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00:04 Okay, so this is the entry for um uh the lecture for our

00:13 on poor elasticity. And so what question that you asked is uh embedded

00:20 here. So let's see if we find it 1st. Let's remind ourselves

00:30 we want to do um quasi static measurements. So this slide yeah.

00:43 this slide shows data which was acquired the laboratory by a friend um uh

00:52 uh with the purpose of verifying that gas man theory. And so the

00:58 theory as you recall, is a that tells us how seismic velocities depend

01:06 the contents of the force. And um it makes a prediction um which

01:13 shown here in red as a function confining pressure. And the the prediction

01:21 done independently expression. And then you the data there which systematically violate the

01:29 . And so uh first let's uh about the discrepancy. You see the

01:36 is pretty big here and it gets be less at high pressure. So

01:41 understand that being due to the closing cracks as we increase the pressure uh

01:47 the laboratory. And this is confining and in this case the poor pressure

01:55 . So there is water in the . But the poor pressure is uh

02:01 . So, uh so the problem that there's a um a discrepancy that

02:10 see here. And furthermore, we infer with a lot of confidence that

02:15 discrepancy is due to the decreasing population cracks in these rocks in this rock

02:21 we're squeezing. But the cracks don't show up anywhere explicitly in gas

02:27 Uh, they're implicitly inside the data shown here. The data for the

02:35 in compression. So this obviously depends how many crafts there are. And

02:40 one too. And here the difference predicted here and it's wrong because evidently

02:47 features, um, there's consequences of cracks which are not included in the

02:56 . And so, um, we remember that the cracks are not a

03:04 of finish. It cracks in the . The pore space in the rock

03:09 complicated, fully connected. Uh, and parts of it are thin and

03:17 and parts of it are, are of roundish, you know, between

03:21 grains. And so we refer to parts that are, which are thin

03:26 flat as cracks, even though, know that they don't really look exactly

03:30 it. Right? So this is long stance. This is typical.

03:35 so it's been understood for a long that this is natural because the gas

03:42 theory serves low frequency. And these are taken in the laboratory at high

03:48 ultra signing means hundreds of thousands of cycle, but hundreds of thousands of

03:53 per second. Whereas the gas monetary its quasi static. And uh,

04:02 , and the statement here says that use the gas line theory Anyway for

04:07 70 years. Um, uh, though it's not even though this kind

04:13 this, uh, lack of verification typical because we say, okay,

04:19 the experiments violate the assumptions of the . We believe the theory. So

04:24 going to assume that at seismic frequencies low enough um uh frequency,

04:31 you know, say between 10 and hertz and uh that's not zero

04:36 but uh that's probably good enough. so that's the argument people have used

04:43 Over 2/3 of a century. So your question asked about quasi static.

04:50 , uh let us skip forward uh the um uh in the final,

04:57 step forward to uh where that is . So, I will remind,

05:15 will remind you that um um The Theory, which was published in

05:25 was generalized by Brown and Karenga in . So, 25 years later,

05:34 to this form. And you can that um um in place of the

05:41 compressibility, it's got something called kappa and something called kappa M. So

05:48 parameters in here. Now, what and Kruger said was that if the

05:55 is only one mineral, and if mineral is an isotopic mineral, then

06:00 uh three things are equal. So that is their result is the same

06:05 Gasman. Uh But this argument by and made the same mistake as gas

06:12 , argued earlier, the gas man a mistake, a logical error.

06:16 this thing is actually wrong, even everybody believes we should instead be uh

06:26 this formula with two primers instead of . And he noticed that neither one

06:31 them is the solid compression. Also are two strange parameters to to and

06:40 that's what it says. We should the brown and result in all

06:44 So then the question is how to determined. And so we don't need

06:49 determine the campus and prime it. Brown and called this the the poor

06:56 . They didn't give names for But uh here's how we're going

07:03 Uh So the first thing we're gonna is put this result into the brown

07:07 result in the Parliament Karenga formula. now you see uh we have um

07:17 compression multi. And and uh still have this campus event. So we

07:26 to you earlier that uh there's a a good argument to be made that

07:32 M. Here stands for means. gonna call this mean compression. And

07:37 the mean between the solid and the . That's what it is. And

07:46 least in this form we got rid this one. So we have only

07:49 unknown Brander. Now this comes directly to your point. We've got we

07:57 to determine these things all of these with quasi static experimentation. So this

08:05 and this one and this one and one we want to determine all with

08:11 static experimentations in the laboratory because the assumed low frequency. So we if

08:19 gonna verify the theory, we should wow, observe the assumptions in the

08:27 . You should do experiments which conform the assumptions of the theory. And

08:33 to do ultrasound, to do a static experiment to determine uh the frame

08:38 voltage. Well, one thing you do is just take uh advised sample

08:43 then squeeze it uh squeeze it with , say with one hertz or maybe

08:53 hertz frequency. Just apply a steady Torrey squeeze. And then you know

08:59 the pressure is. And you measure is the string. And that's how

09:04 determine capital five. Similar thing with and drain. This is what we're

09:08 to need for the seismic applications. so you just have the same sample

09:14 actual water. And of course you to have a jacket around the sample

09:21 that we can squeeze it from the . Uh water from the squeezing doesn't

09:28 into the rock. And that way pressure inside the horse space on the

09:35 sort of depends upon um The framework work itself. It's going to be

09:40 than the confining pressure. It's going be different than the uh pressure in

09:46 grains. Uh And that's part of problem. But at least we know

09:51 now we're simulating what happens as a wave. Those rocks in the subsurface

09:58 because those rocks and sub service, don't have any place to squeeze the

10:03 into or out of. So we that situation in the laboratory with a

10:08 a jacket around the sample. that measurement is straightforward. These two

10:17 are not so straightforward. So let's at them. This is how we

10:23 the solid compression of. So Uh back in 1927, uh th Love

10:37 this here is true to you. do an uneducated test. And so

10:42 means you're squeezing equally on all sides the same pressure. So that's obviously

10:49 the same as uh wave propagation, that's what we want to do

10:53 And when we do an jacketed, mean that we arrange for the fluid

10:58 to be equal to the to the pressure. And the way you do

11:02 is to just to remove the jacket that as you squeeze from the

11:07 uh fluid squeezes into the sample, equalizing the pressure in the pore space

11:14 in the outside. And what love says that surprisingly, if you do

11:20 , the modular, which determines the in volume, is the solid

11:27 Isn't that remarkable. It hasn't got to do with the rock itself,

11:32 only the solid part of the rock . And so that's sort of a

11:37 conclusion. But that's well uh confirmed experiments um over many years.

11:50 Now, when um Love proved this in 1927, he assumed that the

12:04 was one mineral, 1 icy trophic . And in real locks we have

12:10 minerals and all of them are analysts front. So that's why we put

12:13 bar here. And I see I to put the bar here. So

12:21 it says here and not one is when we extend it uh said we

12:26 love serum from head from homogeneous silence heterogeneous silent when we expand when you

12:33 it. It is true that what measure at this point, that we

12:38 it right in here, see what know what this is. We measure

12:42 this is. So we determine what is and what we know is that

12:48 quantity depends upon the Micra geometry and as well as its composition. So

12:53 can't we can't say okay, we uh Uh we have a sandstone with

13:03 ports and 30% magic place. We say that what we measure is representative

13:10 all such sand stones with with that composition because the answer, which is

13:19 we measured, it depends on the geometry as well as the composition.

13:25 when we selected this sample, we that it's representative of a larger

13:29 And so uh even though it depends the micro geometry, which we might

13:35 know very well, we might not how those plastic place crystals grains are

13:42 within the the rock framework. Um might be this, they might be

13:52 we don't know what they are. we have already assumed that when we

13:56 this sample, it represents not just , but a larger formation of that

14:03 um uh sandstone maybe with fellow Maria , maybe something else. And so

14:10 is a non issue. Uh the that it depends upon the microchip.

14:17 already assumed a rock sample has the micro geometry as larger rock.

14:26 Um, here's another note. This a new jacketed dated. That means

14:30 we squeeze the rock, some fluid into the rock from outside in order

14:36 establish that these two pressures are the . So that's not what happens during

14:41 passage of a seismic wave. But argument here is we can use this

14:48 procedure anyway, because the solid compression the same in both the undrained contact

14:55 way publication and in this um jacketed . So that uh and of course

15:01 gonna be doing this at uh quasi frequencies. And it's a good idea

15:06 do it cycle a plane, not squeeze it once and may here

15:13 but to cycle it up and down and down up and down up and

15:16 . Because when you do that, get more accurate. The random errors

15:22 out when you measure over and over over. So, um that's why

15:29 do staff. So the next question how about the mean compression? And

15:37 we can do that also from an drain static, quasi static compression using

15:45 formula, which I won't repeat. a point out too that here it

15:49 the mean compressibility and depends upon the compressibility. The undrained compressibility. And

15:56 quantity B which is defined here as ratio of the fluid pressure to the

16:02 pressure in an untrained experiment. Remember here, those two are the same

16:09 a non jacket experiment. Now we've a new grand experiment and this is

16:14 the experimentally observable. We can we actually measure that. We we don't

16:21 everywhere inside the rock of course, we can uh we can measure near

16:28 surface of the rock in the pore very close to the surface of the

16:34 . And we've already assumed that it's inside that rock sample. And uh

16:43 don't know that's true for sure, we assume it's true. The only

16:50 we can really prove it's true, think, is via numerical experiments.

16:56 here's what we can do numerically. We could make what's called a digital

17:04 of this rock and I won't go the details of that. You can

17:11 can use x rays to determine where the complicated for space in Iraq.

17:19 up to a certain resolution obviously can't the smallest parts of the four

17:25 or the smallest parts of the But you can do a pretty good

17:29 to to define the very complicated interconnected space in this rock. So now

17:36 have a digital model of the rock and then you can squeeze that in

17:41 computer and in the computer you can everywhere in the um, you

17:49 was the local for uh, when you squeeze it from the outside

17:57 uh quasi static compression. And uh, if it's uh, wherever

18:05 natural, it's pretty much the then you conclude that the permeability inside

18:13 rock sample is good enough so that fluid pressure is able to celebrate everywhere

18:21 . And if that's not true and then you say, uh,

18:25 might have a problem here. Uh the uh, food pressure is not

18:33 inside this rock at 10 hertz is at one hertz. Is that uniform

18:41 uh Attentive, it hurts. How do we have to go before we

18:47 this equal? Uh, for pressure it's being a then squished um from

19:00 outside. And so, uh, my knowledge, those experiments have not

19:04 done. Uh, the answer when are done, I think the answer

19:09 gonna be, it depends upon the sample. So, for the

19:15 I think probably 10 hertz is going be good enough with the shale,

19:20 has uh, maybe the same Maybe lower ferocity, but comparable

19:26 but much less permeability. That's the shells are because of their geologic

19:33 And so it might be that for Hertz is not good enough, maybe

19:40 need one hertz write something less. knows? Uh, the experiments have

19:45 been done. So that's how we going to determine the two parameters Campus

19:52 Madison campus of M using static, static compression. And then we do

20:00 uh in order to um Yeah, . Yeah, the grandmothers in uh

20:12 and fingers theory. And so let me see here. Yeah.

20:19 , uh, here your shows that two numbers are not always the

20:27 It looks like they're about the same low pressure, but they become different

20:32 higher pressure. And I'm not sure understand the reasons for that.

20:38 course, as we're as we're squeezing we are squeezing cracks out. And

20:45 anything, I would have expected the . I would have expected them to

20:49 together at high pressure. But who I to say what the rocks should

20:54 . So, this difference here. , this right here shows at least

20:59 this product sample. Uh Gaston is because these two are different and furthermore

21:08 more uh, Maybe even more important geophysics, we commonly don't do

21:18 Why not? Because that's a difficult to do. You have to get

21:22 sample. Suppose you have 40 data you want to interpret it. You

21:27 some 40 differences due to production inside uh, reservoir. And so you

21:34 to interpret that in terms of changing fluids and changing fluid pressure and

21:42 changing ferocity. So uh do that by the theory. And so the

21:49 we almost always use is gas And and when we go to apply

21:55 theory, we don't have a rock to measure like this. So what

21:59 do is we say okay that's a down there in the reservoir and we

22:05 we know its composition. And so can calculate the solid compressibility using formal

22:12 or in the literature. And since formula um don't include the micro geometry

22:18 , all the formula do are given bound and lower bound. And that's

22:22 here. This is called the voice . Voice. This one is called

22:29 void approximation and it's very common to the meaning of these. Well so

22:35 are so close together for this rock is not a big deal. But

22:40 point is the data for for the congressional lies well above the upper me

22:48 upper maximum. So uh that's a difference. So um we have Serious

23:01 with almost every four d. Size interpretation because almost everybody is going to

23:11 using this and instead of this and don't even know about this, most

23:18 you are blessed because you've been given insight into the latest thinking there.

23:24 even even those people who uh don't or care about brown and Karenga.

23:31 they don't know and care about the compressibility. They should know or care

23:36 this difference between measured uh solid compression and the radical, Wow, what

23:49 difference. So you know, if were interpreting 40 data and using the

23:53 privatization, um you could come up a conclusion which could be worth a

24:00 of money to your employer because he might be uh make uh planning his

24:07 , well based on your analysis, might be uh oh planning to uh

24:21 another production platform, spending a couple billion dollars based on your interpretation.

24:30 um this shows that that interpretation could really wrong. And so uh the

24:39 to this is to do a lot experiments like this, see how typical

24:44 is, and also to see how this difference. So does that answer

24:50 question? Yes. And it actually to the reason I asked the

24:56 do you think that this would be much to take on for like a

25:03 ? Um because this is one of first things that I've actually found like

25:09 interesting and I have all of this available to me to use at my

25:15 ? And I was just wondering, you think this might be too much

25:18 take on? Or is this like good capstone kind of thing to do

25:24 I've described you? It's too It's it's a PhD thesis. Not

25:28 capstone project, but I think it be possible for you to do a

25:34 project based on data from your employer your uh stress test. And so

25:43 what I would encourage you to do to uh um organized in your

25:52 what you might think is would be suitable capstone project and then run it

25:57 uh Professor Van and me. And see whether um we agree that that

26:05 make a good capstone project and uh we might modify the ideas. Me

26:13 I'm very confident that your employer will very happy if you use his data

26:19 uh do your capstone project. So um uh you know uh neither Professor

26:29 years Normie are familiar with the assumptions procedures that your company uses but we

26:39 enough background, we can probably bring insights into those and say oh well

26:45 we understand what we're doing, you that um those experiments are done based

26:51 assumptions which were made 50 years ago we can do better now. So

26:57 let's test, let's see how we uh suggest modifications of these procedures Uh

27:08 the 21st century. And let's see would be required to uh buy

27:15 So I would I would encourage you think about how you could use your

27:21 data to uh underlie a capstone project run it by dr and he'll probably

27:32 me in big game. Uh but as it shows here, we need

27:42 dozens of experiments. Uh And um said this is a PhD thesis to

27:49 out the differences here. But I like the idea that you could use

27:57 current data to you understand your job and help your employer understand his data

28:06 . And you know maybe what he do is he can say to his

28:12 , well we were doing these classic and now we're gonna offer you uh

28:18 costs, we're going to offer a product. And so if uh the

28:26 agree that it's worth their money to your bus to do this uh um

28:34 uh works out, then everybody's gonna happy. Even the customers are gonna

28:39 happy because you're gonna be helping them their um situation better. Okay,

28:49 with that let's um get out of . And so yes. And I'm

28:56 stop sharing this and I'm gonna start this one. Okay so this brings

29:11 back to the final lecture um Which on an and uh I want to

29:20 up a little bit to make a treatment of this problem. What you

29:27 here is a real data old. again, probably 40 years old.

