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GEOL6395 Petroleum Seismology - Dr. Zhou 3
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00:00 this quick, uh, little either right now, But, uh,
00:07 first part of today this morning. too. Review anything long chapter one
00:15 you want to, uh, we're or digesting. Are there any questions
00:21 Chapter one? I have a both open in case anybody want to ask
00:31 or were. Okay, I have question on the on the 1st 1st
00:38 on the test. Okay, I do that too. Uh, as
00:43 matter of fact, uh, we go over the way, Can go
00:48 the quiz before you receive the result reading. That's not a big
00:53 We can do that, too. , the purpose here, the whole
00:57 here we do is for learning. , so keep that in mind.
01:01 why, even though it's a long , you should be that bad.
01:05 probably don't even feel it's over. , clearly yesterday we put a little
01:11 . So we finished earlier because we a very short breaks. Right?
01:15 when you're tired, anybody feel Anybody feel need to break something,
01:19 out. You know it, Fine. The purpose is to
01:24 not toe hurry or something. So let's go over the Chris one
01:31 now. I'm just give you the answer, But keep in mind,
01:36 ? Answer is also no unique More than one way. All
01:40 answer. I'm just picking the best . Okay, but feel free to
01:45 . So here is the answer That's into Maria. Can you all
01:52 it? Are you able to see file? The Chris wanna file?
02:01 . Thank you. Yeah, So, uh, keep in
02:06 it's all recorded. So anybody you will have a record. Or
02:11 can always ask me tomorrow, next or whatever next time. No,
02:15 big deal. Well, my job help you guys. All right.
02:20 the way I say this is when given I choose force. Uh
02:28 Definition off statement you're looking for all you want to say is true.
02:34 f best. So the first one tricky. Is that question right?
02:39 first one, because it really This is my life. What I
02:43 the mathematical is a mathematical question. other words, most time they probably
02:50 true because we said available. It the ship we define When the energy
02:57 front loaded, the minimum phase energies old age is a maximum face while
03:03 . That means either from or by . How can you have minimum phase
03:09 maximum phase? So you really Are there any situations that they came
03:13 same? Okay, now the the answers tools. That's because there
03:20 exceptions. The exception is when you a spike. Why did you have
03:26 wide body? Oh, the issue is, um I have a
03:30 Spike has all the frequencies. This also tie with the uncertainty principle.
03:38 , when you have a one spike frequencies all for so which is
03:43 The Commission for Wavering. Well, require more than one frequency. Why
03:47 frequency? The spike is very Spike is extreme type of war We
03:54 once I spike. I mean just just one value. The body can
03:58 anything. Okay, last non zero be minus one plus one can be
04:03 one million Doesn't matter. We count as a spy. If you have
04:08 value in the time to use except location in their non zero value,
04:13 kind of spike okay, We cannot that. So when you have that
04:19 , he is a symmetrical on zero is also minimum face is also maximum
04:26 . It just cannot face constant in way. All right, that's the
04:32 exception. Why, that's that's kind tricky you to think about it on
04:36 question. Most times people don't get right because they don't think that
04:40 But I'm just pointed out with summarizing we learn about the relation between
04:46 space frequency space. You call that demand and frequent movement. That's why
04:53 talk about discussed yesterday about uncertainty Okay, but I don't like the
04:58 basically says about the energy spray or duration, the length off the signal
05:07 time versus the same signal infrequency. are received a call. If you
05:13 the length or duration off in I'm frequency off the same signal.
05:19 constant. We make a one The other one will be longer.
05:23 you make another one longer is shorter that's around the line principle, which
05:28 expose expos off off self to The reason to design this question.
05:33 , so that's the first one let enlarge this a little bit so you
05:37 see more in detail. I don't your view, but I'm assuming my
05:42 and your views large. Okay, we have time to cook,
05:47 Like I said, it's all way slowly. Wake up. I think
05:52 your wake up already, but your not totally 100% of functioning. You
05:56 still dreaming or something. You are recruiting? Recuperating, right. We'll
06:00 that in the morning. So this a discussion you feel feel free to
06:05 . Ok, Any questions? So don't feel rule the only way because
06:09 wait together to work as a Okay, so the number two you
06:15 , the number two is about the , which is our definition about
06:20 Okay, By the way, this concept, what we defined is divided
06:26 the high frequency by downstairs, low . So you're going to raise
06:32 and then you talk about the power to the index the power exponents off
06:38 . That's for the octave. So you divide, uh 5 50 by
06:45 , you got that 10 developed by also 10. So the ratio is
06:50 same but the racial saying we call us the same bandwidth. Okay.
06:59 of course, I'll just give you range of frequency, which, in
07:03 way implies is what we call the frequency. In other words, 5
07:10 . In that case, the first five is the low Connor fifties
07:14 calmer. When we say corner, say, basically, is the minimal
07:17 off this signal minimum or maximum range the signal. Not that the whole
07:23 if you think about the future you full values than the minimum frequency is
07:29 is not a minimum of the signal below the full, below the low
07:34 , the signal strength already decay. it's not a full signal anymore if
07:40 think about travels on the ship. in reality, we never have a
07:45 travel. So it's inter interpretation. the experts or the Geo finishes archaeologist
07:51 decide what is the lowest acceptable frequency . So you get idea.
08:01 third one, exploration to official cover off, but not all good condition
08:06 zit for because we cover everything most operators will, uh, are will
08:14 both amplitude on the face. But true if you if you change your
08:20 on, uh uh, because different the face was changed. I can
08:28 ask the question Too extreme about on of number number four. Okay,
08:31 can talk about question too extreme. about other exceptions? Other situation.
08:38 toe agency, but you don't alter face. Other situations? Yes,
08:46 are. Exception. This is were to the first one. Toe will
08:49 one if you have a single So you have you have a monochromatic
08:56 . Like the one show yesterday. coastline way. A single frequency If
09:00 single frequency goes forever. Never but a single frequency. Now,
09:05 you'll just constantly strategy squeeze aptitudes. , then you do not changing
09:13 Why is that? Because it's a frequency. There's not crossing energy across
09:18 frequencies. So why you changed um at produce off the wiggle off
09:24 scoreline waves their face Don't change because didn't change the time. Zero So
09:30 distance from time zero to the near . Still the same same business.
09:37 that's why exception. This also tells why we often do. I am
09:44 on the face operations after. Decompose in tow. Decomposition in tow.
09:51 frequency one frequency of time. if you do always one frequency,
09:58 can easily, uh, Corlett face with time shift. Because the single
10:05 is the relation between where time. ? Yes. And where is your
10:10 or single frequency? Very easy. when I have a model and frequency
10:14 messed up, which is why we the issue about the complex trees near
10:18 end of chapter one. Now, we study this? Well, if
10:24 going to deal with anything in f uh, space, for example.
10:32 , okay. Migration at Kay Ah, those issues be involved and
10:39 faces often, I concept, Like said, very much underutilized. I
10:46 a former colleague here. His name Chris Liner. We're a famous
10:50 Hey, move back toe Arkansas. , why I came back from
10:57 Flunkies attack. Hey, Supervised PhD . Ah, Mr Lee.
11:06 Actually, I was theme master adviser that students in the master with me
11:13 u k g with the cruise liner on, do his PhD. He
11:17 a pattern where the film was pattern using face toe help solving problems for
11:25 . Eso is why area? Very other used, especially for attributes.
11:29 think many of you guys geologists I you wanna emphasizing on issues you can
11:35 about attributes for integrators. And so things you need to know the usual
11:40 What is the fifth batch for Face me. Okay, so the
11:45 one, number five Petroleum reservoirs in typically related toe on conformity is wrong
11:52 community is something about original civilisational environment for covenants is mostly about after the
12:01 . You know, there are genetics because everything's in order. All the
12:05 of our properties alter. Mostly. care about our communities for plastics,
12:13 , you know, six boundary. know, those faces boundary. But
12:18 the continent's faces already different from the de positional issues, the that's That's
12:26 for that question again, you know open for discussion. You can write
12:31 you feel. You know your reason Maria can be convinced to give you
12:36 partial credit. Even you're wrong. okay. You know, I understand
12:42 cannot force you to get give it the falls the battery answers, but
12:46 often answers the gray area between. , I just for the convenience off
12:52 test. This is purpose here just review the concept. The next one
12:58 resolution measures how small a feature can detected. The front, uh,
13:03 said yes here because it's just another of saying the same thing. Why
13:07 this topic about resolution? I show three. There are many,
13:12 many, many ways to define As long you said something. The
13:16 direction. Reasonably. You know, way said That's okay. Seven,
13:23 the time shift Study The time shift you move the trace whole trees without
13:29 . Just our down time shift. , this morning at the end of
13:34 morning, we talked about we talked the static ship, uh, for
13:39 near surface correction. So if you shift a regulate well, that changes
13:45 Beltran Aptitude Spectrum. Okay, it well, if you study the shifting
13:53 privilege, you are not changing the special because your energy didn't change.
14:00 when you're shifting, you change Zero The times use order one time
14:06 . Alter your face by trial. be will be will be altered.
14:10 why. Circles. You see that you have a wiggle, for example
14:17 record wave, you just move. without anything. Just move shifting.
14:21 up dance You have the constant amplitude . You didn't change anything special
14:28 I I would slide to show you privilege. The special. It looks
14:34 a triangle. Which one slide? that on. Uh, so that's
14:39 trying Will never change. But if shifting in time, your relative,
14:45 know, we go to the time changes so your face special will
14:51 So face, that's what. Tired where? Time zero? Yes,
14:56 both monochromatic away, even for Because every individual frequency coming that
15:04 So every frequency company How far the near I speak to the time zero
15:09 the face angle. Okay, last . I'm raid the radiation pattern off
15:17 gone. Array becomes smaller at the frequency. This reversed that slide.
15:22 show four lower hemispherical projection off Aragona so ankle will lower lower frequency there
15:30 . The reason there smothers the the lower frequency, the longer,
15:36 , wavelength period off the energy because longer, uh, equivalents. So
15:45 air guns have more chance of overlapping each other, so they're kind of
15:49 smaller, more filtering effect off each . They're kind of a cause or
15:55 size each so they recover each Which is also the reason why it's
16:01 to go toe higher. Uh, . Because when the source relation pattern
16:07 the, uh, now, I the word omni. Directional on the
16:13 is the words to say there's their around angle, no change environment.
16:19 is very hard. The only way can think to do that for the
16:24 to inventing figure array of South air , more air guns, more tender
16:30 guns. Well, that will be more expensive logistically in control.
16:38 so I can go back here, any more questions later on in order
16:41 you. But I'm goingto go through compare contrast the differences. Okay,
16:47 a minimum face relate versus maximum face . I'm just saying, Why is
16:54 front loaded for minimal face? but I'm trying to elaborate a reason
17:01 . Why? The front of the . It's a minimum difference between the
17:07 off its frequency component. I don't don't know what you understand. What
17:09 mean, why not have a baby , you can imagine is a superposition
17:15 many individual individual frequencies. They step the top of each other. So
17:21 frequency has his own well that he face time zero. Okay, what
17:28 saying the minimum faces among those of components. Their difference between them
17:35 What a difference. Different minimize We difference measured by the distance to the
17:41 . Zero. So there, for close to the peak. The time
17:46 are very similar between them. Which those frequencies, their peak, are
17:52 toe on top of each other. you face, which is why they're
17:59 loading. Because from means measure from zero, right, So New York
18:03 zero all the frequency, all Although they're different wavelengths. But they're
18:07 laughing, so they have all They have all constructive interference together.
18:15 just one detail. I just want review here one more time on the
18:20 face is other way are on, their frequency difference is maximized. So
18:25 maximum differences, That's why they don't at all. They cancel each other
18:30 the very end. That's why they're loaded. Okay, Now the second
18:39 face off a model connect wave on face of a village. I'm just
18:43 recording from the slides. Face of monochromatic way. A single frequency depends
18:48 the interval between times zero on there speak. Um, use the words
18:53 . I mean, the distance. mean the distance. Right?
18:58 on the letter is a ship. just copy from my from my
19:04 Last one Face special in instantaneous face one's a little bit tricky in the
19:10 both are simple. But if you for difference, you have to think
19:14 that difference. A face that far the The variable is frequency is
19:21 Frequency vary with frequency. In instantaneous face the function. The viable
19:29 time dysfunctional Time. They both talked face but they're different space face actually
19:37 with the, you know, You know one of her's to her's
19:41 so on but time The other one one. When you see these words
19:48 , which means is functional time. have instantaneous face You can have instant
19:56 use amputee use the instantaneous. Anfield also called envelope. Just two names
20:03 the same thing. All right, my quick review of the Chris
20:11 Any question of discussion, Those I add a happy I was still continue
20:19 dream, right? It's all you know, just we're just doing
20:25 . Wake up and you can come here again if you something over to
20:29 in the name of time. Let's stop this one. Move on.
