| 00:00 | Um OK. OK. So I not checked your um questions, but |
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| 00:11 | do that now. OK. So are some questions from the le uh |
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| 00:30 | , so she says uh uh on lecture from yesterday uh um lecture six |
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| 00:40 | , 5051. It says on it says real interfaces are usually not |
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| 00:46 | but are close to other interfaces Now, we assume that the media |
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| 00:50 | well separated from the other, other . So where is the question |
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| 01:00 | Why would you need that? Oh they have different layers, we |
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| 01:07 | we have layers one on top of other and they're all very close together |
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| 01:13 | layer thicknesses uh less than the We, we're going to assume that |
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| 01:24 | layers are continuous. Yes. And , we assume they're perfectly, perfectly |
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| 01:30 | . Uh That's what we did We, we assume they're perfectly flat |
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| 01:34 | a mirror. Uh uh So uh in the real earth, they might |
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| 01:40 | be perfectly flat. We, we're take that up today. But what |
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| 01:44 | your question? Why is it Uh Well, it's because uh uh |
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| 01:57 | layers are are uh laid down over time. And if you have a |
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| 02:03 | which is 10 ft thick, it uh uh be uh 10 million years |
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| 02:08 | the uh uh uh beginning of the for that layer. And the beginning |
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| 02:15 | the next one, I'm I'm not I understand your question. Uh So |
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| 02:21 | have so many layers and we have on all scales. What we like |
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| 02:26 | do is we like to um assume within each layer the medium is |
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| 02:35 | So that means we can apply our which we derived so far, we |
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| 02:40 | the equations only for uniform media. so what we do is we uh |
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| 02:47 | assume the the media are the medium uniform within the layer. And then |
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| 02:56 | on uh on the, the next above and below, it's again uniform |
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| 03:01 | different constants um uh for velocity and and amplitude et cetera. And so |
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| 03:09 | we have separate solutions for the wave and those uh different uniform layers. |
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| 03:20 | then we match the, the solutions at the boundary using the boundary conditions |
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| 03:26 | that's what gives rise to reflections. OK. So next question is uh |
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| 03:39 | lecture slide 108. Uh However, the incident angle is post critical, |
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| 03:47 | is an additional head wave projected upward the propagating post critical refracted wave. |
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| 03:54 | uh oh um why, why is upwards? OK. So that's a |
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| 04:02 | AAA very good question. And uh one that people, um I would |
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| 04:11 | that most people are confused about these . And the reason is, of |
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| 04:16 | , because in most of our we don't have these headways because they |
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| 04:22 | at angles which are greater than the angle. And normally we uh eliminate |
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| 04:30 | angles of incidence from our uh from data sets simply by uh uh ignoring |
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| 04:37 | , right? But let's, let's let's look at that. Uh uh |
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| 04:41 | gonna go back to slide to uh uh lecture six and uh slide |
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| 05:21 | And I'm gonna put this in presentation and then I am going to share |
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| 05:29 | screen. OK. Rosa, can see that slide? OK. |
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| 06:16 | OK. There it is. So is my planter and let us um |
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| 06:30 | I should go. So this is previous slide and sorry, just a |
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| 06:44 | . OK. This is the previous . And so you can see here |
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| 06:47 | uh in rays you can see the ray here and the refracted uh right |
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| 06:54 | and the reflected right here. Uh haven't shown any converted waves here. |
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| 06:59 | This is the only D waves showing then uh uh the corresponding uh wavefront |
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| 07:07 | like c so you can see how thing is, is curved like |
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| 07:12 | So uh that sort of implies, it, that there's a, the |
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| 07:16 | up here somewhere up here somewhere and uh uh um here's the refracted wave |
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| 07:25 | um you can see that um can you see that um this uh |
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| 07:32 | can you see this, this ray is uh uh has bent closer to |
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| 07:42 | , to the interface than the incoming indicating that the lower medium is faster |
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| 07:48 | the upper medium. And then here's reflected wave front. Uh Like so |
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| 07:58 | , if the infinite way was post , it says there's an additional head |
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| 08:03 | upwards by the propagating post critical refracted . That's exactly the phrase that Li |
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| 08:10 | posted in her question. So, so let's uh uh uh let's look |
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| 08:19 | , here's the infinite wavefront and here the refracted wave front. And you |
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| 08:25 | , in this case, the instant is coming in at a uh at |
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| 08:28 | bigger angle than we had before. the source is over here somewhere. |
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| 08:34 | so uh you can uh uh how you know where the source is? |
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| 08:39 | , you just sort of trace this backwards and it goes up here and |
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| 08:44 | along that ray uh uh uh you take a, a radius from |
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| 08:50 | from this circle. And so, uh that's gonna intersect right about |
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| 08:56 | So that's where the uh the sources this curve wavefront and uh for the |
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| 09:05 | wavefront, uh it's traveling uh with AAA wave vector, which is right |
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| 09:13 | . When you see a dashed red here, you're gonna back up here |
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| 09:17 | pre critical reflections. It goes but at all critical reflections, it |
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| 09:23 | uh according to, to law, uh it's, it uh goes right |
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| 09:29 | here. And furthermore, uh uh refracted angle is complex. What does |
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| 09:36 | mean? It has a real part is zero to me, a real |
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| 09:40 | which is 90 degrees. That's, , that's not. And then an |
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| 09:45 | part which is not shown here on graph, it's actually pointed straight |
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| 09:51 | And so uh this refracted wave is faster than uh the infinite wave it |
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| 09:59 | the medium. Uh And th this faster than this one, that's what |
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| 10:04 | says right here. And uh uh , since it faster, it gets |
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| 10:10 | of the um uh of the incident . And so you can't have |
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| 10:18 | a, a AAA wavelet, uh wavefront here is the refracted wavefront. |
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| 10:24 | , you can't just have an ending . Uh um uh That would not |
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| 10:30 | the boundary condition. So, in , in this situation, the boundary |
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| 10:35 | imply that there as this thing moves , it ripples the interface up and |
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| 10:43 | and makes this wave here, which what we call the head wave and |
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| 10:48 | propagating upwards at this angle. So question is, what is this |
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| 10:53 | Well, you can see here that uh the uh uh over Nigerian interval |
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| 11:00 | T this thing gets ahead of the wave uh by uh uh uh uh |
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| 11:06 | , the instant wave by this uh here VP two delta T. And |
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| 11:12 | the same time, the, the wave goes up and VP one delta |
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| 11:17 | . And so that provides all the you need to calculate this head wave |
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| 11:24 | right in here. And that turns to be the critical angle. |
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| 11:29 | this only happens for curved wavefront, the wavefront are um planar interface, |
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| 11:38 | it doesn't happen. That's why we talk about those When we talked about |
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| 11:44 | uh plane wave reflectivity and plane wave transmiss. This happens only post critical |
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| 11:53 | he had this wave going up. , the question that Lily asked is |
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| 11:57 | um does it go up and uh not down? Well, uh uh |
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| 12:03 | it went down, suppose it started and went down somewhere. Well, |
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| 12:07 | that um uh um that's not what boundary conditions say. The boundary conditions |
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| 12:15 | that this wave has to be tangent this reflected wave up here. And |
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| 12:25 | I think that's all I want to about these post critical refracted headways because |
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| 12:34 | we normally exclude them from our We certainly record them, lots of |
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| 12:39 | . And, and how do we that? Well, we design our |
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| 12:46 | acquisition so that the maximum angle is suitable angle for uh for the target |
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| 12:54 | . Uh May maybe we wanna say angle is 45 degrees at the target |
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| 13:02 | . Well, what that means is for the same maximum offset, same |
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| 13:08 | length for shallow reflection. Those angles are gonna be bigger and they might |
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| 13:15 | bigger than the uh uh local critical . And so there would be this |
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| 13:23 | of arrivals coming in at the shallower from the shallower events using our conventional |
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| 13:33 | are conventional survey geometry. But normally we do is we just draw a |
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| 13:41 | uh uh uh somewhere um uh on , on the gather, we draw |
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| 13:48 | line and we say to the uh uh uh at shorter times, we're |
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| 13:55 | ignore those high angle um reflections, the head waves. So, uh |
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| 14:06 | that has historically been the practice of . However, I do think that |
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| 14:14 | that's a mistake, maybe we should looking at that data instead of throwing |
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| 14:19 | away. So it cost us uh money to acquire that and we just |
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| 14:25 | , throw it away without ever looking it. Uh uh uh So here's |
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| 14:29 | opportunity maybe for some student who has an idea, what could we, |
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| 14:36 | information could we hope to learn from uh shallow refraction data? And would |
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| 14:44 | be a useful, would it make for my company? Um So, |
|
| 14:50 | uh that has not happened yet. , I would say that nobody has |
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| 14:56 | taken a close look at those shallow offset reflections, but maybe there's some |
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| 15:05 | in there, who knows? So let me then um uh minimize |
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| 15:25 | I lost my mouth coffee. So to minimize the and uh look |
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| 15:36 | at my inbox. Uh here is , here's a question from Mesa. |
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| 16:02 | . Uh I'm good morning professor. question is regarding quiz one in less |
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| 16:07 | six. Uh So let's look at where one in lesson six? So |
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| 16:14 | am going to um, ok. to the slides and I'm gonna go |
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| 16:21 | to her. OK, back to beginning. Uh And here is um |
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| 16:44 | , I think what I wanna do you know, you're gonna stop |
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| 17:05 | OK. Then I'm gonna start sharing . So I said, can you |
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| 17:14 | this? OK. So now um let's go back to your question. |
|
| 17:22 | read the question uh where one lesson answer is false for all stress components |
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| 17:31 | be continuous at it and elastic But the, but the displacement is |
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| 17:38 | . Could you please elaborate more on ? What is happening at the |
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| 17:42 | OK. So uh uh uh let's at this slide. C uh This |
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| 18:00 | um uh the first question in So the boundary conditions at the interface |
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| 18:09 | tactic media are continuity of stress and . Is this true or false? |
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| 18:14 | uh So the answer is it's false uh um let's see here. Um |
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| 18:25 | me go on to uh the next and it'll help us understand why the |
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| 18:31 | is false here. This is the question, second question here. Uh |
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| 18:42 | as uh says, all compounds of must be continuous. Is that true |
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| 18:46 | all? So that one is So uh think about that, if |
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| 18:50 | had a uh um uh hm a in any component of displacement at |
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| 18:59 | at the boundary at the interface, that would mean that is that the |
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| 19:05 | got torn by the waves. If a AAA, if it's a dis |
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| 19:10 | it's a jump and displacement X then it means it's being torn um |
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| 19:16 | the horizontal direction. If it's a displacement, uh if it's a jump |
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| 19:22 | displacement component X three, then it be torn vertically. And so of |
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| 19:29 | , rocks can be torn. They be um um um they can be |
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| 19:36 | but not by seismic waves. Uh uh they're fractured, for example, |
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| 19:42 | a uh um uh a fracking there were intentionally introducing discontinuities in uh |
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| 19:52 | in displacement in, in the media uh open fractures in the medium which |
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| 20:00 | do by increasing uh uh the pore in, in, in the me |
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| 20:06 | the medium by injecting fluids at high . But it doesn't happen with a |
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| 20:12 | wave. Uh uh Number one, the seismic waves are uh have such |
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| 20:20 | stress increments going with them. And two, since uh oh we arrange |
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| 20:27 | that way, we arranged to have which are uh strong enough to send |
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| 20:31 | signal to our most distant receiver not strong as to uh fracture the |
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| 20:38 | So let me uh so this is for all components of displacement. This |
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| 20:43 | not components of stress of strain, of displacement. I'll, I'll go |
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| 20:49 | to the uh previous slide. So says continuity of stress and strain. |
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| 20:54 | we weren't talking about strains. we were talking about displacement and now |
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| 20:59 | gonna go forward to let to question and the next one of question |
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| 21:04 | OK. All components of stress must continued. Is this true or |
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| 21:09 | And so this one is also false we uh uh we saw in the |
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| 21:17 | uh slides, we saw that only components of stress had to be uh |
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| 21:25 | . Um They are those components of which have the uh remember that stress |