29:32 what we've done is taken a reflection data where all of these events started

29:38 moving out down this way and then corrected them all uh short offsets using

29:46 hyperbolic flattening formula that you really And then we were left with this

29:51 hyperbolic overcorrection at the forest since it bending down and bending up and so

29:58 need to bring this back. So was the way uh was first proposed

30:07 handle this back maybe 40 years And they said okay let's add another

30:13 to the taylor expansion. This was hyperbolic term, add another term but

30:20 um not so long ago, maybe years ago a colleague and I said

30:25 modify this by putting in this term uh based on our physical intuition and

30:32 simply gonna modify this and it's gonna we're gonna choose this parameter and this

30:40 Beverly to uh uh behavior at very . So that's where we're going to

30:49 it. And then uh that argument sort of independent of an ice ax

30:56 . But that colleague same colleague, name is Shrunken Russian name, he

31:02 a colleague of my chemical and he to become um professor at Colorado School

31:10 Mines which despite the name has a good geophysics department incitements as well as

31:16 . And so his very first student was a guy named Oak Leaf and

31:23 guy was here on campus this last . He is now a famous professor

31:28 in Saudi Arabia. And so he this formula. Previous formula. So

31:34 let me back up. So in previous form and we got coefficient here

31:39 a different coefficient here. But now see we have only 1 to 14

31:45 to determine. And we renamed So instead we renamed this one here

31:52 of plus 84 we named it minus ada so that ada would turn out

31:57 be a positive number. And it's same ada down here. Isn't that

32:01 . And uh what is ada in of the anti central parameters which we

32:06 earlier, epsilon minus delta over one two delta. And here's the student's

32:12 . And uh so this was almost years ago, almost 30 years

32:18 Um so, uh that's fun. this is only for a single and

32:26 traffic layer. And so um we have that situation in the subsurface.

32:33 uh oh, before I come to , I'll just remind you of uh

32:43 with the previous uh previous formula. It's complicated and we don't need this

32:51 anymore because uh we're gonna have the quantity here. And when we determine

32:56 , it's gonna also determine this. , the reason I'm showing you this

33:05 . And it's a topic version is whole 4th order term in the iC

33:12 case of many isotopic layers. It from ray bending as the wave goes

33:19 through that overburden with all the And so, you know, that

33:23 same sort of effect is gonna be there when we have an eye

33:27 So um uh all we're going to is we're gonna change uh notation a

33:36 bit of uh So to find that two star we're gonna talk. This

33:41 the same hater that I showed And the deal is once we determine

33:46 one. It also determines this. here is what the community has learned

33:57 do over the years since al Khalifa . We use it basically the same

34:03 with an ada effective here and a here. And uh we're gonna uh

34:09 these as a function of vertical incentives . And so when we do

34:18 we're going to find a time varying of the affected. And how do

34:23 do that? We flatten the gatherers far offsets. And but you know

34:29 this is going to include the remaining as well as the anti section.

34:33 you have to correct for that if want. If you want to know

34:36 the anasazi is, you have to for that. Uh You don't want

34:41 just assume that uh when you determine from your workstation by flattening to gather

34:47 that's all due to anti psychic has bending effects in there. So uh

34:53 is how a good way to look the previous graph and just choose uh

34:59 mute function there and just uh don't at the fire options. And then

35:05 the neuron instead to determine that normal out velocity as a function of time

35:12 . You see they did a pretty job and then here's the deal with

35:16 number fixed now you determine it affected function of time to flatten these cabins

35:23 see pretty good and flat all the up here. Not not all the

35:27 completely um all the way out to . And also you can see some

35:33 events here. These are probably not you're probably not reflected the ways they

35:41 maybe convert waves. Who knows what are. And so that's how we

35:52 it And so then dis repeat it we want to reduce the antisocial parameter

35:59 as a function of um time in the different layers here. Got to

36:05 a calculation to separate out the re effects from the anti psychotropic effects inside

36:11 . I didn't give you the formula that. That's a more advanced course

36:16 you can understand the principle. So would we determine delta. Remember delta

36:25 hidden inside the move out velocity Lossy printer. It's combined with vertical

36:34 inside the short spread, move out . And so how can you um

36:43 those two separate. Here's one way do it. And so this is

36:47 from my friend at dp Richard Clark this is actually data at Valhol and

36:54 is uh data like it says your stack gathering. You can think of

36:59 as uh two D. Although it's uh three D. Day to think

37:04 it as two day and what we are pre snack gathers. So we

37:09 , So we have here uh the from 0-4, 0 to far,

37:15 too far. And so uh you they are not flat. Matter of

37:22 it's terrible. Uh Every one of reflectors is not flat. Here's something

37:27 are straight but none of them are . And down here it's very

37:32 Down here is the famous um gas above the Valhol Reservoir and the Valhol

37:40 down here somewhere and over geologic Um Gasses linked up into this overburden

37:46 collected in these intermediate rocks and the and data quality of the p waves

37:51 . So you can't see anything. never mind that. Let's let's just

37:55 here when we have good data And so uh the question in your

38:00 should be since these things are not , why did clark bother to uh

38:07 uh calculate them and present? Well the answer. These wells have the

38:15 vertical velocity. How do we know ? We have dozens of wells in

38:19 field and we can measure the vertical everywhere in the field just through Bs

38:27 bs bs and those boreholes. So know the vertical velocity. And use

38:31 vertical velocities to uh calculate these Now, if the gatherers were flat

38:39 the next step would be to you stack them together. But if you

38:43 that for these that would be a idea because the staff would be very

38:48 because they're not flat. So uh Clarke being a clever guy and then

38:54 what he called a residual move out . So he modified these vertical velocities

39:03 that they uh the gathers do get . And so that that in so

39:10 he uh he determined the move out separate now from the vertical velocity which

39:16 already knew from all these vsp birth dSPs everywhere. And so now from

39:22 difference he can compute death. And oops, So let's see here these

39:29 here looks like about 8% here, here, about 2% here And about

39:38 here. See down here, you know what it is because these are

39:42 bad. This data is so We're not going to believe this at

39:46 . Maybe we don't believe these. can believe these two. And look

39:49 here, that's a zero, that's ocean up here, that's the

39:55 So I will remind you that these these data here are taken from ocean

40:06 seismometers. So this first data is at the bottom of the ocean.

40:12 so I'm gonna sign a value of for Delta in the ocean and he

40:20 what is the value of peak velocity the oceans. So that's a good

40:30 for measuring adult uh in uh blocks this. And so you can see

40:36 it's got pretty uh pretty poor vertical . So um that is always a

40:47 when you're determining velocities and anti static from arrival times. You always get

40:54 vertical resolution. And if you try do better vertical resolution you always start

41:02 uh lots of thin layers which are high. And just below it is

41:07 thin layer which is too low and that layer which is too high.

41:11 it becomes unstable when you attempt to uh achieved too high resolution. So

41:20 is too smart a guy to do . So he settles for what the

41:23 are gonna give him and he sells her poor vertical resolution. So if

41:28 want higher resolution you've got to look amplitudes which we're going to do later

41:34 afternoon. So we already talked about and so I'm gonna skip over there

41:41 I am going to show you which I did not show you

41:45 So let's uh think about this. you are processing your risks and you

41:53 to uh process data, recognizing the of antisocial. So I'm gonna show

42:04 only the simplest case where it's a D. Sub surface and it pulled

42:09 a stop. Now maybe it's not anti psychotropic. So uh maybe it's

42:15 one D. So then those workflows obviously be more elaborate. This is

42:20 fairly simple realistic case. So the thing is as I said gathers uh

42:25 the maximum um offset in the gather approximately the depth of the and then

42:35 determine the move out velocity from the move out in these short spread

42:41 Then you unmute the gathers determine a from the 900 block move out,

42:47 talked about that. And uh then separate out the antipsychotic apart from the

42:54 that you measure. Remember we got bending effects inside here. So there's

42:59 formula for that and uh introduce now parameter ada from uh that's not hyperbolic

43:12 yeah, what's this? You have time, a time section. You

43:16 to have a depth section but you have the right um uh velocities for

43:22 for converting time to death. What have is to move out velocities which

43:27 different from the vertical velocity but that's you have. So you're making a

43:31 from time section to an apparent death using this move out velocity, you

43:37 , it's wrong but it's a step the right direction. So then you

43:42 guessed what is delta. So a time ago, uh at this point

43:48 would have guessed well uh let's say initial guess for delta zero. Well

43:54 easy to do but we can do these days because we're gonna probably be

43:58 with defense contractor and that guy will , well we've looked at uh data

44:04 some of your competitors from nearby wells after a lot of work they decided

44:10 uh um oh die for delta at horizon at the reservoir level is about

44:21 . So let's use that as our guests as rs 3.5%. So then

44:26 gonna uh stretch the data. Now gonna migrate because we might not be

44:35 uh in the most accurate might not the best way. This is the

44:38 time we migrate and we're gonna migrate time data into the time section to

44:46 adjusted death selection. Yeah. Now uh ready to show that to our

44:53 are showing to our clients And say it's time for you to drill up

44:58 ball and everything was showing you in steps thing. It's probably gonna be

45:03 but it's probably not gonna be too wrong. So you you drill the

45:07 , you spend maybe $10 million you a bsp in the hall and now

45:12 have a true vertical velocity. And you uh you have the comparison at

45:20 um for every reflector of the vertical , vertical velocity and the move out

45:27 . The ratio here is uh So um you're gonna stretch this image

45:37 this astronaut for delta. Mhm. um um actually I said it wrong

45:47 since you know this as a function time, you can deduce the value

45:51 delta from little farmer that I gave earlier or I just heard thunderhead,

45:57 all hear thunder, it's gonna rain here, I wanted to do

46:06 Uh so uh this is um our serious estimate of delta and we have

46:15 nowhere in your hair, nowhere up have we estimated? Excellent. And

46:22 we can compute it because we have we have ada here we have ada

46:28 here we have delta. And so we can compute epsilon at the

46:33 So this is a nice quality Uh I think if we compute epsilon

46:39 it turns out to be negative, probably did something wrong and so go

46:44 and check our work and uh there's lot of things we could get

46:48 but I'm gonna assume that most, time it's gonna be wrong. And

46:54 most of the time it's going to larger than delta. So that step

47:03 works on. And now that we both, we have good estimates for

47:06 these images. Now we do a serious migration. Yeah, got a

47:12 depth image using the correct values of and delta. Yeah, I remember

47:20 everywhere we've assumed here one dimensional honest topic. So maybe this is

47:25 time to say, okay, now we have three D. Data,

47:29 start looking at the three D case might not be polar honest,

47:33 it might be as smoothly as you . So this is just the

47:40 So we did this quiz before I . And so now I want to

47:44 about uh tilted polar and instead of polar. And um does anybody have

47:52 questions about what we're talking about so ? No, I mean that we

48:04 have time for this next talking. um suppose you have rocks and you

48:15 you process them in the way that just talked about and you can see

48:19 there on your sidekick section, those are not flat. And so if

48:24 dipping layers like no, like you might say, okay those dipping

48:29 that at one time in jail in time they were flat, they were

48:34 psychotic then they're still antipsychotic now. now they're tilted. So what effect

48:41 that have on the image? So this situation where all these uh rocks

48:49 these layers now. And so these the symmetry planes, parallels in the

48:54 . Here's the symmetry axis. And these wave fronts, here's your

48:59 These wave fronts are not circles going , uh it's uniform, but it's

49:05 uh anti psychotropic. So these are psychotropic wave fronts going down here.

49:13 so you can see in this case are tangent to a horizontal reflecting plant

49:18 here, not over here. So if they had been icy tropic,

49:27 would have had this situation instead, imaging a point here. And so

49:32 that means is that every point in migrated image is displaced horizontal because of

49:41 tilted and I see traffic backed. not only do we make, if

49:45 ignore the anti sanctuary, we make to death errors. Now we're getting

49:51 positioning errors because of neglected. And said, so this is,

49:57 Um, a real world situation which active, uh, 20 years ago

50:07 I first made this figure maybe still . I'm not sure if this is

50:11 in Canada Professor. Yeah. This isn't in our slides. That's

50:21 So I just added this, not to charge. I will send

50:27 the Okay, Thank you. Um, so, uh, this

50:35 east to west, across the, is just to the east of the

50:40 Mountains. So imagine here off to side, we can't see any

50:44 but off to the side of the Mountains. And they have these thrust

50:49 thrusting up underneath the planes in Alberta in Saskatchewan. And of course,

50:58 , the ocean has come across here , and flatten this. Uh,

51:02 wrote us all off. But, , so it's fairly flat on the

51:06 here. But they, uh, knows the rocks down below our,

51:14 , dipping upwards and they all kind flatten out here. Um, they

51:20 a name for this baseball plan I forgot. But, so in

51:26 days, uh, the big plan to explore for reefs. Here's here's

51:32 reef here and explore for reefs using data, analyze, uh, common

51:39 . And these people, if they I Satrapi, they're going to be

51:43 a mid point right here. And gonna think the reef is here.

51:48 they're gonna walk the drill right into edge of the reef. Because they

51:52 that at the edge of the that's where hyper Carpenter's gonna accumulate.

51:57 because the race are really uh propagating tilted and ice traffic bodies,

52:04 the actual reef is over here. see, the image got just got

52:11 uh from here to here. And they when they drill here, they

52:17 find any reef. And so they to make a side track like this

52:21 find the reef. And so that's several million dollars for the side

52:25 So that was the problem which was by smart juices student At the University

52:34 Calgary about 30 years ago. And this is what he did to solve

52:38 . He made in the laboratory model um uh huh subsurface situation. And

52:50 made it out of plastic. So , he's got a piece of plastic

52:57 here with a false in it here stick here. And this thing

53:01 He wants to image that with uh sources and receivers spaced all along

53:07 That says 500 m. But actually uh in the laboratory. Uh the

53:13 distance is about uh about 20 centimeters . It's uh I think it's about

53:20 think it's about a meter or two in the laboratory. And so he's

53:26 high frequency uh, sources all along on high frequency receivers. And he

53:32 them out a long distance like which scaled to be uh similar to

53:39 it would have um scale in the . Of course it's going to be

53:44 frequency. So he's not really interested the rock physics. This is plastic

53:48 all that rocked. And in the , what does he have in the

53:52 ? He's got another piece of which is an isotonic and it's a

53:58 of plastic which you can buy uh you know where to buy it on

54:03 internet. It's called fennel light and anti psychotropic and has cut it.