20:33 , I'll stop showing this one. go toe the Latin. Thank
20:42 So let me get this, give myself stop correctly. My 10
20:48 . E better using pain. Better the paint color properly. I don't
20:53 which way. So today we're gonna basics, thoughts, morning. Better
21:00 , Which is different Way to say . Our processing. Okay, so
21:03 three sections as we as we see the slides. Let me choose my
21:07 . Right? Uh, my Not a good anymore. Okay,
21:15 the last one, the third we were short. So we spend
21:19 most time, probably on 2.2, we talk about started with the,
21:25 no, a normal world. So, uh, I'm going
21:33 I'm going toe review some issue uh, this morning on the first
21:39 Our, uh there are quality I repeat again, you can always
21:47 with any questions. Feel free. . Eso remember yesterday we talked about
21:53 five factors. You said the first single North ratio resolution on coverage and
22:01 on. Okay, so excuse Go ahead. Your screen Because I
22:06 see your screen. Okay. I forgot to sure, I will
22:14 lecturing. So that's why I need help young people like Maria.
22:19 One second. Let me make sure other one. Because I have I
22:24 a chapter one open Also simultaneously. , this time got right. Thank
22:33 . Thank you. You saved Okay. Eso today we talk about
22:42 things. Morning about 33 sections. like I said, but you didn't
22:48 it. They focused on the second conclusion College in north separation.
22:54 the last one. We're sure as we will are take a break after
23:02 year. About one hour. we started a thirties you can expect
23:05 the first grade. Uh, but 35 minutes from now. Okay,
23:12 we talk about the quality issues and it's all these efforts. It
23:17 towards improved SLR resolution. So? pre processing prefrontal process refer toa preparation
23:27 . Okay, before the main processing , the mean one can be very
23:31 . For example, the meanwhile usually be migration. Okay, imagine or
23:36 be, uh, a bill or be some kind of Ah, special
23:43 . Like scent in the water. we got to determine what is
23:49 Signal that we want toe enhance. wasn't me noise that will harm the
23:57 . So we try to suppress as as we can. We have considering
24:02 on the cost. Mexico's inefficient. , so we often have to
24:10 you see? Okay, For under give example detecting errors because data
24:16 in, people said, if you the if you can't, you see
24:21 right. Low data into your If your software system you already done
24:26 than half the job, So pre a big part of this is a
24:31 is very qc about what's going on they all have. Have you cannot
24:35 anything they tell you until you check . There are lots of things can
24:40 wrong between the field that are coming your shop. People can miss label
24:45 , for example on also were often situations in the field are lost.
24:51 no record. Okay, I can you one example. One time I
24:56 processing were speaking assets. This is best means the vertical sesame profile.
25:03 receivers are cemented into the wall. , On three components I spend.
25:13 time I found issue there eventually realized happened. There's a deal on
25:18 upside down. So the Z is down. So your your ex wife
25:25 like this. So you are the is just messed up. So nobody
25:30 you this, So you have to out Otherwise there's something wrong, something
25:34 . But what's wrong? Right? you have to go out of the
25:38 basically looking for consistency, things that sense or not sorting data. And
25:44 doing this thing and so on. I'm not going to go. Everyone
25:47 in d. P. I just to show you a typical task.
25:51 have, you know, we call up in the final problem on do
25:57 know, quantified issues? Document. if down those if you finish those
26:02 loading it up properly, everything makes . You don't most job already the
26:07 of the metro easy. Okay. example of offshore, for example.
26:14 about sauce? Which were location time era GPS. Time can
26:19 comes down, Can be wrong. flag reversals. Polarity reversal. Incorrect
26:27 . We talk about definition, the , you know, data coming,
26:31 . Somebody label them that. Our . Right. You know, as
26:34 know, that our country was wrong . Human error, Right? Most
26:37 human error. I recall a long ago I got the wrong grades.
26:42 called in register office. Oh, is coming. The era. I
26:46 no data entry. Don't Don't blame . Okay? Don't change your age
26:51 be No, I mean, it be human era. So those it
26:56 right? And shifting. Array You know, you name it a
27:00 of issues, so but let's look concept. That's the concept. Now
27:06 knowledge about time cereals signal serious. we often into your physics and
27:13 We're looking through the data aside. function showing by the three impressions.
27:20 , So before we talk any you can look at the figure The
27:24 says the following the left F t , let me get my pain
27:31 Oh, this time consuming will pay option. Okay, Pan,
27:35 letter will be fine. Faster. can see I'm hesitant, person.
27:40 always change your mind. Okay, about it, Right? So this
27:45 your source. This is your fire . Uh, shot. You have
27:50 things, maybe record, maybe. else you can imagine, this signal
27:56 through the geology from talk going So service bouncing back on getting a
28:02 . So this is our model of going on. We say our record
28:07 trace is I, uh, result this source Echo bounced back from the
28:16 strata class sticks, whatever sensed on bouncing back. This is what we
28:24 . So this is very simply money , But still, there's some signs
28:28 . They're physics here. This is actually works most time believing on
28:33 because we've got a very low So everything and simplify on we might
28:37 a simpler geology. Everything. Layer is a simple kind of one dimensional
28:43 wiring model. So to express this thing into mathematical forms these are two
28:50 here, the first one in time in time in time fashion time.
28:55 signal wise function as a frequency is same signal We just say to two
29:00 wheels. So f here's our This is that here the sauce relate
29:06 X is our geology then X here only one dimensional. It's like yesterday
29:12 a fishbone. I finished. I'm . I still using my pants.
29:18 point is nice, but I can can I can draw things simultaneously.
29:24 start using pain. E can draw . But of course, as a
29:29 yesterday, I can quickly make a . I'm good in, like a
29:36 . Okay. The X here basically a one d function. Uh,
29:41 Susie, but we can call that the time. Okay. At a
29:45 or time. So I can t minus those regular activities. Basically,
29:49 marks the boundary. If you go solved sentiments or hard sentiments, you
29:55 party, the harder one South one be negative. So I call i
30:00 was a fish boom function It's called function. Okay, well, first
30:06 , a function of time or Rosie the US. So when you have
30:11 one, I'm sorry. Using X now, Ex Fine. So this
30:15 the reflectivity here. This is the , it that an oyster.
30:23 So this articulation and our results, here is record. This is what
30:27 see here on the same expression can showing transforming toe frequency domain using Fourier
30:36 , you get the same thing. Capital B is the Fourier transform.
30:40 function, lower cases, the So we just get used to the
30:45 notation first. All right. Very . And then you can start doing
30:52 . This is why we can You talk about this one. I'm starting
30:56 something very conceptually. It's a relatively concept. The conceptual match fielder or
31:05 the future Magic Futre is a concept people using toe clean up the
31:13 Okay, so if you look, back to our problem here in order
31:20 go from G to recover the in other words, recover this X
31:26 , which is a fishbone passion. need to somehow kind of squeeze
31:29 uh this is This is this is is too broad. You want to
31:33 out sweet. Okay. And, , they are theory shorts that if
31:43 can if you can find out the time reversal off the privilege right now
31:51 like this. It's kind of time . Like I'm tired result here.
32:00 , Okay. Kind of time. off that one. Basically, you
32:06 all the coherence off the coherence off off. The really? Because the
32:12 . If you correct those two, minimizing the space for increased resolution.
32:19 are increasing solution. Okay, let give you example. This,
32:23 this is a good thing about car , okay? Stop. Mhm.
32:31 can show you one example later We can fly back to examples.
32:40 this case, we show you a . Okay, we'll have a viable
32:47 pumping the ground website, sending a usually from low frequency toe high frequency
32:54 this. There are many different way . Functional design, Very normal or
32:59 high frequency are very low frequency. so on, so forth.
33:02 everyone, this is a four different of off brand with range everyone all
33:08 called sweep I sweep just means you changing frequency. And so this is
33:14 is we're becoming very long. most times certainly record, you
33:20 old days. It's only about, , maybe six seconds, because too
33:26 , too deep we don't care. a sweet can be very long,
33:30 it can be 15 seconds long. sweet they can be very, very
33:35 . 15 seconds. 10 seconds. , very long. So sweet is
33:40 longer than your record. However, magic thing here, when you're doing
33:46 correlation auto coherence. I used the the correlation cars interchangeable because auto currents
33:55 correlation coalition is normalized Colorations. if you maximizing Mac, everyone becomes
34:04 becomes manners. Why, that's all cooperation. Okay, but if you
34:10 all the correlations, in other you have the same function correcting
34:15 You get very much like we call , uh, arms. Uh,
34:20 almost like, you know, future record lately, this man is
34:25 very narrow, you know, like milliseconds 1000.1 seconds for the central
34:32 So this example that when you correlate convo conclusion college and at the same
34:40 just reverse the other you will be to squeeze the resolution much higher.
34:47 is concept off behind why we do the future. Okay. I'll just
34:53 you a little example first before we back. So let me switch
34:57 This is a good thing about having PPT. I mean of this
35:03 So let me read this one. if you can follow the reading.
35:06 don't like the impacts, but let's say if you can follow up my
35:10 . Islam going back toe. So in the field of telecommunication,
35:17 massive future is obtained by correlating on riblet with the time serious to detect
35:26 presence off the Waverley. So the is that you give me wiggles.
35:31 want to detecting to you contain this . Way. So I do
35:35 We have a high correlation is that have this big break. Okay,
35:39 is when you do that. This this is the same thing as you
35:43 Equivalent toe Come all with the times with the conjugating time reverse version of
35:50 useful to your college. What it is complex but most times not
35:54 So you don't worry about conjugating. the time reversed the reason with all
35:59 ways because Time River if you if come out to thing toe riveted
36:07 involved in time reverse. That's the thing as Correlation. You will see
36:12 a moment we'll talk about in section . We talk about computer conclusion.
36:16 coalition Convolution is the same kind of , except one of them's time
36:24 Time of race means the first point last point last point. First
36:30 Okay, so this is the reason don't like them tax years because they
36:35 the operation with the concept. The is through correlation, all the
36:42 You can detect the signal. You make the whole thing of high
36:46 That's the concept. But they call a magic filter. The reason is
36:52 we don't know what the sources we we don't know what's the What's the
36:55 day. So we're guessing. So take the whole thing in Data says
36:59 do also can reverse understood why what ? That's the reason. But
37:07 trying maximizing the signal enhance the Okay, a little confusing here,
37:16 you can see the idea so I'm to show you some examples off natural
37:24 . Okay. This is a recall showed you yesterday. The last
37:28 The one here. This is the she just remember. I talked about
37:33 GC. I first make the trace infuse. And then I'm making every
37:41 of similar. I'm actually enhance the E g c Basically. Okay,
37:46 great. But if I enlarge my box area red box area put actress
37:54 . Okay, you You see why don't see the same thing anymore?
37:58 that stretch the time, right. this we go here, This one
38:03 . You see, Samos that we there. All right, so this
38:09 same way you can see this is I got kind of a front
38:13 so it's kind of like the sort minimal face working. Okay, But
38:21 don't like the minimum face one because interpreter. I like to change this
38:25 tow. Symmetrical zero face with Okay, so I simply found a
38:32 future matching those too. I can I find a relation between these
38:37 You can think this also take a development order. Okay. I want
38:44 to take a one development other than that one toe the same thing.
38:49 I I find it much future between two guys. Basically basically a ratio
38:55 is a function. Okay, I that function. Come all with the
38:58 trace. So what I get everyone becomes a musical. Were
39:08 It's not about detail. Mathematics. just want to focus on the concept
39:13 now, which is the thing You another detail because someone else can develop
39:18 . You just use it there. . No reason. For most of
39:22 toe Togo down. Castillo, the . You can match whatever you want
39:28 match or you can using the concept detecting signal extracting signal. The beauty
39:34 this process is the noise in The noise term here, the end
39:40 because noise random. So this effect what kind of remove the noise So
39:47 has a very clean up clean in effect, cleaning up. Is
39:52 okay? Let's go back to our figure. Yesterday we talked about the
39:58 talk about right? Yes. So we do this? Well, once
40:04 found out the the bill points trace year being you have a city CMP
40:11 her full that you could do the one normal move up the purpose for
40:19 are several several objectives. First objective to obtaining, uh, higher signal
40:29 because you're stacking, you move out , then you can see the alignment
40:34 reflections. Whereas the other unwanted for example, multiples, uh,
40:41 waves will not be on the same . So he's taking the models
40:46 That's one purpose. So I can a post data data sets for emerging
40:52 common purposes also to divide the so the second velocity. Because the problem
41:00 geological use off geophysical data if you to know the right depth right
41:07 So if you only see the time , there's no control where they are
41:11 depth. So you got to find lasting. So the two million purpose
41:18 Nemo is the preparation for the snr signal reflections and to survive in the
41:25 velocity. So let's do that. some example of being a large Be
41:33 . You can see the point. , so there's the inside issue on
41:39 fourth issue for being size is determined reality. Yesterday someone asked me about
41:45 off data points. This is kind a point or head comes Uh
41:53 Before the simply number off with points being, we don't want it for
42:00 be too low. Okay, even in two d, you
42:05 Want to be less than 10? example, in three D, this
42:08 called three D two D means align d means the area. Okay,
42:13 know, this is three D three . You know what? I have
42:16 than, say, 30 or You wanted. The more the
42:20 of course, but more expensive, ? So that's a typical case.
