VideoPoints

• ••• • •• • ••••• • •
GEOL7333-Seismic Wave and Ray Theory - Day4 09-03-2022-Part2
Help Tour
© Distribution of this video is restricted by its owner
Transcript ×
Auto highlight
Font-size
00:05 So here we are on the afternoon September three resuming the the discussion about
00:15 reflections and refraction. So what we this morning was uh what I'll say
00:22 a major topic for expression. Geophysicist analyzing the amplitudes from uh subsurface reflectors
00:34 using the same methods uh perhaps with insight than our standard in the in
00:42 industry. So now I want to return to uh the same topic with
00:51 different aspect, which is the reflections the free surface, not from interior
00:59 but at the free surface. And it's normally the surface, the interface
01:03 reflects them because it's uh has the contrast, you know, air above
01:12 uh rocks or water below. So because of that, it generates a
01:19 of surface related multiples, which we'll about multiples in the next lecture.
01:26 the marine contact, it generates source and receiver ghosts. Let's make sure
01:31 know what those are. Uh in marine survey, the sources are towed
01:36 one m below the sea surface. uh the or maybe on the ocean
01:44 . Tell us to keep that uh . Uh and the sources are are
01:53 somewhat deeper, like maybe five or to 10 m in depth deeper.
01:59 the reason that's toad deeper is that it's towed too close to the surface
02:04 the bubble expands it breaks the surface loses all the pressure. And so
02:11 that might be a good thing. the the general consensus is it's better
02:15 keep it deeper. So that bubble going to expand and then actually it
02:22 and expands again and contracts again over over again, making a complicated source
02:29 time signature, but we know how deal with that in in processing so
02:34 can convert that to it effectively an source using process Professor. Yes.
02:42 we supposed to be looking at Einstein now? No, we're not.
02:47 thank you for that, I always that. So uh uh let me
02:55 again to share the screen properly. , how can you see this?
03:09 Yes, Okay, sorry about As we were talking, I was
03:14 , I think we're reading off of right now. Uh do you hear
03:21 ? So uh again, I did do it. Right, So first
03:27 me do it properly here. But I think I'm still not
03:34 let me back up here. Do see where it says with reflections at
03:41 free surface? We're still looking at . Okay, so again, I'm
03:46 it wrong, so forgive me. okay, now I can see reflections
04:25 the free surface and now we're in mode. So sorry about that.
04:34 of the shortcomings. Presuming like this not really as conversant as we should
04:40 for the technology even after two but I've got to get back so
04:47 hear a lot of thunder at my . Do you hear the thunder at
04:50 house? It's about to start and just looked at the radar.
04:56 So I am downtown. And if north, you'll get it in maybe
05:02 half an hour now. Like I , the free surface is the surface
05:07 reflects the most energy. And in it generates surface related multiples. We'll
05:12 with that in the next lecture, generates in the marine context. It
05:18 source ghosts and receiver ghosts. um, The source goes ghost happens
05:26 the uh, sources told about 5-10 below the surface bubble expands and contracts
05:35 expands and contracts. We have clever techniques to convert that source time signature
05:43 effectively impulsive signature in the data that look at. Um, but let's
05:52 only the first uh impulsive um The first expansion of the post That
06:01 energy both down and up. The that goes up, goes up five
06:06 and reflects off of the sea surface goes back down again. Following the
06:11 with a few milliseconds delay. And called the ghost. And then we
06:17 the same thing on the receiver The receivers are towed a bit below
06:23 free surface and uh upcoming wave hits receivers. And it also uh
06:33 as by the receivers up to the reflects back down and has received
06:37 So that's the receiver coast. um, those things are important because
06:44 reflections of the free service are so if we have our receivers on the
06:51 floor. The same thing is But we use different techniques to correct
06:55 it because of the much longer um delay in the water column. It
07:03 be uh significant fraction of a full uh in the water column before the
07:10 ways to receive. We have different for doing yeah. In the land
07:18 , let's consider the land, ordinary land. And we have a vertical
07:24 phone. Remember we have a three your phone, let's do that.