54:07 the symmetry axes are like this. it's simulating the situation that we had

54:14 with dipping anisotropy above reflected. And he um did his scale seismic survey

54:27 . And look here. The image everywhere in the wrong place. Um

54:32 , here's the top reflection should be here. Uh, here's the

54:37 you can't even see the bottom reflection , but here is the top and

54:41 of reflectors from here. But the is over here. Uh here now

54:47 say, oh well, you just the wrong philosophy. Of course.

54:50 knew what the velocities are from separate experiments on this Overburden. And you

54:57 see his inside here. These are image point gathers flatten using the same

55:04 that he uh used to make the image. And it's pretty flat,

55:10 personal flat, pretty flat. So the quality control looks good here.

55:15 he's still uh gets uh way of wrong energy. The next thing he

55:21 was he did, instead of doing ice a tropic imaging, he did

55:28 using the assumption of dipping anisotropy. furthermore, he knows what the anisotropy

55:34 because he can measure this stuff So here it is. And so

55:39 now you can see the uh autumn in the right place. Top reflections

55:44 the right place, fault is pretty in the right place. And um

55:54 . The quality control um isn't much . So in this way it proved

56:04 the erroneous drilling results in the field from incorrect assumptions about the uh the

56:14 the old bird. The correct assumptions dipping anisotropy and how in the

56:22 how would you know what is the actually to use? Well, you

56:26 to do three D. Experiments not the experiments to figure that out.

56:33 , having shown you this um successful verification of the theory which was then

56:42 the way it was applied in the uh successfully for many years, you

56:46 a lot of money for a lot oil companies Um over the past 30

56:52 . Even so uh there's a real with this kind of analysis. And

56:59 it states if the beds are then the tilted polar on ISIS is

57:05 not a plausible scenario. T I would stand for uh tilted

57:11 Or from unlabeled but not a very that's the way it's tilted polar.

57:16 and so um this is usually not plausible scenario. And the reason is

57:22 here in this picture. Uh This a picture from a beach in uh

57:29 England and you can see it's dipping . And it used to be uh

57:36 assume that before it was dipping, was uh didn't have these joints in

57:43 . And um it was polar anti . But now it is dipping and

57:48 it does have the joints. And conclusion from this picture is the same

57:54 which causes the dip also opened up the rocks. These um joints which

58:02 coincidence are lined up in the strike the strike direction. So the

58:08 So these beds are no longer pulling the topic. They are Ortho Robin

58:15 their Children. Or so we're gonna more about or ceramic sympathy later.

58:22 um this idea tilted transaction was very for the last 20 years. But

58:30 then people have realized that it's probably a good idea because probably whatever technique

58:37 caused the dip also caused fracturing and fracturing lined up with a structure like

58:44 one is so this is a good to break. And uh sorry it's

58:57 2 30. So this is an time degree. So let us break

59:01 10 minutes and come back in 10 to talk about polar anti psychotropic

59:08 So with that I'm gonna where we off except that when I do this

59:16 of thing uh it does not keep with me. Mhm. Okay.

59:29 polar and subtropical A. Vm. since most rocks are anti psychotropic,

59:34 should be doing this kind of a analysis all the time. But you

59:38 see very quickly that we don't as as you see the difference is caused

59:45 the presence of an eye. So is where we left him for it

59:50 in lecture six we talked about uh and we talked about the Avio reflectivity

59:58 and some simple trigonometry with three different , intercept, gradient and slow.

60:06 you see here this is the trade between p wave jumps and share module

60:11 with the minus sign here. This what makes a video analysis so useful

60:16 interesting is this trade off right here the gradient. Yeah. Remember this

60:28 case study that we had uh we did find that uh when we look

60:33 a two D seismic section with an anomaly in the middle of it.

60:39 we uh draw a yellow box around we have this cross block which is

60:45 cross block between uh intercept and gradient the seismic data which underline each of

60:54 image points. So this is migrated data but behind every one of these

60:59 is uh gather and uh so this the attitude intercept ingredient for every point

61:09 this. Yellow box shows up as yellow yellow duck somewhere here. Then

61:17 mhm interpreter in this case, my Sin draws another green box. Another

61:26 this time green and according to his um judgment, there are no hydrocarbons

61:34 this green box. So when he this green box, some of these

61:37 points turn on and there's always a cloud of green points inside the yellow

61:44 Dutchman's yellow planet here. And uh green points represent points from here where

61:53 are no hydrocarbons. And of course wondering whether these, an african anomalies

61:59 from hydro congress or not. So by the theory for um um characteristics

62:10 A. B. L. Which went through in lecture six.

62:14 he selects these here in the third , mostly in the third quadrant.

62:20 as soon as he selects these points uh before with uh purple lips and

62:28 soon as he does that, those looks to see where those purple points

62:32 from here. And look, they occur at the top of the

62:37 And so these are identified as anomalous on uh Iraq physics argument. But

62:51 data is all received amplitudes and there been no corruption in here in any

62:58 for um uh there's been no correction any of the propagation effects which also

63:07 the amplitude as a function of No, for example attenuation. Uh

63:11 example geometric spreading. Although those, to decrease the amplitudes and the function

63:17 offset because of propagation through the overburden nothing to do with reflectivity. But

63:25 we that's what, that's the kind data that underlies here. All

63:30 all these um points here represent intercept gradient for amplitude in the data.

63:39 they don't represent reflectivity, but even when Pranab selects these points out board

63:47 to the lower left of the little trend and select those these books over

63:54 . And if they had been scattered here, he would say, oh

63:58 just noise. But they don't They all came from the top of

64:01 structure. So it looks like we a great um um workflow for identifying

64:14 departments from um uh from a video , even though we know we're neglecting

64:23 lot of things, all those propagation . And also we're uh we're neglecting

64:31 socks so, but it looks like works. So uh well, there's

64:39 one clue in this whole frame that something's wrong, which is the slope

64:45 this um Green cloud is too What when you look at reflectivity calculators

64:54 rocks in the laboratory you get a of points like this. Um um

65:03 elongated cloud of points with a negative like this, But it's usually it

65:09 a slope of 1-1 -1, but looks like it's -5. So when

65:16 showed you that one way, uh uh point, we can correct for

65:24 that. As mentioned, I am to do that right now. Uh

65:28 me here. I'm going to um , I am going to go back

65:37 this. Can you see this trigger ? You see my kosher movie?

65:47 sir. Okay. Uh watch me power point processing to correct these

65:52 All I'm gonna do Sorry about I didn't mean to do that.

65:58 , just gonna grab this finger right and square it up like that.

66:05 furthermore, I'm gonna get this out the way. Okay, so now

66:12 see that as the slope of So when I did that I just

66:19 changed the length of the uh I changed the uh the gradient divided

66:33 the innocent for every point here. that's what is a common characteristic of

66:41 one of the physical effects that we . For example, consider uh geometric

66:49 . That changes the uh that affects gradient of amplitude as a ratio with

66:58 intercept of amplitude. And I just that and I corrected similar things like

67:04 empirically just by power point process using facilities given to me by mr Bill

67:13 and look, the anomalies are still and they still come from over

67:18 So what it means is that we found a work flock which works to

67:25 these anomalies, even though it makes of mistakes in the physics. And

67:32 that's a good thing. Our our here is not to uh determine the

67:40 at the reflectivity, it's at the surface, it's to find oil and

67:44 and we have a workflow that does . But maybe um we have to

67:51 even better if we corrected um those of problems. So um I I

67:59 say that when you neglect anisotropy uh this up, I should say that

68:07 also changes the gradient with respect to intercept. And I corrected for the

68:14 be here uh right now. But question is, could we do even

68:20 better job of a. B. . If we did it using more

68:24 physics. So before I go back , I want to repair the

68:29 I just did to my uh I that's good. So now I'm going

68:38 mhm. Um show you something So this is the linearize anti psychotropic

68:50 with more efficient. This is the problem as we had before, except

68:54 now uh the overburden is considered maybe anti psychotropic and below the reflecting

69:01 Maybe that's also uh psychotropic. And , the formula looks very pretty

69:08 It's got three coefficients. It's got economically. Uh That's great and the

69:15 appears right here where these coefficients now different in the first place. The

69:22 now depends specifically on the vertical So that's sort of uh expected,

69:29 . Now look at the gradient, depends that explicitly on the vertical jump

69:36 vertical velocity and explicitly on the jumping marvelous. But look, here's a

69:42 a new term And same thing down . I derive these terms for the

69:49 time, I think in 1981 maybe you and all were born and immediately

69:58 knew there was a problem because I that this term here, which will

70:03 neglect even today, we always neglect term. It's small compared to

70:08 So this is the jump in antiseptic delta between the reflecting bed and the

70:15 bed. And that's gonna be a , a lot less than one.

70:20 look, all these terms are a less than one. We assume there

70:23 a lot less than one when we the legalization. And so that means

70:28 this term, whether we included or could make a large relative contribution before

70:38 um uh describe that in more Let me point out to you what

70:45 of you might have seen with sharp here. I have a subscript w

70:51 these angles. So that's what this is about here is uh an actual

70:57 um half space down here. Source over here, way from going

71:03 And so you can see that since an anti psychotropic subsurface. Uh the

71:08 goes further in the horizontal direction, goes in the vertical direction because uh

71:15 is positive. These philosophies horizontal velocity than a vertical loss. Now let's

71:21 ray out here. So here's the . And look, the ray is

71:26 perpendicular to the boyfriend. If the front were a circle, this would

71:31 perpendicular, but it's clearly not. that is called the wave the right

71:38 . Now you can measure this um wavefront in a different way of making

71:44 tangent here and perpendicular, that. so that angle is the way front

71:49 . And you can see by this is a smaller number than this

71:56 . So we have a formula to those two. Uh here's the formula

72:01 I'm not going to derive that for obviously, but uh it involves delta

72:08 ate a prime number. Eight of means uh simply epsilon minus delta without

72:14 by one plus two delta. Uh notation that we did before. And

72:22 are the anti static parameters of the . So that's uh um uh obvious

72:31 of non spherical wave fronts. It's once you got maybe not obvious before

72:39 do it. And so what we for uh we need for the formula

72:47 previous states. We need this, need the wavefront angle because we were

72:52 playing waves. And so um this uh in reel um uh in real

73:03 , we never have plain ways but always we always have carved raise like

73:08 and the curve ways are a superposition many plane waves. And for this

73:13 of the away from the biggest contribution that, some um uh many different

73:21 waves is this one which is convicted the way from this point. So

73:26 the the angle that we need for formula. But when we do ray

73:32 , which we always do to convert two angles, we always come up

73:37 this great direction because we're tracing the and that means that we're uh for

73:44 the ray angle. So I'll just you, we we never measure reflectivity

73:49 a function of angle. What we is received amplitude as a function of

73:55 . So one of the things we to do is convert offsets to

73:59 And then we do that by ray through uh the overburden using an assumed

74:05 field for the overburdened. And when do that, I find uh as

74:11 rate goes down through the layers, following the raid direction. But then

74:16 have to make this sort of correction that into the formula the leadership.

74:25 . Remember that formula and said do we did before. So what we

74:30 want is these uh these three jumps uh properties jump in vertical velocity,

74:39 , shear wave velocity and jump And to do that. Use these

74:45 per formulas from uh Changeable calculus and what you see immediately here is that

74:53 anti santa is in here. But have three equations and five unknowns.

75:00 uh the equations give you numbers for curvature for the intercept and for the

75:07 . So that's three equations. But unknowns are 1, 2,

75:12 4 and five. Shop right, solve this system. Three equations and

75:25 unknowns without making assumptions. And of the assumption we normally make is these

75:31 entropic contributions. Zero, but that's not a good idea. Especially in

75:36 we have talk reflection off of the reservoir in the sandstone reservoir for

75:43 the anti sodomy is going to be close to zero but in the overlying

75:48 Uh it might be five or So the difference thing can be not

75:53 compared to the other terms in the . So I have here an anti

75:59 aereo exercise which I want to go with you here in front of you

76:05 then you uh you have the mhm have the Excel spreadsheet which you downloaded

76:16 the blackboard and you can follow through this by yourself uh later. So

76:25 me just stop this at this point get out of this and stop

76:38 Okay, now you can watch me I Yes, father, I can't

76:50 my screen now, but that's Um Yeah yeah this is what I

77:29 . Okay so now I'm gonna share screen again, share this room.

77:50 so I think you can now see Excel spreadsheet which is called res and

77:56 dot XLs. I hope you've downloaded from your from the Black more.

78:02 remember it's got different exercises down at bottom. This is the disclaimer which

78:08 that you can have this for free you can share it with your

78:12 No problems. Just keep this uh keep this with it. You know

78:23 you want to change something go ahead change it mm don't take this part

78:32 . So in here are many different exercises which we have many of which

78:39 have not had a good chance to look over uh and particularly we didn't

78:45 over this one before I do the part, I do want to show

78:49 this. So uh this is uh uh topic velocity as a function of

79:05 um where you input the values. so you know that uh anti psychotropic

79:13 depend upon put cookie and stiffness is alfa beta and you probably don't have

79:18 good way to uh guess those intuitively you do have a good way to

79:26 intuitively put in data like this so me um I'm gonna expand the view

79:35 yeah okay that's better now so what have here is opportunities to input by

79:52 , a value for for vertical velocity a value for the velocity ratio.

79:58 these are sort of typical values uh the sort that you might see.