42:26 way mentioned about those spray. So the CMP, if you have a
42:32 area, the being older reflection rates be confident on the same location.
42:39 that's great is the central focus, you cannot guarantee is always flat so
42:45 they're keeping you could have dp You spray, you have this spray.
42:50 is another reason why I say about about technology. Uh, some people
42:54 this red flashing point of dispersal. don't know. People credit too many
43:00 simply means the spray off refreshing point the keeping location. So that spray
43:06 zero here on but nausea here. regardless, if you have a CMP
43:12 sprays minimized compared with common shot better common syndicator, you can even
43:18 you know, impression. But more that. This is assuming count
43:21 you know, leaner leader of But that's not always case anyway.
43:27 give you a concept. Eso Let's through the process. The left
43:33 I'm showing the model the right I'm sure you the example.
43:37 Okay, so the left side a here, be here. I show
43:42 only one, uh, half off . I show you the right side
43:48 data here and sees both sides. a is that model space B is
43:55 terra space. Well, as a space, that means across action Cross
44:00 you hear, you have a receiver shot. So, assuming constant velocity
44:04 simple reflector here, your reflection re will go down bouncing up,
44:12 That's that's your this kind of model because it's a model is in the
44:16 to man. But for this how you'll see here arrival energy will
44:21 like this. This is refreshing. is refreshing. This is also a
44:26 , maybe deeper factors that they're two , right? You also have the
44:31 rivals. You also have ah, way. So there are the energy
44:36 . I'm showing for here only one . But it's looking a real example
44:40 to side. So here is the level is for survival. Okay,
44:47 rival means the P baby coming Typically they are there any ways of
44:53 race off some of those refreshes? , we call them refreshing, called
44:59 survival Anyway, then you have This one's refreshing reflection because geometry most
45:06 looks like because it's a hyperbolic because the because the roughly constant velocity they
45:14 be Exactly You have a body. this is refreshing. This is all
45:18 are reflections All these reflections However, of those who are flashes might not
45:24 primary fleshing Some of us may be reflections bouncing more than once will be
45:29 similar In there we can move Move out means how much the varying
45:35 the officer. Okay, eso move means how much body was offset.
45:42 those those other things. Those local here. Those ground rules.
45:47 those air service waves are Grandal's. we say here, ground those.
45:51 , So you have ground. Those ground very, very, very low
45:57 . So there, near the vertical . Remember, this plot is offset
46:02 is distance from the source. Harland . Where to go skills time.
46:08 we have high velocity. They go to vertical. I have a low
46:13 that goto more flat. I'm I was wrong. I just said
46:19 . Higher velocities go this way. velocity goal where you go? Let
46:25 get myself a pen. I'm thinking thing I'm saying something different and that's
46:29 the Jews. So let me get pointer back and getting my color right
46:38 color red color. Not sure about times. Okay? No worries.
46:43 can We can come back here. ? If you join me if you
46:49 If you see this Great triangle Going down as a great color.
46:56 , if you draw a triangle what see, uh, if if I
47:00 that triangle on the sides here, is my heart attacks upset. This
47:09 majority. Okay, so we He is, uh What? They're
47:16 ass divided by identity. Right? that's one situation. Very small distance
47:27 a long time. So the slow . But if I draw another triangle
47:31 the other side on the first this is eternity. This is that
47:40 are X. You can see it's high velocity, right? So I
47:45 figure out which one's which. This gentler slope is high velocity on the
47:54 slope is low last because of where goes time. Horizontal is distance,
48:04 ? Okay, so that's always That's often true. The problem,
48:10 which one you compare with because every of travel is always That's why.
48:15 Here we joined the way we The flashing is like triangular every
48:21 That's why I had to in travel , because going, going back,
48:25 down, coming back so two However, the director, I want
48:30 travel on surfaces one way. This piece of bread, right? Walk
48:36 one way South Constant. This part is the arrival. What? Let
48:42 clean up my my plot. maybe too late now. So in
48:49 case, we should all how many six different ways. Let's go one
48:57 one. Why head away? Waves one, travel down. Travel
49:02 speed and on the lower interface, coming back because of refraction.
49:08 So in this place, But it's refreshing This one. This guy
49:12 you know this This guy here, is the hard way. Okay,
49:20 . P the arrival here, p , Where is it you want to
49:26 to be here? All here? little there actually still keep going toe
49:33 . But it's not the first arrival . The headway behind Faster.
49:40 he's a here. He keeps but he becomes slower now. They're
49:45 than the headway anyway, Coming coming . Okay, The sort of on
49:51 is as wave, which is also along surface, but much slower
49:58 It's very hard to see here because were a week. If there If
50:02 the s wave here you will see will be roughly doubled. Angle off
50:08 roughly. Maybe here that might be . The reason I'm doing this because
50:18 a rural farm, P way typically as fast as as way for sentimental
50:28 . Okay. Typically twice if you about harder, lock like grenades.
50:33 , that's not have any more. 1.7 squirrel, too. I'm
50:38 Square off wall. North Square to off for three. Squared off.
50:45 is 1.7. The hard rough, ratio. Well, baby,
50:51 The software typical is to people s PBS capital to. Okay, so
50:57 p Yes, roughly two. So that's why I said that my daughter
51:06 here is s way for survival. very hard to say. You consider
51:09 a bit the coliseum. Okay, the sort of one. The first
51:15 here. I'm going here. First is refreshing. There may be over
51:19 depend on which one. Okay. example, this one here, this
51:24 here, the people, they are more flat because geometry, if you
51:29 very, very deep, they got , like, plan way. Let's
51:31 very flat. So it's all uh, flying around Events are
51:37 So the velocity of a ball triangle . That triangle here, top
51:43 This is talk about appearing a Not true velocity there appear on this
51:48 , but they're not really lost. ? Because, for example, is
51:54 reflection. Go to way. The threat wave only go along surfaces.
52:00 one way you cannot compare this The lens is different. They're
52:05 Lines are different. So you That's not trouble. Last. That's
52:10 we say two of velocity for the . So they appear to be
52:13 That's very fast, okay? Or we are wrong? Depend on what
52:17 you talk about it? The last will last two down here. There
52:21 airwave. Your air baby there was . Both of them shall on
52:28 But there are very different. airwave waves in the air travel in
52:34 air. Very low speed, but constantly in tow. Interactive with the
52:39 Because Grandma have some, uh, your service so that energy will be
52:46 , but they're very small. So , somewhere, Very low velocity because
52:51 needed something like mm 330 40 m 2nd. 1000 ft per second.
53:00 there we were, very slow, service They want faster there.
53:04 Typically between sure wave and P That's the speed they going sometimes even
53:10 then share wave. But so traveling on surface And so all this
53:16 here? Certainly. Okay. We'll Are certainly. Both are.
53:24 Any questions, folks? Well, , Right. So the more try
53:31 fly them like this is another Same picture show here again. This
53:35 the people anymore. This is African , which is using question, toe
53:41 and reflection. Okay, there's another , which is triangular question. You
53:48 see what I'm saying here. So goals making the the ghost making the
53:55 flat. Okay. Before the no another flat. Okay. Why,
54:03 important because it wants the flat. you can stack everybody every trace.
54:08 right side here you can stacking along direction. If you stack, you
54:12 one single trace. Imagine that the events will be enhanced, right?
54:18 need any events along direction of enhanced events, which is particular or
54:23 those will be surprised. And that's purpose of more for one purpose.
54:30 other purposes were lost because of where go from non flat to flat.
54:37 is more you have using velocity you different last, You're flashing different
54:43 For example, I actually to hear so flat because my last is
54:50 So through China era you can see velocity will flatter reflections on. Then
54:55 drive the blast. So the process two things flooding events okay, way
55:02 enhance the signal reflections the same time the see which one will flat more
55:08 developed a velocity that will also called velocities Because we're stacking them together.
55:16 got it. So if you start , you can only one trees
55:22 Now this trace what we called Paul Post factories or stagnant trees There many
55:28 valleys, their methods For example Paul migration Palestina Granting the input traits will
55:34 those factories. So very, very trees left very high Snr Very few
55:42 because only few trees left. so I'm sure you have some some
55:48 some example off the velocity analysis. , before the break. So that's
55:54 one, people. We take a . Most off people like my
56:00 you will spend a few months of this thing, you know, stacking
56:03 . But you guys maybe lucky you do this. So I'm just past
56:06 guys. This is boring process going you. Okay, but to learn
56:11 idea is not is fun if you've this already. Anyone down stacking large
56:16 already before? No. Let me if you've done something already.
56:21 You can share experiences. So this the middle one is called a
56:28 Okay. Similar plot. Sooners Actually, it's a summary. Off
56:33 try different velocity. Remember? Here tried many velocity flatten. I go
56:37 , there. Everyone tried to have . Fly them. Okay, flight
56:42 for every location you can travel, you. So here's a stacking
56:46 Sean, talk for low on left , toe. Higher. Right
56:50 We have a five kilometers per second . So on. This is from
56:54 module. So for every single velocity number 500 seconds, you are See
57:00 result off the result here. Maybe case five probably depend on which
57:05 Some events. This was still the time as data. Just like
57:09 Same times they are. So they're in this case, their flag.
57:13 ? They're flat here because we're using This trade track. We're using this
57:22 . Okay, on what we're showing is the the name of semblance means
57:29 usually have velocity to no more than taking events that measure energy. So
57:35 if the events align off flat like one, energy will be higher.
57:40 you you construction with very each You don't cancel each other, so
57:45 will see both eyes. Both are those circles high amplitude events. You're
57:51 ours. Okay, Some location. don't see highballs. Sometimes they don't
57:57 side. That's because depend on which . For example, right here.
58:02 lo modelo bottle here. That means location The earth is not flag and
58:06 don't seem anything. Call it You don't seem anything that align Horizontal
58:11 energy will be very low. This a real data. So we basically
58:17 using this stacking result as a way measure where the loss you should
58:23 This is completely automatic. I you can automatics on computer so you
58:27 try different philosophy simultaneously. You'll see eventual flashing other, you know,
58:32 flat going that way are going which are the way they go.
58:36 you will see and you also have do detail. You have to do
58:39 training to cut off even far away there something more stretch. Okay,
58:46 some influences. So you're using you . You don't go too far because
58:51 something which they're not reflections anyway. they are. They will come up
58:55 second together to contribute to the siblings , so that might not help you
59:01 . Okay, so in this I'm showing you three examples. The
59:07 long call is the original data. , middle after local filtering. Remember
59:16 of phone numbers. Low frequency, corner hike are high corner and high
59:22 . Almost be fielder. Almost feel is also a triangular. I
59:26 what it called the troubles are the . The last one, the lower
59:31 off the high cut filter. I'm showing the effect off filtering data.
59:35 can see the data. This is sort of a lower one. You
59:39 see it's a much lower frequency, ? This was low frequency. This
59:45 a high frequency on top of one ones original. I'm just showing example
59:51 federal frequency on a semblance resolved. do this. Just worried by our
59:57 . Are we picking the right Why? I say picking ready
60:01 I'm gonna talk about picking the balls kick in the balls. I'm used
60:04 picking that about asking what that The following. Okay. Remember horizontal
60:11 . What he calls time. So any bows out your life, for
60:15 , this will die. That means that time, which is a 2.5
60:22 , the second velocity is what, six. So your final result of
60:31 velocity is a velocity as a function time. This time the travel time
60:38 velocity function about two way travel time going T w t. That's your
60:45 immunity. So starting last dysfunctional to child. Why second, with all
60:51 defined for reflections, peaceful reflections? we we have that contains the order
60:58 . Like I said a certain whatever else. But we want only
61:03 to do refreshes. That's why we . Mm. Oh, So the
61:08 reflection will be flag. Other energy be no flag. So when we're
61:13 is other energy will be surprised. get it? I hope it's not
61:19 complicated for you guys if you see first time Kind of complicated, but
61:23 idea shouldn't be okay. So this why this is how it arrived in
61:27 the stacking velocity. If you go also data on top one. This
61:34 data you might you might wondering how back. So how come I'm I'm
61:39 here? I'm kind of They're also here. What about those?