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| 21:33 | area. So uh the components of which has to be ingenuous are those |
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| 21:42 | which are aligned with the interface. let's assume the interface is horizontal. |
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| 21:47 | means it's specified by a vertical arrow specifies uh the direction of the surface |
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| 21:55 | it, to the normal, to vector. OK. So that has |
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| 22:01 | three. So what we just uh uh learned is that uh subs uh |
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| 22:07 | stress component 31 has to be uh continuous across the interface and also stress |
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| 22:16 | 13 because the order of uh of of the indices doesn't count doesn't |
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| 22:25 | OK. So we can say the thing about 23 and 32. And |
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| 22:29 | can say the same thing about So those five components of the stress |
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| 22:35 | have to be continuous or across the because they have uh uh uh the |
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| 22:41 | area is uh aligned with the OK. So did that, did |
|
| 22:50 | um uh answer the question, Yes. II, I think |
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| 22:58 | And I have another question. I know if I, I understanding |
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| 23:03 | but I, we are thinking about , just one point, right? |
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| 23:10 | 11 way, say it that But what is there like in the |
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| 23:17 | interaction between all of all of those at the interval? It's like uh |
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| 23:25 | my mind, I I it's not clear to me exactly what happens or |
|
| 23:35 | we are considering that it's a right? In all the, in |
|
| 23:40 | , the physical properties between the two , the upper layer and the bottom |
|
| 23:46 | . That's what makes the reflections. huh So let's go forward to uh |
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| 23:52 | this time. Uh I wanna go to the slide which shows the picture |
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| 23:59 | um uh uh for all the different together. Yeah. So this is |
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| 24:08 | uh th this is what we And uh remember this did not work |
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| 24:14 | we assumed that we had one for incident, one incoming wave and two |
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| 24:22 | waves, we found out that we have enough E equations to evaluate all |
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| 24:29 | constants. What are the constants that to be evaluated? Well, there's |
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| 24:33 | displacement and there's the, the wave and uh uh above and below. |
|
| 24:41 | so, um we didn't have enough there. So what we did then |
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| 24:47 | uh once we came to the understanding I hope, by the way, |
|
| 24:57 | uh here is a diagram that uh is explaining how we're uh how we're |
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| 25:04 | the angles. And um uh this kind of like the diagram that we |
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| 25:10 | before concerning post critical uh uh reflections curved wavefront. And so this is |
|
| 25:21 | different because the wavefront are flat. so I didn't say here whether this |
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| 25:26 | angle is post critical or pre but it doesn't really matter if, |
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| 25:32 | long as the wavefront are flat, if they're curved, that's when we |
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| 25:36 | into the issue of the uh additional waves that I I mentioned earlier. |
|
| 25:43 | let's go on here. Um uh , here's how, here's where we |
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| 25:53 | that we didn't have enough uh uh equations to uh uh uh determine all |
|
| 26:01 | parameters. So what we did was uh assume, OK, let's assume |
|
| 26:07 | also uh a reflected shear wave and transmitted shear wave. And sure enough |
|
| 26:13 | gives more uh uh uh uh complexity the picture. But now we have |
|
| 26:22 | the same sorts of boundary conditions and we have uh uh four equations uh |
|
| 26:29 | uh for evaluating all these concepts and turns out to be enough. So |
|
| 26:37 | your question is uh uh uh you said you're not quite sure what's |
|
| 26:43 | on. So, so let's walk here, this incoming wave is |
|
| 26:48 | it's hitting the boundary and it's jiggling boundary up and down and sideways at |
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| 26:53 | same time. And so, uh that jiggling is what excites the upgoing |
|
| 26:59 | the downgoing waves. And um uh energy here has to be partitioned, |
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| 27:08 | incoming energy has to be partitioned among four outgoing waves at um uh the |
|
| 27:18 | conditions assure that that uh happens properly um uh we have uh uh so |
|
| 27:29 | amplitude for the reflected wave and so for the transmitted wave, reflected s |
|
| 27:35 | s and all of that um is determined by the boundary conditions. |
|
| 27:43 | you can imagine that it's pretty complicated uh uh solve all those many equations |
|
| 27:49 | solve all, all those uh those chars cons. So you, you |
|
| 27:56 | that, that we didn't really solve at all. We did uh uh |
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| 28:01 | directly for the uh for the And we found that Snell's law applies |
|
| 28:06 | equally for all of them. Um so here is the answer to uh |
|
| 28:14 | happens uh how all those considerations, of displacement and of stress work together |
|
| 28:25 | provide air. This is only for upcoming uh reflected P wave. And |
|
| 28:31 | uh corresponding uh uh in terms for retracted P wave and the reflected uh |
|
| 28:41 | wave and the reflective S wave. it's all pretty complicated. So that's |
|
| 28:46 | we didn't uh show the derivation. I see here, wanna back up |
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| 28:55 | here. So this is the guy finally figured it out. His name |
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| 28:59 | Zur and I want to back up a little bit more. Oh, |
|
| 29:06 | . Remember here uh uh about the . So, did you look at |
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| 29:10 | movies? Yeah. So, were you able to look at the |
|
| 29:18 | ? Yes. Yes, I Ok. So, so uh uh |
|
| 29:23 | since uh Carlos is not here, gonna sort of uh he some time |
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| 29:29 | until he uh finishes with his meeting gets online. So, what I'm |
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| 29:33 | do right now is to um show movies and talk about them now. |
|
| 29:42 | let us see if that works. thing I wanna do is uh you |
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| 29:57 | , I want to, I think gonna stop sharing here and I'm going |
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| 30:02 | help you know that presentation presentation off mouse or the mountains. Yeah. |
|
| 30:55 | , the mouse only here. you can uh help, help |
|
| 31:36 | Uh uh you see my, my is only trapped inside here. How |
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| 31:42 | I get rid of that? See now it's trapped inside here. |
|
| 31:54 | Yeah. Right. It just greens can see the disease. So, |
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| 32:18 | , and then start. Oh Thank you. OK. So, |
|
| 32:41 | , ok. Now, uh when see this movie playing? Oh |
|
| 34:00 | you don't say that. Ok. I'm gonna um you could, you |
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| 34:07 | not. OK. OK. So lets see. Keep out. |
|
| 34:33 | OK. So I, I think can see it now. Oops. |
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| 34:38 | uh OK. So what you see is uh in, in, in |
|
| 34:48 | movie you can see the uh the P wave is, is a |
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| 34:52 | wave with the, the displacement in uh uh plane of the, of |
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| 34:59 | uh figure. Uh just a second in the pan of the figure. |
|
| 35:05 | so here it is uh oops uh me get myself a um Can you |
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| 35:18 | my mouse, can you see my ? OK. So here's, here's |
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| 35:23 | P wave down here and the transmitted wave, here's the reflected P |
|
| 35:28 | it's polarized longitudinally. So uh that's we call it a P wave. |
|
| 35:33 | the uh the sheer waves are here red. And you can see that |
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| 35:38 | this case, the polarization is uh cross line to uh uh uh it's |
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| 35:45 | it's transverse to the wave that uh uh lying in the plane uh but |
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| 35:53 | to the wave vector. Now, uh so mead it can you uh |
|
| 36:00 | me why it is that this angle uh between the, the sheer wave |
|
| 36:06 | the normal this angle right in Why is that a smaller angle than |
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| 36:11 | angle between the reflected wave and the . That's for you, for |
|
| 36:26 | Uh I, I want to hear thinking out loud. Yes, I |
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| 36:35 | trying to think that it, I mean, I think it's related |
|
| 36:41 | that it goes with the refracted. right. And we can say a |
|
| 36:47 | thing about so uh so the short to that question is Snell's Law. |
|
| 36:54 | so then the longer answer is that uh uh S Snell's Law says that |
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| 37:01 | , the ratio of the signs of two angles, this angle and this |
|
| 37:05 | is the same as the ratio of , or the, the same as |
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| 37:09 | ratio of the velocities. And since sheer velocity is smaller than the P |
|
| 37:14 | velocity, it means the sheer wave has to be smaller than the P |
|
| 37:18 | angle. How much according to snow's . And you can be sure that |
|
| 37:23 | put this together um uh did it properly, you can see here. |
|
| 37:29 | Well, you can see here this this uh uh P wave is traveling |
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| 37:35 | three times as fast as the share . And this P wave velocity is |
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| 37:41 | about twice the uh uh the sheer velocity here. Uh So that, |
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| 37:48 | ex, that explains why um the sheer angles are smaller than the |
|
| 37:56 | angles. Now uh uh to you , uh can you see that this |
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| 38:02 | here or uh uh uh then uh uh here's the question for you. |
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| 38:09 | is the lower medium faster in P that and the upper medium or |
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| 38:20 | it's faster. Yes. And so do you know it's faster? |
|
| 38:26 | So, so what she says that can't hear, but I can hear |
|
| 38:31 | . It says that be uh because angle here from here all the way |
|
| 38:36 | to the normal because that's a bigger than from here or all the |
|
| 38:41 | So she can see that with her , it's a bigger angle. So |
|
| 38:45 | must be a bigger velocity down here uh and up here. So there's |
|
| 38:51 | way to check that all you have do is look at the uh at |
|
| 38:55 | deformed here. Here's the wavefront right and here's the sheer wave front right |
|
| 39:00 | and it looks like it's gone about as fat, right? Yeah. |
|
| 39:05 | , uh so that's great. Uh , um I think that there's not |
|
| 39:10 | more to see on this one, I'm just gonna finish, let that |
|
| 39:16 | and then I'm gonna uh hi Ma I'm going to bring up the other |
|
| 39:30 | . Yeah. And now I'm going share the screen here. OK. |
|
| 39:44 | I think you can see this movie well. So let me play |
|
| 39:49 | So this one is uh more isn't it? So let's stop it |
|
| 39:54 | here. OK. So, uh here is the incoming wave and you |
|
| 39:59 | see that uh um uh the source was back here somewhere and here is |
|
| 40:05 | , uh the uh refracted wave and , um uh you see also it's |
|
| 40:14 | a little bit faster. Can you here that because of this pink right |
|
| 40:18 | , you can see that this one going a little bit faster. |
|
| 40:22 | we have these two other wavefront. so the question I have for, |
|
| 40:26 | for you Brisa, which one of two wavefront is the reflected P |
|
| 40:33 | the shallower one, the shallow. . So this one. So uh |
|
| 40:40 | uh uh how do you know that it's faster? Oh Yeah. |
|
| 40:48 | Yeah. OK. That's good enough it's faster. OK. Uh And |
|
| 40:53 | , furthermore, you can tell by , the uh the way these curving |
|
| 40:58 | now, um so uh le le this uh must be in the, |
|
| 41:05 | re reflected sheer weight. Am I ? Ok. So now tell me |
|
| 41:12 | , where is the transmitted your It's not showing. Yeah. Uh |
|
| 41:20 | it be, would it be that for this lower medium? It's uh |
|
| 41:26 | ocean water? And so there would no um uh uh shear wave in |
|
| 41:32 | , in the um in the And would that be a possible |
|
| 41:41 | Could this, could this be a down here or if, if it |
|
| 41:45 | a fluid that would explain why there's sheer weight, right? So, |
|
| 41:50 | tell me, is, is that , a good explanation? You don't |
|
| 41:55 | so. Why not? You have speak more loudly. The salt. |
|
| 42:20 | , I'm, I'm still not hearing . You speak very softly. |
|
| 42:26 | while you're thinking, let me turn brace. Uh, I, is |
|
| 42:29 | a reasonable thing to, uh, this as a fluid down here? |
|
| 42:35 | yes, if there's not a, refracted wave and wave? Ok. |
|
| 42:43 | , uh, I, I know you're thinking. You're thinking, |
|
| 42:45 | maybe this is just upside down and uh the ocean is on top and |
|
| 42:51 | , not necessarily that it's the but it could be a, a |
|
| 42:54 | that has fluids in it, OK. So, OK. |
|
| 42:59 | in our business, we have uh uh media uh containing fluids in pores |
|
| 43:08 | . We, we haven't talked about yet, but we, that's the |
|
| 43:12 | the topic for uh um uh the um Saturday morning is what happens when |
|
| 43:18 | have uh fluid in the pore space the grains of rocks. But uh |
|
| 43:26 | now thinking in terms of hook in with the homogeneous media. Uh |
|
| 43:32 | Uh uh what you say is this be ocean. Uh this could be |
|
| 43:38 | here. And uh um uh in fact, it could be the |
|
| 43:46 | . Now, all we have to is figure that if it's the |
|
| 43:49 | that means that the figure is upside and this way is really upwards instead |
|
| 43:54 | downwards and we could do that. um now tell me uh um uh |
|
| 44:02 | back to you. Uh Would it reasonable to consider this fluid to be |
|
| 44:07 | this, this layer here to be looking at these waves? And you |
|
| 44:13 | there is no uh sheer wave propagating here. Uh So, is it |
|
| 44:20 | that this is a fluid? I didn't hear you. You think |
|
| 44:25 | is possible? Uh OK. So it's possible, uh didn't we say |
|
| 44:32 | this uh um uh velocity here was uh uh uh down here than it |
|
| 44:39 | up here? OK. So, you can tell it's faster because of |
|
| 44:44 | little kink here in the. Uh uh that means that the, the |
|
| 44:50 | is tilted towards the interface. Uh So uh it is reasonable to think |
|
| 44:57 | we have a fluid down here, is actually faster than the fluid up |
|
| 45:03 | , the, than the rock up . Well, probably not. |
|
| 45:07 | can uh can you think of any where that might be true? We |
|
| 45:13 | a, a faster fluid then uh where the he wave velocity in the |
|
| 45:20 | is faster than um uh uh uh uh it's faster than the P wave |
|
| 45:29 | in the rock. I don't think . We have cases where the uh |
|
| 45:33 | the P wave velocity in the fluid faster than the shear wave velocity in |
|
| 45:38 | rock that's in uh uh uh that's encountered in the borehole in uh uh |
|
| 45:45 | recent sediments where the recent sediments are very soft and slow. Uh And |
|
| 45:52 | a case like that, you can a borehole through there and we have |
|
| 45:56 | of bar, we drill a lot bore holes and, and through rocks |
|
| 46:00 | that because we're looking for oil and like that. And in those |
|
| 46:05 | it can easily be the case that new wave velocity in the mud is |
|
| 46:11 | than the shear wave velocity in the surrounding. So we talked about how |
|
| 46:17 | deal with that. And uh um uh s Slumber guy makes a lot |
|
| 46:23 | money by helping us to solve that . But I conclude that there is |
|
| 46:29 | ser there's no reasonable scenario where the wave velocity uh down here is uh |
|
| 46:38 | than the P wave velocity up And at the same time, no |
|
| 46:42 | way. So what I think is uh the, the uh whoever drew |
|
| 46:49 | cartoon got lazy and he, he want to show the uh the refracted |
|
| 46:55 | wave down here. OK. one more question, um can you |
|
| 47:05 | here and see that the, the , the wavelength here in the sheer |
|
| 47:11 | is less than the wavelength in the wave? Does that make sense? |
|
| 47:24 | let, let's let me turn that you uh uh uh Mercer uh uh |
|
| 47:29 | we have a reflected sheer wave here you can see that uh uh this |
|
| 47:34 | in depth right here. And so can see that, uh, |
|
| 47:38 | the, the, the wavelength, , and the reflected shear wave is |
|
| 47:45 | than the wavelength. And the reflected wave, does that make sense? |
|
| 47:53 | think not. I think they it's the same, right. |
|
| 47:58 | it should be the same. Uh . Why should it be the |
|
| 48:05 | Because there is not, ah, a, that's a very interesting |
|
| 48:12 | So, let me, uh uh I, I was gonna switch |
|
| 48:20 | to the other um lecture six, I think you have it in your |
|
| 48:25 | , we show those models of incoming and outgoing waves and so on. |
|
| 48:31 | we had uh uh for each we had a, a plane wave |
|
| 48:37 | and the plane wave expression it had either the I omega T minus K |
|
| 48:42 | X uh uh um the frequency is explicit in those in that |
|
| 48:54 | And furthermore, we decided that if gonna match the boundary conditions at all |
|
| 49:00 | , we have to have the same for all uh waves. But that |
|
| 49:09 | that mean that it's gonna have to different wavelengths for uh the different waves |
|
| 49:15 | remember the uh the, the wavelength equal to the uh uh velocity divided |
|
| 49:21 | the frequency. So if we have same frequency and a smaller velocity |
|
| 49:28 | we have a smaller ch uh So means that the, the wavelength uh |
|
| 49:34 | be um uh smaller for sheer. . Now, let's think about |
|
| 49:42 | So, oh, so I want to remember this conversation when we uh |
|
| 49:52 | about the lecture later this afternoon. what we said about sheer wave Waley |
|
| 50:01 | shorter than key wave wavelength? So with that, what I want |
|
| 50:10 | do is uh uh uh kill this I want to uh uh catch up |
|
| 50:20 | something that I, oh here's No, that's not. Th that's |
|
| 50:26 | down, Lily is showing her OK. So uh that, that's |
|
| 50:33 | . So, uh we, we we'll um stall for time while Carlos |
|
| 50:39 | finishing his meeting. He should be here in any month. So, |
|
| 50:43 | I want to do is I want show you um the spreadsheet which uh |
|
| 50:53 | did not um uh uh which I to discuss in class. So I'm |
|
| 51:07 | to show you this spreadsheet and the thing I'm gonna do is do |
|
| 51:13 | OK. Share this. So can see the spreadsheet here? This is |
|
| 51:20 | there are many worksheets and uh uh is the first one and it has |
|
| 51:25 | disclaimer that says that uh uh anybody use this so you can share this |
|
| 51:31 | spreadsheet with your friends if you like whether they're uh uh uh no matter |
|
| 51:37 | , who your friends are, you share them with us. If you |
|
| 51:41 | uh Rueda. Can you see Yes, I can. OK. |
|
| 51:47 | now let's look at uh the first the uh worksheets. OK. So |
|
| 51:56 | is uh a spreadsheet that does the for you if you want to convert |
|
| 52:01 | velocities and all these other elastic constants we talked about in the first |
|
| 52:07 | So, uh see, uh so in kilometers per second and this is |
|