07:29 components your phone on a stake uh in the ground. And uh so
07:37 call that exactly at the surface. mind that uh instrument packages, maybe
07:44 inch or two above the surface that going to neglect that. But uh
07:48 incoming way comes up and reflects and some of its energy going back down
07:55 . But all the time it's doing , the instrument is recording. So
08:03 does not record the incoming way, records a combination of both the incoming
08:08 the outgoing waves altogether. They shape surface together and the instrument is recording
08:14 . So we need to understand how uh number one, we need to
08:22 uh oh Um the waves interact and two. There's gonna be an implication
08:30 that for how we um um interpret . So, because of this strong
08:40 , uh the big difference between uh the interface and above the interface at
08:48 free surface, we can't use the theory that we just used. So
08:53 got to consider the application at the surface of this complicated expression which comes
08:59 and richards at the free surface. we have an upcoming wave so that
09:07 air is uh subscript two because it's the other side of the interface.
09:16 we think that the incoming wave is going down and so subsequent to is
09:22 the lower war medium. But here up the incoming wave is coming from
09:29 . So the uh the air on other side of the interface is zero
09:37 both P. And S. And for density. Now you look at
09:41 formula and you can see those things in the denominator. So we can't
09:45 divide by zero. So instead we're to consider the limiting behavior of this
09:53 as these quantities here approach zero. as they approach the what we're going
09:58 find that it makes uh We can that issue and we never have to
10:05 the issue of dividing by zero. the first part of this program is
10:10 . We're gonna consider the uh we're consider the effects this into these uh
10:21 coffees, B, C, A D. That's what we're having.
10:26 here is the definition of A. so I have to do is set
10:29 equal to zero and set this equal zero. And we're left with only
10:35 other chart which is this go through other um coefficients like that and they
10:41 simplify substantially because uh the quantities with to oral zero. Yeah, let's
10:52 this. The cosine of Theta two defined as the square of the
10:56 one square root of one minus the squared of theta two. And the
11:02 of theta is equal to P X VP to uh that comes from Snell's
11:08 and we already know that VP So this becomes something I one and
11:13 same thing with the co sign for of theta four. Remember these are
11:18 angles on the other side of the . So these are the angles up
11:23 the air. Next thing we're gonna is um uh these coefficients here and
11:30 is the definition, I mean uppercase here is the definition of um e
11:39 remember what we're considering is a case VP- two is not zero but it's
11:44 , it's much smaller than this. since we're dividing by a small
11:48 we can neglect this term and keep term only. So that's this Co
11:57 is one that COVP- two. That's the Lebanon case because VP- two is
12:04 lot less than VP- one and then we're gonna let it go all the
12:08 to go. So the same thing these others, They simplified down because
12:15 these uh special case. So then quantity D, Which is this um
12:25 here, because here is the definition of D. And we put into
12:32 definition, these uh special cases that just saw, for example,
12:38 Is this one and f. Is one? And the product is this
12:44 ? And you can see that uh among these two terms. These two
12:51 come come from these two terms, you can see the comment in here
12:55 the product of one over V. . Two times V. S.
12:59 let's factor that out. Okay, now we're all ready to go back
13:06 this complicated expression and we're gonna find dominant terms in here in the case
13:12 we're Okay, man? Yes. , so we already decided that this
13:21 of this v. p. two the uh um the non denominator this
13:29 dominates over this one. So we're gonna set this 1 to 0.
13:33 way, we're gonna set this 1 0. And then putting in what
13:40 just found for F. And Uh was in here and then we're
13:46 factor out uh The Denominator v. two times v. S to put
13:54 right over here. And uh so you see, we have um we're
14:03 dividing by zero here, but that's gonna lead to infinity because of
14:10 Uh let's look at what we just for d. This product, what
14:18 uh discovered in the uh two pages , that product is not infinity,
14:26 it's this. And so uh putting all of that into the reflection coefficient
14:37 we just simplified it, we get expression and you see here nowhere here
14:43 we dividing by zero? We have small, slow this parameter here,
14:50 going to account for the um offset . And to the extent that these
14:56 are not one, that's also the dependence. But let's look at normal
15:01 and at normal incidence that this is be a zero. And so we
15:06 c squared, this is gonna be zero. So we get c squared
15:10 notices minus one here, so that normal incidents, we get The reflection
15:16 is zero actually, etc, reading and I read it wrong that normal
15:22 , the reflection coefficient is -1. that means that a normally incident term
15:31 all of its energy exactly. Back . None of them gets propagated into
15:37 uh into the enter the air. , um that's a normal incidence.