80:03 me just change this one here and gonna put in here um 2500

80:12 When I enter watch all the grass , All the graphs change. So

80:20 over here on the right side are bunch of tables which drive the grass

80:25 , you don't want to look at tables. Uh I think normally you

80:29 make good guesses for vertical p wave and for vertical velocity ratio here,

80:36 got a 3.0 let me put in . Uh yeah, let me put

80:42 here uh 2.5. Watch again how changed. So now uh those are

80:50 which you can probably pull out of head now. Uh here are the

80:56 parameters, dalton, epsilon and And you can uh even though you

81:06 you can't tell me off the top your head proper numbers for the and

81:13 you can probably say that uh epsilon the number, say between zero and

81:22 . So I'm just gonna sit here be 19%. So I'm just gonna

81:27 this slider and move it so much . You see as soon as I

81:31 that, all these curves changed. now we've got epsilon 15 15%

81:36 Let's assume it's even smaller. So we go, 3%. So everything's

81:43 , answer in the same way, you can change all of these anti

81:48 topic parameters and you know, intuitively gonna be small numbers bigger than

81:53 Uh Maybe not bigger than one, I mean to say bigger than

82:00 maybe not bigger than zero. Look for delta, it allows you to

82:04 minus delta, negative deltas, um for epsilon and not for gamma,

82:12 it does permit you to have small of negative delta. So I invite

82:17 to play around with that at your later. But most of the time

82:22 is gonna be positive. So let's it where it is. And so

82:27 what I uh given in the grass three graphs for V p v S

82:35 here in green and V S H purple according to these parameters. And

82:43 these are the exact um um expressions were derived first time in over a

82:55 ago in terms of these c alfa here. So what I did was

83:00 converted these five parameters here into these parameters here and put those into the

83:08 equations. And that's what you see . Now, what you see over

83:14 is the difference between the exact expression the weak approximation. So almost universally

83:21 days in our business, you always discussing an Exxon tribute with the assumption

83:28 is weak and that's a really good . But you might be wondering to

83:33 just how good is it? So just look here in this example that

83:37 have an example that I showed up . So um for the P wave

83:44 the uh is the dark blue, this one here is the P wave

83:49 . And so the this is the between the exact minus week as a

83:53 of angle. Yeah, Daniels are showing, I don't know why that

84:02 . Uh, it goes from zero . Oh here here here, the

84:08 right here in the middle. so uh so now let's look at

84:13 P wave here and it starts off zero error Between exact and weak at

84:20 inserts. And then as, as get larger and larger. This error

84:26 from the assumption of small Linus oxygen bigger and bigger and here gets to

84:32 a maximum and that turns around and the other way. But look

84:36 this is a five five m/s error 50 degrees. So, you

84:45 in uh most uh, common world acquisition um, uh, angles the

84:55 angles on the reservoir are gonna be bigger than this. So it makes

85:01 difference in five millimeters, five m second out of some 2500, Maybe

85:10 600. So it's a very small It's a very small air for the

85:23 acquisition designs that we use today. um, you can uh, play

85:34 with a smart for example. Let's uh make a bigger case. Let's

85:39 epsilon bigger and let's make belts are . So I'm gonna make delta three

85:46 than absolutely. As soon as I go of this, watch all the

85:52 . Okay so now what's happened is everything has changed. And here's the

85:59 now at uh at 45 degrees. this is 45 degrees. Now the

86:06 error is a minus five m per . Still very small compared to the

86:14 the absolute value. So you are gonna conclude I have to play around

86:20 us a lot that uh errors that encounter because of this assumption a week

86:29 are really pretty damn smaller. Pretty small. So uh with that,

86:36 I want to go to the next which is a real exercise. So

86:46 so now uh this input is similar not exactly the same in the cartoon

86:52 we have a red incident media and reflecting medium separated by this reflecting

87:01 Perfect reflecting horizon. And uh sliders and below. The reflector asked you

87:08 put in here the way the P. Zero the vertical velocity ratio

87:15 the density. We need that. delta and epsilon we don't need,

87:20 is going to be a p wave a problem. So we don't need

87:24 for this. And so whenever you select one of these numbers with

87:34 what you're selecting is shown out So let me just grab this and

87:39 them smaller block as soon as I go watch that number to the right

87:50 here. So that's what we picked . A blessing. And um now

87:58 the first thing we're gonna do is going to set all the anti social

88:02 to be zero. So these two already zero. Let's put this to

88:06 zero. And this one, okay now the curves down here, we

88:17 um Oops first are not uh changing look what it says, automatic update

88:48 links has been disabled. So I'm enable the content now. Okay now

88:55 see here um now I want to these, wow this is broken,

89:07 spreadsheet is broken, so this is one that you have and um okay

89:16 I put it out there just a or so ago and I never bothered

89:20 check that it's uh still working. here's what we're gonna do, we're

89:26 stop sharing this and we're going to I'm gonna find on my computer,

89:36 gonna find a uh version of this which is not broken. So uh

89:45 course I use this lots of other find an example. Okay so this

90:27 works. So I'm going to now my screen and what what I'm gonna

90:32 of course is to uh tonight after course is over, I'll put a

90:41 spreadsheet on what? So 1st I'm share my scream. Okay, so

91:01 is um sam spreadsheet like it was and now you can see that uh

91:13 all these uh parameters up here in in the corresponding parameters there, you

91:18 see that delta and epsilon are both in the upper media, delta and

91:23 are both zero in the lower And you can see this reported on

91:27 to the right side and also what were reported, implication for ada and

91:35 implication for headed down here and also implication for a vertical competes. And

91:41 implication for vertical shear modules coming from um I said around vertical shear velocity

91:51 from this vertical p wave velocity and vertical velocity duration. So all that

91:57 good. And so now you see here uh reflectivity equation which um looks

92:08 of similar, I think this should be surprising to you. And so

92:13 um it's a simple curve calculated in standard using innocent gradient or slope.

92:24 it's always assuming I sought to be we were said the isotopic parameters are

92:31 zero. The anisotropy parameters zero. now let's assume this is uh reservoir

92:39 down here. But now let's assume incident medium is a shale with a

92:44 zero anisotropy in there. So let's this and put in a little bit

92:49 anti Satrapi. And so as soon I let go of the cursor,

92:55 the curves down below, watch how change bang. Now I want to

93:01 in a little bit of epsilon. , wow, that's bad.

93:09 so now what have we got? uh we have down here,

93:22 Um uh several purse, so this is the ice, a tropic

93:27 so this one is assuming uh that calculated in the same way that you

93:34 do almost everybody in the industry does and it's got a positive, it

93:41 a positive signature. Uh you that comes from the parameters we put

93:48 here and maybe that's the wrong numbers uh scenario of sandstone or shale,

93:55 never mind that you can adjust these and I heard you to play with

94:00 uh in your free time. but the main thing is that when

94:06 include the anti sox beat, everything after this, there are actually two

94:12 here, one calculate the right way one capturing the long way, so

94:17 right way is done with uh wavefront uh data. And uh that's mean

94:28 uh the wrong way is done with random purple and you can see that

94:36 this particular case they're almost identical. the important point is here is that

94:44 this model with a little bit of in the over bird, see this

94:50 anisotropy 9% in delta and 11% in That has made a huge difference in

94:59 reflectivity. This looks like if you to drill this. This is what

95:04 call a positive a leo ah Mhm because it's got a positive intercept and

95:16 positive ingredient and a positive character. is because looking good here accept that

95:23 how we see it was all due what the subject. If we do

95:28 same calculation including the anti sox tickets , there's no no Avio effect at

95:35 . So this this shows by the um Uh reports out to the outside

95:52 is given by 6%. That's this in here And the curvature is

96:02 But when we put in there the speak it goes from um 6% to

96:11 . Almost flat. And then the uh the character is a minus 2.5%

96:20 of crap. In other words we huge changes in captain reflectivity depending on

96:30 or not we put in a little of antisocial. So um let's put

96:36 less interesting, let's put in delta 5% whatever that's 4.5%. So still

96:43 differences. And now you can see some visible differences between the green curve

96:48 the purple. So now let's consider bottom reflection. So let's uh so

96:58 let's assume that the upper medium is fronting. Now I'll put an in

97:08 morning. Yes and see how it the curves in the other way and

97:18 changes it so it looks even more but that's uh do the uh much

97:26 than uh then you would have from topic theory. And so you might

97:34 noticed as I'm retail re computing these , the um actions changed, that's

97:41 automatically by. And also notice here the maximum angle is 45°. So uh

97:57 spread, she then uh confirms what can see from the formula. So

98:08 now going to share the screen with power point file and I'm gonna go

98:27 into presentation mode and then back And so when I first showed you

98:40 funnel um you can see this is a really big problem when we ignore

98:46 because even though we don't know what is, we can know intuitively that

98:52 going to be a number a few but these numbers are also a few

98:56 . And so whether or not we this could have a big effect on

99:01 uh the uh ingredient could even change algebraic sign of the gradient. That's

99:10 . So uh I first discovered this Formula about in 1981 and uh let

99:25 remind you that uh I told you story last time about how I am

99:31 the inventor inside of em echo of leo and as soon as we discovered

99:38 valuable it is for finding oral. project was taken out of my hands

99:45 was put into the hands of a senior researcher. But I thought to

99:52 um yeah mhm doing this analysis in of ice. A tropic rock

99:59 What happens if the rocks are anti ? And so I derived this formula

100:06 convention 81 but I couldn't figure out way to determine this one from the

100:12 or this one. This one's not important because you know, normally in

100:18 we don't consider this curvature term because data is so noisy that we don't

100:25 a good estimate of curvature in the . So normally we only consider this

100:32 and this one and I could not out how to turn this one in

100:36 of the day. And so um the project was taken out of my

100:43 , uh I went on to other and this problem laid to be unsolved

100:50 32 years, 32 years. And finally after I left during that time

100:57 course BP bought Amatil and then I from BP and joined the University of

101:04 . And at the University of Houston had a Uh student who was quite

101:11 and so together we solve this problem it was 32 years after I first

101:18 the pilot was. I'm gonna show that solution next stage presence. So

101:28 what's the problem to analyze a leo while we account for an ice actually

101:33 of just wishing it will go So here's the issues uh we're gonna

101:39 up using logs as well as seismic . So the problem of the logs

101:45 they do have high resolution and accuracy they don't measure. And it's actually

101:51 in the simplest case the vertical rate on. So consider horizontal layers with

101:57 vertical world war through there. So the velocities that reduced from there have

102:04 red paths, owner. And so we use surface surging travel times,

102:11 have, we always have low special for anisotropy parameters like Delton. I

102:17 you that and I say half an ago or an hour ago by now

102:21 I showed you that the calculation of by my colleague Richard Clarke at DP

102:29 Valhol data and you had poor vertical for determining delta. So you're never

102:39 get a jump in delta what I delta delta from that kind of

102:46 And when you look at service section , they are affected by many factors

102:51 it's just not feasible to do deterministic . Many factors. We talked about

102:56 of them before. Attenuation in the geometrical spreading in the overburden transmission losses

103:02 the overburden. Uh you could name half a dozen more and you're just

103:07 feasible to correct. We solved this in 2013. And so uh published

103:18 solution here in uh expanded abstracts of scG annual meeting in 2013. And

103:26 you can look it up uh and if you want, you can write

103:31 down just remember 2013 and my name uh you'll find it. So um

103:39 wrong, wrong, Lynn was student our department here and this was her

103:44 stasis. Pretty good master Stations. we call this convolutional description of a

103:52 propagation, or we have the signal the way it starts off with a

103:58 source strength and a certain initial wave and then it goes down and it

104:03 and comes back from many different players it gets received by instrumentation and then

104:09 on afterwards. So, you can uh many different complex things in

104:15 particularly this operation here, very hard to uh make a realistic uh

104:24 which determines uh everything which is going as it propagates now, similar for

104:31 this. So most of these uh change with angle. So when we

104:38 here with our sets, most of depend upon this. Uh this angle

104:44 . Now, this is not the angle, this is the angle at

104:49 eventual reflecting. So, I should uh here, but um um as

104:58 uh think about these things and think a series of reflections in a size

105:06 and uh in that series of uh example, uh suppose you had

105:17 suppose you had a series of reflections five major reflectors. And so as

105:25 the wave goes down from number three number two. Say from number three

105:30 number four. This is going to a little bit. This one's gonna

105:33 a little bit but this one is to change a lot. So the

105:37 thing that uh changes rapidly down through series of reflectors is the reflectivity and

105:48 these other factors change slowly. The exception to this statement here,

105:56 reflectivity. So now uh it's common take the surface besides me. Um

106:06 data and normalized to reflectivity. Let remind you how uh how we do

106:14 . We uh have a uh war for V. P. And

106:23 S. And densely and foot by , very high resolution. And so

106:29 between every two um of those measurements can find a delta V.

106:35 And average VP. And um we compute the reflectivity uh foot by foot

106:44 the measured properties in the locks using ice, a tropic formula that I

106:51 you earlier. Foot by foot. then we can take that and involve

106:58 with a wave lips from um from surface sizing data. And now we

107:04 what we call reflectivity seismic ground which in there only the effects of reflectivity

107:12 have any of the effects of propagation there. And it's gonna have the

107:21 aptitude In that. Uh it's gonna a number between uh say uh 0.1

107:30 -10. They're gonna be small But meanwhile you compare with the seismic

107:37 and those are always large numbers. look at any seismic data on your

107:42 , you mouse over one of the and you're gonna get back a number

107:47 1000 and minus 1000. So obviously seismic data on your work station differ

107:53 these reflectivity seismic grants uh by numbers the order of 10,000. So in

108:02 to compare, we've got a normal . So let's normalize in a in

108:08 thorough way. Let's measure the surface . Avio intercepting curvature to the

108:16 Send that gather when reconstructed from And we're gonna normalize three times,

108:23 know, a normalization factor for the . Another one for the greater and

108:27 one for the curvature. And we're to apply that to the seismic um

108:32 data. And we're gonna do it a function of normal business travel

108:39 So we have these three normalization factors various long term time. But uh

108:49 uh normalization very slowly as they go from here. Um both due to

108:56 and propagation effects. And the only that makes a rapid variation in those

109:03 curse is the reflectivity. So Lennon normalized the seismic data circus sessions only

109:15 that part of the normalization which very . Uh let me just say that

109:21 , these normalization functions, we have of them they all vary with

109:26 So since they vary with time, have a four year spectrum, rapidly

109:30 parts and slowly bring parts. And we ignore the rapidly growing parts.

109:36 we get slowly vary normalization function. we normalize only with those. So

109:44 that way we correct the propagation and and we'll leave the reflectivity unchanged.

109:52 that's quite a clever idea. I very pleased when they came up with

109:56 . So let me show you how works. For an example. This

110:00 directly from MS lens um master And so this is for the HBO

110:06 R two as a function of travel , vertical travel cancer goes down from

110:13 milliseconds to 700. And so this the um seismic flow. The seismic

110:22 with a gross normalization. We divided 10,000 or something like that. So

110:27 can put this curve on the same with the reflectivity. So this one

110:35 um and red is the synthetic psychotropic slope catholic from logs, ice

110:43 And you can see that these two different. And so now we normalize

110:50 seismic slope to this um reflectivity we could point by point. But

110:59 we uh we do it only with frequency portions of the of these uh

111:10 functions. If we didn't if we just took the ratio of this to

111:17 , we would normalize out everything. would normalize away all the provocation

111:23 And we would normalize all the anti effects and we would learn nothing.