| 52:14 | for VP uh three kilometers per Uh le let me just uh exchange |
|
| 52:20 | and I'm gonna put in here 3.2 now watch when I do that, |
|
| 52:26 | watch, uh what changes, as soon as I hit enter some |
|
| 52:31 | are gonna change. Not this one not this one because those are |
|
| 52:35 | those are independent sense of quantity, look down in here uh, to |
|
| 52:40 | which things change when I hit. . Ok. Here we go. |
|
| 52:46 | . Ok. So you can see VP changed and, uh uh, |
|
| 52:52 | uh uh uh uh and also, the mood changed, didn't it? |
|
| 52:59 | Let's go back now, I think mood change. So let me, |
|
| 53:09 | . Um, yeah. Is that ? So here we go, I'm |
|
| 53:15 | put the VP back to three. . Ok. So, uh |
|
| 53:24 | so we have, uh uh uh changing your VP of 3.2 and it |
|
| 53:39 | that the mood changed. Oh, . Uh huh. So we |
|
| 53:46 | uh uh, you see, I, I ha I have not |
|
| 53:50 | V PV S and row instead I VP velocity ratio and row. So |
|
| 53:57 | I changed the, uh the VP changed the uh uh uh uh uh |
|
| 54:03 | changed the velocity ratio, which changed uh the sheer velocity with and that |
|
| 54:09 | the uh sheer models here. And these other things were changing also. |
|
| 54:14 | uh uh uh also notice over here to the side it tells you what |
|
| 54:19 | means in feet per second. So, uh that is uh um |
|
| 54:27 | uh uh an Excel worksheet that does you all the arithmetic that we talked |
|
| 54:33 | in the first lecture. Uh So might be useful to you some uh |
|
| 54:44 | time. Um uh Anyway, this it all does, it just does |
|
| 54:49 | , the arithmetic. So now let's at the next worksheet. So this |
|
| 54:55 | a ricer wav. Th this is what we uh uh discussed uh previously |
|
| 55:01 | the course. This is the formula the Richer wavel. I remember this |
|
| 55:05 | named after a famous dishes. This named Richer and I'm gonna scroll up |
|
| 55:13 | if I could find my mouse, my mouse. OK. So uh |
|
| 55:22 | this work away only has one number . The only thing that can be |
|
| 55:28 | here is uh the uh the mac called the, the maximum frequency. |
|
| 55:33 | , you can see that there's lots frequencies here. Uh uh But this |
|
| 55:37 | the uh the frequency with the maximum . So uh let me uh scroll |
|
| 55:43 | here. This, I think I show here. No, I |
|
| 55:50 | I, I don't show the um the fourier spectrum. But th th |
|
| 55:56 | you look at the fourier spectrum, has a maximum at this frequency. |
|
| 56:01 | let me just change this here to more typical seismic frequency. So I'm |
|
| 56:06 | so watch the graph when I hit , see how it uh um spreads |
|
| 56:14 | . Uh So this is uh a frequency and, and this is in |
|
| 56:20 | by the way, not, not . And so uh um you can |
|
| 56:26 | that be laser. So this, think is probably not gonna be useful |
|
| 56:32 | you, but I just put it here because that's what I needed to |
|
| 56:37 | some of the subsequent worksheets. So let's look at a common midpoint gather |
|
| 56:43 | we're uh we have uh you can that this guy that each has um |
|
| 56:51 | wavefront that looks like uh Bricker And here uh you can uh it's |
|
| 56:58 | same uh recorder wheel that I had uh the, the previous worksheet was |
|
| 57:04 | . So it's just a coincidence that also has 50 her. Now we're |
|
| 57:09 | it here at two milliseconds. So sample it again, uh sample it |
|
| 57:14 | uh um typically at four milliseconds. I'm gonna change. Uh mm hm |
|
| 57:39 | , I um I think I did sample this. Uh uh You can't |
|
| 57:44 | the sample now. That's set. you see up here that the formula |
|
| 57:50 | from the, the, it's the , uh that's deceptive here. Um |
|
| 57:55 | should um uh uh correct that. by the way, um there was |
|
| 58:04 | mistake in this spreadsheet, not this , but another one which I corrected |
|
| 58:11 | morning and uploaded the corrected one to uh to canvas this morning. So |
|
| 58:18 | you downloaded this spreadsheet, uh you throw that one away and download again |
|
| 58:23 | you'll get the uh the correct uh correct spreadsheet and, and don't do |
|
| 58:30 | right now, don't do it uh evening, do it tomorrow. Uh |
|
| 58:35 | this evening, I'm gonna just correct cosmetics so that this does not |
|
| 58:41 | it sort of does imply here that can adjust the sampling rate as you |
|
| 58:47 | . But uh you can't and how you know that? Because there's this |
|
| 58:50 | here uh which is uh uh showing uh this is calculated um automatically, |
|
| 59:02 | can't adjust it. A uh uh at, look, look at the |
|
| 59:08 | and look at uh this and I'm to adjust the uh normal instance, |
|
| 59:14 | times. Watch what happens when I this when I turn, turn, |
|
| 59:18 | it arrive later. So you see everything got adjusted uh uh uh the |
|
| 59:26 | uh Excel machinery. I did a of everything. And so uh this |
|
| 59:35 | really uh change much at all. So, but let's look at |
|
| 59:39 | at the uh this, this change move out velocity here. And I'm |
|
| 59:44 | change that to uh say um Now watch, watch the no graph |
|
| 59:54 | our enter. I know. So , it moved out less. Why |
|
| 60:00 | that? Because uh uh the faster goes uh the the faster is uh |
|
| 60:05 | velocity here. Uh the sooner it . So it doesn't affect uh uh |
|
| 60:14 | , this is the R MS not the vertical velocity. So it |
|
| 60:18 | affect the vertical arrival time, but did affect the move out. And |
|
| 60:22 | can see this um uh blue curve the move out and then you can |
|
| 60:31 | it goes through the peak here and doesn't go through the peak anywhere |
|
| 60:35 | Uh Because um yeah, that's actually , the point uh rob this point |
|
| 60:47 | here is arriving at the same time the, as we speak here. |
|
| 60:51 | OK. Uh I, I think point I would gather is uh not |
|
| 61:00 | uh not interesting to you, but , let me ask you to your |
|
| 61:07 | . Do you see AAA difference in here as a function of offset your |
|
| 61:17 | ? Do, do you see Really? Do you think that? |
|
| 61:24 | so yeah, so to uh to eye, this a rival Appleton is |
|
| 61:33 | than the arrival amplitude here, but not, that doesn't have anything to |
|
| 61:38 | with move out. Does that's, just amplitude. OK. Now, |
|
| 61:43 | to you brace that. Does it to you like the, uh |
|
| 61:47 | the maximum frequency of this offset? , wow. Is that the same |
|
| 61:54 | frequency as we have here? it looks different. It looks the |
|
| 62:02 | . Yeah, I agree. It the same. So, uh, |
|
| 62:06 | now look down here at the bottom , we're gonna do the next spreadsheet |
|
| 62:11 | is gonna be showing NMO stretch. , you can see that the uh |
|
| 62:18 | um uh distant wavefront which has been out now. So it's the, |
|
| 62:24 | guy that is flying and now you easily see that this wavelength uh this |
|
| 62:31 | um uh th this wavelength um as lower uh uh uh has been stretched |
|
| 62:41 | to this. So it has, lost apparent uh frequency just from moving |
|
| 62:48 | just from removing the move out. that's called NMO stretch. Are you |
|
| 62:54 | with that? So it comes just we have uh uh adjusted all the |
|
| 63:01 | times here to correct further reflection. so that uh that stretches the uh |
|
| 63:09 | , the times um at far off . So it looks like it's lost |
|
| 63:20 | . So, uh let us uh look at that, uh le let |
|
| 63:26 | make a, a smaller um uh out velocity. So the effect is |
|
| 63:31 | . So I'm gonna put here OK. So the, the effect |
|
| 63:37 | more, we didn't change the uh the flattening, it's still flat. |
|
| 63:43 | uh it is definitely lost frequency. this happens whenever we um uh correct |
|
| 63:51 | out. And what it also means when we do um uh migration, |
|
| 64:00 | are stretching uh uh uh we're, stretching the wavelength and migration as |
|
| 64:07 | And so that's normally corrected for But we don't want that. |
|
| 64:12 | we don't want to simply add up uh uh uh wavelets uh and stacking |
|
| 64:19 | uh they have different frequency content. uh if we do, we'll get |
|
| 64:25 | fuzzier stack traces than we uh really . And so uh uh when we |
|
| 64:32 | a modern migration uh techniques, they uh uh uh methods in there for |
|
| 64:40 | reducing or eliminating uh the effects of of uh stretching caused by the |
|
| 64:49 | We can talk more with uh uh that with as a show coming |
|
| 64:56 | OK. Let's look at some You saw a picture like that like |
|
| 65:01 | um uh in in the lecture. so let me uh come over |
|
| 65:09 | Ah look here here. It shows the sampling rate is not an input |
|
| 65:16 | . That's what I'm gonna do back that other sliders to make it look |
|
| 65:20 | this so that you'll see. nobody will think that that sampling rate |
|
| 65:25 | adjustable by um uh by the So I'm gonna make this to be |
|
| 65:32 | higher frequency uh uh wave. And I do that, uh you look |
|
| 65:38 | see how it changed the um uh it changes the interference between those upcoming |
|
| 65:48 | down going ways. Here we I'm ready to hit enter. |
|
| 65:56 | I didn't see any change at I know I did not see any |
|
| 66:03 | at all. Can you check that there's gonna be? So I'm |
|
| 66:11 | change it a lot. I'm gonna it back to 30 Hertz. |
|
| 66:17 | yeah, it did change, it change. OK. So here we |
|
| 66:21 | 30 Hertz wavel and you see the pattern um is here with, as |
|
| 66:26 | wave is going down, you can it's going down, this wave is |
|
| 66:30 | up when they cross the double and because uh they interfere uh constructively uh |
|
| 66:40 | and then they just pass through each like ghosts. So now I'm gonna |
|
| 66:45 | down and here the same thing with uh uh waves of opposite clarity. |
|
| 66:55 | now you can see that I have up here by uh um making the |
|
| 67:02 | the graft didn't handle itself, So I'm gonna have to go back |
|
| 67:06 | here and change this back. I'm change it to 50 Hertz. That's |
|
| 67:11 | we started with. And then I'll down. Yeah. So this one |
|
| 67:17 | so funny. So when I did changes before they simply moved some of |
|
| 67:22 | wiggles out of the picture, which not really what you want. So |
|
| 67:26 | think this is remarkable that when you two waves interfering with opposite polarity. |
|
| 67:32 | one going down and here's one going and opposite polarity obviously. And, |
|
| 67:38 | when they intersect, it looks like is happening. So the displacement here |
|
| 67:44 | zero, but the uh particle velocity not zero. So there's still a |
|
| 67:50 | of action going on inside the even though the displacement is zero. |
|
| 67:55 | sure enough, uh uh it shows as those things uh leave out the |
|
| 68:01 | side. OK. So that's maybe . Um uh But it's basically what |
|
| 68:09 | saw previously in the lecture. So let's go on to abnormal few wave |
|
| 68:16 | out. Now, this is an um which is different than um um |
|
| 68:26 | in style than what you saw So here, uh we have the |
|
| 68:31 | is in, in, in these blocks and we have three layers, |
|
| 68:35 | red layer, yellow layer and a layer. And in each layer, |
|
| 68:40 | specify the velocity with a slider. you can take your slider like |
|
| 68:45 | So let me grab that and when move it sideways and you see the |
|
| 68:50 | uh uh uh at the right it says 2610 and that's now |
|
| 68:55 | So I'm gonna let go now and bunch of things change down here. |
|
| 69:00 | uh Never mind that you can, can adjust uh uh all over the |
|
| 69:06 | uh uh the inputs in the same . And so uh I'm going to |
|
| 69:16 | I trust. Ok. Now le see what we have here. I |
|
| 69:22 | not done this for a while and select a move out case by adjusting |
|
| 69:31 | sliders and, or the thickness of . Um, let's see, where |
|
| 69:37 | we adjust the thick question? here's, here's the last thing. |
|
| 69:44 | . So can I suggest that I'm to make it uh instead of uh |
|
| 69:56 | , 1000 I'm gonna make it to um, 1500 see what happened. |
|
| 70:03 | . Wish me luck here. I didn't see anything change at |
|
| 70:24 | Yeah. Mhm. Ok. never mind that then. Um uh |
|
| 70:47 | see what uh well, what it here. Yeah. Do any of |
|
| 70:53 | curves look weird? OK. So would say these curves look weird if |
|
| 70:58 | reduce one or more velocities until the weirdness goes away. What have |
|
| 71:04 | discovered? Ok. That's a good . So let's uh um um what |
|
| 71:11 | did was we made all these uh , so let's make them slower. |
|
| 71:26 | . That doesn't look weird. Now. Oh, yes. |
|
| 71:31 | no. Says what have you Uh what we discovered is that |
|
| 71:40 | if we put for the input model which is too fast, then we |
|
| 71:46 | weirdness. So uh let me uh see if we can uh track it |
|
| 71:53 | . Why did it uh uh what was it? That was |
|
| 71:57 | So I'm gonna uh um take this one here and uh uh, increase |
|
| 72:02 | a little, a little bit. this curve here got longer, but |
|
| 72:06 | still looks. Ok. A little more. Yeah, a little bit |
|
| 72:26 | . Ah, now it's weird. little bit less. Ok. So |
|
| 72:50 | weird is going on and we don't yet what that is. So, |
|
| 72:55 | go, uh, uh, further down, look at some more |
|
| 72:59 | . Maybe we'll get some clues. top layer is different from the |
|
| 73:05 | How and why? Um oh looks me like it's uh different from the |
|
| 73:21 | . It has a SAS. It has a small uh Yeah, |
|
| 73:35 | know, look at the, at , look at the legend over |
|
| 73:42 | we have um uh three possibilities for uh in yellow and two possibilities for |
|
| 73:53 | in red and in green, but one for uh or uh the uppermost |
|
| 74:01 | color. Oh OK. So, let me, let me um go |
|
| 74:16 | here and I'm gonna increase. Now uh velocity in the green layer you |
|
| 74:24 | uh uh did you wa wa watch green curve down below um uh uh |
|
| 74:29 | here, watch it. So I'm increase the P velocity a little |
|
| 74:34 | Yeah. And you see the curve going up and the move out is |
|
| 74:48 | there. The uh the Excel recalibrated . But uh we don't, didn't |
|
| 74:55 | any of the weirdness that we saw . Oh, now we're getting some |
|
| 75:01 | . OK. OK. So, let's see here. Oh, that's |
|
| 75:11 | weird. OK. So now can see there uh uh they down here |
|
| 75:20 | uh uh some Africa, what we T three extended and T three R |
|
| 75:29 | extended in is in dashes and in uh and uh uh T three R |
|
| 75:36 | is and dots. So I'm gonna down a little bit more. So |
|
| 75:42 | the curves above the exact travel times the solid lines. the hyper hyperbolic |
|
| 75:50 | is in dots. That's this one in dot And the fourth order extension |
|
| 75:56 | in dashes. So it says is extension a better approximation than the |
|
| 76:04 | Well, maybe but not much according this. Uh It looks about the |
|
| 76:10 | uh uh in in this case. So the next question is, can |
|
| 76:17 | select a case with no non hyperbolic out? I had to select the |
|
| 76:29 | with maximum 900 about OK. So of these questions are things for you |
|
| 76:35 | play around with after class. And uh so you, you remember the |
|
| 76:46 | uh the weirdness that we had uh I think I want to leave that |
|
| 76:52 | to uh to you to think about weirdness experiment around. See where the |
|
| 77:00 | comes from. Go back to where were talking about the uh move out |
|
| 77:04 | hyperbolic move out and non hyperbolic move and see if you can uh answer |
|
| 77:10 | question of uh of where does this come from and answer all of those |
|
| 77:16 | . We'll talk about that um on um Saturday morning. So, |
|
| 77:23 | those are, those are good questions uh uh to, to leave for |
|
| 77:28 | all to figure out on your I'm gonna go. Right. Oh |
|
| 77:31 | by the way, um uh there's , there is more move out |
|
| 77:41 | more, more answers here. This shows the uh uh uh yeah, |
|
| 77:51 | input that we provide this is um the uppermost that's red. This is |
|
| 77:58 | orange and this one down here is green. And uh you can see |
|
| 78:03 | uh that for the um uh for lower two layers, there's both an |
|
| 78:10 | value which we're setting here and A an NMO value which we're calculating according |
|
| 78:18 | the previous formula. And over here are calculating what we call a to |
|
| 78:25 | back when we uh uh looked at out, we calculated AAA non higher |
|
| 78:32 | extension using a uh using a new called A to star, which we |
|
| 78:40 | from um well, that it, governed the, the far offsets and |
|
| 78:50 | completed the value of a star from near. So when we did |
|
| 78:56 | we were making some approximation. And uh uh the answers to some of |
|
| 79:04 | equations are related to those approximations. I'm gonna give you this to play |
|
| 79:11 | uh this evening and we'll talk about more when we come to class on |
|
| 79:18 | morning. So for now, uh look at the next spreadsheet. Uh |
|
| 79:27 | this is uh uh one which is uh different and um and maybe, |
|
| 79:34 | it's interesting, maybe not. Let's here at um uh at the |
|
| 79:42 | this is a depth profile of velocity this is obviously P velocity here. |
|
| 79:48 | can see that PP velocity and sheer here. And you can see that |
|
| 79:53 | a water layer here. So there's sheer velocity in the water layer. |
|
| 79:57 | so where are these velocities coming Uh It says here, it's using |
|
| 80:03 | following parameters. So this is implementing data set where some uh phd candidate |
|
| 80:11 | a lot of rocks, pnvs And then uh uh uh approximated the |
|
| 80:24 | of all those many, many measurements made in terms of uh uh the |
|
| 80:32 | of the rocks and the f uh the fluid properties in the rocks and |
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| 80:37 | the clay percentage of the rock. first, let me just change this |
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| 80:43 | uh uh this is the ferocity of surface and the surf as the porosity |
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| 80:49 | going down, the uh as the is going down, the process is |
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| 80:56 | to um uh change of course. that's gonna happen in a natural way |
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| 81:02 | the earth. And here we're trying simulate that uh in, in this |
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| 81:08 | . So I'm gonna change this from who has 30 I watch the curves |
|
| 81:14 | I hit when I hit enter, , what a big change. So |
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| 81:19 | when we have less porosity, we faster velocity if that makes sense. |
|
| 81:26 | now let's uh here is the porosity great, great depth. So let's |
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| 81:31 | say here, this porosity at great is uh only gets down to uh |
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| 81:37 | to 5% but to 10%. And can see how that affects the loss |
|
| 81:43 | the, when the, when the down here is, is higher than |
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| 81:47 | uh the density down here is gonna uh and the, the density is |
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| 81:53 | be uh higher when the price is , the density is gonna be |
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| 81:59 | And so the velocities are gonna be . Now look up here in the |
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| 82:03 | line, you see uh we have straight line here, it really should |
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| 82:06 | constant but um uh with a, a jump, but we uh ignored |
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| 82:12 | here. So, the shortcoming in , in the spreadsheet now between the |
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| 82:22 | and Greek depth, how does the velocity change? Well, it changes |
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| 82:27 | to an exponent which we're setting down . So let me just uh uh |
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| 82:32 | this here and uh see as I the uh that changes the rate of |
|
| 82:38 | and so on. So, uh uh is uh um are useful works |
|
| 82:47 | for deciding what should be a, sort of reasonable velocity for um uh |
|
| 82:57 | for sedimentary rocks. Uh um A sedimentary rocks doesn't include uh carbonate. |
|
| 83:04 | these uh uh the, these these numbers here uh uh in in |
|
| 83:10 | table are being driven by the input and the input down here. And |
|
| 83:17 | uh that summarizes a, a lot experiments in the laboratory. So, |
|
| 83:22 | this is uh a valuable um the for you to decide uh if, |
|
| 83:31 | you're looking at real data and then you're getting, seeing a certain velocity |
|
| 83:37 | uh does that make sense in terms the properties of plastic rocks in the |
|
| 83:43 | or not? You can use uh worksheet to help you decide that, |
|
| 83:49 | question. So now what, I wanna leave it at that and |
|
| 83:56 | uh uh show you on the other , the other worksheets here. This |