15:48 about at oblique incidence? Well, we get too oblique instance, we're
15:53 uh the same calculation for the converted coefficient. This is the definition of
16:01 as we define it. Several pages . Many pages back at the free
16:06 , that one this one reduces to Uh this using the same approximation as
16:16 just did. And now let's consider special case of normal incidents. And
16:22 thing is a zero zero. So get uh conversion coefficient and normal
16:31 That's what we found before. And we still have that and so that's
16:38 hard zero now. Um Okay, let's uh remember that this surplus receivers
16:49 all these three things all together at same time, because while it's recording
16:55 incident way, the reflected wave has left yet and the converted share wave
17:00 not left. So vertically incident what is this, this some of
17:07 , the recording uh instruments is given this here is the sum of the
17:13 , uh factoring out the W0, in here, the reflection coefficient for
17:21 oh uh Normally incident p way uh here we just decided that's a
17:32 And so uh the outcome of all is that some of the waves uh
17:39 due. So this is what is measured by the instrument at the
17:45 it's the twice the incident at. that's what we meant at home.
17:55 that's part of what we meant when talks about the interaction of the wave
17:58 the free service, the free service the amplitude because it includes this reflected
18:07 as well as the incident, interesting that our instruments uh are located at
18:16 point where the where the signal is insurance. Now let's consider the same
18:27 and that's true. Uh What we said is that's true for uh any
18:33 insurance, no matter what's below. service. As long as we have
18:37 above it, that's what we're going get for the normal it's away.
18:41 let's consider the special case of the environment. And so uh in that
18:46 uh the incoming, the sheer the velocity and the incident medium is also
18:55 . So from the previous work, can decide that this uh four case
19:03 is zero in this special. And remembering that this is what we um
19:10 derived for the for the the wave , car fishing. And now let's
19:17 assume this quantity is zero. But we assume that D. Is
19:23 So uh this thing disappears. And thing disappears for all incident angles,
19:29 matter what is the value of piece act, no matter what is these
19:33 of these other things? Because of D squared out here. That goes
19:39 and we'll have some C squared over squared with a minus one and there
19:42 is. So in the marine environment get the reflection coefficient of minus one
19:48 all angles, all internet shopping in bleak wave coming up to the bottom
19:55 the sea, to the sea surface the bottom is going to reflect
20:01 And at the uh going back downwards the same angle first, back
20:08 no matter what is the incentive Now this assumption assumes a flat sea
20:15 . I suppose there are waves on surface of the sea. So that's
20:21 to what we call a rude ghost because the sea surface is not
20:29 That makes a complication. Which we want to go into in this
20:35 But I'll just remind you that uh here is that the C circuits is
20:45 perfect flat plane interface. Maybe not , especially in winter time when the
20:52 is blowing and so on, the are high. So you know,
20:56 the waves are only one inch, cares? But if the waves are
20:59 10 ft maybe that makes a And so um that's something for you
21:04 keep in mind if you're looking at data taken um under weather conditions.
21:15 . Um See service might not be . And what happens if you're doing
21:21 survey and it takes several weeks and weather is changing during those weeks,
21:26 conditions might be different at the beginning survey. The towards the end,
21:33 something that you might want to keep mind. You know, we make
21:36 these assumptions and they are more or plausible. More or less most of
21:42 time. But not always. It's a good idea. Whenever you see
21:46 puzzlement in the data to think about did we assume didn't happen that might
21:52 happening in this in these data. of course similar argument is gonna show
22:00 converted wave is zero for so uh uh now here's a little quiz at
22:10 free surface on land. Uh which these answers gives uh It is
22:24 Uh Stephanie, I'm talking to Um Wouldn't it be d cause it
22:31 our PP of zero is negative That's correct. Okay, that's
22:38 Normal minus one. Um This is true in general and this is never
22:48 . So you are correct? None these good analysis. How about at
22:54 ? The only difference here is we're sea instead of on land. This
23:02 is c Yeah, okay, now is an interesting um this is an
23:12 public and you know, before I to this topic, I want to
23:17 this, stop sharing and I want um um show you those movies that
23:34 didn't show. It turned out that the files were fine. Only I
23:39 trying to open them with the wrong application. So when and I did
23:45 get the chance to put them in blackboard yet, I'll do that.