111:31 um what we do is we take seismic slope here and we see that

111:38 has a rapid variation and slow We normalized only with a slow

111:45 And with that we find this green . So the green curve is approximately

111:52 to the red curve but different at single point. Now the differences are

111:58 smaller. See this point here is difference of about 30% from zero.

112:04 uh here its uh the opposite So we're gonna attribute these differences to

112:13 . And um the reflect differences in seismic data here is the seismic data

112:21 normalized and it's not equal to what's from them. Uh huh From the

112:29 because the logs didn't have any anti piano. So we're gonna contribute this

112:34 here as being due to missing quantity dolphin. And this is delta delta

112:41 . So in that way we estimate delta everywhere. Well, we don't

112:47 to know delta delta, which is jump in dalton. We want to

112:51 dalton itself. So we were gonna do this here is from her thesis

113:01 is the Dr. Delton. Never this for a minute. So here's

113:07 derived values of Dalton. And uh down here at the scale goes from

113:12 -20%. And notice right here. look at these logs. So here

113:24 have a gamma gamma ray log. not a gamma anasazi log, it's

113:29 gamma ray log. And uh we it that such logs identify the shammy

113:38 . And so because the savior layers lots of radioactive species in there,

113:45 emit gamma rays, they're not Of course you don't have to worry

113:49 you pick up a piece of but we can measure the gamma radiation

113:54 the radioactive minerals in the shale and those in a log. And here

114:00 is foot by foot. And so we see high values here, um

114:05 means it's a shell. You low guy is here is a sandy

114:09 because in a sandstone uh there's no inside of a porch crystal for a

114:17 radioactive iron like for example. So those thorium elements get segregated into the

114:24 over geological time. And so the stones have low gamma ray signature.

114:31 this is the in fact the reservoir they were exploring for. And we

114:36 that the sandstone. So we're going assume the gana inside that um uh

114:44 is zero. We could have said 3% but we just said zero.

114:51 then we add up all the golf dolphins which we arrived from statement data

114:58 we have this predicted curve here. so you can see that where we

115:03 sale content in the gamma red We're predicting high delta. So that's

115:10 confirmation. Um we can't measure delta the subsurface any more accurately than we

115:18 doing. But this is a confirmation when we measure delta in this way

115:24 has um uh it makes sense in of the pathology in the walks

115:34 So I was quite happy with this when she first did this, but

115:40 Stewart in our department is a much hard nosed individual than I am.

115:46 he said what? You have only predictions. That's not so impressive.

115:52 so MS lin said this is her thesis. She said, well sir

115:57 all that we had said uh the peters out here. Of course it's

116:02 true that the logging companies don't log entire world. They only log in

116:07 interval where the client pays them to it. So Professor Stuart says,

116:13 I know this this area, this is in Canada and I know this

116:19 , we have lots of uh logs blocks of nearby wells and the same

116:25 . Find one of those logs that in higher uh you know because of

116:31 variations in the intervals. And uh had that. So that's what she

116:38 . There's a nearby log shows a interval, Sandy intervals. She's predicting

116:45 sandy interval and predicting the Shelley interval well. So uh five out of

116:51 . Pretty good. And uh department her uh master to me in

117:00 maybe 2030. So I wanted for to continue with us to go on

117:08 a PhD degree. I thought that was outstanding master's degree, but she

117:16 I'm quoting here, she says I'm of being poor, I want to

117:19 get up, go and get a . So she did and she made

117:24 lot of money for uh working for service company. But I have to

117:30 they didn't appreciate her as much as should have and they didn't challenge her

117:38 projects, which uh she was smart to do. And so eventually she

117:45 unhappy. And um so she came to the department about three years ago

117:53 she did do a PhD and and was not happy, but uh she

117:59 a different project than this one. thought this was a great project for

118:03 , but she wanted to do something , so that's what she did.

118:07 so now she's uh has her PhD she hasn't felt, I think they

118:15 recognizing her more appropriately, uh maybe of her of her higher degree

118:24 she's quite a powerful woman and uh a great success. So now the

118:34 of Houston has pattern on this. so since the ideas were mostly my

118:40 , uh I could have insisted that own that intellectual property, but then

118:48 I had insisted on that I would had to pay the lawyers to get

118:52 patent. And so uh I didn't to do that. So I said

118:57 university you can I will agree that you own this idea. And so

119:04 university uh signed all the paper and university then paid for a patent and

119:11 is now uh um hood. And so now um when a company wants

119:22 use this idea, they have to they have to um negotiate with the

119:31 of Houston to pay the University of world series for the use of this

119:39 intellectual property owned by the university. , so that's uh not um something

119:49 happen to do what they like to is to uh play around with it

119:55 decide whether it's going to help them oil and gas. And so when

119:59 do that uh inside their company without doing it for profit. If they

120:06 it for research, they don't have pay the anniversary. But as soon

120:10 they decide that it does um um uh uh who's a little better and

120:20 be fooled by uh thinking uh looking data and deciding that it's um uh

120:33 anomaly. Maybe it's only uh and anomaly. And maybe they can save

120:41 from drilling a dry hole. Doing , smarter jbl and so that's the

120:47 it works When they do pay the , it's only a few percent uh

120:57 and it's usually worth uh working a to do. So the university has

121:07 office called the Office of Innovation I . And the way it works is

121:16 , um, whenever university people have idea like this where they think it

121:22 have commercial possibilities. They have an to reveal to the university this

121:31 And then there's a committee and the says, well that looks like it's

121:36 interesting idea, but it doesn't have commercial uh, uh, possibilities.

121:42 we'll just let the, that student that professor have the idea or the

121:48 might say, oh wow, this have tremendous uh, commercial uh

121:55 We will uh, we will apply a patent, will pay for all

121:59 patent stuff and then, uh, inventors will be rewarded with small rewards

122:07 the university will reap major financial benefit um, the ideas that our people

122:16 using our resources. So in that , the university hopes to offset some

122:23 the costs of running a university, know, uh, buildings and

122:30 professors and everything else. And football gotta pay for that also.

122:38 , and so I think that the probably does not make a lot of

122:47 off of its patent portfolio. The now owns hundreds of patents and they

122:55 , uh, probably their income from conventions because patterns, probably several men

123:03 here. But then they pay for , uh, the office of administering

123:09 this. I think that they probably probably not a big money spinner from

123:13 university for the university. But they it anyway, hoping that sooner or

123:19 they'll have a blockbuster blockbuster invention that along. And of course uh in

123:26 , most of the um economic activity Silicon Valley comes from this kind of

123:33 ideas spun out of the uh local most notably stanford and has had uh

123:44 uh fact not only that uh economy but the entire world. And so

123:55 example the technology that we're using today computers and zooming and stuff like

124:02 that was basically out of that process over the past 40 years. So

124:12 uh take a little quiz here. Let me turn to you MS del

124:19 . Um Sex here. The anise on HBO was not recognized for so

124:26 . And even still today most people ignore it because A. B.

124:31 C. All of the above. um uh What do you think about

124:36 A. It's true. Yeah. and travel times is true love.

124:44 about being also true? So now suspecting D. But we gotta check

124:52 C. Already um uh what's your for C. Yeah. So when

125:00 like Hampson Russell normalize uh the seismic uh normalize the segments of the

125:09 And so the logs are based on exercise that forces the agreement with the

125:14 . So um mr wu how do answer this? Mr Yeah that's

125:39 Uh He says B. N. . About. So the gradient has

125:43 delta in there and the curvature has epsilon in there. And even though

125:48 don't use the curvature that's not in question uh the question involves the

125:55 hey Miss del rio for Fox since anise traffic is usually is this

126:08 Yes that's true because we just sit that it's not in the intercept at

126:13 . So that that is definitely So now mr same question but one

126:20 is different which is right here say it again? Yeah I'm gonna

126:33 that false. Although we don't really . But you can plausibly you can

126:39 that that term delta delta which is estimated is probably in there. We

126:45 uh don't do the proper analysis to it. But I'm gonna say this

126:51 uh not usually small, it's usually . And uh by the way let

127:00 just give you some anecdotal evidence. The society of the july, the

127:08 Society of Houston G. S. . Is the local affiliate for the

127:14 . E. G. And you should both be members of that,

127:19 your dues is maybe 50 bucks a . And you should go to the

127:23 and network and learn something from those . They have lots of what they

127:30 special interest groups. And uh each those has maybe 10 or 50 members

127:37 it which are local geophysicists talking about topics and one of those of course

127:44 A. V. L. And um uh they have uh maybe monthly

127:53 and they have active discussion groups and the discussion groups every few months there's

127:59 who says I'm unable to uh to my surface seismic audio effect using the

128:10 reflectivity tools and the logs that I what is wrong. And so uh

128:16 the answer to that is that well neglected and because that's not in the

128:23 and you didn't do the um procedure was stepped out by living cops.

128:35 That's you Miss del rio. This also true. Well it's probably

128:42 Um but we don't know it's probably but it's not because uh well let's

128:51 here uh If we think about the , if we think about the reflectivity

128:57 , it's true. I want to about the data, we don't really

129:02 because the Davis are nice. back to you. Mr I think

129:18 true. So tell me your thinking . So you have a delta buried

129:38 death. So you know the depth can calculated duration of everything you said

129:50 true except that we normally know this with coarse resolution. We know it

129:56 averages over course intervals. And so don't know how it varies rapidly over

130:04 smaller. All we know is the average value average over portion of this

130:10 100 m uh thicker maybe 200 m . And what you want here is

130:17 jump. And you're not gonna get jump from an estimate of this with

130:23 resolution because it comes from moving And so you're familiar with estimating philosophies

130:32 move out. And you know that those velocities are smoothly very because their

130:40 over force uniforms and as the averaging moves down delta uh uh changed of

130:51 . But um um during a corresponding of delta, it's also gonna be

131:00 smoothly. So it's not gonna give a jump, it's gonna give you

131:09 averages over course animals, so that is false. So now um so

131:18 is a good time. Um uh a little break. So we're gonna

131:24 now and pull around our central the as another land a century. And

131:29 let us come back here at Uh four point. So I will stop

131:38 here and I will stop my video when I imported uh that spreadsheet calculation

131:52 my other course. There are some which were cross references not done on

131:59 . So I'll fix those up later , I'll have that in your

132:04 But this evening, so let us share the screen and come back to

132:17 week as a brothel and such. , so he's not working. I'm

132:30 have to stop sharing and I'm gonna to yeah, okay. Remember we

133:18 about this uh scene. So this a really good picture Uh uh and

133:25 it shows is uh in these dipping , there are fractures here aligned with

133:31 stress which caused the dip. so um these fractures and uh fractures

133:40 this can appear in rocks even when not obviously dipping like that. Um

133:50 when you have those sorts of or , they always cause as lethal anti

133:58 recent means velocity is changing with asthma well as with the angle of

134:07 Now there's some um a simplification which deeply embedded in the literature which I'm

134:18 gonna criticize. And these are called . T. I. Cracks.

134:25 that means a horizontal transverse Issac. never possible in the sedimentary context because

134:34 the following argument, you could have transverse I saturate from a single aligned

134:40 of circular fractures. That is Penny fractures. Penny shaped country all lined

134:45 together all vertical within an otherwise ice . Background possibly you could have that

134:53 this was actually a reasonable approximation 30 ago when I first came across these

135:00 . However, there are no circular anywhere. The most important factors are

135:06 the joints which I showed you in previous slide, which ribbon shape rather

135:11 punishing. And uh in the sedimentary , the background is always an

135:17 So at a minimum, you want be considering a single set of vertical

135:22 shape fractures within and otherwise polar and media that's not what H.

135:30 I. Is. And so I reviewed the paper just yesterday from some

135:35 who uh were uh working on this . Uh this problem has been uh

135:44 for 30 years. They were suitable years ago but not today. Matter

135:52 fact the first papers that I ever um Asma had that assumption in

135:58 But it's been a long long time that was an appropriate assumption. So

136:04 you hear people talk about H. . I. You know immediately that

136:08 don't know what they're talking about and can go on to do something

136:13 Now the most realistic approximation for fractions rock has shown here. Orthe aerobic

136:19 section means the anisotropy of a So I mean the antipsychotic characteristics of

136:25 brick. So this is uh an photo taken somewhere in the southwestern United

136:33 and you can see the layer and can see the joints and you can

136:39 the other set of joints. So there you can see or Saronic

136:46 Now there might be still further joint . Yeah it might be still further

136:52 here. Maybe that's a joint. set of joints. But let's let's

136:58 only or ceramic symmetry. Yeah. north atomic symmetry we have a stiffness

137:08 which is more complicated than we have anti century. Remember this is the

137:13 stiffness matrix that we have for polar sokrati. Uh And it's got uh

137:21 cost the um with the diagonal here it's got a lot of zeros out

137:26 . Uh And so the thing that this polar and the topic is that

137:32 two are the same. So uh the direction for direction one is the

137:39 as coordinate direction too. So east the same as north and vertical is

137:46 . And so when you count up number of different independent quantities in

137:51 there are five independent quantities. Count , right, 4, 5 independent

137:59 . Whereas if it were I shipped uh it would look like this the

138:05 pattern, but there would be only independent numbers in here. Uh launch

138:11 . The longitudinal modules M and the modules view. So we went from

138:18 , a pizza polar anisotropy. We from 2-5 um independent elements. Now

138:27 talking about or ceramic symmetry, which shales or thin bed sequences with either

138:34 or two orthogonal vertical practice. And this has nine different primaries kind of

138:42 . And so it looks like it's complicated. And in fact, the

138:46 time I attempted to deal with I gave up because it was so

138:54 complicated. But that was because I smart enough. And from my colleague

139:00 , whom I mentioned to you he's smarter than me and he showed

139:04 the way forward. So orthodontic symmetry the symmetry of a brick. So

139:11 uh imagine you've got a brick sitting and it's got um principal directions along

139:19 axis and along this axis and along axis. And normally if it's sitting

139:25 in the subsurface you don't know how orienting. Maybe you know which way

139:30 one is oriented vertically, but you know whether this one is oriented north

139:35 northeast or what all you know this is not increased. So what's function

139:43 ? Oh by the way uh this not the right hand according. So

139:48 your hand up to the screen with finger in the X. One

139:52 curl your fingers around to the extra and you'll find your thumb pointing down

139:58 the X. Three direction if you're it right handed. And if you're

140:02 it left handed you come to the conclusion. So um that's why it's

140:09 important to remember even if you're left you gotta do this kind of stuff

140:14 in uh Miss del rio, are right handed? Yes sir. Okay

140:21 you're gonna be okay, Mr wu you right handed? Okay, So

140:27 gonna be okay? Well my sister left handed and she can never get

140:31 hang of it. She thinks that should be adopting the Uh Convention of

140:37 handed coordinate systems. Uh but I statistically only about 10% of us are