61:45 this is capable of experience. It out the primary flushes. Well,
61:52 have a higher velocity than the Multiple, multiple reflections. So very
61:59 . You see a lot of multiples the same area or laughing with the
62:05 . But there are velocity will be . So when we pick up,
62:09 eyes were typically picking the both around high end, high velocity and another
62:12 end on In a way, I'm show you here for so filtering what
62:17 am doing hypertensive tutoring. You can my my result of picking. Same
62:21 are very stable. Okay. I put you guys to exercise. Make
62:30 hands dirty. We don't have time that. So I'm kind of summarizing
62:33 results for you guys, but that is very important. You can You
62:39 learn something quickly from someone there. else who spent three months got this
62:46 . It was a little lower, there is the same Say easy,
62:51 . Music Goal, Right? I'm it. Easy. Calm musical for
62:55 guys. So you need toe. yourself in the situation and try to
63:00 the detail of them. Said the . You guys are smart. I'm
63:03 you can figure out. I'm just sure you got that point. The
63:07 point so you can cook it back off my normal analysis, slides back
63:13 , makes you understand everything I You can bring the issue back.
63:16 have questions. All right. On . Here's here's illustration. Why the
63:24 has a low velocity. Okay, this is a two plots combined
63:29 Mm. Insert here. Shots be at This is a model space.
63:36 sorry. This restaurant is data. don't know why this thing happens.
63:42 bleach. Don't worry, but you see the Let me Let me stop
63:46 point that I'm just using the The point is easier. Now. I
63:50 cause trouble. So this is a or model space. So sauce here
63:56 the left side. Receiver on left . So this is a primary reflection
64:01 people. Reflector. This is multiple yellow reflector. Okay, It happened
64:07 be that this multiple arriving the same as the primary a deeper adviser happened
64:14 be. That's where they're arriving Okay, but what we're saying is
64:19 there move out of different the the popular like this, like
64:25 the multiple will be slower. The they're slower is geologically their comfort.
64:33 . The velocity model usually increase with . Overall, the shallows elements is
64:38 slow velocity and deeper sentiments. even though they are exactly the same
64:45 , the shadow part is the lower . So multiple spend most time in
64:49 shadow part than the primary off similar time. So multiple was always slower
64:57 primary because the mother poll they didn't deep. They just stay the shuttle
65:05 . Let me repeat it one more . What I'm saying is,
65:08 even when the travel path off the here the same length as primary travel
65:15 1200% lens, the total length, same lens, this one going
65:21 going up, going down again, up. So we're saying the total
65:26 off the second daughter multiple Samos, total lands on the primary. Even
65:30 the case. Your your time for primary will be much faster. High
65:35 because it's part of the geology is velocity. There were very rare exceptions
65:45 times always true because of physics. , if you go to geological
65:54 if you look at any area most , the the last increase with
65:58 Of course, they're detail in other inversion sense of that. But
66:03 they're increasing death because compaction because pressure effect combined geologically combined. That's the
66:11 why we're picking high velocity for the with we think those low lost both
66:19 are you the border close and there more than multiple. There seems like
66:25 convert away. We're coming coming down P way coming back your way Sure
66:31 people again. Even we only recording , p waves. But the way
66:37 can go down to pee Goto here year goes to here here and go
66:41 p. Okay, there come other . But all those other events multiples
66:47 motivates their arrival times that you should slow velocity than the primary delay,
66:55 actually is one reason why the industry using primary reflections as a signal?
67:02 it's a kind of mawr era free free because I want to go to
67:07 is nice using other events. But more prawn toe era is very hard
67:13 identify them. So as a simple , if we cannot identify the signal
67:23 if you using the wrong wire you the fire, you can create more
67:30 . So we're gonna take a But we're gonna come back this point
67:35 it's a 9. 40. Why we come back? 9. 50
67:40 be okay. 10 minutes. All , Now we can ask. We
67:45 discussed question an issue. Yeah, come back, maybe. Okay,
67:55 going toe to toe the sharing Make sure. Well, on the
67:59 page where it is here. What? So we were actually tried
68:13 one slide because that's all over one . One part of the sea.
68:16 okay. We probably already have too information. So we were here.
68:23 would break. Uh, let's Yeah. And make sure I can
68:31 all my I can see who Who there. Okay, Okay. No
68:37 . So when we are doing Uh, in the really real
68:45 we can look whole thing like this . Okay, so it is a
68:51 home. I'm showing you the city number, which is famous, The
68:56 Basically basically it's a way we organizing to the profile us the way to
69:04 the distance. All right, so it's a city city number, that
69:09 the distance along the profile to the . You can find out the lens
69:15 between the CDP numbers which is basically size the same peeping sides. That's
69:22 the rial distance, for example the European sizes say 10 m. Then
69:28 can multiply that, say, the , converting toe GDP versus distance.
69:35 in this plot, I show you sea locations, the velocity semblance off
69:44 locations. Okay, so then computer , you can get a sense.
69:49 , Semblance three horizontal is always the really cause the same time. Time
69:57 travel time. Okay, so this you can see the quality off velocity
70:04 in this example. The the both are very cluster. Let me very
70:11 . So that means a lot depending . Very good. You can say
70:15 low velocity increased depth. Remember? said, increase the velocity depth.
70:21 to the right is higher velocity. this is actually I'm using Ponder
70:25 I almost forgot. So the velocity lower here. The increased quickly and
70:33 that. Okay, so this this a this example shows you how real
70:39 with pick stacking velocity. Okay, their issue about that accordance and so
70:50 , so forth. But later we will discuss issue about what's the
70:55 between stacking velocity versus the Rio So let me go back Thio the
71:03 decision one more time So I talked Bob. Beginning will ask the flat
71:09 so on. So when I talk flatness like from here to here flatness
71:14 . That's taking velocity. You can what happens. What happens is for
71:20 flatter for example this one here without flutter in order to flatter and flatter
71:25 it was like this. Okay, we flat the other one. So
71:30 ? We're What's the magic? What is that we are assuming from the
71:35 flatter on upwards to the source which receiver and shot on surface All the
71:41 between flatter, good service South You've lost this constant. That's photographs
71:48 me will also mean a single velocity order to do the flat. That's
71:54 stacking velocity stacking velocities, A single assuming for flung the reflector. You
72:03 the data from that point on? all the way to service. So
72:08 , czar, arbitrary velocity we're It's an average of everything evolved.
72:14 the second lost. Okay, on clearly is not really accurate because most
72:20 from surface down before the flatter, virus increasing, decreasing whatever. Keep
72:28 . So using on average is not very good way. So later
72:33 we'll try to convert from the stacking back to the, you know,
72:39 velocity. Which is the velocity defined each later off Australia. How?
72:45 sorry. I just have one Yeah, on yeah, on these
72:50 slides we when we do the enemy the lost analysis or apply the
72:55 the last thing we we do both CP domains. So we only correct
72:59 the effects of the travel time with . But here these are shots.
73:03 the building here. So each traces from a different location. It is
73:08 all from a CMP, right? , yes. I'm showing here as
73:14 common shot as a way to illustrate events. But we do this on
73:19 sea. NPR's yourself. Okay, a little bit more detail.
73:25 but the stock is ready. In a sense, this is
73:28 This is shot better. But you do You can do that for
73:30 Get it as well. This is coming together. I'm showing Come
73:36 So this taking from cruise liner, colleague is, ah, book,
73:42 , But the same thing. We do this, uh, field for
73:47 coming together. We do this for together, but you can apply the
73:53 concept using Comstock it if you want reason we don't do come together because
74:00 spray, because we're flashing my not from the same location on there.
74:06 can also see many other issue For example, You see, this
74:09 what you go stuff here. This work alignment here. Many work
74:14 Yeah. Okay. Those are static problem. That means near surface
74:21 , for example, there's nobody There's little hell there. So this
74:26 shifting off the events. This is I end up today in the third
74:31 off. Discuss. Stay steady. . Okay. Study correction.
74:38 Lighting those events. Is topography stuff that? Yeah. Okay, now
74:46 on. So, again, this here, even though they're not
74:50 I mean, they're increasing their still velocity. They're not a true
74:57 Okay? There's a lot of using fat events. They're kind of assuming
75:02 evolves constant. Okay, there's an of colonies here, but we can
75:09 . But I'm just showing once you , which is, uh, this
75:12 a two d survey, so the distance of GOP from origin,
75:18 is the distance. But you add from the origin. Okay, so
75:22 want to the survey, for here's your to deserve a line here
75:26 top here. Origin here shot So as is the distance shots to
75:34 , if your keys here and she's from that location on your phone all
75:39 way to the origin. So that's and s. So you can using
75:43 simple formula, computing from distance off slammed us into the middle points on
75:50 as his offset M. Smith It is a mathematical way. So
75:55 average distance off your phone on the is the midpoint. The difference between
76:01 off on on the shot is the . Just some detailed measuring. Because
76:08 might see this kind of situation often who knows you are, you
76:13 exposure to the data sets and resulting always issue commitment, consulting, for
76:22 , on building I saw one on reason is that is the issue is
76:27 very simple is because we always wanted . We want to see we want
76:31 high speed. We don't want We're so so most time we have
76:40 . We have using 13 format for . You might heard something called a
76:44 y 60. You know, so . See why format and typically those
76:50 sets format started with something called the Header Header is like a general description
76:56 the former. This is like a like survey geometry and harmony shots,
77:03 server, brother, you know, and so on. Uh, that
77:08 is in the header, all And it is at a lot of
77:12 . There. I put into the paper they're talking about, I think
77:20 white format. So if you care detail about silver former, you can
77:24 it. There's a published by C . There differently revisions. All
77:31 So the data are organizing in the the far headers, followed by Chase
77:39 there, followed by trees, Trees Is the information about that one
77:46 Okay. One trip just for I saw countries here I sought
77:50 which means many points on a legal legal came from Where is the source
77:56 this wiggle where the receiver is legal so on so forth Okay, so
78:02 zahau trade Scatter in riel processing like We do parallel processing in the sense
78:11 don't want to solving every point We sorting all the trace. So in
78:16 way, for for a task golf common together into the same together I
78:24 have a sort of trees Haider's because header contains the X Y location off
78:32 N s. I can use this for completing the middle point offset.
78:38 when I'm actually sorting, I'm only the whole trees a piece of time
78:43 I don't have to worry about This is kind of a vector processing
78:48 vector process is very efficient. I can also underway. So this
78:55 a detail I don't want to Because for this great course, there
79:00 not be time goes on those Uh, in my lecture on their
79:07 about most like issues I just mentioned , you know, eso you wanna
79:15 , uh, c m c m or C d p gathered toe.
79:19 this line 11 point. They also , convinced severely under sample,
79:27 due to whatever reason, com promising of the stack. So irregular spray
79:34 in my cost or even aptitudes some issues. Okay, You don't have
79:39 those because I'm just giving some soft . It is not. This is
79:43 a very important side, but I to give you exposure. Difference I
79:48 a moment ago about the stacking velocity not the true velocity. Here's a
79:55 example into your physics when he says example. We mean it's not a
80:00 data is a theoretical model. So left. One is called interval
80:06 asking. Okay, now it is steps. So this is like model
80:13 , You know, in 3000 m , 2000, 1000. Okay,
80:18 distance, CMT CMP distance here is and so on Both. So everybody's
80:26 is, uh, one kilometer square . So they're slightly vertical.
80:34 maybe two times? No. So have scratched. We call this interval
80:41 because the color here, unfortunately as with a slower the color bar,
80:46 black colors five will ask me the colors Global lost the grace between.
80:52 this one is assault is assault So it has a very high velocity
80:58 kilometers per second on their low velocity on top on the low, they're
81:03 high velocity and some low velocity Okay, so for interval for into
81:09 velocity Goto I'm as well a city using. This are arm s,
81:16 , equation, which has been very . It's a it's a dividing for
81:20 . Basically, the layers of velocity with well layer of velocity square square
81:29 waited by the layer interval, death or time. Then some of
81:35 toe together, layer by layer until point you want to talk about the
81:40 another lot of if you how to by words. You have a textbook
81:45 look at, you can see my it in detail. Andi, if
81:50 want to convert back Florence, second artist lost you toe interval velocity.
81:59 might using something called a peace formula X this formula. Okay, But
82:05 not a very stable way to convert no, unique. That's always the
82:11 . The result is now unique. , so there's always issues when I
82:16 flung, stacking will ask you uh, even low velocity so you
82:27 see the right side here, in case, very smoother computers, the
82:32 among the issues. Why we cannot back there many issues while the
82:37 Yes, uh, assuming for sauce here. A music one sauce
82:46 December here There were assuming it's constant . Therefore, is a perfect
82:52 right? Like this. I call we ship letter we re past.
83:00 , we have a velocity real velocity always increasing with that than the same
83:08 . The same receiver with us. is not be with us is more
83:13 you. Okay, can curb. the curve? Because they can enjoy
83:23 velocity faster can write faster the They're not like of street line.