23:51 uh you can uh you can these work for you if you have the
23:57 application and I'm not sure what applications have for showing movies. But if
24:02 get an error message like we just earlier, it's because it's the
24:07 And so what I'm gonna do is yeah show the movie. And the
24:24 thing I'm gonna show is called S. P. And S
24:29 Well dinner all night used the wrong again. Sorry, I have to
24:37 it with which works. So for , I'm using something called cool file
24:47 and I think it's free. Uh you don't, wow, you don't
24:55 it. I think you can find on the internet for free. Or
24:58 maybe something else that you have on computer or viewing movies in mpeg
25:05 Um That'll also work. So let now show you this. I'm gonna
25:15 , I'm going to span the zoom , share my screen and I'm gonna
25:25 that viewer. Okay, so you see the application, what I'm going
25:36 launch it. Okay, can you this movie? Yes. Okay.
25:44 it again. Okay. And in is uh now these are showing,
25:54 only way I can do it is don't have a way to uh repeat
25:58 . So I'm gonna have to trigger and over again. So this is
26:01 the displacement of the way, it's a way front, it's the
26:05 And you can see the way of down and reflecting back up and going
26:10 And now look at the little red . Uh Can you see that uh
26:19 it goes on now it converts to can you see the shear wave going
26:22 in red? There you go. transmitted in red see the little circles
26:31 oscillating side wins as it goes You see that? Uh Yeah,
26:39 . Oh I know, but what want to do, I'm going to
26:43 that. Okay now it's uh on screen. Oh okay so here we
26:54 . See the shear wave uh converted moving slower. Okay so I will
27:08 this to uh the black warm and can do this for yourself and I'm
27:15 stop sharing this and minimize this The other movie this way, Front
27:36 , this one's more interesting. I'm share my screen, expand the
28:02 you can see the movie already to . Oh Watch This one. So
28:10 is uh a wave coming down from upper left. You see it's coming
28:17 from the upper left and the bright moving to the lower right, that's
28:22 incident way and it's curved. It's like the plane waves that we have
28:28 , it's definitely curved. So now can see uh let's contract on the
28:36 on the transmitted wave so frustrating the mr wave and you can see that
28:42 has a little kink at the Uh But it's um um uh Not
28:52 at all at all, I would . Yeah I just learned how to
28:57 it. Uh I'm gonna advance it little bit more or so, you
29:03 see the pink here. And so this up here is a circle whose
29:09 is over here and this uh this is a circle whose origin is um
29:18 in here somewhere and you can see radius of curvature. This is a
29:21 bit different than the radius of curvature because the velocity is different down
29:25 but the apparent velocity is the same both modes. You've got to have
29:30 two wave fronts, the uh this and this one they've got to travel
29:37 horizontally along the, horizontally along. . Now let's look at the reflected
29:50 . So here is the reflected wave and I know you're accustomed to think
29:55 a reflective array which is going up this record. This is a reflected
30:00 front, so maybe a little bit in front, but you can see
30:05 it's a circle with the same radius curvature as this one and the center
30:11 that circle is down here. This what we call the mirror point
30:15 So this apparent source down here, the center of this circle down here
30:22 is uh the mirror image of the source, which is over here
30:28 And so uh this wavefront has a and a trough and a peak in
30:33 conflict. So now this part here the converted share waves, how do
30:38 know that? It's because of moving , you see uh this one is
30:43 ahead and so this is a convert right now. And uh do you
30:48 a converted way of going down? don't see one. Uh let's uh
30:56 the uh I do not see a way uh, in transmission.
31:14 uh, whoever made this calculation, think did not include that. So
31:20 a special case of the lower which doesn't have um, converted transmitted
31:30 special place. Okay, so, , I encourage you all to play
31:36 this on your own tonight and during the week and uh, stay
31:46 it until, until nothing more is . I'm gonna share the screen.
31:55 . Um, what's your, and we're gonna talk about critical angles.
32:05 so, um, first thing I you're thinking is that we don't have
32:16 angles in our data. Well, that's true and maybe not.
32:22 uh, in our data, we we normally know what depth range we're
32:27 for. So we're looking for a , that's about two kilometers long,
32:35 km deep, something like that, three km deep. And so we
32:41 out um, receivers. So that links, I have a corresponding maximum
32:49 when, when I was young, I was your age, it was
32:55 decided to have a maximum offset to approximately equal to the depth to the
33:05 . So that means uh, 2 km alone. So about the
33:14 I came into this industry, we a V. O. And so
33:19 if we want to have um, want to study the, the offset
33:25 of amplitudes. The popular thing to is have, um longer offsets.