|
| 84:03 | uh mm this is for converter waves it's the same sort of a |
|
| 84:11 | but now with converter waves in So we're not gonna talk about that |
|
| 84:16 | anymore. Well, if you have questions about that, um you can |
|
| 84:22 | me uh later, but for now sort of running behind on time. |
|
| 84:29 | uh that has Carlos joined us No, Carlos is not here |
|
| 84:36 | Well, OK. So I think we need to do is to uh |
|
| 84:44 | I'll just tell you a AAA little about these last two worksheets uh to |
|
| 84:51 | you the truth. I'm not sure I have this r uh second r |
|
| 84:57 | worksheet in here. I think maybe one is not uh uh needed. |
|
| 85:03 | think that's redundant to the other I, I'll look at it and |
|
| 85:08 | Brown Kinga thing is uh one which will talk about. Come on. |
|
| 85:16 | , for now I'm going to, , get out of this and I'm |
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| 85:23 | to uh open up the uh lecture . And so what we're talking about |
|
| 85:44 | its complications. OK. So do see the lecture file for less than |
|
| 86:33 | ? With? Mm. Yeah. . That's, that's right. That's |
|
| 86:41 | . Yeah. OK. Now, and presentation mode there and now I'm |
|
| 87:14 | share the screen. OK. So you should be able to see |
|
| 87:26 | Mhm. Me too. Oh, we take. OK. Is that |
|
| 88:02 | ? Yeah. Yeah. Oh Let me uh step through some objectives |
|
| 88:23 | then what I wanna do is um a break and maybe by the end |
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| 88:28 | the break, Carlos will be with . OK. So the objectives of |
|
| 88:32 | particular lecture are we'll talk about multiples you probably um know something about multiples |
|
| 88:40 | maybe there's more to learn and you'll , you'll realize that we didn't talk |
|
| 88:45 | about multiples yet in this uh in course on uh raise and, and |
|
| 88:54 | you probably don't know what diff fractions , but we will, as opposed |
|
| 88:58 | refraction, we will talk about that this uh electric. You probably |
|
| 89:04 | you know what a Fra a F zone is. Uh but you probably |
|
| 89:10 | some further instruction here. And I'm gonna let you know that this |
|
| 89:17 | this name here is the name of French physicists from the 19th century, |
|
| 89:24 | F Forel. So the French have way of not pronouncing lots of uh |
|
| 89:31 | in their words. And so that's of them. And the French Al |
|
| 89:36 | also usually put the accent on the syllable. So this is not |
|
| 89:43 | it's Forell. So we talk a about resolution in our business and, |
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| 89:56 | , and I think most of the is misplaced or naive. And so |
|
| 90:02 | , uh we are gonna talk more that here and then we're gonna talk |
|
| 90:08 | uh more complications. What happens when have curved reflectors? That is |
|
| 90:13 | uh when uh uh uh the center is actually, is uh uh is |
|
| 90:20 | down to make it a dipping I suppose it's flat in the |
|
| 90:25 | And as you go to the it uh is deeper. So |
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| 90:29 | it's uh uh uh curving down. talk about that and that is the |
|
| 90:35 | of topics for uh these complications. might not get through all those in |
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| 90:41 | court. So, uh uh but first one is multiples. So, |
|
| 90:46 | I want to, uh, so start, uh, let's have a |
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| 90:51 | minute break here, come back at minutes before the hour and hopefully Carlos |
|
| 90:57 | be with us by that, by time we lost Mesa now and you |
|
| 91:08 | don't have car loans. So I Rosa must have just stepped out for |
|
| 91:13 | moment. I'm sure she'll be back . I think maybe we'll wait for |
|
| 91:18 | to come back. Send me a to say, ok. Ok. |
|
| 91:53 | , um, you'll have to follow on the recordings, make sure that |
|
| 91:58 | get the recordings posted in a good for him. Um So I still |
|
| 92:07 | wait for a few minutes for, state to get back here. |
|
| 94:47 | She is. OK. But now I'm having a hard time controlling |
|
| 95:01 | screen, stop sharing and now that gonna share it again. So, |
|
| 95:13 | , that's right. Is that, that right? The dialogue? |
|
| 95:34 | No. OK. OK. now we're OK. So the bad |
|
| 95:40 | is that Carl Carlos is not gonna able to join us this afternoon. |
|
| 95:46 | we'll just continue. So, uh first topic is multiples. So, |
|
| 95:54 | if you think about it, uh so far we've discussed only direct rivals |
|
| 95:59 | primary reflection. Uh uh We talked body waves and she wa and, |
|
| 96:05 | , and surface waves. But um uh no multiples. You can think |
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| 96:12 | the, the surface waves are a of the class or direct wave, |
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| 96:18 | also you could have a body you know, just traveling horizontally. |
|
| 96:22 | now we wanna talk about uh uh . So here's an example of uh |
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| 96:32 | uh primaries and then a surface related , you can see that uh it |
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| 96:40 | uh bounced at the second horizon all way to the surface bounced back. |
|
| 96:45 | so, by symmetry in this that's gonna be at the mid |
|
| 96:49 | isn't it? But it doesn't have be that way. Here's an |
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| 96:53 | for example of a multiple that never it back to the surface at |
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| 97:02 | And here is uh uh a another uh uh uh sy a synthetic multiple |
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| 97:10 | time coming off of the bottom And compared to this one, of |
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| 97:14 | , uh compared to this uh uh uh multiple, uh this one here |
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| 97:21 | gonna be coming in a lot, lot later, of course, because |
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| 97:25 | gonna go all the way down, the way back, all the way |
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| 97:28 | , all the way back again, gonna be coming uh uh uh I |
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| 97:33 | late, but then, you maybe there's some which bounce off of |
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| 97:38 | shallow horizon up to the surface back all the way to the target horizon |
|
| 97:43 | back up, you can see that of different possibilities have uh uh |
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| 97:50 | this would be uh a long period in which the, the time spent |
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| 97:55 | the um in the, in the and uh and second downward leg is |
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| 98:00 | is a long time. And then a short one for some reason. |
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| 98:06 | I don't know exactly why, but call these short period and long period |
|
| 98:11 | instead of short delay and long delay . Now. So, uh normally |
|
| 98:20 | we wanna do is get rid of . And so the best way to |
|
| 98:25 | , which was invented by He Dick 70 years ago. And so, |
|
| 98:30 | uh let me just walk you through here is a uh uh AAA primary |
|
| 98:37 | And you can see I've got a recorder wi uh without any frequency |
|
| 98:43 | in here and without any aude effect here, it's just uh repeated and |
|
| 98:48 | according to it looks like a hyperbolic out here. And then here is |
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| 98:53 | , a multiple. And so uh arriving earlier, let's uh go back |
|
| 98:59 | look. So this the primary is later. So vertical uh uh arrival |
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| 99:05 | this multiple is earlier, but it's moving out uh more. So |
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| 99:10 | obviously a, a slower moving with slower uh velocity. And why does |
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| 99:17 | have a slower velocity? Well, spending more of its time in the |
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| 99:22 | , slower formations which are the at top. Normally, we expect to |
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| 99:27 | uh uh uh at shallower depth, expect to find slower rocks which is |
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| 99:34 | not been compacted and consolidated so much geologic time. So these multiples are |
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| 99:41 | be spinning more of their time in shall by rocks. So that's why |
|
| 99:48 | slower. Oh Here's Carlos Carlos, made it. How nice we |
|
| 99:54 | We were not expecting you. So, for me, are you |
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| 100:02 | be with us then? For the of the afternoon? Yeah. |
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| 100:05 | professor. And I gonna try to there to watch the recording after we |
|
| 100:10 | . Yeah. Well, we killed time. Ok. Uh, hoping |
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| 100:16 | you would be able to join And we also talked about the exercise |
|
| 100:20 | which you have on your uh uh what you saw on canvas and we |
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| 100:26 | some questions and then uh we OK, we, we've got to |
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| 100:29 | up and get on with that. here is um uh uh a common |
|
| 100:35 | gather showing both of those three You see, here's the primary in |
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| 100:39 | and here's the multiple in here. see there's, well, there are |
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| 100:44 | the cartoon, they're well separated at normal incidents, but at further |
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| 100:50 | they are interfering with each other. you can see how they make for |
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| 100:55 | waveforms. In this case, the arrivals have very similar um uh frequency |
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| 101:05 | and uh uh oh and the amplitude the multiple is less than the amplitude |
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| 101:16 | the primary. Why is that? because it has uh suffered two more |
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| 101:22 | . Uh uh At least two more , it went up and it reflected |
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| 101:28 | up, reflected down, reflected up . So uh at least two |
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| 101:32 | two additional um reflections. And so , it's amplitude, it's gonna be |
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| 101:48 | . So as it drawn here, have no real interference at short |
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| 101:52 | but we have a serious inter interference longer offset. So what we're gonna |
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| 101:57 | is remove the move out according to move out of the primary. So |
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| 102:03 | the primary is flat. And so we just add these, add these |
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| 102:07 | up and um uh uh this would the stack trace here and you see |
|
| 102:13 | that um this far offset trace has additional wiggles in there, which don't |
|
| 102:19 | show up here. That's because they averaged out uh when we added all |
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| 102:24 | together, uh we just uh uh out this little complication here. So |
|
| 102:30 | don't see it anymore. So we the primary and also the multiple is |
|
| 102:38 | . So here it is uh uh we add up all these uh uh |
|
| 102:43 | block traces, uh we don't get for the multiple, but we, |
|
| 102:48 | , it gets reduced a lot because don't add together in the same way |
|
| 102:54 | these do. OK. So that like a really good idea. And |
|
| 103:01 | fact, that is our best technique removing multiples by stacking and migrating with |
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| 103:11 | uh with the velocities of the And so that's a really good |
|
| 103:15 | And that idea was had a long time ago and we've used it |
|
| 103:20 | great success for decades. But here's good idea. Let's uh move. |
|
| 103:29 | remove the move out with the move of the multiple, the, with |
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| 103:32 | velocity of the multiple that's a slower . And so now, uh uh |
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| 103:38 | you see these uh these uh uh arrivals are all now flat and the |
|
| 103:47 | primary is overcorrected. So it still interfering uh out here. Um uh |
|
| 103:54 | we did uh enhance the multiple quite bit. And you can see that |
|
| 104:00 | , this multiple doesn't show this stack doesn't show too much of the complications |
|
| 104:07 | coming from the primary primary did not eliminated, but it did get |
|
| 104:14 | Why is it um um uh why it still there? Well, uh |
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| 104:19 | see it, it is stacking together uh for the shorter offsets and then |
|
| 104:26 | has a larger amplitude to begin with the uh m. So uh if |
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| 104:34 | do this, if we um move out, if we correct from |
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| 104:40 | out using the velocities of the then we get usable stack traces, |
|
| 104:48 | can be uh uh can make useful out of this. And there are |
|
| 104:53 | uh cases where you might want to that. And so yeah, uh |
|
| 104:57 | in your course on uh science imaging in the semester, you will hear |
|
| 105:03 | about that. So um let's have little quiz. Let me start with |
|
| 105:13 | Li Lily. Uh I don't see of the above down here. So |
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| 105:18 | means that all of these are wrong for one. And so, |
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| 105:23 | uh, let's, uh, uh, let's, uh, talk |
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| 105:29 | you about simply answer number A uh, is this one true? |
|
| 105:42 | didn't hear you. Yes. So one is true. Ok. |
|
| 105:47 | uh, let me turn to Carlos. Um, uh, we're |
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| 105:50 | expecting all the others are gonna be because there's no, nothing down here |
|
| 105:56 | says all of the above. uh, uh, uh do, |
|
| 106:00 | you agree? Number one, do agree it's false? And why is |
|
| 106:03 | false? OK. This is Well, Professor, I, I |
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| 106:23 | not sure if I understand this it says, well, OK. |
|
| 106:30 | uh let me put the two parts multiple to differ from primaries because if |
|
| 106:37 | subsurface is laterally uniform, if it's one D subsurface, then the second |
|
| 106:43 | reflection is at the midpoint. Is uh is that true or false? |
|
| 106:48 | , that, that is false. , because it is the case, |
|
| 106:53 | could be true, but it's not the case just like you said. |
|
| 106:56 | . So uh Rosa uh uh over you uh um we're expecting this to |
|
| 107:01 | false. Tell me why it's why, why it's false. Um |
|
| 107:10 | the downward reflection not necessarily occurs at surface. Yeah, it could, |
|
| 107:16 | could come from an internal boundary because showed an example of that. And |
|
| 107:21 | you know, uh this is happening the time, of course. Uh |
|
| 107:25 | the, the, the ones that has the most um uh obvious appearance |
|
| 107:32 | in our data uh comes from where a strong uh internal reflection. |
|
| 107:39 | for example, at a, a an internal interface between uh sediment and |
|
| 107:46 | or between sediment and the salt somewhere the subs. OK. That's |
|
| 107:51 | So, I mean, uh that's for the reason you said. And |
|
| 107:55 | let me turn back to you, . It says uh a simple three |
|
| 108:00 | , multiple has a travel time, is about twice that of the corresponding |
|
| 108:06 | ? Is it a corresponding primary? that true or false? We're, |
|
| 108:12 | , we're looking at D and so we're expecting it's gonna be false |
|
| 108:18 | you know, we've had one So it's false. But why, |
|
| 108:23 | is it false? No, I so. Uh Yeah, it could |
|
| 108:28 | internal, right? Uh uh uh . Uh That's, that's a good |
|
| 108:33 | . Uh So uh Carlos uh over you is, could there be another |
|
| 108:37 | why this uh is FT 31, two of you? Uh Sorry, |
|
| 108:55 | what I think it could be false it's been, it's traveling with a |
|
| 108:58 | velocities. Uh So, uh uh even though the, the travel path |
|
| 109:05 | about twice, the travel time would be longer. OK. Yeah. |
|
| 109:11 | then let's go on. Um Next is uh to you Brisa multiples differ |
|
| 109:18 | primaries. Um uh Is this Uh part a or uh uh only |
|
| 109:27 | this true that multiples differ from primaries they arrived before the corresponding primary, |
|
| 109:34 | is false because not all that OK. So it, it obviously |
|
| 109:41 | is uh arrives after the corresponding primary it's done this multiple pathway stuff. |
|
| 109:48 | let me uh and then pursue you this subject. Uh In the |
|
| 109:52 | I showed you that uh the multiple indeed arriving before the primary uh at |
|
| 110:01 | offset. So uh is that consistent your answer just now? How |
|
| 110:11 | how could it just have days? . Yeah. So I uh I |
|
| 110:18 | uh I showed that as a cartoon um I, is that a reasonable |
|
| 110:24 | for me to do or, or , did I do something that's really |
|
| 110:28 | back then, you know, 10 ago? Well, I was looking |
|
| 110:35 | the slide number six and there the , I mean, the multiple arrives |
|
| 110:42 | the primary. Yeah, that's But you, you, you just |
|
| 110:45 | me that this is uh uh uh statement is false. And so, |
|
| 110:51 | on slide six, it uh uh was um a multiple arriving before a |
|
| 111:00 | . Is, is that consistent with answer here? You said this one |
|
| 111:05 | false and you were correct. I say yes, yes. But I |
|
| 111:12 | , it's not, it's not always case. Yeah, not always the |
|
| 111:16 | . Yeah. So that, that that was showed arriving early back on |
|
| 111:21 | six must have been from some other reflector, right? It, it |
|
| 111:26 | made it down to uh it, , it doesn't arrive before its corresponding |
|
| 111:32 | , it right arrived after its OK. So uh next one is |
|
| 111:38 | uh but in the previous slide, slide that you were showing when we |
|
| 111:43 | like trying to identify the velocity of slide. Yeah. Yeah, |
|
| 111:49 | you were, you were, you , you were showing that we had |
|
| 111:53 | multiple that was like earlier in time the primary, right? So that |
|
| 112:01 | doesn't correspond to the, to the reflective, let's say, right? |
|
| 112:06 | That, that multiple uh must have from some other primary reflector because it |
|
| 112:13 | before uh the primary that I OK. Yeah. OK. So |
|
| 112:24 | uh uh uh Lily is uh this uh uh this is wrong because it |
|
| 112:30 | moves out uh slower. Uh then primaries are right. Yeah. |
|
| 112:34 | you're correct. OK. So Carlos uh number C uh is that one |
|
| 112:40 | or false? The multiple in? , I wanna hear you thinking out |
|
| 112:48 | , Carla what? Iiiii I I think that that one, that |
|
| 113:00 | could be true. OK. That's . Right. That would be |
|
| 113:04 | OK. So uh bris it, this one better be false. Tell |
|
| 113:08 | why it's false. It's the, the opposite, right? The, |
|
| 113:22 | multiple usually have lower. Yeah, has lower because it has reflected at |
|
| 113:28 | twice and every time it reflects, loses. OK. That's good. |
|
| 113:35 | Number three. Now, when we the traces using the move out velocity |
|
| 113:41 | the primaries. A me, uh of these is true. So, |
|
| 113:46 | we don't have any, all of above, so we're expecting only one |
|
| 113:50 | these is gonna be true. uh Lily, let's uh take up |
|
| 113:55 | first one with you. Uh is that one true? Um That |
|
| 114:01 | false because they are usually under Right. Right. Uh uh So |
|
| 114:08 | Carlos uh for you uh Number Yeah, I would say that that |
|
| 114:15 | is also false because it's the That actually, yeah, because we're |
|
| 114:21 | around here with the arrival times, with the amplitude. So uh uh |
|
| 114:26 | , that one's not affected. So uh uh to you, Brice, |
|
| 114:32 | is it true that uh after stacking multiples are limited? I think it |
|
| 114:40 | false. They are not completely Yeah, they're reduced but they're not |
|