83:32 , so that cause problems for your . You can have a go from
83:37 velocity go better to the interval By this formula, you can have
83:42 era. There are other reasons for Also, for example, you your
83:45 number might change. We don't know was the right number of layers,
83:50 it's very unique, but still people this way. Okay, so this
83:56 sort of era somewhere. I'm going illustrate some examples the same models that
84:01 already have model we can generate data that we can see what the result
84:07 imaging. Example. So here's result wall uh, more stack because in
84:14 old days, people just took it and they got this. That's a
84:18 . You don't walks down. You already have it so you can
84:22 the two model left side. Virtually model. Okay, you might say
84:28 it's not bad. It's not Okay? I mean, kind of
84:33 what's going on. I mean, got a good result. Well,
84:36 problem is the top size. We're the top assault is very, very
84:41 . Okay, you guys, we this octopus. Alright. Tops off
84:45 showing. Very, very well. some salt on is an assault flank
84:51 of problem, This kind of lost . Okay, support was very
84:57 You can see, uh, the bottles like this, Right? But
85:04 bottom showing on Assad is not like . You don't You don't say
85:07 You don't see this this thing at your business is distorted. Okay?
85:15 the velocity was not right. But you do time aggression, you can
85:22 time aggression give you some improvement, still not very much. Okay.
85:26 . Go back. Uh, that's . So they do. This is
85:32 not This is almost back and still back. This is E mean,
85:36 is illustrated issues more GMOs that you to go. That's my graduate.
85:41 is case you have that migration. , there's still time migration and still
85:47 that want to the issue on the world. Even this migration. You
85:53 issues because you have assuming the blast right. That's why the true Velasquez
85:58 is always a big issue. I think I give you offer
86:05 Now let's move on to the next , which is, ofcourse, any
86:09 . Like I said, Okay, keep asking you guys okay? I
86:13 nobody have any issues, right? . Okay, wait, come
86:21 So there here is a clever lifting about the conclusion. Correlation on noise
86:28 . Um, uh, So let first using this example. Maybe maybe
86:33 is not the best example, but Let's see. Let me just
86:36 What do we have? Okay. right. So let's just focus on
86:40 . Is this example No problem. imagine these are two functions F
86:46 too. You want to come all one here have to hear You wanna
86:51 all okay, I'm showing Here are I call this boxcar function sine wave
86:58 , but you can imagine there's a have There's something Interval. Right.
87:03 this postcard maybe composed off, will , uh, well, model here
87:07 because they have to deal with a , so they're not everywhere. So
87:12 maybe have one point here. Next here. Next point here. Next
87:17 here. Next point here and so . See my point. So you
87:20 have something that we call it a function. So basically have lots of
87:27 at a zero. So it will like zero nothing there than one on
87:33 on one on one and so on we're and that's one and zero.
87:39 times you will be like That's for past confronts you, right? So
87:44 the for the sign Similar zero then a bottle here. Ah,
87:49 their value here. Follow their and on. Negative ones and so on
87:54 the point. For example zero here point 801 or 0.8 months. One
88:07 from 80 So something like this this she is. So our job is
88:14 demonstrate How can you compute your The convolution means multiply two times cereals
88:22 . So commotion Samos multiplication just like times three equals six. The complex
88:30 is the not 23 anymore which wants vector otherwise time serious. Okay,
88:38 in a way, the result of two things means like I like
88:42 for example, off like area. each one lens here's lands, one
88:49 learns to know I multiplied together. ? He got this area. So
88:55 dimension changes. So the result of not just convert together is also changed
89:03 . Right. So I'm going to about detail here in the example the
89:08 . Here's one way toe do I keep the boss. Now
89:13 So keep us the same location. any move on my reverse. The
89:20 to the F two. I reversed two. The last point become the
89:26 point. Notice this, uh, example, here, this location
89:32 You notice that sign with this time . The first point become last
89:40 Okay. Why? Well, let spend why, for example, the
89:46 point here. Zero amplitude call I don't know. One, 23
89:54 order. Right? The first point you come up should go to the
90:00 point of the boxcar Banking also one three. So this bottle here.
90:06 the interact with the first body on first so graphically they looked reversed.
90:15 in actual competition that's correct. I the reverse triangle in orderto get the
90:22 point of triangle hitting the first point box. So what I'm saying I
90:30 to reverse them. So this is in the reverse is not a real
90:38 . So you want to do You have to do the competition because
90:41 is complication about the vector off Serious Multiple multiplication. The first
90:46 The last point of different. So got a reverse of all of
90:51 Okay, of course you can reverse . Still box. That's that's the
90:55 . So I'm purposely refused to sign . You can see their difference.
91:01 , Now I'm sure you three moment sliding this reverse the sine function across
91:09 . The first one here the second here. That's around here. What
91:14 computing here is the overlapping area. area of the or happy the area
91:23 the world. I mean Okay, one's tricky one here. Well,
91:27 talk about 31 later on. So area or lapping the area. The
91:32 happy we put that bottle here. volume so that vertical height is the
91:42 off this moment The vertical height of is the area off that or happy
91:56 . For example, if you say is the first one is one half
92:02 is one half the second wife said is too. I'm sorry to one
92:06 11 here. Amplitude. So the of conclusion is the overlapping area.
92:16 , The third one are complicated because letting area already complicated. Why?
92:21 at this is a positive, but is negative. This is also
92:31 So we're saying this negative area cancel part of areas zero only this part
92:39 area next area go to the That's why the land here is a
92:45 the value of one quarter off off sign way. Okay, so it's
92:54 kind of confusing. I'm showing you that evolution is a multiplication or two
92:59 serious. The results there or Latin Also sliding one across, other as
93:08 go on as a result, is conclusion. This is kind of a
93:14 way is very confusing way, but many years, the following you shoot
93:20 one off the other. If you're more of them, violate the other
93:26 . Relativity. For example, this relativity, This one's really you basically
93:32 the village through the relativity. They . They're complimenting each other's or their
93:38 . Each other combined. Any We're okay. Okay, Now,
93:50 don't like this way at all, it's kind of confusing, to be
93:53 with you. I just described this a concept, but for a deeper
94:00 , we want toe. But if go back to my let me let
94:04 let me stop here. If you back to my to my concept,
94:07 got do something like this because because the very beginning, a moment
94:12 I describing the concept off filtering. . So this is detail. That
94:17 here stars conclusion. So we wanted detail of this process. We already
94:23 the concept, you know, regulated source control with the geology give you
94:29 . We just know to the hard . It's like you hear from people
94:34 about living anything. There's three Okay, there's three questions.
94:40 Why? How What is conclusion? is convolution? Why convolution? Now
94:48 looking at how the conclusion. uh, although I prepared a lecture
94:54 , I'm not going using those I'm gonna choosing, going back the
94:57 slides here. I'm gonna get myself wider bar. I will show you
95:02 ? I'll do this myself. That's the first getting my parent.
95:07 again. Uh, this is a part for doing this. If you're
95:12 face to face, this is very . Just draw this again again using
95:17 chalk. But I don't have And also, I'm not choosing to
95:21 . I'm not choosing i color of again. It's not my favorite
95:27 but it's color contrast. Okay. want this ties in my dad.
95:33 , Uh, I'm serious. My one here, f one, My
95:38 is one one one one. I have a five point. I'm
95:49 . Basically, I'm saying that's why one. That's one. That's
95:55 That's why. Okay, Now go my white area. This is why
96:00 have this body of my area, , because toe one hopes I don't
96:08 what I was coming. Follow Is this is how my function looks
96:16 my tool. Uh, if I'm , I can using the different color
96:21 the same color, but not A different color. That's okay.
96:25 try the same color. Let's say gonna I'm gonna choose this one.
96:29 , I'm gonna be totally let's say . I'm not gonna do in
96:35 I just call this, uh, zero marathon about that notice. I
96:44 put the 1st 10 here. Because 00 I don't need to put
96:47 zero useless. I'm also assuming the the same name. Okay, so
96:58 f two bodily is, uh, Mara's Juan. Okay, I recall
97:15 , keeping honest if I'm wrong miss Take. There's no magic.
97:21 , let me know. Okay. to do this? I'll show you
97:27 easy way to do this, which making this as a matrix operation,
97:33 one of them as the metrics. I call this as one example.
97:39 gonna making a bigger mattress here as recording. My value as a column
97:44 111 11 Next role at the same . But do one time shifted after
97:53 1st 10 Have a shift. One 1111 Wow. You will hear the
98:05 one after one more zero. So basically doing a one step shifting over
98:13 trees I report Repeat the same So there's zero here. There's zero
98:19 . Okay. You see what I'm ? I have no more, but
98:23 only have a three volume F I don't need more than the same
98:28 that I can put my toe One zero. That's why I hate
98:36 . I don't know why coming. me that Right. You see what
98:42 saying? What I'm doing, this how you're competing. Conclusion using military
98:48 . Okay, you can do this I can say Oh, I don't
98:52 while I'm, like, absolutely Another way You have to. Same
98:57 . One 01 one zero while So keep doing here. Next one will
99:07 one that will be one That's one be one on day 01 This time
99:16 making my number of column five because a 51 here. Okay. On
99:39 here zero everything About zero. I'm lazy. Okay, you get a
99:46 . So when you multiply Kamal to shoes, you just make all them
99:52 . The one step shifted. We this diagonal matrices. People also call
99:58 topless mattresses populace tautness. If you at tax, you can find the
100:11 . Okay, so you know, if you know how the multiple metrics
100:15 get, you get the answer. ? My first case, I have
100:19 situation here. What do you Your multiplied role with color,
100:25 So? So you can get a result. You can no better out
100:33 times one is one plus zero times plus zero times minus one Still 01
100:44 21 times one is 11 times zero 00 So it's also one on the
100:53 111 Now I can see the Add them together is zero Wow !
101:01 comes in zero. Well, I them still zero on the next 10
101:11 101 time 001 10 minutes. One minus one. That also was a
101:17 . Why? This is my You smart like this other way.
101:27 shows you the same thing in theory practice. Because my arrow, I
101:31 get riser one Everything else. Zero one zero times one still 01 time
101:41 are still one. This one here is matters one I have ever already
101:54 Nobody catch up me. Come catch up Me have era. It
102:00 work if I got era. This here Actually the rule here is very
102:05 . Now because this otherwise all, you simply add up them at all
102:12 rules, you'll get it right. red answer. Okay, so I
102:16 a 160171 Add up the country 100 . Next role. Also canceled.
102:26 . Let's roll. Still. Council the last 12 minutes. One
102:32 So I get the same answer. . What? Looks right.
102:42 you draw I Tom access. You got a while here una Y
102:54 . Zero zero zero. Man. Juan. Anybody else? One.
103:05 looks like it looks like a roughly to the color. I get into
103:09 . I make a mass very So something like this. People like
103:24 . All right, that's my results the exercise, You know, compared
103:29 to answer. Yeah. Sort If you are happy. Guess
103:36 You put more point. You put points, people more horns.
103:48 I mean, it's a supply society I could do. It s
103:53 This is the way I recommend for doing exams are always It's just mechanical
104:05 also pretty straightforward. Any question? not difficult. Yeah, go
104:16 Yeah, Like trying to get the ? Why and how the solution.
104:24 what was the section again like? would you? Convolution Good question.
104:30 always cut. You will try to it. Why? First before before
104:36 to detail is Oh, God, , it's OK. You see that
104:42 I showed here? This is the . Figures conclusion. You're not a
104:52 . You know how you don't. is why Conclusion? Because this is
104:57 you holiday has been controlled. Your you recorded out here g is convolution
105:06 the source on the geology relativity. you're able to do home convolution,
105:14 you can describe this process quantitatively. you can have a resolution or do
105:20 about it. Conclusion basically is the is the new vehicle is how computer
105:30 the filtering process. So if you to describing how the geology is working
105:37 satellite data, you want to be to follow that you can be making
105:41 going on, then can either manipulating clean up the data so you can
105:47 the imaging. Did that Okay, I say or if you feel that's
105:54 enough, you know, this is reason why math is like asking why
106:03 need to do the math. You , I don't like mess. I
106:07 doing mass. Why? I need . It's a way to realize the
106:13 . So I came back. This very efficient The mass has to be
106:17 in a way that really describe the . All right, So, for
106:25 , while I try toe, why this result here? I say the
106:29 on the, uh all the correlation those two off this sweep, we'll
106:37 you this arms. Crowder future Wiggle it. I'm using Claude er
106:43 in this case, and you can this, but you cannot do this
106:49 . But you can actually do yourself you know how to computing all the
106:54 . Another correlation happen to be the as commotion. Exactly the same,
107:00 a way. Okay. So I show the formula of comparison this slide
107:06 the comparison between convolution on coalition Okay, don't worry about the
107:13 Here. It's just again two times wise. A wise X is the
107:18 access relativity on earth. This is formal, awful conclusion. But when
107:25 look at the competition formula and compared the correct formula. They're the same
107:31 . The only difference is this man here. T Moscow T plus
107:38 That's the only difference they have in comparison. So I show you a
107:47 ago how to compute this example are one on one on one with the
107:54 medicine one using metrics. You can the same operation for cross correlation
108:02 Change the sign off. Change the . Another sign another black man,
108:07 reversed Order off the one of those s symmetrical. For example 101 Switch
108:15 101 That result will be called as because the mathematically the formula very
108:22 There's another way to look. Formula left is the integration formula. The
108:28 is the digital formula are described See the y minus k. Here's
108:35 plus K y plus case Cross Florence calories is the same as cross
108:43 If you normalize it, coalition. let me again a couple idea
108:52 Quantify the similarity between two times Look, the similarity if you normalize
108:58 become a correlation If normalized, I normalizing. Normalized by the the Energy
109:06 Modoff X and y you get a correlation. The close cooperation we said
109:14 of all that faith, aptitude, . Remember, I was not 20
109:21 chosen wave to drive the four years for, But im did aggressive too
109:28 already. Let me Let me make you guys follow the whole part.