140:43 handed and the rest of us are handed. So we always do it

140:47 handed. Now what song can realize when you and you look at trying

140:57 derive velocities from that Stiffness Tensor with different elements. She just do it

141:08 a brute force, right? It's . But if you concentrate only on

141:18 traveling in this vertical plank, then um raise obey the equations for

141:29 And it is the previous the previous complicated expressions for velocity as a function

141:39 data. And five reduced without approximation to those for polar anisotropy. When

141:47 talking about propagating in this plane, know or any of the parallel planes

141:53 and we know how to handle polar the previous lecture. And he further

141:59 out that when you specialized they're very general expressions for for population only in

142:07 plant. You may also reduce without . The equations are pulling on the

142:13 and we know how to handle Furthermore. We're gonna assume both of

142:19 two different ones. Can you see that the lines are differently? Space

142:23 and here, That's trying to indicate this apparent polar anesthetic medium is different

142:30 this one? And um so we're to assume that that we're gonna parameter

142:39 each of these in terms of vertical and anti psychotropic parameters just like we

142:46 for polar and ice actually. And we do that for example, in

142:49 13 plants, we have vertical p velocity, vertical shear wave velocity and

142:56 um uh psychotropic parameters which are defined subscript here. Uh just like we

143:08 for the polar on this topic medium that this epsilon has a subscript one

143:13 it's in the 13 plant. And also have sub scripts now for the

143:18 plane, very similar expression. But see everywhere on the right hand side

143:25 these presents a small difference. For , you see a C two to

143:29 instead of a C 11 here And see ε two instead of ε

143:34 And so you see those kinds of everywhere. And of course the vertical

143:39 philosophy is going to be the same both. So if you look at

143:43 you see a total of nine different and you say okay isn't that

143:47 We um we have a solved we parameter ties the problem in a way

143:53 is uh Suitable for progress. But like I said was a very smart

144:01 and he looked carefully at this and saw that nowhere in here do you

144:07 a C12 and there's a C 13 the C 23. There's no C

144:14 anywhere. So the the problem is we have not properly repair amateur ized

144:25 orthodontic system. So shrunken then identified parameter which has two C 12 in

144:32 and it looks like a delta parameter reasons that spells happened. So then

144:42 all directions, the previous velocity has familiar form. It's got a as

144:47 function of data and fine. It a vertical velocity with two anti psychotropic

144:52 precisely like we had before. These uh data is the angle of incidence

144:59 it's not two parameters here. Anisotropy . And these are very young things

145:04 new here is these vary with ASM if you want to know the details

145:09 how they here it is. Uh delta of five has in there the

145:15 want and the delta truth and scott and signs of uh fire. Now

145:23 are all going to be measured from . But I told you we don't

145:28 how this is uh oriented in the . In the ground. We don't

145:33 that the one direction is proud all the east like I showed in the

145:39 . Uh so uh so really this say 5 -550. And we don't

145:45 where 50 is. This direction that's in the ground. But we can

145:50 it out. Sam. This is elliptical variation of delta as elliptical variation

145:58 ASM. And so here I'm gonna you that ellipse in some data.

146:08 Given by my colleague Lynn let me something about Lynn this is another woman

146:17 a different len than I mentioned before connection with the reflectivity exercise.

146:23 Lynn was a colleague of my ankle then she left and Michael to raise

146:30 family and now the family has grown she maintained her activity as a geophysicist

146:39 all these years, ran um boutique firm called Lynn Incorporated. And uh

146:49 has uh she does in specialized processing oil company clients. And so this

146:54 something she did a long time over 20 years ago. And this

146:59 a three D seismic data which has processed by Lynn to uh show um

147:08 image gathers azimuth by asthma. So is 10 degrees as 20 degrees,

147:13 degrees around to 180 degrees asthma. then the rest of the circle repeats

147:21 . So uh Who continued from 180 360 would simply duplicate this.

147:30 Uh let me uh when I this the interval she was she's analyzing and

147:37 analyzed, she's analyzing the velocity, normal move out velocity as a function

147:44 as it. So in the first , I want you to ignore this

147:49 non hyperbolic move out, especially at angles because this shallow section is something

147:57 wasn't interested in. These angles are to be bigger and any given

148:02 These angles are gonna be bigger than here because that's normal with these shallow

148:08 . Um they're gonna have larger So she wasn't interested in that.

148:12 mind that. And now she's flattened these gatherers with the same velocity

148:18 And so you can see that at function at this uh asthma here which

148:24 North 1 50 east. Uh The is correct. And then it gets

148:32 and worse as you go around the and here is really bad and then

148:37 gets as bad as it's gonna get here. This is uh North 60

148:44 . Uh And then as she keeps going it starts to get better and

148:49 wraps around and comes good again. look at this a 1 50 minus

148:57 90 degrees. That nine degrees is what you're expecting from any lips.

149:06 what she was looking at was normal within these planes. And she was

149:10 that varies with asthma in the way uh it should be quite natural to

149:20 out, velocity is equal vertical velocity one plus the anti satellite primary

149:26 which varies as a function of asthma to the formula that I gave uh

149:33 former neighbor a few minutes ago. this this figure explains a very explains

149:46 answer to the to a very important . The question is, if you

149:53 geophysicists are so damn smart with all poor ceramic anti sodomy and everything.

149:59 come 80 years ago they found all oil. So let me just remind

150:08 that uh here we are in the 2022. So 80 years ago was

150:16 . I was born in 1942. father was a geophysicist before me and

150:23 found a lot of oil In the and the 40s and the 50s and

150:28 60s without knowing any of this fancy that I'm telling you about now.

150:34 how come they were so successful at oil, ignoring the use of sophisticated

150:40 . So this figure explains So in days, of course, think about

150:47 father as a young, as a man um, in the 40s,

150:52 years and he stated he was not into the army because he um was

151:00 that he had critical skills and of the army needs to have oil to

151:06 on uh, to supply the fuel the tanks and and the plans and

151:12 . So it was really important for United States to have easy access to

151:20 of or during the war years. um, so he was not required

151:31 serve in the army. He was expecting to find oil, which he

151:37 , He was spectacular oil finder for , first for Western Mexico and then

151:44 pan american petroleum, which turned into . And he was so good at

151:50 oil that when I came along and for a job, they said,

151:54 that's great, let's get another He'll have the same magic touch that

151:58 father did. Well, I'm sure were disappointed I in all my career

152:03 Amoco and BP, I never found single barrel of oil, but I

152:09 find ideas and we've been talking about ideas for the past several weeks

152:16 Um Other people have used those ideas find a lot of oil. But

152:21 was it that my father was so finding oil back in his day without

152:27 of those ideas. You can see directly from this picture in those

152:32 Of course it was a two Air. So they were putting out

152:35 along two D. Lines, not D. Lines. Imagine putting geophones

152:41 this line. They didn't know that rocks down there were Arthur Robin.

152:45 thought they were actually tropic or maybe didn't think that, but they thought

152:49 if they're not actually tropic, we do anything about it. So let's

152:53 there ice in front. They laid their geophones along the line like this

152:57 they arranged the geophones to the maximum here. The geophones is approximately equal

153:05 the depth of the reflecting. So those conditions are only gonna get hyperbolic

153:12 out. So they only have to about the animal velocity. They don't

153:16 to worry about uh non heavy body out because they had short spreads.

153:24 now they found short spread. Um out velocities, hyperbolic move out

153:32 And um the anti was surely there the anti sex was hidden within uh

153:41 major point. They measured uh N. M. O. They

153:46 measure these two parts separately. So they knew was they got hyperbolic move

153:51 and that was good enough for They used that to convert time to

153:55 . Uh and they always got it but they laid that to uh uh

154:03 in the field. And so they just didn't worry about it. And

154:09 since they didn't acquire all these three . Angles here, they didn't know

154:13 this thing was varying as a bunch . So using those uh simple ideas

154:21 that restricted contacts, they did find lot of world. For example,

154:26 father was instrumental in finding the east oil field, one of the largest

154:31 fields in the world, comparable in big fields in Saudi Arabia. And

154:38 it was it was all found um during his time as an act of

154:44 in America. So today we have better data that is longer offsets.

154:52 have three D. Uh data we have 40 datasets. We have

154:58 computers to process all this stuff in father's day, no computer in the

155:04 , there were no computers fifties, computers. First computers started coming in

155:10 the late 50's late And I remember I first went to college in 1960

155:20 while I was still at home, this would be 58 or 59.

155:25 father said let me show you And so he took me into the

155:29 on a weekend. Nobody was there course uh and sitting there in the

155:34 was a large, um, instrument about the size of a

155:43 And I said, what's that? said, that's your computer. And

155:47 said, what does it do? said, it manipulates data, you

155:53 in the data here and it prints the answer over there. So I

155:56 , oh like a big adding And so he said yes, but

156:01 lot more flexible. You can manipulate in lots of different ways, which

156:06 can't do with an adding machine. use your imagination of how you could

156:12 numbers. He said, I think machines like this could be very important

156:18 your lifetime. So that was pretty . Wasn't in 1958 and it took

156:24 years for his vision to mature. slowly and slowly and more and more

156:31 more so now what we have is computers. And not only do we

156:36 computers in offices, we have computers our pockets which we call smartphones have

156:42 technology developed and from that day and sort of saw it all coming and

156:50 his day there are a lot of colleagues who thought it was not important

156:55 they resist the changes. But he the changes and try to figure out

157:01 to use these primitive computers. They primitive um, by our standards.

157:07 so he kept his job longer than colleagues. He retired at age

157:14 Uh, basically the same age as did when I retire. So here's

157:18 lesson for you. Young people uh change, expect the change is gonna

157:24 in your lifetime and embrace it and master the changes as they come

157:31 especially can uh these days. Um people are much better at uh comfortable

157:41 smartphones for example, and old people me. So you need to embrace

157:49 changes. There will come a time uh younger younger people are into much

157:56 technology uh than than your girlfriend. uh you should not uh throw up

158:05 hands and say, well the old is good enough for me. You

158:08 try to learn from um the new . And he got the date as

158:16 you can for as long as you and that will be important for your

158:22 professional success. So now let's think the azimuth, all changes in this

158:33 coming from this. Remember we had uh oh and that's in one dimension

158:45 . So now what happens if you're in two dimensions, X and

158:49 There it is. We've got an term and a wide square term,

158:53 you might not have thought of We have an xy term and we

158:56 three different parameters to determine. And written them in this more complicated

159:02 Uh But you can see there are different three different parameters in here that

159:07 have to determine. So these are is the equation for any lips and

159:16 know what you're thinking. The looks only two parameters and short axis and

159:20 long axis. So there should be two parameters here, but there's also

159:25 parameter which indicates the orientation. That's you need three. So uh let's

159:32 at this picture here. Just a . It so as a function of

159:36 and age is what they call half . I don't know why they did

159:40 , but in three D surveys often about half distance from source to the

159:46 . And we got sources, receivers at all asthma. And we have

159:52 coming in. And I've I've shown pics of the arrivals here and you

159:56 see that I've found an average hyperbole go through this. And so at

160:02 point like this, you should be one noticing the residual and number

160:08 asking yourself are those residuals, no or signal. So the answer is

160:16 they're random their noise and if they're in some sort of pattern, that's

160:22 signal. So let's look for So here's a pattern. These early

160:29 are coming from generally north south directions the later arrivals are coming from east

160:35 in the cartoon. So then let's first thing I'm gonna do is uh

160:42 flatten the gatherers using this average average ground balls here. It

160:48 And now you can see that uh residuals are really quite obvious but and

160:56 know what you're thinking, you're well this has been stretched here,

161:00 look at look at this, see this this residuals here, almost the

161:06 of my, almost the size of arrowhead. And I'm gonna go

161:13 see it's the same size down So when we um flattened it,

161:20 kept all these residuals here. So what we wanna do is we do

161:28 want to stack all these together because get a fuzzy image at that.

161:33 want to do is residual move out flat knees down here and the residual

161:39 out is going to happen as a of uh So you can actually do

161:47 quite easily. Uh The first thing want to do, I want to

161:54 the brain's limited normal, normal move trucks that gathers sorted by asthma.

162:01 , so this is a common midpoint but not sorted by offset. It

162:08 go from zero offset, just large here because its range limited, it

162:14 by ASM and the picks line up some and so you can see

162:21 not all Asmus will be recorded. in our and most three D acquisition

162:31 there are zones like this where no are reported and other zones where lots

162:38 Asmus are reported close by each So you got to plot them with

162:43 proper as well. So this one Is really 91, instead of um

162:52 You gotta plot it right over So you have to plot when you

162:56 this. Asthma started gathering. Gotta them at the right as um and

163:03 can see here that these events are flank. So uh you can remove

163:07 then with a parametric residual movement algorithm has only two parameters in it which

163:15 uh long axis and uh the short and the three parameters long axis,

163:22 access and orientation of the ellipse which implied by this. So let's look

163:30 see how this looks. Um in data, this is val and uh

163:37 is the Valhol reservoir down here and taken off to the side um where

163:45 no interference with the gas cloud. never mind the gas cloud. You

163:49 see it's been muted here. Uh we're not gonna pay any attention to

163:55 and it's been flattened. All of are pretty, pretty nicely flattened.

164:02 . Um and it's a function of Maximov sat here and in this case

164:10 maximum officer is uh at least two three times the depth. Now,

164:21 you look closely here, can you these arrival times move up and down

164:26 that rapidly? And that comes from fact that all as mazar representative and

164:33 one right here which is arriving early coming from a different asthma than this

164:38 here, which is coming late. you see that difference here with my

164:42 , This is an early one and is a label. And uh without

164:48 asthma, you can't possibly imagine this of a jittery arrivals uh without it

164:56 not being caused by an ASM there's else here. So now let's sort

165:06 these uh the ASM, so this one degrees to 360° here. And

165:14 can see these zones here where there's data. Yes. Oh and now

165:23 see there's no uh there's no rapid with asthma. Up here, we're

165:29 to uh there's more there. Can see the early arrivals are here,

165:35 a perfectly flat line here and the arrivals are coming in about here.