| 114:46 | . So you are uh you answer next one as well. So, |
|
| 114:51 | uh I would say that the multiple uh remains uh a problem in many |
|
| 115:01 | data sets. Even today, we lots of techniques much more elaborate than |
|
| 115:08 | ones that we've talked about so far . They're all useful, but none |
|
| 115:14 | them are perfect. And so uh we, we never really succeed in |
|
| 115:24 | multiples. The best we can do reduce. Them. OK. So |
|
| 115:30 | then that brings me to uh one the, the, of the popular |
|
| 115:36 | for uh I, uh I would a popular modern method for uh reducing |
|
| 115:44 | is uh the one which is used the multiple happens to uh hit |
|
| 115:51 | the uh the surface on its uh internal bouncing. So here's an example |
|
| 116:00 | a, of a marine environment where have a primary here in red. |
|
| 116:06 | we have uh uh uh surface related and blue, which happens to be |
|
| 116:14 | . You see uh it's uh uh it's bouncing at the midpoint on its |
|
| 116:22 | multiple routes and then it's arriving uh here at the receiver. But um |
|
| 116:28 | another one an asymmetric surface related multiple and uh both of them ha have |
|
| 116:38 | common that they are reflecting at the at the surface on their intermediate |
|
| 116:47 | And so this is what, so have here um at the University of |
|
| 116:51 | , a guy named uh Professor not in this department, but he's |
|
| 116:56 | the physics department. And uh uh has been AAA major component of the |
|
| 117:03 | uh that says we can uh eliminate these two bound, these two multiples |
|
| 117:12 | we record them. See right here marine environments, we have AAA cable |
|
| 117:17 | close to close to space receivers. we rec we recorded these uh intermediate |
|
| 117:24 | and then we record them again when come, uh uh uh uh back |
|
| 117:29 | to the, to the uh So, because we recorded it, |
|
| 117:34 | can use this data from uh uh , uh in internal, uh, |
|
| 117:39 | these uh shorter offsets to eliminate these . And it turns out that you |
|
| 117:45 | know, you have to, you have to know the velocities. Isn't |
|
| 117:49 | uh neat? Uh, uh, , you can eliminate these multiples or |
|
| 117:54 | least reduce them strongly without knowing what they took. Where are they about |
|
| 118:00 | the interior or uh whatever uh you what, what the velocity is. |
|
| 118:07 | You don't care whether it's uh isotropic and isotropic velocity or what because all |
|
| 118:14 | stuff is uh is included here in recording. OK. I, I |
|
| 118:25 | a question. So the asymmetric multiple be the, the symmetric multiple of |
|
| 118:33 | previous boundary. Like in this it would be the lot of symmetric |
|
| 118:40 | would be the symmetric multiple of the floor. Um No, that uh |
|
| 118:47 | it's a, this would be the primary for the sea floor, |
|
| 118:51 | one right here. Yeah, but then it's the asymmetric of the |
|
| 118:59 | layer of the second. No, a, it's a, it's an |
|
| 119:04 | multiple from this uh uh reflector down . OK. So it, she |
|
| 119:11 | down and goes down and so uh looks like it's really easy here. |
|
| 119:19 | uh uh in the ocean layer uh uniform velocity we know what the velocity |
|
| 119:24 | here. So uh regarded as a , that one is really easy. |
|
| 119:30 | it would make a good image of primary or of the sea floor using |
|
| 119:35 | arrival. But it doesn't, it's finished, it reflects off of here |
|
| 119:39 | a strong reflection coefficient going back Remember we, we decided this the |
|
| 119:46 | reflection coefficient at the sea surface is minus one. So it doesn't lose |
|
| 119:52 | energy in here. And so it back strongly and it eventually ends up |
|
| 119:59 | . And uh uh it seems to um it's always the case that we |
|
| 120:06 | always have multiples happening to arrive at the same time as the uh uh |
|
| 120:15 | as the arrivals, uh the primaries we're most interested in. Now, |
|
| 120:19 | this particular arrival, uh this asymmetric , it's gonna be arriving here at |
|
| 120:24 | uh receiver a lot later than this primary, right? Because it's spending |
|
| 120:30 | of its time up here in uh the shallow region. Um And the |
|
| 120:35 | uh the same is true for the um the symmetry multiple. It's |
|
| 120:41 | be arriving later than the prima primary . But uh we could have drawn |
|
| 120:48 | also for other um uh uh for layers. And I can tell you |
|
| 120:54 | um it seems to be a rule thumb that there's always uh uh uh |
|
| 121:00 | multiples uh arriving at the same time the primary adventure. Talk about Uh |
|
| 121:14 | wanna talk more about this particular case we have so surface related multiples and |
|
| 121:21 | algorithm requires that we record the balance . Now, of course, we |
|
| 121:27 | do that literally. But this is feasible in two D where we have |
|
| 121:32 | spaced receivers uh in uh in uh behind the uh uh directly on the |
|
| 121:41 | between the um source and the But normally in 3D, we normally |
|
| 121:48 | crossline sports uh spacing, both the and the receivers to be a lot |
|
| 121:55 | dense than uh the uh uh the , the in line spacing here in |
|
| 122:01 | D. So uh in a marine , suppose we have 10 cables stretching |
|
| 122:09 | the boat and suppose they're 10 kilometers , the sideways um separation between these |
|
| 122:22 | cables uh totally uh uh normally it's to spread the uh those 10 cables |
|
| 122:31 | behind the boat so that the cross array is about one kilometer across 10 |
|
| 122:38 | long. That that's feasible. And we have 10 um cables in |
|
| 122:45 | it means that there's space uh basically m apart. And uh uh |
|
| 122:52 | with within each cable, we have receivers maybe 25 m separated within each |
|
| 123:02 | . So you see how inherently it's much easier to have closer in line |
|
| 123:09 | of receiver than crossline spacing of receivers because uh o of the mechanics of |
|
| 123:17 | towing cables through the water. if you were doing this on |
|
| 123:23 | you could conceivably have the same crossline as, as in line spacing for |
|
| 123:30 | , you just have to put out lot of receivers and then the same |
|
| 123:35 | is true of sources. You could it uh equally spaced in both horizontal |
|
| 123:42 | . Uh have uh uh lots of and lots of source points. But |
|
| 123:46 | we don't, usually we have uh uh um oh both sources and receivers |
|
| 123:56 | a lot less closely cross line than line just because of the logistics of |
|
| 124:04 | all that equipment. Now, talking about srme it performs, it implements |
|
| 124:24 | theory as invented by the physicists a time ago for analyzing uh uh atomic |
|
| 124:36 | . And so these rays are, are uh not colliding with each |
|
| 124:41 | but they're colliding with the interfaces and off the interfaces. And so |
|
| 124:46 | the same atomic theory has been a adapted to our contact by guys |
|
| 124:53 | Weglein and his students and his And it requires a nonlinear combination of |
|
| 125:00 | various traces. So that should uh immediately make you worried about uh uh |
|
| 125:10 | the algorithm. When you're doing When you're uh uh combining traces in |
|
| 125:15 | nonlinear way, then you're combining the as well as the signal in a |
|
| 125:22 | way. And so that's a And uh uh I it turns out |
|
| 125:30 | uh uh that the uh the algorithm calculation of many terms in um in |
|
| 125:39 | series and the series converges slowly so you have to calculate many terms, |
|
| 125:46 | just one or two. So both those uh uh things are true. |
|
| 125:53 | so that, that limits the application Sr Ma. It's still a very |
|
| 125:59 | tool, but it's not a, final answer. Here's another problem which |
|
| 126:07 | has become like not so obvious. When you are um uh when you're |
|
| 126:20 | the sr algorithm, normally you start the wave equation like this. |
|
| 126:26 | we should start from the equation of which is this and you can see |
|
| 126:30 | got this additional term in here. so if that term is not included |
|
| 126:37 | where does this term comes from? comes from the variation in space with |
|
| 126:42 | to uh spatial coordinates X one X and X three of the elasticity. |
|
| 126:49 | that if, if the elastic, the elasticity uh uh uh the sty |
|
| 126:55 | tensor is uh uh variable in this , it's not such a big deal |
|
| 127:03 | that's all included in this velocity It's not included in the displacement. |
|
| 127:08 | right here, you uh you see included among the differential operators. So |
|
| 127:14 | have only one derivative of the spec X of the displacement and one with |
|
| 127:21 | to acts of the stiffness color So we will discuss the complications arising |
|
| 127:28 | this um tomorrow. Uh But uh people who apply the uh srme only |
|
| 127:38 | this term only. So it's So right there is another mistake that |
|
| 127:43 | make. So, uh that this a, a fairly big topic, |
|
| 127:48 | sure you're gonna be discussing this in uh uh data processing course. |
|
| 127:58 | uh I want to uh to leave at this. Oh Even this. |
|
| 128:09 | after we answer this one question quick surface related multiples are an important special |
|
| 128:18 | because ABC or D look all of above. So as a professional test |
|
| 128:25 | , you immediately realize that uh uh uh it might be that all of |
|
| 128:32 | are true. So uh um let's , I think it's uh Carlo's turn |
|
| 128:39 | is uh is this true, is one part A, is that |
|
| 128:44 | Uh The amplitudes are usually stronger than of internal multiples because of the large |
|
| 128:52 | in elastic properties at the free Is that true? I think it's |
|
| 128:58 | . Professor. Yeah, it is . And, and that helps make |
|
| 129:02 | an important special case. So just review, if the free surface is |
|
| 129:07 | uh in the marine environment, the coefficient at the free surface is a |
|
| 129:12 | one, nothing gets lost. If on land, then you do uh |
|
| 129:18 | have some conversion to share, but uh it's still a strong uh strong |
|
| 129:25 | . So you expect to have uh amplitudes for surface R multiples than from |
|
| 129:31 | multiples. And then we have special , uh uh attempts techniques to uh |
|
| 129:39 | deal with them. Of course, were just talking about Sr Ma. |
|
| 129:43 | that's a special technique. So uh that one is also true. Uh |
|
| 129:48 | So we got two true. So this third one better be true. |
|
| 129:54 | , what do you think? Tell why this one is true. |
|
| 130:03 | it's a bit of a bad uh . It's almost a definition uh uh |
|
| 130:08 | uh um yeah, it's, it's definition of Sr Ma technique which uh |
|
| 130:15 | the uh the recording of the surface to help reduce it. So, |
|
| 130:21 | so, so that's a no So the answer then is all, |
|
| 130:25 | of the above. There's another class uh multiples which is uh important for |
|
| 130:35 | to think about and those are called . So here we have marine environment |
|
| 130:41 | uh uh uh uh the boat uh this way, uh a string of |
|
| 130:49 | here, maybe 10 kilometers long, our source. And you can uh |
|
| 130:55 | can see that the source uh is exactly at the surface, some of |
|
| 131:00 | energy is gonna go up and then go, gonna go down and it's |
|
| 131:04 | follow along behind uh the uh uh , the primary uh just by a |
|
| 131:11 | milliseconds depending on how deep the source being told. So the depth of |
|
| 131:21 | towing is determined by the operator. if he towed it very shallow. |
|
| 131:31 | when he fires the source, it's air gun source, suppose it's only |
|
| 131:34 | m down. So then as he the source, the bubble breaks the |
|
| 131:40 | almost immediately and loses all the energy the air. So he doesn't want |
|
| 131:45 | . So he wants to tow the source a bit deeper. And |
|
| 131:51 | the deeper he tow it, the is this two way ray uh additional |
|
| 131:57 | path right here. And so that that the two way time delay of |
|
| 132:02 | ghost is gonna be uh increased the he uh it, it towed |
|
| 132:09 | And so, uh I, I tell you that uh uh there are |
|
| 132:14 | lot of operating, operating um um , uh operating considerations, but it's |
|
| 132:25 | that the, um, the source towed somewhere between five and 10 m |
|
| 132:32 | the surface. Now, that's more consider how about this, the, |
|
| 132:43 | receivers are also below the sur. so that means there's gonna be a |
|
| 132:49 | ghost coming from this two way travel right here. Um In the |
|
| 133:03 | the rec the receiverr string is at same depth as the source, but |
|
| 133:08 | not necessarily true. The operator can to, uh to draw to uh |
|
| 133:15 | keep the uh uh receivers at the depth of the source or maybe |
|
| 133:22 | more shallow or more deeper. Uh on the conditions. For example, |
|
| 133:30 | , if he, um uh if tow the receivers too shallow. And |
|
| 133:38 | there's waves on the surface, the will be uh uh rocking the receivers |
|
| 133:44 | and down as he uh drags it the water sideways and he doesn't want |
|
| 133:49 | . And so he's uh maybe gonna to uh throw it deeper. Oh |
|
| 133:55 | uh again, the deeper he toes , the longer is the time |
|
| 134:03 | Now, remember that we derived that the free surface of the marine |
|
| 134:10 | the reflection coefficient is minus one for angles of incidence. So just think |
|
| 134:17 | this at a certain frequency which we'll back to in a second, the |
|
| 134:22 | path length of the ghost is exactly wavelength. So let's back up |
|
| 134:27 | suppose this at half a wavelength up half a wavelength now huh for those |
|
| 134:37 | and those frequencies because of this minus that would exactly cancel the primary when |
|
| 134:44 | gets uh uh when it gets right to here. And you can think |
|
| 134:49 | the similar sort of thing here. it's, if it's exactly one wavelength |
|
| 134:54 | and one wavelength down, then it here and goes here. And so |
|
| 134:59 | source code also a source code, first ghost also exactly cancels the primary |
|
| 135:07 | that particular frequency corresponding to that particular . Now, in actuality, it's |
|
| 135:17 | gonna be uh uh exactly canceling but it's gonna make a deep notch |
|
| 135:23 | the frequency spectrum. It's gonna destroy of the frequencies arriving at that special |
|
| 135:36 | . And see you, you, can see back here why it's not |
|
| 135:40 | because this, uh this is not straight up and straight down. It's |
|
| 135:45 | obliquely up and obliquely down. And um amount of this angle up here |
|
| 135:51 | depends upon uh uh how far back the string. We're looking, if |
|
| 135:57 | looking at uh at a receiver uh uh maybe it's uh exactly up |
|
| 136:03 | exactly down, maybe that's a good . But for the end of the |
|
| 136:07 | , it has uh it spends a longer period here. So you make |
|
| 136:15 | notch in the spectrum at that certain . And uh obviously, if the |
|
| 136:22 | depths are deeper, the corresponding ghost is longer, that's the ghost period |
|
| 136:31 | the period where it's almost canceling the . Now, how about ocean bottom |
|
| 136:40 | me, normally in ocean bottom the uh of the water layer is |
|
| 136:46 | deep. We're not talking about five 10 m, we're talking about 1000 |
|
| 136:51 | of water depth. And so if wa if the uh if the water |
|
| 136:57 | is very deep, so that there's wavelengths of sound in the water |
|
| 137:01 | then we, we're gonna be using techniques. I mentioned one of them |
|
| 137:07 | to you uh yesterday uh last week it's called uh uh the co the |
|
| 137:14 | . It's called uh uh using four , ocean bottom sites of presiding four |
|
| 137:22 | , meaning three vector components and one component. And there is a special |
|
| 137:28 | for combining the hydrophone component with the component to exactly cancel each other |
|
| 137:35 | But of course, it's not It's uh uh it's only approximate, |
|
| 137:39 | there is an example of using a technique for ocean bottom seismic to eliminate |
|
| 137:45 | water layer multiple. And you can't that with those streamers. Uh because |
|
| 137:51 | uh the, the additional path length the water is so short. |
|
| 138:02 | So um uh let, let me back to you. Uh uh uh |
|
| 138:09 | at this question and notice here that got none of the above. So |
|
| 138:13 | all of these are correct. Um uh uh Or maybe uh maybe |
|
| 138:21 | but if we have uh more than , uh just keep in mind that |
|
| 138:27 | might, might the right answer might none of the above. So, |
|
| 138:31 | about the first and only in a streamer marine survey, assuming that the |
|
| 138:37 | and upcoming rays have the same angle incidence. Uh Does the receiver goes |
|
| 138:43 | have the same delay as the source ? I think it's, it's |
|
| 138:55 | And uh so it's false and you are correct. But why, |
|
| 138:59 | is it false because of this? are talking about the same angle of |
|
| 139:12 | and they, and they don't have same angle. Um Well, I |
|
| 139:19 | know, I kind of confused if is the this delay. This delay |
|
| 139:24 | uh depends upon the path length above uh uh above the source and above |
|
| 139:32 | receiver, not the angle. So they have the same delay if they're |
|
| 139:37 | at the same depth, the angle nothing to do with it. But |
|
| 139:42 | , the, the, the depth that uh layer of water between the |
|
| 139:48 | source and the surface and between the and the surface, that layer of |
|
| 139:53 | . If that's the same, then gonna have the same delight. |
|
| 139:58 | OK. So coming to you, , uh how about this? A |
|
| 140:05 | in the spectrum occurs at a frequency the depth of the receiver is example |
|
| 140:12 | where the depth of the receiver is to half the wavelength at that |
|
| 140:28 | Mm Yes, that one is true uh it loses uh uh uh uh |
|
| 140:37 | if the depth is one half the and the two way of travel time |
|
| 140:43 | that um surface interval is one wavelength because of the minus one in the |
|
| 140:50 | coefficient that will exactly cancel. Uh uh So uh Carlos uh we |
|
| 141:00 | a one wrong and one right. so that means that uh this is |
|
| 141:05 | also. So this one must be . Um Also, but um tell |
|
| 141:12 | why it's wrong. Yeah, because not, I mean the the |
|
| 141:23 | the recorded frequency is not going to on the under that right. Uh |
|
| 141:34 | say that again. Yeah. So, so, ok, let |
|
| 141:37 | , let me read it again. , so if the source is to |
|
| 141:42 | they receive goals has not at the . Yeah. Yeah. No. |
|
| 141:49 | , it should be false. But mean, if it is deeper they |
|
| 141:57 | would be also a lower frequency. . Professor, I'm not sure. |
|
| 142:01 | mean, for me it sounds like , it could be, I know |
|
| 142:05 | he's not right. But uh for based on what I understood, could |
|
| 142:10 | could be right. I don't Yeah. So this is a trick |
|
| 142:14 | . Mhm If the source is towed , then the source goes will be |
|
| 142:20 | lower frequency. But it's asking you the receiver goes. So the receiver |
|
| 142:25 | has its notch depending on the depth the receiver, not the depth of |
|
| 142:30 | source. Isn't that a tricky So yeah, I was really proud |
|
| 142:37 | that question because everybody gets that one . Yeah. Yeah, because |
|
| 142:45 | yeah, and everybody gets confused in the same way that Carlos got confused |
|
| 142:51 | because um it's a trick question. So I do not guarantee for the |
|
| 142:59 | exam that there won't be a trick on the exam. So you need |
|
| 143:04 | read every uh e exam question OK. So let's see here. |
|
| 143:15 | Chocolate that brings us to internal So here's an example of an internal |
|
| 143:21 | . So we can't uh uh we use MS R MA because we didn't |
|
| 143:26 | this did we, if it had all the way up to the |
|
| 143:30 | we would have recorded it and then could use Sr Ma but we |
|
| 143:36 | So it, it never made it to the surface. So this is |
|
| 143:40 | internal multiple. However, we, can do the following. We record |
|
| 143:49 | date up here. But we know we know the velocity here, we |
|
| 143:55 | uh uh calculate what the wave field have been at any lower uh |
|
| 144:01 | For example, if we know what the velocity between here and here and |
|
| 144:05 | record up here, then we can what we would have recorded here. |
|
| 144:11 | do we do that? Well, just uh follow the wave equation backwards |
|
| 144:15 | that it's what we do and all means is all it requires is we |
|
| 144:21 | uh we have to know the So that's what it says here. |
|
| 144:25 | have to know this velocity in And we also have to know the |
|
| 144:30 | uh uh all the way down to point here where it was uh w |
|
| 144:36 | the internal multiple did its downward So if we only continue down halfway |
|
| 144:44 | we think, OK, uh that's enough. That's not good enough. |
|
| 144:48 | , we got uh down will continue the way and we have to know |
|
| 144:53 | velocity to do that. And if an isotropy in there, we have |
|