109:33 , this example. College conclusion. example is called called Cross College.
109:40 , I can give you more but they have a lifting today.
109:44 part, it's know how how to conclusion. For that reason, let
109:55 do one more time. Let me something different, okay? I used
110:03 with me or anyone scared any Feel free to open for people.
110:08 . I know this is a mathematical is really hard, but you got
110:13 be quantitative if you can, because it's not. It is easier
110:20 know the answer what and why? mean, what and why It's actually
110:25 than ever. It's kind of Answer is to give the solution a
110:31 . Is sometimes using computer sometimes using experiments, sometimes using, uh,
110:42 . Okay, I'm not sure he's tired of call already. I'm not
110:46 . Green color school color let me black color this time. So this
110:51 I'm using mathematical one Say have Serie A. Okay, its function
110:58 okay. On the the value will like a one. So a to
111:09 three eso on a four. So can see I'm just giving giving the
111:16 here. Okay, so the the of conclusion a correlation Can you describe
111:25 something called Aziz transformed? The value be the coefficients than the power Bi
111:32 . For example, this will become a Z. Okay, The Rico's
111:40 Anyone plus a to power Z Well, if you start on,
111:49 starting from one. But if you on zero, that's probably better.
111:53 stuff are zero okay now you wanna ? I can put a zero
112:01 They won power Zito power one on two little power to and so on
112:13 have of my b hopes. Might You can imagine zero You want b
112:24 and so on. There might be Yes, you know Monkey see Monkey
112:32 80 p zero plus p one The power plus be true the to the
112:46 power That's so long now if you over them And the that means a
112:58 times busy. What you get You're . This whole thing here,
113:12 put here Put holes in here to at times this holding here be toe
113:25 . Okay, but I'm not gonna Is simply collecting the terms under conditions
113:32 Zito zero power, Which means constant on bond. The collection in terms
113:38 power one A power on collateral terms power to that's all. So you
113:47 collected terms. This is how we prove this is right or wrong.
113:53 you have lots of monetary conditions. can spend time short of detail But
114:00 is where I show you why metrics . Why is it works?
114:07 So I'm gonna make myself metrics. not I'm not gonna sell. But
114:12 me say that might be vertical was zero. Do you want be to
114:21 put this way all the column. putting a zero A one a two
114:33 saw Then I feel the box. first ones to pay zero a zero
114:45 . They want zero a few zero three and so on. You can
114:55 what a good same zero. Keep . A the next one. B
115:02 zero. This was me too. zero. Do you want a
115:10 You want a tool? You won three. I gotta be any faster
115:16 hopes I don't like that. Be a one. This is a
115:26 You can see the error. this is one thing good about metrics
115:29 error. You can easily find it . Always be too. So the
115:35 number column member was correspondent to the role in the column. Okay.
115:43 We spend the time doing this. me show you the nice thing.
115:47 I've got a 10 color, I go back to my red color.
115:52 Dr Red. Okay, Now you draw the there are gonna go this
116:01 . You're looking for terms. That is powered one Saudi. The addition
116:08 the two conditions together. Well Tau zero. Here. One
116:14 Two there. So the first one be this guy here because you add
116:20 . P zero is zero right So you have a B zero on
116:26 zero. Now, this one here to be 180 on B two b
116:34 a one. So here, that's you have. So here you have
116:41 zero a one plus be 10 on third while you have to as zero
116:53 one a 108 to those three terms still there because the addition off the
117:02 becomes the sirve. So in other , the competition result shows you how
117:09 orangey add up things together. this process is exactly what I'm talking
117:20 . Efficient way using the metrics. I shifting my f y here this
117:28 if one upon my after here, is a more clever way to do
117:35 . Actually, both of them. same thing. Remember, I think
117:39 my both car in tow. Wah wah. Now here's a 10
117:49 That's the same thing as I'm doing . So this, uh, we
117:54 these transform operation the Samos the same this metrics operation, you can prove
118:01 the same process is lengthier background because time spent, we don't go
118:11 but the underlying idea of how is important because you know how that you
118:19 You can You can do the job you want. Not the concept.
118:23 don't know how to do it. still not able to deliver right or
118:29 else give you a software algorithm, might push the wrong button. You
118:34 even tell what is wrong from That's the problem. This is the
118:40 between geology and geophysics. We are quantitative. You can get it.
118:47 not that hard. It just be . My secret for living masses.
118:52 patients, they're not a cigarette Because patient just like you guys are looking
118:58 . You got a understand Which one's . Okay, so anyway, if
119:07 do a sweep, you have sleep . You know you can compete in
119:12 cross correlation. You can use the , for example, using spreadsheet
119:17 make a program or using meta. you can do this job.
119:22 I'm gonna talk about concept off Three more. I think we're a
119:26 bit ahead of time. No time in My goodness. Turn for
119:32 Give me a few more moments that can have all break. Okay,
119:36 your best question feel free. This is very important. So once
119:40 know this, you can This is of future. If you look in
119:43 special man, you can talk all The low pass high pass side Liu
119:49 pots and so on. His name's filter and so on, So on
119:53 filters And again the same concept featuring already. This is called a conversion
119:59 filtering Samos conclusion. Okay, Children conversion and then you can see the
120:07 conclusion model. So you have earthquake Butoh dislocation off fault This is
120:14 this location function. Then you can earthquakes stops so the finite then they're
120:21 few the Coliseum Mexico spreading. That's future. Now you have a generation
120:27 the medium. Now you have another spreading radiation pattern. So this whole
120:34 combined give you the software with Come out here and give yourself Maybe
120:41 come out with structure. Give you assault instruments yoga. Finally, give
120:47 a small grant. This is slightly tells you that our simplify the way
120:55 thinking system a grand is a conclusion reflectivity with the way blade. It's
121:03 a huge apart mentioned because from your combined with all those factors, combine
121:11 your family. We asked petroleum engineer geoscientists. Try to see the
121:21 We have toe remove all the other . All of them together. So
121:26 do take a dirty We do crack . We say That's bubbling. Which
121:31 it? Waited all. It's actually more complicated now. You want to
121:37 out of detail? Their fluid you know, rock properties that z
121:43 complicated. Okay, so then here's way to show convolution. Maybe you
121:49 this way. Okay, let's say like this way. This is your
121:53 function here on top. £50 a on you can see the baby right
121:59 . Okay, That's your big I said, Well, come multiply
122:04 the first letter, then you. way with the multiply you Can you
122:09 ? Same with multiple signal One using one There. This one signal better
122:15 . A single ones. Here is same reputation off the first one by
122:22 polarity. Reversed, minus and empty a smaller because it's smaller empties.
122:29 also see this guy here? That is this one, right? I
122:38 this guy here as the one sour guy here is that one This whole
122:47 do arable Basically you have a reputation the same wave late according to the
122:53 coefficients at a plus minus or by scale that is plotting to relocation shifted
123:01 finished, you add up them You're stacking together. This year's taking
123:05 whole thing together downwards. So every you you have plus amount of value
123:10 together is some together. This is final result. This is another way
123:16 looking convolution. So I'm I'm showing how many ways now the first one
123:21 a graphic one the second one's The third one is this transform.
123:27 was the first one, so I showed a different way off. Completing
123:34 . A revolution is actually very Part of all your physical that are
123:38 is the same thing as Futural. , that's why I spend all time
123:47 . Any questions or issues. let me show you something juicy
123:52 Okay, here's one example off. that is some program from convolution.
123:59 you a correlation. Can I Okay, The first traces the deputy
124:05 log. Here's the law school I told you multiple identity with la
124:10 impedance. So here's important block now don't generation the Chinese impedance off
124:17 independence with death. It's reflectivity Refreshing confidence with that you can
124:25 Always label It is with great introducing sunsetting trees, the red colors that
124:34 . Then you can tie that with trees. This is exactly how we
124:41 fascinating world high, You hear? word says me, Walter, this
124:46 how you turn. Start speaking, . We're logging tired. How?
124:51 were logging Assessment World Heart. That's most important part off Geophysics for
124:59 Andi, here's some examples. Uh, the rest are here.
125:05 red colors. That's 91 floor. , the white color background assassin.
125:12 taking this wonderful on some work I a long time ago, so just
125:18 show your idea, okay? I this is a good time. Taking
125:23 break time flies. I don't know much. I don't want to give
125:28 too much math. That too much . Then you get more confused.
125:32 let's take one more break. We'll back 11 about that. Okay,
125:39 be 11. See you. Thank you, Maria. Okay,
125:55 we were talking about the water. , So a lot of concept
126:01 I don't need to go to So now the next one we talked
126:06 the future re so quickly goes The feuding idea is very similar.
126:11 know, once you get the multi than the filtering part of will be
126:16 along. So I have about one left because we do our crease.
126:23 an unknown if you to finish well leave earlier. Maybe even longer
126:30 So it's time to talk about Right? So we scheduled to
126:35 uh, 12. 30. Now start again. One here. So
126:41 repeating like yesterday. So in the , I will usually try to stretch
126:46 bed, make sure we deliver the . But if you feel too
126:51 let me know. You know, can throw it down. So let's
126:55 the deal. Okay, So here the where we were Continue from where
127:02 are, we were here. We to come only when the filtering and
127:07 on, as you say. A of reputations. But some of mathematical
127:13 escaped here because, you know, is another way to show the filtering
127:18 . Interest response. This is no from, uh, this picture.
127:25 sorry, this picture e s this this picture is saying Okay,
127:32 with both scarf comes your way. model. One way to show the
127:35 thing. This one shows you the between filtering. I relate.
127:42 my pointer. A city Always. always cannot find very quickly here,
127:50 that's the same model we saw And this is why example filter in
127:54 detail. You can express it in . Block diagram on. We don't
127:59 not required a menace. I'm just you something you would probably see somewhere
128:04 . Okay? Eso The future has three functions, which is the
128:11 multiplication and addition Stories just means you them there for a while because they
128:17 their stay inside multiplication, which is right at the increase decrease off,
128:24 assigned reverse polarity. Now, I . You do summation. So adding
128:30 as a detail of filtering process on detailed mathematical ones. But I think
128:36 already confusing enough, so I'm I'm gonna dive into this one,
128:41 ? So we'll just move on with one. Unless you, some of
128:46 one is not modified or having to about it. There are many,
128:52 filters on Here is the one table Boxer. It was, uh,
128:57 eso. There are many names for s o all them based upon contribution
129:05 filtering idea so you can usually apply using Fourier transform. This was
129:12 Dft send for discreet foreign transform. is a fast Fourier transform. So
129:19 , it's a way to track for frequency and applied operation there.
129:24 I'm going to show you some So this is some detail of how
129:27 do this. It's all efficient way computer. So, uh, GMT
129:35 . It is very fast, but a problem with the dft, which
129:40 , uh hmm, like a chief the call that gives ears.
129:50 So in other words, when you a function which has the,
129:54 shove age, uh, there will a miracle era because the reason is
130:01 forest transform using harmonics, which means sign way coastline waves, which are
130:08 waves, most continuous waves. It's difficulty describing the sharp boundary like a
130:16 alcohol maji using sign way. Because not. They're not. They're
130:20 continues. Okay, here's the illustration that because that gives ears. So
130:26 true answer should be box. But you see sign cozy, you will
130:30 over shooting under shooting on two Okay, so the reason we describe
130:36 is when you apply future using those Ah, boxes you can causing problems
130:44 near the shop ages so you might something called the paper ta pr
130:51 So, in other words, making triangle. Uh, how about reducing
130:56 lot on those, uh, over keeps ears. So something like this
131:03 taper What do I e There were . Okay, so that's why we
131:09 reduce problem either, uh, either D or three D or multi
131:16 This is often be used. You heard something like f k filtering f
131:22 . You know things. This is often used. Let me talk about
131:30 k here little bed, So f for frequency. Case stands for
131:37 Okay, the concept that is very simple. You have originally for
131:43 , Shah Gator, you have ah X, you have time.