165:41 this year is coming just above this off here, this trough is coming

165:49 later. So it's that uh she this arrival plotted quite close to this

165:55 that would make the considering arrival like summer, but it's sorted by

166:01 There's no more jitter. I want um and focus on attitude behavior and

166:16 see this azimuth, this aptitude behavior also very strongly as a function of

166:25 bad things. You see that So uh here we have an asthma

166:32 is strong, weak, strong, , strong, you can't possibly have

166:36 kind of variation within a vo expression we saw before, just a sine

166:43 term and the sign of the fourth . It doesn't happen. It have

166:48 most one piece of uh of amplitudes . Strong, weak, strong,

166:55 and strong. And look asthma sorted limit. So you can see that

167:04 amplitudes in some directions are very strong not so analyze that. So now

167:11 gonna do asthma thing and that's the ceo. So um let's think of

167:25 video only for moderate austin. So this curvature turn on him. So

167:31 the reflection coefficient looks like it did except that Dalton is a function of

167:36 . And also the sheer models is function of asthma. And here instead

167:41 having two times V. S. , we got the S. 10

167:47 V. S. 20. These the two different share um uh two

167:52 verticals share module I uh which coming breaking down um grazing down there um

168:04 ceramic symmetry into two separate planes of anisotropy. This is one fear of

168:11 , vertical shear velocity, one of and that's the other. So if

168:16 want to know what what this variation here in this variation here. I

168:24 an expression for that but I don't to discourage you by showing you a

168:28 expression. Uh Let us just say this gradient can be expressed in uh

168:38 the form of a term which is of asthma. And another camera depends

168:45 the square of the side of the referred to some um reference asthma with

168:53 coefficient here, which we're going to ? So uh this asthma, the

168:59 of the grade can actually be Here's our was our first look at

169:04 again at available Um um um 20 ago. And so here we have

169:14 uh incident angle. So this is sort of that you're accustomed to looking

169:21 . It's got one peak, not several peaks, one trough only

169:25 several shots. And you see there's lot of scattered around there now

169:32 Um Here's something you might matter. look at this, that's a data

169:37 there, that's not part of So and you see something like that

169:47 you want to just ignore that but don't want to ignore it. Um

169:52 you don't want to uh ignore it because it's convenient. What you do

169:56 before you start analyzing this statistics of noise, you set up criteria and

170:02 say we're gonna ignore things if they outside of our of our criteria.

170:08 for reasons we don't know what it , maybe it's a false instruments that

170:13 just going to ignore those. So ignore that. And then we fit

170:17 curve through there using formula like you're with. And then we ask ourselves

170:26 this residuals is it signal or is noise? It's random, it's

170:34 but if it's got some sort of pattern to it, that signal.

170:38 what kind of pattern are we We're suspecting an asthma attack pattern.

170:44 we take this, we take the gradient for every one of these,

170:48 the same intercept and apply gradient for one of these points. And plot

170:53 here as a function of asthma. you can see that some Asmus is

170:58 and some it's low and there's still lot of scattered, there's always scatter

171:03 pre stack data. But here you see a clear pattern and as a

171:08 pattern which is telling you that this simple. So look at it in

171:17 proper way you find the patterns. that's what you do when you're confronted

171:22 noisy data, you look for patterns in every conceivable way you can think

171:29 and if you're lucky you'll find it we did here. So uh so

171:35 as a little variation is responsible for uh as little difference as you see

171:42 , this is uh brightest Appleton's here this is the different attitudes and it's

171:50 degrees separation from another 90 degrees. uh it's uh strong again and another

171:58 degrees, which we that's exactly the variation of. So let me put

172:09 up on a Amen. So this a valhol and this is about 500

172:20 by about 1500 m here. And see in every pixel here. Uh

172:26 plotted a little arrow without an error . And so that is giving the

172:33 of maximum Avio Grady. And then contouring up those and uh presenting that

172:42 the color overlay. And so the here goes from zero as local variation

172:49 200% as a little variation. So Zeros are places like here and the

172:56 is a place like so uh see this in this patch here, all

173:04 directions of maximum gradient are more or the same. So what that means

173:10 if you are traveling along here with two D. Survey that 40 years

173:15 , Oh see maybe there's a right here, maybe not. Um I

173:20 looking for right angles. So now you're traveling in this direction and a

173:24 D. Survey 40 years ago, would definitely notice it when you came

173:29 this area. You can see a a real uh phenomenal however if you

173:35 along this way you wouldn't see anything all the variation is in this

173:40 Remember that the gradient is effective and points in this direction. So we

173:49 this and uh but we didn't know it meant anything. There was no

173:56 service confirmation. So years later we better data and so this is also

174:05 value also data from the top of reservoir And what you see here is

174:12 map, it's about five km by 15 km. And you can see

174:18 red lines here. So these are lines of um life of field seismic

174:26 varied, 2500 ocean bottom side of receiver in the mud about a meter

174:36 along these lines. And we, brought subsurface tables to the platform,

174:44 is right in here where things are in those days. There was a

174:49 platform right here. And from there was sent to the shore and also

174:54 another table, not by reader. so then here in colors, we've

175:01 up the same, uh, azimuth of a real great. So there's

175:11 lot of places here which are navy . And so those places are places

175:17 the data is so noise that we believe the results at all. And

175:23 right here this is the gas cloud the gas is in the overburden over

175:28 center of the, of the Uh, the data quality here is

175:36 bad. We can't see anything. in order to hide that from our

175:39 , we painted all enabled. Now is the previous picture, Right?

175:45 have a previous life exhibition. You see there's a patch of color here

175:54 to what we have. So The value uh, show 100% different.

176:02 here, who you see why? 100%. I would say that

176:05 we did a better analysis at this in 06 than we had. So

176:12 zoom in on that. And so see places, by the way,

176:15 see the cables are here and you see there are zones here where they're

176:21 uh all white. And so uh uh indicating maximum aereo gradient variation and

176:33 there's a narrow transition zone and its in another direction. Mhm. So

176:40 we interpret that is we're gonna we're interpret that in terms of fractures on

176:45 like so and then fractures going like separated by narrow offenses. But here's

176:51 zoom into the southwest front, same of path. So we did this

176:57 Houston, my colleague shaw and myself we didn't know what it meant.

177:01 we sent it to our colleagues in barking. And a couple of weeks

177:06 uh I'll show you what he sent a couple of do this. Uh

177:14 an example of a place with a , clearly defined as a little various

177:21 there's a lot of noise but there's uh as a variation here. And

177:30 is the data set that went into offsets chasm. Here's a case where

177:38 a similar noise, but you can't this um uh Phillips, this is

177:46 a flat line here that this does an elliptical variation, but we obviously

177:52 believe it because the noise is so . And so there are standard ways

177:56 statistics you to decide whether or not want to believe the parameters you get

178:01 of this fit, given this kind noise. And so where the confidence

178:06 less than 95%. We just painted dark. This is what bark would

178:13 us back a couple weeks later. is the same map. And I'll

178:17 you later about this map. Same with a different color bar. So

178:22 of um instead of navy blue, white. So wherever you see right

178:27 , we don't believe it. And it's got on here the wellborn

178:31 So the platform is here well go down about two km and then it

178:37 horizontally to reach to all corners of reservoir. And you see here the

178:43 of color. So the amazing thing this is that every one of these

178:48 ends in a patch of color and of them there are no patches of

178:54 where there are no boreholes. And the we found here is that these

179:02 of color. I gotta tell you more thing. Uh they let's look

179:08 this one. Um they drilled this and they drill it with a complicated

179:15 like this to end up exactly where want it in the racing part and

179:20 they perforate the ends of it with devices so that they can produce only

179:27 the end of this. Or maybe gonna inject either way they're gonna be

179:32 of injection of production only from the of the bottom. So here we

179:39 a good confirmation of uh some service that the uh huh advanced your physical

179:53 that we're finding here, which are azimuth variation of the offset variation of

179:58 amplitude Is coming from something that we about. Uh at this point these

180:06 have been in production for uh 20 . And so this is the result

180:12 Production from this zone around here over years. And I have to tell

180:17 one more thing. Uh the reservoir a soft chalk, so when it's

180:24 with oil, it uh is able hold up the overburden. But when

180:30 withdraw the on we lower the pore in the reservoir, as to the

180:37 top framework is not strong enough to up the overburdened by itself. So

180:43 overburden crushes the reservoir making fractures like , there's of course um an ambient

180:52 you so the fractures are not um aligned or uh joints like I showed

180:59 the photograph an hour ago, but are preferentially aligned by the uh by

181:07 stress. Um That's good because as reservoir, as the overriding questions the

181:18 , it re pressurized so you can more oil. And so as a

181:24 of that, this field has gone being a one billion barrel field,

181:29 it was when it was first discovered years ago. Now it's a five

181:34 barrel field, they produced about 3.5 so on. And you can do

181:41 because reservoir maintains depression because if you're by the old burden because the reservoir

181:50 is so soft without the pressure to them hold up. Let me show

181:57 this one right here. This one when they put this borehole here,

182:02 thought they were going to produce from area around here. But evidently all

182:07 oil came from off here to the , evidently there is a premier grocer

182:11 in here which they couldn't see in seismic. So all the oil that

182:15 up this world came from here. obviously what that means is that there's

182:21 opportunity to put another ball. So um you see here lots of

182:27 that you don't see them all uh stuff reservoir collapses the overburden sags down

182:38 it breaks tomorrow. So boreholes only a finite lifetime and this is only

182:45 the ones which are still alive. over 100 bore holes here. And

182:50 uh so now uh this was done um oh oh six and so now

182:59 a new platform over here to the which I'll tell you more about

183:04 Okay, so that's all about What about this one? Well this

183:12 um Said I told you came from geophones so we spent $25 million dollars

183:19 bury these earphones in the mud with expectation of doing frequent time lapse,

183:28 , numerous time lapse surveys recognize that you do uh 40 time lapse survey

183:38 the conventional way to go out and a three D. Baseline and then

183:43 go out to a year or so uh and acquire the first time

183:50 And when you do it in that , the second one cost as much

183:55 the first. In both cases, have a large push graphic vessel towing

184:02 which are gonna be screaming behind about kilometers. And there might be an

184:07 of a one km wide 10 km big powerful book to pull that through

184:13 water. And so that is And so you might never do a

184:19 one because it's so expensive. So idea that BP had was to spend

184:25 million dollars up front burning the earphones the mud. And then you can

184:31 around shooting seismic data into these earphones only A small source boat. It's

184:37 towing 10 km of receivers, it's turning a sorcery so it can be

184:42 cheaper and so you can do it times. So these are the first

184:46 a life of field seismic. And these are the first to buy now

184:51 over 20 so uh they have is movie with 20 friends in it showing

184:58 the uh field is evolving uh every months. Fantastic uh advance and four

185:08 . Acquisition and processing technology. And by now they they instrumented the other

185:16 of the field which is over here . So now let's look at the

185:22 here between the second survey and the and you can see it's got patches

185:27 color everywhere in the same places. of course these are all calculated

185:33 Every one of these points is calculated others. And of course independent like

185:37 . And so what that means is can form simple differences. So these

185:41 the differences between two and one. this is a few months of production

185:48 hearing all these uh these changes happen a few months of of production between

185:54 and two. So uh think about we're doing here the work um we're

186:04 a very exotic um geophysical signature and looking at differences of differences or

186:12 And you would think that when you at all these differences you would very

186:16 become overwhelmed with uncertainties and it would nothing. But in fact when you

186:22 at this you see it does make sense. So and furthermore we can

186:28 a lot of money out of this recognizing which parts of the reservoir have

186:34 drained, which parts have not And so it's a very good case

186:41 the best uh even today in the showing how uh advanced geophysical technology can

186:51 economic um advantages to the operator hundreds millions of dollars. Mhm. Reese

187:04 of course are not. Orthogonal factors I showed him the picture. Here's

187:10 picture showing a more complicated fracture All of these fractures here are vertical

187:19 you can see the angle between them not named degrees. So that doesn't

187:24 for Thoreau pick an ice factory that mono clinic and a century. It's

187:29 complicated and not uh not feasible. we're not even going to discuss it

187:36 this point. So running short on here. But I do want to

187:44 about this topic sheer waste that we before about what happens to a plane

187:53 at uh um reflecting interface. And in that case we were talking about

188:00 p ways. But uh you can if you had an incident S.

188:04 . Wave polarized out of the plane upon uh you know medium like

188:11 you're expecting a reflected S. Wave and transmitted issues. By

188:17 if it's if the incoming wave is SV way for its poor in this

188:22 then you get in addition to reflected transmitted SV rings, You also get

188:27 and transmitted P waves. So everybody looking at this, this is the

188:32 we want to do it. So in about about the time that I

188:37 um until early eighties uh counter film a horizontal library. They said let's

188:46 shear wave surveys, just like we p. Wave service. All we

188:49 to do is have horizontal vibrators so instead of vertical vibrators and we need

188:55 have horizontal earphones. Uh Well uh it so that uh vibrator is transverse

189:07 the line and the receivers are The line waves are gonna go down

189:15 without coupling to pee. At the from back is an S.

189:19 Way and cross line motion all the cross line signal owner. So um

189:30 did that they invented the vibrator and went out in Oklahoma and they acquired

189:36 kind of a survey and they got absolute garbage and they did it again

189:41 again and got garbage and they said know there's something here we don't

189:46 So let's put together a consortium of to figure it out. So they

189:51 together a consortium of about 20 companies amicable to share the cost of sending

189:57 kind of film crew around the country this kind of a survey. And

190:02 they came back they found that uh did about 20 surveys which about 19

190:11 them were garbage. And the only was yielded interpret herbal data. So

190:19 killed sure way of exploration back in . So and only survived uh in

190:30 like universities and Amoco had a research . We had long since we had

190:38 all of our acquisition equipment to the companies. Now that sounds like a

190:43 idea because our payments then paid for profits instead of ours. But when

190:49 have an asset like a crew. You've got to keep it working all

190:54 time. You find out that it you instead of you owning it,

190:58 gotta keep it working all the time the payroll is accumulating every day.

191:04 the interest on the capital equipment it's best to um, outsource both

191:12 and the expenses to a service company then to contract with them uh,

191:18 and when you need it, um way that you're not having to pay

191:24 people and equipment standing around idle. we had done that like every other

191:29 company, but we retained one group um research purpose. So we went

191:38 to um, uh, well, did that research crew here and there

191:44 different purposes. And this one we to Pennsylvania. And you see here

191:49 Pennsylvania. And the site of the . And this survey was done with

191:56 kind of S. eight screw along line here, vibrating false line

192:03 And then uh, here is uh line almost perfect guitar over here is

192:13 , it's almost perfect. And of we're vibrating foster. So the geology

192:20 this area is folded mountain range. there's a mountain range running here.

192:25 mountain range running over here in the down the middle and obviously down the

192:29 , there's a road and the crew following the road. And then right

192:33 this place where there was another road the mountains. So that's what they

192:37 . And they gave this um uh to the woman uh Eloise lin that

192:44 mentioned earlier. Uh smart energy physicist and her husband was working then for

192:52 . She was working for Amoco in and she found a very pleasant result

192:59 she followed me up. She heard I was also new with the

193:04 Now I have been uh publishers in but work was done I think in

193:09 or 81 look at this result that found, I'm gonna back up I'm

193:14 show you half of this line compared half of this line. And then

193:19 going to show you the other two first half of the first one.

193:23 this is a half of one half the other line. And this

193:26 um sure we get acquired like I an S. H. Style.

193:31 and very very similar. Well it it was an M. O.