| 144:57 | know about that. So you see lots of opportunities to make a mistake |
|
| 145:03 | uh uh for the uh downward for internal multiples professor. But by saying |
|
| 145:10 | to know the near surface velocity, that mean all the velocity above that |
|
| 145:17 | multiple generating horizon? Yeah. we don't need to uh uh we |
|
| 145:28 | know all the all the velocity all way from the surface where we record |
|
| 145:34 | to the interface, which made that uh melo. And so, depending |
|
| 145:42 | how deep that is, that might a real challenge. And then, |
|
| 145:45 | know, uh uh uh velocity determination really um a weak point in uh |
|
| 145:53 | most seismic processing, we can get approximately, but we can't get it |
|
| 145:58 | , especially when we realize that the velocity in the real rocks is |
|
| 146:04 | an isotropic. And so our uh uh if we don't uh understand the |
|
| 146:11 | anti velocity in this layer, then gonna only be able to do uh |
|
| 146:18 | downward propagation uh with some errors. so that's why it's much more problematic |
|
| 146:27 | handle the internal multiples. So you , uh Professor Joe might have some |
|
| 146:34 | for you on that. So, which of these statements are true? |
|
| 146:50 | , uh we don't have all the , but we do have both of |
|
| 146:53 | above. So it could be one true and one is false, one |
|
| 146:58 | false and one is true, both true. But uh uh maybe neither |
|
| 147:03 | is true. And, and in that case, uh uh we |
|
| 147:08 | up here at the bottom. So me say uh uh go to you |
|
| 147:12 | be it. How about uh uh A? Is that true? I |
|
| 147:21 | that is true. Yeah. So true. OK. Uh But we're |
|
| 147:26 | done yet. Uh um uh So le how about Lee? Is that |
|
| 147:32 | ? OK. Just a second. . Uh You think they're always |
|
| 147:49 | I I, yeah. So, yeah, so that was false. |
|
| 147:55 | that means C is false. And uh uh d uh better be |
|
| 148:01 | Uh uh um Carlos, why is false? Yeah, because we can |
|
| 148:09 | the multiples if we know the velocity the layers above. Well, uh |
|
| 148:15 | uh I'm gonna say the statement is . Um uh Because uh uh we |
|
| 148:23 | uh uh we can't eliminate them but can reduce them. Uh Why can't |
|
| 148:28 | eliminate them? Well, they don't at the surface. So we can't |
|
| 148:31 | Sr Ma. Uh But uh we reduce them if we make an estimate |
|
| 148:37 | the velocity of the subs. So I'm gonna say this one's false |
|
| 148:44 | . Now, this brings us to topic which uh I think you probably |
|
| 148:50 | not familiar with at all. Uh me uh has anybody here ever heard |
|
| 148:56 | concept of friendly multiples? He has . Yeah. Uh Yeah. So |
|
| 149:03 | can tell you that uh uh um it used to be that we all |
|
| 149:09 | about friendly multi culture. Now, of us don't. But here, |
|
| 149:14 | the situation. Uh So uh in N normally where we are exploring, |
|
| 149:21 | are many layers spaced more closely than seismic wavelength, but each one of |
|
| 149:29 | reflects some energy backwards. So uh just imagine that you are uh um |
|
| 149:37 | in a, in a target 10,000 down. And that means that in |
|
| 149:42 | overburden above that target are many thousands , of layers. I'm talking not |
|
| 149:50 | dozens, I'm talking about thousands of above your target reflector and every one |
|
| 149:59 | them is gonna reflect some energy backwards . And then this scattered wavelength is |
|
| 150:05 | be scattered downwards again by the nearby above, right. So uh uh |
|
| 150:11 | consider uh a target horizon at 10,000 , consider uh uh uh a a |
|
| 150:19 | at 500 ft reflecting some of the back up. And then at 490 |
|
| 150:25 | , there's one reflecting it back down . And so, uh it |
|
| 150:30 | it's going downwards, but it delayed that uh in a two way um |
|
| 150:37 | uh multiple and because it's got uh uh reflected twice on average, it |
|
| 150:46 | the same polarity. So uh uh , if it's uh uh uh |
|
| 150:52 | on average, it has the same . And so these two waves uh |
|
| 150:58 | the primary and the uh the one is, has this two way um |
|
| 151:05 | a delay, they have the uh same polarity. So they partially reinforce |
|
| 151:11 | other with a small, small That's why we call them friendly |
|
| 151:17 | Uh Every one of these has a amplitude, but when you have lots |
|
| 151:21 | lots of them together, they take of the energy out of the |
|
| 151:27 | And what we see on your workstation not the primary, even though uh |
|
| 151:33 | I I your boss calls it the and your colleagues call it the primary |
|
| 151:39 | not a primary because most of the in the primary has been delayed and |
|
| 151:45 | out of the primary arrival by these multiples. And they were first discussed |
|
| 151:51 | these two gentlemen, o'doherty and Anstey 1971. So let me draw you |
|
| 151:57 | picture. This picture is way over in the first place. And you |
|
| 152:03 | see it's, it's not uh uh Snell's law at any of those |
|
| 152:13 | But the simplification I don't wanna talk now is the fact that normally what |
|
| 152:18 | is that every one of these upper , you have a reflection upward and |
|
| 152:24 | down another reflection downward and making a from all the many, many layers |
|
| 152:32 | here, they all uh uh end with um um clarification down at the |
|
| 152:40 | angle with a little delay and um superposing mostly constructively and the same thing |
|
| 152:50 | on the way up. And can see how this gray is not as |
|
| 152:58 | as this one? That's my attempt show you that the amplitude is gonna |
|
| 153:02 | less here and here is the direct which comes up. And this has |
|
| 153:07 | any energy in it because most of energy has been delayed by this process |
|
| 153:14 | generating peg leg multiples. So this is gonna arrive first, but it's |
|
| 153:21 | the very beginning of your wavelet. you look on your workstation, when |
|
| 153:26 | have a, a, a AAA arriving in a strong reflection event, |
|
| 153:31 | uh only the first little toe of is the primary and the rest of |
|
| 153:36 | , all of the amplitude that you measuring for a vo and you can |
|
| 153:40 | with your eyeball and making up the peak in the uh uh in, |
|
| 153:46 | that arrival, that's all coming from propagating interference, constructive interference between all |
|
| 153:54 | multiples. So this was invented by . He, he was the real |
|
| 154:00 | here. I think o'doherty was a colleague and I don't know what ever |
|
| 154:05 | to o'doherty, but Ansty was a GE physicist uh uh when I came |
|
| 154:12 | the business. And uh frankly, thought he died 20 years ago. |
|
| 154:18 | look at this here. He is 10 years ago. He was honored |
|
| 154:24 | uh the Eage and I made it point to get myself into this picture |
|
| 154:30 | all these great geophysicists. Uh so you'll uh recognize here uh Anders Robinson |
|
| 154:37 | just died last year and this is Helbig who's still with us and uh |
|
| 154:43 | much uh active. And this is Zoki, all these famous guys. |
|
| 154:48 | so I wanted to get myself in same picture. So I went up |
|
| 154:51 | and enjoy it. So, Ansted the one, he was a great |
|
| 154:58 | of geophysics as well as a practitioner geophysics. As far as I know |
|
| 155:03 | still alive, retired. Now, is not retired. Helbig is still |
|
| 155:09 | , but I think Anstey is not juices anymore. I think he's uh |
|
| 155:14 | his garden and I always OK in . So thi this description that I |
|
| 155:25 | gave here, that is sort of very theory explanation, but the effect |
|
| 155:31 | better described by wave theory using tools we've already uh assembled uh and |
|
| 155:38 | starts from the equation of motion. we showed this just a little bit |
|
| 155:43 | the equation of motion says on the that the acceleration of a particle is |
|
| 155:48 | to a wave equation uh uh term . And an additional term here. |
|
| 155:53 | you can see that since there's layers , uh uh we're gonna have a |
|
| 156:01 | variation of um uh of elasticity. consider uh uh uh we do a |
|
| 156:10 | over J equals 123. How do know that? Because we have J |
|
| 156:14 | and J up here. So repeated means that uh repeated index means that |
|
| 156:19 | summing. But for the, the J equals three term, uh this |
|
| 156:24 | be a derivative of the, of stiffness tensor with respect to depth. |
|
| 156:29 | that's exactly the layering that we just . So we will talk in lesson |
|
| 156:35 | about how this effect is a better uh than uh the ray theory explanation |
|
| 156:45 | I just gave before we can still them um uh friendly multiples. But |
|
| 156:51 | since it's uh since the wave I , and since the wave doesn't necessarily |
|
| 157:01 | a high frequency compared to the uh thickness, we really don't wanna call |
|
| 157:08 | . Uh We don't wanna um um this in terms of wave theory, |
|
| 157:15 | we wanna drop that high frequency approximation talk about it in terms of wave |
|
| 157:21 | , which we'll do in, in on. So here you can actually |
|
| 157:29 | it. So these are the downgoing arrivals in A VSP. So normally |
|
| 157:34 | uh no, normally when you look A V SS P, you are |
|
| 157:37 | at the reflection arrival. But of , the, the VSP tool is |
|
| 157:42 | the downgoing arrival as well. And we ha have here four traces vertically |
|
| 157:48 | four traces uh vertical. Uh And are the verti vertical components and you |
|
| 157:54 | see it in the shallow trains, are lots of um of uh events |
|
| 158:01 | down, all of these are going . And so uh uh at deeper |
|
| 158:08 | . Uh you, you see there fewer of them. And furthermore, |
|
| 158:11 | , we've lost high frequency and that further down and we've lost a lot |
|
| 158:17 | frequency by down at 3.5 seconds, seconds. Uh So these are |
|
| 158:24 | uh uh actually, so some of might be going up, but many |
|
| 158:27 | these are going down and they, , uh, they smear together and |
|
| 158:41 | and each of them has its own delay. We call that a peg |
|
| 158:46 | delay because it's a uh such a part of the total travel time is |
|
| 158:53 | that uh multiple section segment there. we called those peg leg multiples, |
|
| 159:03 | leg delays. And of course, even this is not uh uh you |
|
| 159:09 | the uh the uh loss of high here that uh is best caused called |
|
| 159:16 | apparent loss of high frequency because most the high frequencies are not lost due |
|
| 159:23 | attenuation converting the elastic energy into No, they're caused instead by this |
|
| 159:31 | or all these little wavelets are superposing each other with small delays, uh |
|
| 159:37 | out the wavelength, uh whether uh loss of uh frequency uh uh is |
|
| 159:45 | a generation or real generation, it's losing the high frequency. And so |
|
| 159:51 | are the spectra for those uh uh the, the shallowest trace deeper trace |
|
| 159:57 | the de deepest trace here. And can see that all the high frequency |
|
| 160:02 | is and gets lost. So what learned from this is that what we |
|
| 160:09 | detect is really the propagating constructive superposition all the friendly multiples, we call |
|
| 160:19 | the primer really it's the friendly multiples . Now this pattern, what velocity |
|
| 160:32 | this pattern travel with it travels with we call the Backus average velocity slower |
|
| 160:38 | the ra theory average of the layer . So the primary is going down |
|
| 160:43 | back. Um uh Well, depending how thick the the rays are. |
|
| 160:49 | let me just, I dropped that uh statement about the primary or what |
|
| 160:55 | can say is that in real the velocity is given by the back |
|
| 160:59 | average of the individual layer at velocities regardless of how thick or thin the |
|
| 161:07 | are. So let me explain about back as average. Here is a |
|
| 161:14 | uh uh uh of a course bedded . How do I know it's co |
|
| 161:19 | ? It's because by uh by my , uh uh these layers are thick |
|
| 161:27 | to the seismic wavelength, right. gonna have a seismic wavelength coming up |
|
| 161:32 | . And here is the seismic wave these are successive um uh heat in |
|
| 161:38 | uh um uh in the infinite wavefront below. And you can see the |
|
| 161:44 | here is smaller than the layer thickness here. Uh You see here as |
|
| 161:49 | sonic log where we have a, slow velocity and a fast velocity uh |
|
| 161:54 | uh one for each layer. And we're gonna receive this up here. |
|
| 161:59 | Here's our transmitted wave. You can the transmitted wave has a lower |
|
| 162:05 | And we're gonna ask ourselves just what is the velocity through this |
|
| 162:12 | Well, so um uh first, do it in a civil way uh |
|
| 162:17 | ray theory. So, uh uh , we just said this, we |
|
| 162:22 | the uh uh the wavelength is shorter the layer thickness. So this is |
|
| 162:26 | legitimate to use ray theory for So here's, we're gonna define the |
|
| 162:33 | as the total thickness divided by the travel time. And then we're gonna |
|
| 162:39 | that into layers. We got layer and layer travel time. And then |
|
| 162:44 | gonna eliminate the times in terms of layer velocities here. Each time is |
|
| 162:52 | by the corresponding um uh thickness and can talk about one way travel. |
|
| 162:59 | this is a one way thickness uh divide by the local velocity and then |
|
| 163:05 | gonna invert the whole thing. It like this. And now this looks |
|
| 163:12 | an average, doesn't it? Uh it's a weighted average where the, |
|
| 163:17 | the weights are um given by the thicknesses. And what is it that |
|
| 163:23 | uh uh averaging within each layer, averaging the inverse of velocity. That's |
|
| 163:29 | what it says right here. So we have a uh awaited some divided |
|
| 163:35 | the sum of the weights. So an average. And we're gonna uh |
|
| 163:39 | do you note that with angle brackets this inside it tells what's being uh |
|
| 163:44 | average. And uh uh we'll just , um, we, we'll assume |
|
| 163:51 | uh when we have this notation, assume that the weights of the layer |
|
| 163:59 | and shone here. So this is uh I, I think that this |
|
| 164:08 | an intuitively obvious derivation uh the the ray theory velocity through a thick |
|
| 164:18 | of uh uh thick layers. So let's look at a thin bedded |
|
| 164:24 | So in the cartoon, it looks same, but you know, it's |
|
| 164:28 | uh regarded as a thin bedded sequence the infinite wave it has a wavelength |
|
| 164:36 | than uh layer thickness and the transmitter uh coming up here with AAA shorter |
|
| 164:46 | it's gonna be recorded up here. let's derive the velocity through this |
|
| 164:56 | Well, that's very complicated to So we're not gonna derive it. |
|
| 165:01 | gonna refer you to uh this is the Backus uh velocity. And you |
|
| 165:08 | what a mess it is. It's the square roots, it's got inverses |
|
| 165:12 | inverses in here. What we're averaging uh uh the inverse of the density |
|
| 165:19 | the velocity squared. And then we're um dividing all that by the uh |
|
| 165:27 | uh by the average of uh And this was first done by a |
|
| 165:32 | named Backer George Backer in 1962 is uh uh Brice is his name well |
|
| 165:45 | in Slumber Shade today. Iii I know. I think you're too |
|
| 165:54 | I think that he is retired many ago and he was working at the |
|
| 165:59 | um research center and uh I think retired before the research center moved to |
|
| 166:09 | . Anyway. Uh The reason I his name is because he has a |
|
| 166:14 | who was also a geophysicist. That was named Milo Vus. He was |
|
| 166:19 | professor at the University of Texas in . Also a very distinguished guy with |
|
| 166:25 | long uh career long history. Many uh uh including uh among his students |
|
| 166:32 | a name that you will know from at the University of Houston. Professor |
|
| 166:38 | was a, a student of Professor in the University of Texas back in |
|
| 166:43 | day. So we call this uh uh uh Milo Bacchus was uh a |
|
| 166:49 | clever guy, but he was not mathematical as brother George. This is |
|
| 166:55 | Bacchus average here that you see here was due to George. He was |
|
| 166:59 | a mathematic highly mathematical guy. Milo much more intuitive though. Now we |
|
| 167:06 | this back as averaging, but we call it Bruggemann averaging because the |
|
| 167:11 | exactly the same result was found by in 1937 you see 25 years |
|
| 167:21 | Well, the reason we don't call , the Bruggemann average is because Bruggemann |
|
| 167:27 | the very poor judgment to publish this in German in 1937. And so |
|
| 167:35 | after that, uh there was a and everybody forgot all about uh the |
|
| 167:40 | science during the war. And then , Bachus uh uh uh drive the |
|
| 167:48 | thing. And I don't think Bachus knew how to speak German, but |
|
| 167:52 | somebody who did know how to speak said, hey, uh you know |
|
| 167:56 | this, this result was derived 25 ago in Germany. And um mm |
|
| 168:04 | um nonetheless, it's, it's called back of sandwich. No, I |
|
| 168:12 | , oh Steve, I is this ? How does this one compare to |
|
| 168:20 | one that we just did? Here's one we, we just did right |
|
| 168:25 | . And so both those on the slide. So uh the, the |
|
| 168:31 | theory velocity good for coarse layers as uh so much simpler than the uh |
|
| 168:39 | wave theory velocity good for thin So where did we assume thin layers |
|
| 168:49 | , where did we assume thin That all looks so simple and |
|
| 168:55 | I I suspect that when I was this narration, you were thinking uh |
|
| 169:00 | wow, this is so obvious. is he going into this like so |
|
| 169:04 | depth? So somebody tell me where are from here in layers. Where |
|
| 169:10 | we resume high frequency? Really? you have any ideas? Oh How |
|
| 169:20 | you Carlos? Any ideas? I , it looks so obvious. It's |
|
| 169:28 | what else could it be? Where we assume high frequency? How about |
|
| 169:33 | , did you see where we assume frequency? I think it's pretty uh |
|
| 169:43 | well hidden here. So this is this is where we made the |
|
| 169:48 | When we did the uh when we the total travel time up to individual |
|
| 169:54 | time, we assume that the wave going up through uh uh the layer |
|
| 170:01 | , then up through this layer, up through the next layer and so |
|
| 170:04 | one at a time. And so how we added up all the total |
|
| 170:10 | time to uh uh make this But that's not what happens if the |
|
| 170:17 | is low compared to the the then as it comes up to the |
|
| 170:26 | one, that's OK, but it up to the second one, it's |
|
| 170:29 | , it's still inside the first right, as the leading edge of |
|
| 170:33 | wave gets into the second one coming from below, some of the wave |
|
| 170:39 | still in the um um uh in first layer. And when it gets |
|
| 170:44 | to the third layer, some of is still in the second layer and |
|
| 170:48 | of it is still in the first . So it doesn't go layer by |
|
| 170:54 | like we implied right here, it them all together, squeezes them all |
|
| 171:06 | . So that's why the back is is different than the Great theory. |
|
| 171:14 | you're entitled to ask. OK. what is the relationship between these |
|
| 171:19 | And so, uh at this this is a good time to uh |
|
| 171:23 | doing physics. And uh um I'll out to you that everything I've been |
|
| 171:29 | about in the last few minutes is , not geophysics. It's old fashioned |
|
| 171:35 | , it's classical physics, but it's physics and we're gonna stop doing |
|
| 171:40 | now and start doing geophysics. And uh the reason we do that |
|
| 171:46 | when we start doing geophysics, it's we're trying to uh make a approximation |
|
| 171:53 | assumptions so that we can simplify complicated like this into something that we can |
|
| 172:01 | understand and apply to our real So here is the Geophysical assumption we're |
|
| 172:07 | make, we're gonna assume that the among the various layers is small. |
|
| 172:14 | then OK. So here is, is uh uh uh uh here is |
|
| 172:20 | variation layer to layer uh in And why is it small? It's |
|
| 172:26 | compared with the average velocity of the stack. Uh uh This ratio is |
|
| 172:35 | average of the, of the velocity the jump, the the difference in |
|
| 172:41 | delta v in each layer compared with average for the whole layers. And |
|
| 172:48 | we're gonna square that and then we're average it all up in these uh |
|
| 172:53 | brackets. And then we're gonna end with this fairly simple expression because we're |
|
| 173:02 | to assume that this small quantity is small that we can uh use tailor |
|
| 173:09 | approximation. And we can ignore higher terms in this same um uh in |
|
| 173:17 | same ratio. So we're gonna assume the uh the fractional difference in geology |
|
| 173:28 | difference in velocity is a small number compared to one. And we're gonna |
|
| 173:34 | whatever high order terms might uh come of this. And then we can |
|