131:48 I'll see em together. Something time . So this is two d x
131:54 to D you have one? You here like this. I'm just talking
131:58 You went there. Okay, if you if you apply two dimensional
132:04 transform, your tea becomes frequency. , my God. Frequency angular frequency
132:13 your X becomes with number K So that's where the F K came
132:21 Omega or can be replaced by F f k it stands for frequency.
132:26 a big number with the number is similar to frequency. Frequency is
132:34 uh, harmony cycles per time as frequency. Right? How many time
132:43 ? Homeless cycles per one second, example. Time. One second.
132:49 50 years, the 50 cycles away one second. That's the 50 hertz
132:56 numbers. Very similar is harmony wave per lands units. For example.
133:08 violence per one kilometer that zone, ? Okay, now let me Let
133:17 ask you one question. I'm not , you know, answer. But
133:20 just challenge you. You see, thought this trying asse always line here
133:26 this way. But this line after deep in this other way. You
133:31 why Salmon goes over here? Over . You know why anybody? They're
133:44 of like a perpendicular, right? , why is that? One thing
133:53 discussed yesterday is very profound. We that, uh, our certainty
134:00 We said this morning also, we something very late in times of
134:05 very short dementia relation will be very in frequency. For example, a
134:12 in frequency. What we were riding advance. But I something very narrow
134:17 frequency, like a single frequency in like sine function forever, you
134:23 the monochromatic way, Andi, that's . The same principle apply toe multi
134:31 . I applied that most dimension. see this perpendicular, uh, particular
134:38 between the two slaves in the uh, x g distance and time
134:48 the new frequency wave number? The are particularly yeah, yeah. So
134:58 saying particular abuse. This direction is long, right? That's for
135:04 Here is very long along in the X two man on the same direction
135:09 be very short. These directions were across the the events and that the
135:17 were along. But there are some differences. However, you have
135:25 most events go through zero because zero low frequency are loving number. So
135:31 have to start on zero. So not exactly everything the same there,
135:35 in cannot. Symbolically, but they're go from go through 00 in f
135:42 means low frequency, low frequency, number. Long prevalence Basically.
135:50 that is a long way away from is high frequency and high number with
135:56 observation. Okay, so here's an . Off data in TX. I'm
136:05 this data incense cartoon. I If show you that I will be very
136:12 . So you have a lot of here in in Tiesto, man,
136:16 events have lost. Lost the signal on. But when you go to
136:22 transfer them in tow, dimensional through dimensional first transform, it will have
136:28 space. There's nice separation of Why? Because the original events in
136:37 key extra man Tiesto Man, they different slope, their angle different.
136:45 the f k space. The events rearranged. According toa, where there
136:51 pretty slope original t estimate So the of the low, uh, the
136:58 velocity ground roll over here I have the noise will be there and so
137:04 so forth. So events will have better chance of separation. Okay?
137:11 repetitive of separation. But that's a thing. The drawback, however,
137:18 the sun will cause on wave. are pure article events. So you
137:24 make sure you don't go beyond their because you go beyond that period there
137:29 themselves again, again. That's called . Alias. Okay, So
137:35 worth a DNC areas the husband, you don't want to go beyond
137:41 Didn't beyond their past minus cycle, . If you're beyond, there will
137:48 areas you can artifact. Okay, word aliases kind of Australia word.
137:56 just means the frequency component, distorted or being misidentified, Miss
138:09 Okay. For example, if you you someplace not insufficient, you can
138:13 the, uh, high frequency in low frequency you alter them.
138:20 There frequently changed that. The words anything. So alias the signal are
138:25 that their frequency components are moved, frequency their their their author on.
138:33 arbitrary, Which is wrong. on there's a mother processing processing.
138:39 don't need to show DPR because you not most you guys, not your
138:43 , so that's okay, you also, this is not that important
138:47 For what? We're concerned. multiple example escape. I just show
138:53 some example. Okay, here's A few guitar stack. Surat
138:59 Australia, on this example off. data F K. Filtering so before
139:07 after. So this is just trying remove some of the ground role noise
139:13 the stack section. This is, , actually what was quite dirty
139:17 Not not in fancy. Just the filtering northeast. The quarrel are very
139:23 dipping events. Uh, those Cubans , different events. So by African
139:28 , they just removed. Just let think anything different Steep because they're not
139:33 geologists were gentle, very gentle, the results were nice. Nice
139:40 But if you geologists, we're still that this is love. The
139:43 Okay, this is not a very idea. So you gotta have a
139:46 , right? To for your uh, toe to solve.
139:53 uh, this one go back to very important, which is size me
140:00 . I keep saying this again but I'm sure the detail here.
140:04 this time the left black color curve the impedance curve, Remember? Impudence
140:09 , uh, uh, products off times translating on the very close this
140:17 . Okay, To wait 12. to weigh refreshing time. So for
140:21 presidents, we can derive the relatively that can call. Always vibrate,
140:28 . Okay. And then you can them with a producing the system of
140:35 this case is number five. Number is the result of conclusion number
140:40 This is the conclusion off privilege. your creativity. You can say this
140:47 . You can also say it's the field heard by the privilege. Give
140:53 number five. Okay, now four six other sesame trace near the world
141:01 logging World war for comparison, you say this is very excellent correlation.
141:06 high correlation. So we have very tired than the last ones in the
141:12 suppressing 567 So these are a mystery , why we care about this?
141:20 , here's the reason. Okay. showing you here. A seismic section
141:27 from data alone Surface the arable, here. I think verticals is
141:32 Okay, Uh, in milliseconds, know, one second here. Two
141:36 here. Sleeping here. So the seconds later a sense position here showing
141:42 lot of events. So you want say Oh, what do you
141:45 what? The geological age. How interpret you care about those things
141:49 Which is great. But the problem , as I said, the quality
141:54 on not only resolution, but also are in the right location. Are
142:01 real events or not? In the war, the best way Among the
142:07 ways, one of the best one the best ways is sex Muto
142:12 Which means you have well here from well, here, from where you
142:17 impedance on relativity derived. And if can tire tradition from, well,
142:24 call that a small ground just like were here, showing that one there
142:29 you can tie that with the This is a lot of the best
142:34 ever seen. So you can see are very good time. So even
142:38 , even here, even here, all of them are tired Very well
142:43 their this ties. That here. , but majority of entire very
142:50 this is almost like a training dirt gold. I'm saying that assessment section
142:57 useful, but, you know, really that's control onto your tie.
143:03 you tie, then you're suddenly becomes because they can. Really? Because
143:08 well logging Give your ground truth. can tie with the study graphic,
143:13 with rock samples. Core samples, ? If it's actually types that that
143:19 everything to see Princess Me. Probably . Riel. Not really really the
143:23 off relativity geometry they also choose for the location that will be great for
143:34 drilling plan. If you're gonna feel with a seismic, you have very
143:38 confidence now. So this is extremely now that process off suddenly water high
143:48 the skill off one. We just just win, namely Correlation Conclusion.
143:55 use both of them. We use coalition's producing the same program here
144:01 well, well, well logging, coalition toe. Quantify the similarities and
144:08 where we use those. That's why was going on time for about conclusion
144:13 you feel this way that way because very important. Okay, so there's
144:21 about details about Well, hi. don't have time to go through
144:25 but I'm just list to give you key factors for certain. Wockhardt,
144:30 I wouldn't be surprised if you find job in oil company one time,
144:35 job will be set in the This is very technical. It's not
144:40 easy job, even for experienced because there's anything can go wrong.
144:47 , so there are some noise Lots of noise there. So I'm
144:53 again on move on here. But can be color noise can be white
144:59 depend on special properties. There are methods, more separation methods, some
145:05 model driven. Some are data Okay. And going to the example
145:12 . You saw this before. I to show you another way to look
145:17 the same data. You something before is a comment together, right?
145:22 applaud this upside down because the originals . I'll sit down. So
145:26 Time's not done? Time's up Going up. And the point is,
145:33 coming, Communist model. How do go from this data business model?
145:37 the question, Right? So you to study the first to see what's
145:42 on. Uh, data here, for survival is here. Okay.
145:49 this is a refreshing highways. This a reflection here, so just simply
145:54 with data. You can see, most prominent official in the data is
145:58 reflection. Because we care about which refreshes very strong. Can you
146:03 the headway? Well, we know head away because by reflecting approaching the
146:09 rival, that's where we caught a point. That's where. So critical
146:15 . Okay, You know, You're so here on the profile you
146:24 . Have ahead. Wave on that is called a When the first time
146:28 the head away. That's the critical . Okay, here is critical distance
146:35 the flashing overlapping with the first rival that point his head away.
146:46 He wants your head wave until beyond critical point. Okay, so my
146:54 here is OK, this is Because if you're fleshing But if you
146:58 about the Boston model itself, you to find out what's the value of
147:03 velocity? For example, we won with three, So here I'm showing
147:09 a quick, dirty way. The we one way to be three using
147:15 grade first break means a p way earliest. But first breaks very complicated
147:24 different power points, they mean different very close to the source. They're
147:32 arrival. Traveling on service. We them right away the right away.
147:38 . I'd rather be traveling or likely the Thursday which also traveling on
147:43 This is certainly this ground rules of way the way we are. Those
147:48 traveling on our service, they're going way on this part of the near
147:56 First break, most three, threat of legs. But then close
148:02 the, uh, critical points starting , uh, her way. So
148:10 will become the first viable? How way this guy here is going down
148:15 travel along here is like the head traveling on the high speed part.
148:20 right, here. Although the total longer, but because of high velocity
148:25 below. So this wave become faster this point here, that's right away
148:34 the head wave, aligned together with way refreshing here. Headway. Because
148:40 is refreshing. This headway there are similar. They're very close to each
148:46 . That's why they're crossing each other . Okay, so it's just like
148:50 argument. So I'm joined here. finals. We want be true with
149:02 . Remember my body calls time. husband knows distance. So every triangle
149:08 close there, huh? Horizontal Most X. Right. So you have
149:14 appearance velocity you can dividing. There but that he gave you the
149:21 Can you tell that last year the red box here? Can you tell
149:25 the body most of the lost value notice But there are t Here's one
149:37 . Here's a five kilometer So the of the triangle Cardinal length Look here
149:44 about 1.8, right? So the here is 1.8 kilometer per second Makes
149:57 because horizontal part of the triangle is In this case, I'm estimate is
150:04 seconds At 1.8 kilometers. Maybe you not right. Maybe 1.7, I
150:09 know. Close to 1.8, approximately kilometer. The vertical part of triangle
150:15 one second, So you're credible. is slow. It's the 1.8 kilometer
150:22 second right At the same talking, can look at the size of triangle
150:30 green triangle here by measuring the horizontal vertical on to see the apparent
150:37 This one clearly was higher than one one high velocity. I don't
150:43 I didn't compute. Maybe 2.52 point ? I don't know exactly. On
150:49 third one, we three the blue even faster because over a very small
150:54 , then verticals time, you have much longer. Distance. Okay,
151:01 three kilometers per seconds? I don't exactly. Maybe even beyond that.
151:07 the key? Interesting point is you estimate those velocity by this way.
151:12 you know where they are in the here is we want, which is
151:15 last year surface. Here's a big , which is velocity The bottom
151:21 First later, before the critical point is critical wine with three is we
151:27 the off the bottom layer on So we want smaller than way to
151:32 to smaller than with three. So increasing the steps. So this shows
151:39 I quick way to estimate near surface using first break. Okay, this
151:51 very effective, but the drawback uh you cannot go deeper. It's
151:56 the You gotta have reflections, strong . Uh, in order to do
152:02 on, if you don't have enough , you cannot go very D.
152:06 only the very shallow part. Any . We're happy, right? Are
152:16 , I'm sure. Let's keep going I can show you some more
152:22 Here, I will try to slow here, just showing cartoon. So
152:27 put here the same thing. How see before. I'm sure you some
152:31 quick credibility ways here. Cut the Utilities next plan throw away because we
152:40 want to using the first grade because are not reflections. So for
152:45 stack of reflection profiling. We often away the first grade part because the
152:51 music Okay, also, if you have time, you underground for
152:58 you know, urgency off produce We also do crack away, off
153:03 the, uh certainly There's a certain which is to interview. Okay,
153:09 can also doing program if you So we're often piece one. We're
153:14 the data we have here. We're to stay those data we got
153:21 This is a make a quick anyway using the selecting the reflections on producing
153:31 . Okay, so I'm just already you some flavor processing. You can
153:36 fancy ways, but this is Anyway you can see the concept.
