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GEOL7333-Seismic Wave and Ray Theory - Day7 09-16-2022
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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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