| 173:39 | this small um um uh this simple . And you notice here that this |
|
| 173:46 | always gonna be a positive number. layers are gonna be faster than others |
|
| 173:50 | some are gonna be slower. So of the delta vs are gonna be |
|
| 173:54 | and some are negative, but we're square all of them and average them |
|
| 173:59 | . And so this thing is positive of this minus sign here, the |
|
| 174:05 | wave uh velocity is shorter than uh uh less than the short wave velocity |
|
| 174:14 | this is positive. And this is minus. That means that the long |
|
| 174:18 | velocity means that the correction term is . And uh uh um the uh |
|
| 174:26 | wave velocity is shorter than the short velocity. Now, of course, |
|
| 174:35 | one, we, we can measure in, in uh uh sonic |
|
| 174:40 | But what we need in is for seismic data, we need these long |
|
| 174:44 | wavel velocities. So when we're when we use sonic logs to calculate |
|
| 174:50 | band velocities, we do need an set. We, we can't just |
|
| 174:55 | this measured sonic data and compare that a seismic. No, we need |
|
| 175:00 | make this correction that's needed for the . And we need to uh to |
|
| 175:07 | uh uh calculate, well, we , we can measure this from a |
|
| 175:11 | log and we can calculate this using sonic log because if from the sonic |
|
| 175:17 | , we can get all the interval um uh and calculate this. And |
|
| 175:26 | this correction factor is the friendly multiple that uh uh Nigel Anstey told us |
|
| 175:36 | uh 50 years ago. Now, this um comparison between um Sonics and |
|
| 175:52 | . The second I have a phone coming in, don't need to take |
|
| 175:55 | one. That's a fishing expedition. a um it's a very common thing |
|
| 176:04 | you do it. Uh look at surface seismic data, do your velocity |
|
| 176:09 | . You've got a nearby bore hole you've got a Sonic log in that |
|
| 176:14 | hole and you wanna compare the, Sonic with the se uh So uh |
|
| 176:21 | when you do that, uh you're , then the, the size and |
|
| 176:27 | are gonna be slower than the sign velocity you're expecting that you're gonna have |
|
| 176:31 | slowly changing size and velocity. So changing with depth, maybe even piecewise |
|
| 176:39 | . And then if you look at Sonic log, you're gonna see all |
|
| 176:42 | of uh rapid variations, but the variations should be on average, they |
|
| 176:48 | be faster velocities than the sonic and seismic because of this term here. |
|
| 176:56 | that's sort of a mathematical statement, there's some real world issues here. |
|
| 177:01 | uh Let's think of uh what um else could interfere with that comparison between |
|
| 177:11 | and sonic. Well, in the case, uh the uh sonic log |
|
| 177:17 | measuring uh velocities very close to the and the seismic um waves are measuring |
|
| 177:24 | uh uh well away from the that's pretty obvious. But uh uh |
|
| 177:32 | , here's one you might not have about as the drill bit is going |
|
| 177:39 | , making the borehole. It uh chews out uh the uh the |
|
| 177:45 | but maybe it damages the rock and outside the ball, who knows. |
|
| 177:55 | And it might, and furthermore, it might be um uh injecting uh |
|
| 178:05 | mud into the porosity of the uh of the borehole formation rocks. And |
|
| 178:16 | that, that could slow the waves , I can find the ways. |
|
| 178:20 | another one. It could be that rocks just are intrinsically um dispersing |
|
| 178:28 | It could be that simply because of high frequency, never mind the possibility |
|
| 178:34 | damage, never mind the bilateral He . Just because of dispersion, the |
|
| 178:42 | frequency scic waves might be traveling with velocity than the um seismic wave s |
|
| 178:50 | dispersion. Here's another one which you not have thought about if the s |
|
| 179:00 | are coming from a VSP tool. one thing. But if it, |
|
| 179:05 | if the s velocities come from, out, then that introduces the, |
|
| 179:11 | concept of anisotropy, which we don't about that yet. But you will |
|
| 179:16 | by um uh by the end of 10, so quick quiz, um |
|
| 179:31 | of these are true notice here, have all of the above. So |
|
| 179:35 | think uh it, whose turn is now? Uh forgot whose turn it |
|
| 179:40 | . I'm uh uh Carlos, I'm pick on you. Uh not to |
|
| 179:45 | number eight, which of these statements true. Individual friendly multiples usually have |
|
| 179:50 | small amplitudes since they are internal. those are the individual peg leg multiples |
|
| 179:57 | make up the friendly multiple arris They usually have very small amplitudes since |
|
| 180:02 | internal multiples. Is that true? I think it's true. Yeah, |
|
| 180:09 | true. But we're not done yet uh uh there's this possibility here. |
|
| 180:14 | brace that. How about you? number B? It says many, |
|
| 180:18 | internal multiple super pro constructively to make amplitude even though each one has a |
|
| 180:26 | small amplitude. Is that true? is true. Yeah, that's |
|
| 180:30 | OK. So uh uh now here's easy one for Lily because she knows |
|
| 180:35 | we got uh these two truths and one better be true. Tell me |
|
| 180:39 | why it's true. Says the friendly delay has a vertical velocity given approximately |
|
| 180:45 | the Backus average of the individual layer velocity. Well, uh, you |
|
| 180:50 | , that's just what we derive. I'm gonna let you off the hook |
|
| 180:53 | that one. Really? So, , yeah, that's true. |
|
| 180:56 | all of them are true. uh, that brings us to, |
|
| 181:01 | , uh, the topic of their and I think this is a good |
|
| 181:05 | for a short break. So let's here for 10 minutes and we'll be |
|
| 181:11 | at 25 after the hour. So wait just a s a minute or |
|
| 181:19 | until Brice gets back here. She . OK. So now we're ready |
|
| 181:30 | talk about the fractions, I would . Yeah. So what are D |
|
| 181:44 | ? Uh It says here whenever there's localized elastic discontinuity in the media. |
|
| 181:51 | let's think about this, see this here. So imagine that um uh |
|
| 181:57 | have just a, a wedge of and everywhere else, it's uniform. |
|
| 182:04 | so this is what we mean by localized elastic discontinuity. And so here |
|
| 182:09 | have an incoming wave from the upper . OK, sir, as it's |
|
| 182:16 | down AAA away from the, the there. Uh It's uh not affected |
|
| 182:24 | the edge at all. And so can see that all of these wave |
|
| 182:28 | that looks to me like uh um couple of, of rer rer wavelengths |
|
| 182:35 | I put together anyway, they're they're all the same here. I |
|
| 182:39 | here. Uh And that's what's incoming . Now over here where it's uh |
|
| 182:49 | , there's more of it in more waves coming in along the same direction |
|
| 182:53 | here. And those are being reflected of the flat surface here. And |
|
| 182:58 | see these waveforms are just like these form. But all this other energy |
|
| 183:06 | in is in the picture and that from those are the fractions and some |
|
| 183:13 | them are, are, are some of them are curving around |
|
| 183:17 | behind the wedge and some of them , are uh coming back at steeper |
|
| 183:23 | . See uh uh here, the angles, the, the angle of |
|
| 183:27 | here is the same as the angle incidence. But these are coming in |
|
| 183:31 | at other angles. And you can that there's a transition in the waveforms |
|
| 183:37 | . It, it's a, a complicated um transition zone and then eventually |
|
| 183:44 | the amplitude peter out same thing is down here in, in this area |
|
| 183:49 | , there's uh uh the waveforms are and then the amplitude uh um gradually |
|
| 183:56 | away. Some of them actually uh backwards and some of them are forwards |
|
| 184:04 | , but at sufficient distance uh uh the F out outboard out here, |
|
| 184:11 | they, they uh uh move, s merge these diffraction in here, |
|
| 184:18 | merge smoothly with the TED wave out . So, uh OK, let's |
|
| 184:28 | at another model. So we have AAA block of, of wood sitting |
|
| 184:34 | table. So we're gonna do, , uh, uh, a se |
|
| 184:40 | line along this way, uh, , outboard of the block. And |
|
| 184:46 | we're gonna do another one, across middle of the block you can see |
|
| 184:50 | is the trace of the, uh, across the top of the |
|
| 184:53 | and out the other side. As matter of fact, we're gonna do |
|
| 184:56 | one first. So, uh, , along the center line here, |
|
| 185:00 | are the reflections from out here, are the reflections from out here here |
|
| 185:06 | the reflections from the top of of the block. You see, |
|
| 185:10 | Of course, they're coming in but look at all these other things |
|
| 185:17 | and here and down here, those all diffraction coming from these edges here |
|
| 185:27 | here and on the other side. , uh um I, I should |
|
| 185:37 | uh uh uh these are zero offset . So it's uh just straight down |
|
| 185:43 | straight back up. So now let's at uh uh along the line he |
|
| 185:47 | here, see, and that looks uh uh straight and clean. |
|
| 185:51 | nothing like this on line B. this one comes because it's going right |
|
| 185:58 | the center line. This one is , but look here, there's something |
|
| 186:04 | on here even though uh uh the is uh uh the acquisition line is |
|
| 186:12 | from the block, some of the instead of going down and coming |
|
| 186:19 | It's most of it here. It coming down and coming back, but |
|
| 186:25 | of it is going off to the and then back into the receiver here |
|
| 186:30 | line B and that's the stuff in . So you, you see, |
|
| 186:36 | can still see the block on this right here even though uh the acquisition |
|
| 186:47 | was away from the block. how we're going to uh uh understand |
|
| 186:54 | , uh um this is one way think about it when you have a |
|
| 187:03 | plan without a discontinuity. Without it's a complete reflecting plank. That's |
|
| 187:14 | reflecting the plan here. And here have an incident wavefront and then a |
|
| 187:19 | wavefront, obviously, this wa this wavefront got uh the reflection from an |
|
| 187:26 | wave that was coming down here and reflected back in this direction, it's |
|
| 187:31 | a plane wavefront coming down here and back here uh equal angle of |
|
| 187:38 | And so, uh uh what Huygens that this is a Dutch name, |
|
| 187:44 | know, it's Huygens with the s uh yeah, single man's name |
|
| 187:52 | And he pointed out that uh that you have uh uh this reflected wavefront |
|
| 187:57 | can be considered as a superposition of coming off of every single one of |
|
| 188:04 | points, never mind that they're all together. Uh If you uh put |
|
| 188:09 | uh uh do the, do the and you'll find that if you have |
|
| 188:13 | uh diffraction from every one of these points, they, they uh superpose |
|
| 188:21 | um uh along these lines of these here which, you know, e |
|
| 188:27 | from each point and that makes up reflected weight. So, um um |
|
| 188:40 | , uh uh a little um uh on this point which of these statements |
|
| 188:46 | true and we got ABC or all just two. So let's start |
|
| 188:53 | Uh I think it's uh uh uh Breda term read beta first. Uh |
|
| 189:01 | Look at answer a uh is this ? All P diffraction are caused by |
|
| 189:08 | of P velocity in the subsurface? is, that is false, |
|
| 189:18 | And why is it false because it's about the velocity? Oh no, |
|
| 189:25 | ho ho how about if you had , had a discontinuity and density with |
|
| 189:29 | same velocity? Uh Wouldn't that make P uh uh uh A P |
|
| 189:37 | Yes. Yeah, that I, didn't say that explicitly but uh uh |
|
| 189:43 | uh I think that should be intuitively that when you have any discontinuity in |
|
| 189:49 | subs service of any of the um properties like uh uh V PV S |
|
| 189:57 | anything. And of course, an uh extensions of that, then you're |
|
| 190:02 | get diffraction. OK. So, so that one is false. And |
|
| 190:09 | so uh coming to you then how about B and elastic discontinuity acts |
|
| 190:16 | a source point activated by an infinite radiating energy in all directions with different |
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| 190:24 | and phases. Uh uh So uh that what an elastic uh discontinuity does |
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| 190:44 | ? Well, I can barely hear voice but I'm going to uh uh |
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| 190:51 | I think uh uh so uh do you have a different answer? |
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| 190:58 | think for me, for me, uh I would say that B is |
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| 191:03 | . Yeah, I, I think a good verbal description of uh the |
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| 191:08 | pictures that we just showed. uh back to you Bria A ray |
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| 191:14 | M mi misses the pinch out of se sedimentary wedge by more than a |
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| 191:21 | of a wavelength is not affected by pinch out. So let's go back |
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| 191:28 | and here we have the pinch out uh um uh uh we don't see |
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| 191:35 | wavelengths on this, we see uh wiggles in time. So there are |
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| 191:39 | distances here. Um So, uh I think um I think I did |
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| 191:46 | discuss this point. Um um But , it's true, right? |
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| 192:00 | it's uh it's not true. Uh , if you're, if you're more |
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| 192:06 | one wavelength away, you're not but uh more than uh but just |
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| 192:12 | uh uh one quarter of a wavelength , it, it is affected. |
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| 192:16 | , you know, I didn't discuss uh fully uh because of the pressures |
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| 192:22 | time. Um But uh well, could be, is uh the only |
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| 192:28 | of these, which is true uh to, to uh uh learn more |
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| 192:35 | the quantitative aspects of the fractions. gonna refer you to the, the |
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| 192:40 | by, um, uh, the and Jill D which I've referenced. |
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| 192:46 | , yeah, this book here. . Oh, uh, you, |
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| 192:50 | can, uh, let, let ask you, uh, uh, |
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| 192:55 | , Lily, do you have this ? He literally has it. |
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| 193:00 | Carlos. Do you have this No. Uh, it might be |
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| 193:06 | good idea for you to buy, can buy it, uh used on |
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| 193:10 | for maybe 20 bucks. I don't . I think you should buy |
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| 193:13 | It's a good book with lots and of stuff in it that um uh |
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| 193:18 | don't have a good time to talk here. Uh How about you? |
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| 193:22 | ? Do you have this book? , I don't have it. |
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| 193:26 | So, uh you should buy also , and uh what I'm thinking |
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| 193:30 | uh that it might be that uh will pay for it. Uh But |
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| 193:35 | , I'm not sure. Ok. that brings us to F Fornell |
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| 193:42 | So let's just suppose the reflecting plan not perfect. So we have, |
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| 193:50 | , we have a source point here we have a reflecting point here. |
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| 193:55 | If, if this is a uh perfect mirror down here, uh uh |
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| 194:01 | gonna have only reflection from this spot we call that a specular reflection. |
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| 194:08 | , if the, if the reflector not perfect, then from this point |
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| 194:17 | , you're gonna have not only this , but you're gonna have this one |
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| 194:23 | and this one here and this one coming back at all angles with all |
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| 194:29 | um amplitudes and different waveform. And uh so, uh uh uh in |
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| 194:42 | is that if the reflector is then a radiating, radiating wavefront with |
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| 194:48 | source at point X received refracted arrivals in all directions, including this one |
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| 194:56 | towards the source. Each of these is delayed according to its own path |
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| 195:03 | . So um uh we're gonna uh in particular about the uh the uh |
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| 195:11 | the delay on this one which heads back to the source before we do |
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| 195:17 | , I want to ask you Uh Is it reasonable to think that |
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| 195:21 | a, in a, a real environment like we are exploring for oil |
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| 195:27 | uh in the subsurface in Texas, we expect the reflectors to be perfect |
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| 195:33 | this? Perfect or imperfect like Yeah. So they're gonna be imperfect |
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| 195:40 | uh in some sense, they're gonna imperfect, they're gonna be the, |
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| 195:45 | , the result of, of a sedimentary process. And so, you |
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| 195:51 | , it's not gonna be perfect. has been uh uh out uh in |
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| 195:56 | subsurface polishing these reflectors down there to them ref reflect perfectly. So we |
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| 196:02 | expect that this kind of stuff back reflection back towards the source is gonna |
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| 196:09 | and every single uh uh reflecting horizon have in the subsurface in the real |
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| 196:18 | now because of this feature, it's proper to say that um uh waves |
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| 196:28 | from a point like we did earlier the course, there is an imperfect |
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| 196:33 | and uh uh some of the uh from this source are gonna come back |
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| 196:39 | the source. They're not gonna, of them are gonna reflect here |
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| 196:43 | like uh uh uh like we talked earlier, but some of them are |
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| 196:47 | come back to the source. And , um this fellow fell, uh |
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| 196:55 | defined the circular area in, in uh uh uh uh I'm showing |
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| 197:02 | here a cross section through a The circle is lying in the plane |
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| 197:06 | this, of this reflector here. It's the circular area around the secular |
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| 197:15 | reflection point A. So, if the, if it were a |
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| 197:18 | mirror, you would only get reflections to this s from this point A |
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| 197:25 | if it's imperfect, you're gonna get reflections uh uh uh uh back from |
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| 197:31 | from everywhere on this plane. But those uh um within AAA circle with |
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| 197:39 | as a semi radius. No, , the, the, the, |
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| 197:44 | , the circle has AAA radius A B and uh uh this is the |
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| 197:50 | limit of that circle. So imagine penny lying on the table here that |