153:41 are other offensive One has, like . Tao is slowness is a pretty
153:47 . Topics It is a slow so we can produce by using original
153:52 manners. This p here, slowness . Uh, this is an excess
153:59 sources. You're all set. So means of our velocity. So that
154:04 this means basically the offset divided by outside of development velocity. So this
154:10 the P. So this will give the slow off the events, how
154:15 give a slope of events. People called it a slam stack, but
154:19 just too many different names. I want to confuse you. So we
154:24 called the leader move out. Basically something flat so you can use in
154:30 transform. So he becomes, she becomes Tao on X t combined
154:38 the p, the slowness. so then it's like for something that's
154:45 . So I'm just giving you a show. Your idea. So this
154:48 the original Better. Okay. Events as, uh uh, have a
154:54 curve. Right? So if you part topic to become those will be
154:59 separate on the main idea of toppy toe. While the reason for using
155:05 is toe based on the slope you might say some events you want
155:12 some because you don't want. Maybe separated. For example, we're often
155:18 a topping space. Your multiple reflections be in different locations from your primary
155:25 they have different slow. So people also using copy to do,
155:32 multiple separation multiple multiple suppression because they using, they want extracting the primary
155:39 for emerging. Okay, there are ways to use this. I had
155:44 students. I have a students recently Kauppi toe do better attenuation que estimation
155:53 the curious dimension was old was contaminated the or hanging or burning, in
155:59 , including multiples. So he was Kauppi to the separation on which found
156:05 be very effective. So we're often small technically this once, once more
156:11 help us has the signal reduced That's the main purples. Okay,
156:21 last one is very sure. I give you a concept about how to
156:25 near surface. Your service is always not only for land data, even
156:32 Marine for near Shore Marine you can a problem too, because we're show
156:38 Gulf Mexico or some lakes. You , floating can slow area Continental slope
156:46 . You can have a steady Okay, I'm sure you this
156:50 Piece of line here. You can the different geology if you go to
156:54 you can see the rocks. You can imagine the excitement serving those
156:59 . The quality gonna be problem because lots off near service violations.
157:06 Ghali's there's they're not even nice place you. Like this paper area.
157:14 put yourself receivers on the topography. problems. Okay, so in the
157:21 , we do this. Okay, have desert desert area, so
157:25 So we do a lot of those . The problem is the near
157:29 because the low velocity and also undulation going through this dirty glass, your
157:35 gonna be impacted by this. So typically called data data means the surface
157:44 which we have our source on So one way to do this is
157:49 called vitamins, which means you go original statue, where true South Korea
157:54 trying to kind of projecting what is to be below this dirty glass either
158:00 floating that you are flat at So you try to kind of peel
158:04 off so you can go from there see where they already is on their
158:09 . Way of doing this. on this is one slide missing.
158:13 just spend the a few minutes to make a slide. But I didn't
158:18 enough time. So my next slides , very busy. Very, very
158:22 . You can see. Obviously it . This is about a very,
158:25 busy. Maybe you said this is to busy. I can't read
158:28 But my problem is I know after to my lecture for 23 hours.
158:37 think you're interstate awful. I don't that it works for that cause
158:43 Okay, a tous time. If do face to face, I'll say
158:48 can't be monkey. See, monkey whatever I say said yes.
158:52 yes, that's my fear. so I'm going toe elaborating a
158:59 So first of all, what is correction? Okay, That just means
159:03 you're shifting things. Whole trees down, statically whole thing up,
159:09 . Okay. Remember that trees, friend. We talked about. Where
159:13 it? Remember the treated we talk ? I think the question,
159:18 armor. Remember? You asked me question about that. The flattening come
159:22 shout together versus, uh, same together. We talked about the
159:28 offers. Remember that one? Do see those vertical lines here? So
159:33 can do this? Corruption by studies . That's what we talk about
159:38 So we come back here. That's what we say now. So we
159:42 to do some studies shifting to credit this. Okay, so we're here
159:48 , so I put this lot show your idea, but in a
159:51 way of doing this, you can refreshing aesthetics, which is long prevalence
159:56 , Uh, basically, we find how much we can shift. That's
160:00 we're looking for. We want to out the whole much We can shift
160:04 that trace, but there are Many will agree with this. I'm
160:09 the whole class one slide. That's problem. So we have a refreshing
160:15 , reflection, aesthetics and trim There also solves receiver studies. There
160:20 many. Many of those, but ones are three refreshing reflection on trim
160:29 . Refreshing is using first rivals doing square fitting for the arrival times of
160:36 flat reflections using refreshing time. She'll also pick the time actually finding where
160:43 state is on financial. Okay, those two are easy. The difference
160:49 refreshing because it's powering past more hard refreshing or horizontal. So they're more
160:55 reverence, refreshing. The result will more short women because, myself
161:01 I mean the space in between the , we're shop shop nearby.
161:08 the last one train aesthetics. This basically as statistical methods were basically
161:15 Labels doing correlation, a shifting So kind of arbitrary neighbor to neighbor.
161:23 refreshing is very long spacing. Long reflection is a small spacing, maybe
161:32 or 20 trees. Teams that is close. Just neighbors. If you
161:41 in that, which one gonna Most efficient? Yeah, dreams that
161:44 most efficient. The problem, is very actually is shifting.
161:49 there's no physics, so you have huge impact, but it's a big
161:53 . You can make a lot of lot off shoes Mistake's because you can
161:57 if the wrong thing right. generally speaking, most people like to
162:03 them looking for which was better, and so on. That's a big
162:08 . Then they're looking all the result combined. So that's a general idea
162:14 the static prosthetic processing. I'm done . Okay, but I want to
162:19 you the fancy way. Now there's fancy way. But Thomas Medics,
162:25 is Thomas. Thanks, Paul. is actually taking the arrival times.
162:31 using the wrong time doing tomography, means deriving a model. I've lost
162:35 model for the whole field. Your . They're using a glass bottle to
162:41 the correction. So you see, fancier. I'm not require you to
162:46 all the detail here. I'm gonna you some kind of relaxing at the
162:49 of the result. My main go for this section. Introducing the study
162:56 on a common way of doing So you already hear one talk about
162:59 about it, the flashing aesthetics, , aesthetics, train statics on Thomas
163:06 four methods. You need to memorize . This is that some detail?
163:12 this is example tomography. The top . My initial model. Uh,
163:18 I can still be my point. what happened. My point here.
163:22 this is initial model with four This is ah, lost value meter
163:28 meter per second. So it's very . Velocity 600 is very, very
163:33 . High velocity below. Right this is a two different tomography once
163:38 constraint constraints. We can we don't to see that you feel this is
163:44 one. We can we Don't because we can We can call this
163:46 later on. Okay, this is of show you tomography. So flying
163:51 model you actually interacted with work for . So initial model, this is
163:56 model. This is that synthetic This is many packs that you want
164:01 Melo that working for. So it's you are approaching, right?
164:08 Okay. And this is resolved. , you can see what Not much
164:14 , but if you look deeply or actually you can see there's something
164:17 So initially there some events here. is very lousy that, as you
164:21 see much, but after unconscious you see some events here,
164:27 This is constrained tomography. So That has very hard to say.
164:31 much improved? But I'm sure you can say something now better here than
164:36 . You can say what happened that , that's some artifact that those events
164:41 the real events, reflection events. can also see another way.
164:49 this is This is I shall get . This is what data you can
164:56 . Whether that should have a hyperbolic . But they're not a very hyperbolic
165:00 kind of there, but they're not clear. This is other Sandy,
165:03 , correction. This is after constraint tomography. You can see the front
165:10 which once more, which is one symmetrically e think tomorrow is more symmetrical
165:18 the hyperbolic occur. You see It is very small, tiny
165:25 but I feel that it is very activities. Okay, official other
165:29 The commercial companies. This is my we can compare. So there more
165:34 one way notice here. Okay. is here. Can't see it.
165:45 better ones. One with the We'll see more everything. Hyperbolic.
165:49 more right. Answer once. The hyperbolic is not the answer. Another
165:56 thesis CS to another company company. . And some other comparison. More
166:04 . We're done. I'll skip The last one there Too much in
166:13 in the name of time. So saw. I don't want to,
166:18 . Bo w down Put that I always want to leave a few
166:23 for any question because we cover a of ground. Do you? Not
166:33 . What is the constraint for the ? Demography upholds. There are many
166:39 to construct them. In this I didn't I don't have anything.
166:43 imagine. Construct using the flashing shallower they're not uphold here at all is
166:48 death area. Sandy, Um, not know awful. You cannot uphold
166:54 uphold their the same collapse. There's . Yeah, it's very challenging
167:00 Actually, this company thinks is not by me. I I give them
167:05 methods. They compare their very happy the answer. Uh, there are
167:10 countries coming here. They're the best for Thomas Athletics. But this kind
167:14 call me this was a long time . More than 10 years ago,
167:17 even 20. They call me the told me the answer. My
167:21 my methods better than two companies. want your name, but they're the
167:25 tool. Mm hmm. Thomas, economy. I don't want to
167:32 I don't want to say somebody else worse than mine. That's what I'm
167:35 . Because maybe I'm lucky this But anyway, you are rather this
167:41 could become doing research, right? just want to give you idea that
167:45 surface is really, really, really . If working for a company to
167:50 data like that permanent basis, for , our Middle East. My
167:58 Static headache forever. You come to 50 years ago. Three years ago
168:06 . Same issue, some improvement. huge. Yeah, but Thomas,
168:13 is right now the best way. I was working for Exxon, I
168:20 my clothes in my early cause for they put in their products. So
168:26 was using my clothing. Excellent. Thomas status that time. Not
168:29 I don't know. They were I I was there a long time
168:33 Middle nineties? Yeah. I didn't thing for them imagining. Even though
168:39 only spent a year and a I think my coat was such a
168:44 . Almost automatic. They don't even a model. They feel they can
168:48 out. I would like to be professor. So I come back your
168:55 . Did you work with Chuck? ? Lots of people. I don't
169:01 of people. Many people I I think many people know Already
169:07 No, there's one guy. I one paper with you guys about the
169:11 shift you can find yesterday. Not . Right? Top officials compared to
169:17 a zero case, The guy named murder. I was with him.
169:23 retired long ago, but he was very famous. He was another formal
169:27 president. In 1979. He was SED president. It's a big
169:34 Next very famous guy. Yeah, work together, you will see more
169:39 his name's. I've seen some more on a conclusion. But anyway,
169:44 lot of things covered here today, this morning, as usual, but
169:49 focus that you can see, I a lot of focus on the
169:53 There's something really simple, but you did not. And also the connection
169:57 conversion on the coronation. You'll see again because I want o repeat the
170:06 concept. You got to see them , again, again. So you
170:09 it. You know, it's always way in the beginning. You you
170:15 to know? What is it You ask question. Why do
170:19 Why is useful? But eventually I truly that useful. You want to
170:24 a little bit about how you don't it, But you need another
170:28 So you know, other people do . Maybe you can be a
170:32 but you should know your work I think the right thing. Our
170:35 thing. That's what I say. know what you're doing, right?
170:40 can't know what you're doing. Any questions? Anybody? We do have
170:48 more Chris today, so I just a few more minutes. People will
170:52 to create same star yesterday. Same . Okay. Gonna be to support
170:59 , gonna be compared differences of terms things like that. And I ask
171:04 to compare, for example, Trim versus reflection. Statics, for
171:09 I'll give you slide it already So can do that. Slide. Any
171:15 questions, folks? You're gonna be out the quiz again. The queen
171:22 be showing in the blackboard. if you can accept to it if
171:26 not, I'm gonna email you. not saying it on blackboard. So
171:30 you could email, that'd be It's not there because times their put
171:35 11. 50 around 50 in four Everything time. You know, I'm
171:44 of program my time by my everything on time. But I'm already
171:50 already today because I have a lot you guys need to tired, So
171:53 tryingto so this early. So let send you by email anyway. Osama
171:58 it. Let me, if you question close this. I'm gonna I'm
172:03 show the show the question. We send you to your email about that
172:08 I'm not sure you guys can, I'm not sure all of you guys
172:16 ableto see the blackboard just few So let me raising with Blackboard.
172:21 I'll feel the recent race e getting your your your names here first.
172:27 the problem. Always take time. , my goodness. Where is
172:37 One second. Almost there. I'm trying to follow your law.
172:45 vision rule. They don't want me email you guys by open email.
172:49 wanted me to see me about That's why I have a copy.
172:53 do all the stuff. You it's a strange way. Okay,
173:01 got it this time. Cure Oh, my goodness. I e
173:20 else or is my cue tool I'm than than than the that. Because
173:31 So where? So what can I ? Yeah, Maria should be
173:44 Yes, I'm here. Yes. you guys see it? You be
173:59 see by emailing all Okay. Okay. Good. Whoa. I
174:17 know. I'm not doing this My eye hurts after steering this screen
174:21 that for this law, you So let me go over again.
174:26 time eso let me share that so can go on with it. Where
174:32 it? Yeah, you guys can it, right? Okay, let
174:41 go backwards. Let me talk about . First, I'm gonna give you
174:45 one more question. Last one. giving one question. Come all going
174:51 times serious before the
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