --> 01:05:46.410 So here it was perfect polarization, so we want to add noise 01:05:46.410 --> 01:05:49.460 coming from the drilling pad, for example. 01:05:49.460 --> 01:05:52.390 [chuckles] Okay. That’s something we want to do. 01:05:52.390 --> 01:05:57.390 But I’m not sure it will really improve the things, this case. 01:05:57.390 --> 01:06:01.390 The only way I see it would bring -- like, would be more precise 01:06:01.390 --> 01:06:04.980 is because we are going to keep all information 01:06:04.980 --> 01:06:08.850 correlated together, okay, with this covariance matrix. 01:06:08.850 --> 01:06:13.940 And we are not going to split and try to differentiate 01:06:13.940 --> 01:06:15.930 azimuths and inclination and so on and so forth. 01:06:15.930 --> 01:06:18.440 But we are going to keep the whole thing together. 01:06:18.440 --> 01:06:23.140 This may be the main difference in this case. 01:06:23.140 --> 01:06:24.400 - Thanks. 01:06:28.420 --> 01:06:30.400 - Anyone else? 01:06:33.900 --> 01:06:36.520 All right. Let’s thank Emmanuel again. - Thank you. 01:06:36.520 --> 01:06:38.720 [ Applause ] 01:06:38.720 --> 01:06:40.940 - And we’ll get coffee. 01:06:42.180 --> 01:06:46.260 [ Silence ]