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| 197:56 | see half of the penny. And uh the uh the, the radius |
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| 198:02 | B is is uh defined by Mr to include all the, the diffraction |
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| 198:10 | are delayed by less than one quarter a wavelength. So, so here |
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| 198:16 | have some unknown depth here. This the radius of the first for |
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| 198:22 | Uh And by definition, that's the limit here. So uh they're delayed |
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| 198:29 | 1/4 of a wavelength. So this uh uh 1/8 of a wavelength difference |
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| 198:35 | uh in Iraq and Pat back And so what is the length of |
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| 198:40 | uh uh uh of this radius? , why Pythagorean theorem? It's the |
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| 198:48 | of the squares of uh of uh mean the, the length of this |
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| 198:56 | ? Let me back up, uh know, the length of the uh |
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| 199:04 | the hypotenuse, the square of this is equal to the square of this |
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| 199:09 | the square of this. So that that this term here is the square |
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| 199:15 | of the square of this one minus square of this one. And using |
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| 199:20 | tailor approximation that comes to this. you do is where this thing inside |
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| 199:29 | uh square root and throw away the terms. Uh uh uh And |
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| 199:36 | you let, uh sure you don't , I take it back. I |
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| 199:39 | misremembered, there is no tailor, uh there's no tailor expansion here. |
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| 199:44 | simply square this and this minus Z cancels out this Z squared. And |
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| 199:52 | you're left with is this term Now, why did fell choose this |
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| 200:01 | ? B as the outer limit of first fell zone top going way out |
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| 200:11 | ? Th that one, the fraction there would have uh no way out |
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| 200:16 | . Fractions uh uh from there would a delay of, of uh if |
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| 200:21 | were so far that they have the of, of 11 half of a |
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| 200:26 | compared to 1/4 of a wavelength. is 1/4 of a wavelength here, |
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| 200:32 | I'm I'm saying it wrong. This 1/4 of a wavelength for the two |
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| 200:39 | uh athlete. If it were uh a a half of wavelength, instead |
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| 200:47 | would have opposite polarity and that would interfere with this one destruct destructively. |
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| 200:55 | one is sort of halfway into the so fell, designed that one to |
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| 201:00 | uh the edge of the first fernell . So I said this is a |
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| 201:07 | question for you. Uh If if in our data, if in |
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| 201:15 | data, we're getting arrivals back from of these points inside the Trell |
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| 201:22 | coming back to any point in the uh uh uh at the surface. |
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| 201:30 | it go that going to affect the ? And don't we have to uh |
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| 201:36 | that into account when we're doing a now, this is not an a |
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| 201:42 | problem because th th this is a A that uh recording point. But |
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| 201:49 | of course, we're gonna be able do and we will do shortly um |
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| 201:53 | uh same sort of thing for offset receiving points offset from source points that |
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| 202:01 | gonna bring in a bo and uh uh don't you think that all of |
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| 202:07 | non specular reflections which are happening in are gonna affect the attitude? |
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| 202:15 | maybe so, and so, um much uh you know, that sort |
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| 202:21 | depends upon how imperfect this mirror If this mirror is only slightly |
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| 202:29 | then maybe those uh uh delayed arrivals affect the aptitude very much at |
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| 202:38 | you know. Uh oh um Also uh of course, the uh these |
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| 202:47 | uh travel time considerations, not amplitude . This ray is gonna be coming |
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| 202:53 | after the primary reflection from A. is that gonna be interfering with uh |
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| 203:01 | our amplitude calculation? Well, that upon um uh the frequency and, |
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| 203:09 | the depth and everything else. uh uh the answer is that it |
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| 203:14 | , might be something we should worry , but let's not worry about it |
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| 203:19 | now. OK. Now, normally of our data is not zero a |
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| 203:27 | . So uh uh mostly we're, considering uh issues like this uh when |
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| 203:32 | have a finite source of Z And so then the first fell zone |
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| 203:37 | is gonna be that uh uh uh uh a circle here here, you |
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| 203:43 | the other half of the circle and course, it's like a penny lying |
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| 203:47 | the plane of this table. So only see the edge of it. |
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| 203:50 | uh But in two D, it like this. And uh uh so |
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| 203:56 | all the diffracted arrivals from both this and this side and constructively or semi |
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| 204:04 | um to uh the specular reflection received here offset from the source part. |
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| 204:13 | what does this imply for a VL , that's the same question as I |
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| 204:18 | before. Now, I will re you earlier, we talked about converted |
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| 204:29 | , remember what we said about converted that uh uh as rude waves |
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| 204:36 | Because when you have an incident plane incident upon uh uh uh perfect reflecting |
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| 204:46 | , you get uh uh isotropic above below, you get a reflected py |
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| 204:54 | sway, transmitted PNS. All of is coming because of the um boundary |
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| 205:01 | which were used to match the solutions both sides in the uniform area on |
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| 205:08 | sides of that inter and, and about it. Now, how about |
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| 205:18 | convert? So that reflected s way a converted way, right? In |
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| 205:28 | P outgoing asked, that's a converter . And we talked about the conversion |
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| 205:33 | for that. And I gave you exact um uh answer for the for |
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| 205:41 | um amplitude of the uh reflected converted he asked, converted. And we |
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| 205:51 | about, I gave you the exact and I also gave you the uh |
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| 205:56 | expression, which is analogous to what learn about, uh uh which is |
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| 206:03 | to the way we think about the amplitudes. It, it's in terms |
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| 206:09 | uh uh uh delta VP and delta and delta density, I gave you |
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| 206:14 | expression. And I also showed you linearized expression and I pointed out that |
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| 206:22 | normal incident, the amplitude, the says the amplitude must be zero and |
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| 206:30 | can think about it this way that um I'm gonna go back here, |
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| 206:36 | about it this way for a normally , he way it's not shaking the |
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| 206:40 | sideways at all, only vertically up and down. So there's no |
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| 206:47 | there's no conversion to share at um instance for this, for this uh |
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| 206:55 | uh for the uh way of coming the source down to here, that's |
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| 207:02 | that's moving the boundary, not only and down, but also sideways. |
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| 207:07 | that's what, that's what um creates uh reflected share weight and the transmitted |
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| 207:16 | way, but that doesn't happen at incidents. Well, now let's think |
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| 207:23 | this and I'm gonna actually show you actual data. So this is converted |
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| 207:29 | data. Um So this is the , I think this is a land |
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| 207:35 | , a land survey and it's uh got uh three component geophones uh lying |
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| 207:43 | the surface and it has uh uh an impulsive source. I think it's |
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| 207:48 | impulsive source coming from Viber size. you know, we we process the |
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| 207:54 | to make uh uh that driver size source to be effectively an impulsive |
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| 208:02 | So think of an impulsive source in land environment and think of a two |
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| 208:10 | survey. So we have all the are spread out in in two D |
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| 208:15 | this. OK. Now let's look the data, this is data from |
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| 208:20 | horizontal component of that two dlan data as you recall. So, so |
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| 208:32 | is measuring the convert way as you . Um uh we're expecting opposite polarity |
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| 208:43 | on the two sides of this common gather. So this one has had |
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| 208:51 | one had uh uh the negative offsets been multiplied by minus one. So |
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| 208:57 | should be symmetrical like a P wave ll as if we were recording that |
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| 209:04 | the um on the ver component. this is not the ver component, |
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| 209:09 | is the horizontal component. Sure. you can see that it is sort |
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| 209:18 | symmetrical. But now I want you concentrate on the normal incidents terms |
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| 209:25 | Those are strong arrivals from a normal in the converted sheer ray at all |
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| 209:38 | different in each depth. But um all of these depths have strong uh |
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| 209:46 | coming in in at uh um uh insects. The, the, the |
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| 209:54 | says this can't happen but the data that it does happen at least in |
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| 210:06 | instances says data like this is So this poses AAA severe problem to |
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| 210:16 | of our thinking about reflectivity because we should under this is an exotic data |
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| 210:24 | , right? This is converted But when you think about what's causing |
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| 210:30 | , some of these um uh some the explanations are going to involve um |
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| 210:38 | um uh P wave A L. for example, one explanation of this |
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| 210:47 | that these reflectors down here are imperfect reflectors with uh f forel zone arrivals |
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| 210:56 | back to the uh uh receiver in incidents from rays which are traveling which |
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| 211:03 | uh intersecting the uh the reflector at finite offset and some of the energy |
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| 211:12 | coming back as a Trell diffraction event back to the receiver at uh the |
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| 211:20 | offset. So if that's true, think what uh uh uh what that |
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| 211:29 | for um P wave A vo that that a good fra a good fraction |
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| 211:39 | the energy that should be reflecting like reflections like we talked about in chapter |
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| 211:49 | , that's being converted to sheer when shouldn't be. But you know that |
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| 211:54 | has to be conserved. So all this, all of this anomalous sheer |
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| 212:01 | energy converted wave energy which is showing here has to come from the other |
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| 212:09 | waves, which means the reflected P , the transmitted P wave and the |
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| 212:15 | uh uh transmitted shear wave. So would be amazed if none of this |
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| 212:21 | shear wave data didn't get taken away the upcoming reflected P wave, which |
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| 212:29 | what we're analyzing in terms of a and, and uh uh uh taking |
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| 212:34 | very seriously. And we're drilling uh expensive wells based on a vo uh |
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| 212:41 | verification of the, of the We spent a lot of money ignoring |
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| 212:48 | . Uh uh We spent a lot money in our business drilling wells following |
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| 212:54 | which says that this thing is not , but it obviously is possible |
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| 213:00 | at least in some circumstances. So need to understand this. Sometime some |
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| 213:10 | student may be here at the University Houston. Maybe elsewhere is gonna figure |
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| 213:15 | what's causing these anomalous convert sheer wave at near normal incident. And under |
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| 213:23 | circumstances and what are the implications for wave A vo all the rest of |
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| 213:29 | are doing D wave A vo uh and naively ignoring that something like this |
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| 213:35 | be happening. But I'll say it , this anomalous energy that you see |
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| 213:40 | at near uh normal incidents has to coming from the other outgoing waves. |
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| 213:48 | not the outgoing T wave? That's that should be very worth now, |
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| 213:55 | it's a wave propagation phenomena. For , there might be uh on this |
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| 214:01 | horizon, there might be uh sand sand dunes in a ripple mark |
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| 214:06 | on, on the uh preserved over a year as part of the sedimentary |
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| 214:12 | , there could be erosional effects and of the sedimentary process, those are |
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| 214:18 | wave proper. Those are geologically uh phenomena which can cause differences in wave |
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| 214:25 | propagation or solution might come from the . Maybe the instrument, the |
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| 214:32 | the recorded here recorded uh uh had uh call the signal coming from the |
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| 214:44 | uh verte component to the horizontal component come from the incoming wave, but |
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| 214:50 | came from, you know, the instrument design or maybe the wave is |
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| 214:55 | to the, to the, to ground. So if that's true, |
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| 214:59 | gonna be affecting the uh the reflected wave amplitude also. So we're gonna |
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| 215:06 | looking at that and say, here's an a vo effect. Maybe |
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| 215:10 | not an a vo effect, maybe an instrumental imperfection uh effect. So |
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| 215:15 | see how um uh important this can . Uh I, I show this |
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| 215:22 | every class I ever teach because I'm that somebody is gonna help me solve |
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| 215:27 | problem. I don't know the Well, we're almost out of |
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| 215:33 | out of time. But uh le uh as, as a matter of |
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| 215:36 | , uh we are out of My wife is waiting for me |
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| 215:41 | So I'm gonna leave this quiz for and uh uh uh I'm gonna give |
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| 215:47 | a, an extra homework assignment uh Saturday morning, tomorrow morning, nine |
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| 215:53 | , we'll start off with your questions with your um, a analysis of |
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| 215:59 | quiz is number seven. Ok. that, that's where we're gonna take |
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| 216:05 | . So, um, let's call it quits for today and then |
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| 216:10 | will, um, um, continue tomorrow morning at nine o'clock Eastern |
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