193:39 was the uh imaging algorithm of the . And uh it was good

193:46 Well there's pretty good uh pretty good here and pretty good imaging here.

193:51 look at the thai point they tied shallow and then a mistimed begins to

194:00 and down here the mist i is 61 milliseconds, wow both of them

194:06 good but that they should be the and they're not the only uh main

194:12 is different here. This is uh midpoint stacking S. H. Data

194:20 on each line and we all thought would look like this. I was

194:25 the other two from Carson this uh one is pretty good. This one

194:30 a lot more noisy but you can see the uh oh. Mr.

194:41 . Uh huh. I want you think about this. This is uh

194:45 of uh common midpoint guidance. But want you to think about this in

194:50 of um vertical incident. Only think it in those terms. The only

195:01 different here is the angular polarization of and traveling right? So uh you

195:10 do this for yourself. Uh Take bunch of business cards, put a

195:15 band around here to keep it And imagine here a vertically traveling away

195:21 . So the all of the hand the wafer and the fingers indicate the

195:28 . So these business cards represent vertical . And you can see this some

195:35 deforming the rock. Like this takes of the zones of weakness. So

195:40 wave experiences the rock is compliant and moves slowly. Meanwhile if you have

195:47 the same uh practice in the same with a way of traveling in the

195:53 way vertically but polarized along the You see it can't take advantage of

195:59 zones weakness. So this way experiences rock as stiff and it travels

196:07 So because these two ways are traveling different speeds launched at the same

196:13 they're traveling to different speeds. We that sheer waste. So normally we

196:20 have um you don't know there's fractures there. So let's do uh two

196:30 . Line on this line. And gonna do an S. H.

196:35 and we don't know it but there's in subsurface online like this. So

196:42 to the equations of uh tropic wave , this wave traveling vertically polarized in

196:52 direction, can't propagate at all. . But what the rocks say listen

197:00 I'm not gonna let that one propagate all. But listen I'm gonna do

197:04 vector decomposition of this displacement effect into direction parallel to the fractures and this

197:12 perpendicular to the fracture. Just sines and co sign. And I'm

197:17 allow these two ways to propagate um and reflect and come back. So

197:31 of these modes does propagate down each its own speed. And so the

197:37 one to come up is this one here. Well we don't have a

197:40 phone pointed in that direction. We have one point in uh horizontal

197:46 But suppose we were very clever and also had in line components also.

197:52 we could uh we could uh uh much of this one according to science

198:01 process and so much of this and split second later up comes the other

198:08 and we have the same gear phones there. And so we record these

198:12 things. You see these are the components uh of the upcoming waves and

198:20 don't know that wave is down We launched it in this direction but

198:25 an upcoming wave here or in this which we don't know about and we

198:30 this data here and here. So a representation of that, uh gonna

198:41 a cross line source and across line , uh we've got a strong impulse

198:50 , that's this one right here. at the same time we got spike

198:58 here, that's hers. Yeah. a split second later we got these

199:09 impulses coming up and so this is good time to uh say what happens

199:18 really the anti sox zero. So delay is zero. So this uh

199:24 slides up to here. This slides to here and see this one exactly

199:29 this one because they both have a on the pro side and this one

199:33 together because sine squared, so did same thing with the online source.

199:45 got a different set of vectors, so and we can make a matrix

199:52 see by to see matrix from this . So this is putting uh those

199:58 spikes together from the in line Cross line source. Uh Offline source

200:04 line receiver. Cross line source in receiver and so on. So you

200:09 we have a matrix of data here here is what it looks like in

200:17 data except that these aren't stack Not vertically insert traces but uh you

200:25 see here that we get our line this uh this is our life and

200:31 have a four to see by to matrix of of reception here, wiggles

200:37 wave forms real data. And uh two the the S. H.

200:46 Yes it's serving that. It used be done all the time. Was

200:52 one right here with sources cross line receivers crossing. And this would have

200:58 an SV survey. Never did that because it was obviously we shouldn't do

201:03 . And also we never did this with mixed max cross line and in

201:08 receivers because that should obviously be zero you're having the sources in line and

201:14 cross line but valley look here is zero, it's just as strong as

201:20 others and here's another mismatch component just strong. And we discovered this using

201:29 research party uh in uh in Um and this figure was made some

201:39 later by my friend jerry Bodnar but such a good figure. I wanted

201:44 introduce him at this time. And then what we did with using and

201:49 the way all of none of these sections is interpreted to see all of

201:56 look terrible here. Uh But then we did is we uh we did

202:03 operation called Alfred rotation named after my Rusty Alfred at chemical and we did

202:10 mathematical rotation of this uh to see to see dataset at every um uh

202:19 rotated the whole dataset uh about the axis, the same rotation for all

202:27 position at all times. And we did uh locational matrix of the sort

202:34 you saw earlier in the course and did one degrees, two degrees and

202:39 on. And then we found a angle or look this off diagonal

202:45 All zero just noise. And this all zero just noise. This is

202:50 interpreted. You can see these reflectors through here and this is also interpreted

202:56 but this one is uh Arriving sooner this one. So by that rotation

203:06 uh we've arranged for all of the energy to be appearing on one section

203:14 and all the slow energy appearing on other section. So if we had

203:20 the data with sources and receivers oriented this, they would have been only

203:26 mode uh publication fast and slow according whether it's from this way or this

203:31 . But we didn't know before we started how the uh the fractions were

203:40 . So we discovered it by discovering magic Alfred. And I'm gonna back

203:45 here. Now I'm gonna show you that this angle here is the angle

203:52 the uh that the acquisition direction the was going along here. And now

204:01 gonna point out to you that are in the subsurface here like so which

204:06 parallel to these virtual receivers and perpendicular . Uh So we did that so

204:16 transported um the data has recorded into we would have recorded if we'd known

204:22 fractions were down there. So We that in the early 80's and attempted

204:44 secret for um uh five years. I think I told you the story

204:52 how we revealed it um to the . E. G. And a

205:00 technical session at the ScG in 1986 the chemical anti chapter face session reveal

205:09 stomach to the uh larger community. at that time we suspected that it

205:21 suspected that the effects that we were in the data across by tractors in

205:26 subsurface. But we couldn't prove So this was the data set here

205:34 proved this is taken in um um texas. Just to the west of

205:41 , near the texas near the texas of Giddings. And uh down here

205:49 the often chalk, it's a famous formation stretches across thousands and thousands of

205:55 miles in central texas and further east Louisiana. Well known to be uh

206:04 good producer of oil or it's fractured not. And so this data set

206:10 acquired with the to see by to shear wave acquisition that I showed just

206:20 . We did the Alfred rotation. so this is the fast section and

206:24 is the whole section and you can the slow section is coming in a

206:30 bit slow. And so this delay is coming from on uh fractures in

206:37 old bird. And then it gets be a bigger uh bigger july as

206:43 go deeper. And this is the again. So let's zoom in on

206:49 zone and you can see the amplitudes are pretty continuous here for the fast

206:56 . So this to the section. think again, vertically propagating shear wave

207:02 the polarization parallel to the fraction. , uh this wave is fast because

207:11 does not take advantage of the zone of the zones of weakness and above

207:17 is a share. And so the , the chalk is a hard

207:22 not like the val home truck. so it has a strong uh reflectors

207:28 of position along the city alone. this fast direction determined why? Um

207:38 the over word. The overburden is is determining this fast direction.

207:44 let's look at the slope section. slow polarization direction is also determined by

207:49 uh ordered. But look right here's the often chalk inherit strong

207:57 Week. So the implication is that a place like this, there are

208:05 which weaken the chalk. So that this uh polarization. And in this

208:14 the uh the fractured limestone has a impedance to the shale up above.

208:19 not much different. So when we absence of reflection, we call

208:25 Presidents are Francis And over here there's Francis. And over here, this

208:31 is uh independent of whether this fraction not. So this looks like a

208:37 detector detector at the horizon. We're interested. It's not caused by anything

208:44 above. It's happening right here at reflectors. Okay, that's the the

208:50 . So here's the proof. This the the same data with the representation

209:00 a mythos, first horizontal bar So, uh, here is a

209:07 accurate representation of the borehole trajectory. this time we were just learning how

209:13 deviate a well horizontally. And so had, since it was our first

209:23 . Well, we had a smart sitting there on the well site,

209:29 the operations. And uh and this of context, what you have the

209:35 well head, you have uh old close to the uh most to the

209:42 , right where the little earth and making a mud pit maybe 10 ft

209:50 . And when the mud comes out the bar hole, you dump that

209:54 into the mud pit and then you circulate from that mud pit.

209:59 so the challenges are sitting there looking and he um he noticed something sparkly

210:06 the mud, He reaches in with hand into the mud and pulls out

210:12 mud and there in the mud is little sparkly crystals with perfect uh crystalline

210:21 like diamonds. And so this is sedimentary environment. How can you have

210:27 little crystals in a sedimentary environment? only way you can have that is

210:31 you have open fractions in the ground water circulating the open fractures and

210:40 out of the ground water, perfect on the edges of the right,

210:48 then the drill bit comes along and it all off and spits it up

210:52 with the mud come to the And the geologist, smart guy sitting

210:57 watching and says, oh I didn't that, what's that? And he

211:01 a mark in his um long Okay, so it as this well

211:10 drilling, he's making marks in his here and here, but no marks

211:15 and here. And look up here , we see tractors here in for

211:21 and the first fractions here, but here. So no Francis here.

211:30 immediately we realized that we can detect fractured immediately we realized that uh our

211:40 Atlanta shock is caused by orient fractures the substance. We can detect them

211:46 they are, how they're oriented. we can we know where to,

211:53 know where to drill in the often and nobody else in the industry knew

211:59 if they drilled into our fraction swan going to produce oil and nobody knew

212:03 to find the fractures except us. also knew from the story, I

212:08 you last week that Exxon uh was soon find out. So we proposed

212:15 Chicago that M. F. Should buy up the mineral rights to

212:22 entire often chopped play thousands of square In those days. It would cost

212:30 have cost us about $100 million dollars was a big sum but we could

212:35 handled it uh huh. In those the cost for the mineral rights was

212:43 $25. An ancient we could have uh mr Williams probably don't realize that

212:53 the United States the soil beneath the land belongs to him not to the

212:58 States But normally the farmer doesn't have capability to um produce that oil.

213:07 what he does is he signs a with their own company to explore on

213:11 land and then to drill on his and they give him an up front

213:16 in this case $25 an acre. if they find oil on his property

213:22 produce it then he gets a fraction the profits. And then so that's

213:27 way um uh works in the United . So we proposed that NFL should

213:35 up all the mineral rights in this area of texas and Louisiana because we

213:41 where to find the oil and the shop nobody else did that proposal was

213:50 all the way up to Chicago management it was rejected On the grounds that

213:56 didn't trust our technology and on the that the price of oil, who

214:01 , who knows what the price of is going to be in those

214:04 it was about $10 a barrel and knows what the price is going to

214:08 . So, um, they rejected proposal. Uh it's too bad because

214:12 we had uh done that, uh, we would have made enormous

214:19 . Uh, my guess is profits $500 billion, $500 billion dollars from

214:25 . Uh, we've done that a years later. Amateur would have bought

214:30 instead of answers and we didn't know , but the zone down here is

214:40 the Eagle ford shale. And these , Eagle ford shale is one of

214:44 largest producers in the United States of via fracking well, in 1986 we

214:50 know about tracking, but we would got the rights to the uh,

214:55 ford shale for free. So with uh, added that lost opportunity for

215:02 , fl was about a trillion Of course, it's hard to estimate

215:06 numbers like that. It was very by any calculation. So,

215:13 because of the uh, the Eagle shale down there, the cost of

215:19 mineral rights is about $1,500, an , So nobody can afford to buy

215:26 all up today. So let me show you a little bit of theory

215:33 this. So, uh, the instance reflectivity uh is uh delta Z

215:39 two Z. Bar except it's And instead of being pregnant, that's

215:44 obvious. And uh that's uh without that's for the uh as mode and

215:53 the slow mode, there's an additional here coming from the asthma. All

215:57 difference in Azimuth lanai century at the . And Uh this can be comparable

216:04 this. So the uh difference between and this could be of the order

216:11 100% as you saw in the So small differences in um uh subset

216:20 properties make large differences in the So that brings us to another

216:26 but folks, we have one out time here. So I don't want

216:31 uh to broach this uh topic. me just see here. Uh if

216:38 anything that we can do. I think there is. Certainly I've

216:57 finished with this. Again. This a and you can see that a

217:06 of underwater and receivers here. And is the on the drilling platform.

217:14 you can see here uh every pixel , we've we've plotted that uh implied

217:20 orientation of implied french. And you see the uh the pattern here.

217:34 , circular pattern. So the story that when we produce oil from this

217:40 , we uh uh the reservoir cannot up the overburden. So the overburden

217:49 . And so the sea floor And so there's a substance bowl here

217:54 the sea floor. Uh it's about m deep by now and it's a

218:02 100 m across. And so that's by the production. And so it's

218:09 all the pipelines and everything which is the sea floor here. If one

218:14 those sea floor infrastructure pipelines were to and put oil into the Norwegian north

218:21 , the Norwegian government would be very with BP. So they've abandoned this

218:26 platform and and um instead they put platform one here and one here.

218:35 much difference should this be? you can tell the dimensions of the

218:40 both from the sea floor, but can't tell the dimensions of the damage

218:45 beneath the sea floor except with data this. And so this is from

218:50 wave data uh from the same like field seismic data set. And so

218:57 analyzing ways which are extensions of the that I talked about before and they

219:03 that the this indicates the uh direction cracking in the subsurface 1000 m

219:11 So that indicates that if you put board hold your next platform right here

219:15 maybe here, that's a good thing do. But you wouldn't want to

219:18 it here. So, another example operationally important decision which can be made

219:29 uh use of advanced your physical. um so here's a summary of the

219:37 psychotropic ideas here. Uh It made Socrates is usually small, usually weak

219:44 the in the substance. It makes order effects and arrival times. Large

219:50 of absences and completely new effects and waves and converted waves. When I

219:57 a new effect here for example there's share waves instead of one new

220:03 Large effects means that HBO uh gradient change uh the algebraic side of the

220:13 with possible small changes in. Uh that completes the list of topics that

220:25 are going to consider in this Uh The first seven topics were what

220:30 call classical ways and raise. And last three topics were uh where topics

220:38 which introduced more realistic um analysis into into your understanding. So with that

220:47 gonna call this um uh course closed I am going to send each of

220:55 a final exam by email And I also post onto the blackboard in the

221:04 lecture. And after a couple of the corrected uh spreads gonna take me

221:14 couple of hours from that because you to look at it. So with

221:19 I'd like to thank mr Wu for his help and thank you Mr Del

221:23 for her attention and wish you well the exam, the exam will be

221:29 at midnight on Wednesday a week from

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