33:33 we've got to have longer and longer . And so these days we have
33:39 as much as 10 kilometers long for a three kilometer depth right now.
33:48 it's true for the for the horizon interest. We never we never include
34:03 which are imply after we've done our all converted offset angles. We don't
34:09 to have any angles in our Any incident angles in our dataset,
34:16 at the receiver. Uh no incident the interfaces. We don't want to
34:22 any incident angles in our data which uh post critical or even near the
34:29 because we know that if if we those kinds of angles, weird things
34:36 now consider this. Maybe we could smarter and we could learn something from
34:43 near critical post critical angles. That's good topic for a graduate student is
34:51 consider what we might learn from the which is intentionally excluded from our from
35:01 consideration. Like I said, normally we limit the length of the off
35:08 . I uh just don't those receivers in out of the field, save
35:16 by not uh installing receivers that we want to use the data from.
35:23 , there are, there are lots cases where that is improved. For
35:31 , suppose we're doing an ocean bottom , uh maybe as far as we're
35:38 a land service and so we put a bunch of geophones in a
35:43 We're gonna do three D. In uh in this year, of course
35:47 gonna do three D. You can of to day if you want and
35:51 put out our receivers and then uh for that we don't and I put
35:59 out online uh on stakes in the . And then we start vibrating.
36:07 don't vibrate in the middle of this . We don't we don't start our
36:12 in the middle of the array. don't start our vibrations uh at the
36:18 of the array. No, we our vibrations outboard of the array.
36:22 this is to get what we call proper migration aperture. So we start
36:30 so maybe we'll start our vibrators, two or three kilometers outside the
36:37 And then we work towards the right and forth lines of uh uh horses
36:45 so on and according to all those . And then while we're and then
36:51 we're doing it we passed through the the array. And pretty soon we're
36:56 in the middle of the array. then we pass out the other side
37:01 we're vibrating from the from the other . But everything to do is while
37:05 vibrating, say we're vibrating to the of the array. Our vibrating and
37:12 closer to the array with every shot . We've got our crew working and
37:18 installing more receivers in the ground on east side of the race. So
37:25 start off to the west and we're our way east and as we're working
37:29 way east, the crew is installing and more vibrators to the east.
37:33 then as we get in the middle the array and proceed through, we
37:38 to pick up those uh, those most receivers and uh move them around
37:47 install them again ahead of the shock . So we call that rolling the
37:54 and this is very common. We a finite number of receivers and so
37:59 gonna put as many as we can the ground and then we're putting more
38:03 the ground to keep ahead of the . So think about that.
38:09 I say we start three km west the array and suppose the array is
38:17 km wide set, supposed to eastern is uh three km east of the
38:27 , Western of the Western. Now , so that means that as we
38:32 vibrating, we have um offsets of kilometers three kilometers of of no receivers
38:43 then three kilometers and receivers and we're more 3.13 point two etcetera. And
38:49 we, as we are working. so we have in our data set
38:54 long offsets in this case six kilometer . And in many cases we can
39:01 2030 kilometer offsets in our data. , because of the way we operate
39:09 the field, answer nationally. The thing we do is we had to
39:14 away those far far Austin's, but we don't throw them away. Sometimes
39:21 keep them in the computer and we don't look at them. So that's
39:27 crime that, that's a crime that be uh punishable by death because we've
39:34 good money to acquire those. And it's, it's a real shame if
39:40 not a crime, it's a real to not even look at them.
39:43 the reason, of course we, , look at them is we have
39:48 in our thinking and embedded in our and, you know, our analysis
39:52 everything. The idea that we have and moderate offsets maybe for our
39:58 but not really, not really very . So we don't have normally most
40:04 incident angles at the target horizon in analysis. So if we have them
40:11 our data, let's just uh, in the archives somewhere don't even bother
40:19 at them. Well, so that's real opportunity for a university like
40:23 Uh, we can talk, we talk to these oil companies who do
40:28 and say give us this very long data. We'll have some smart students
40:34 at it and maybe they'll come up something interesting will cost you much.
40:40 should give us access to the maybe give us a few bucks to
40:44 for the graduate student scholarship and so . It's gonna be a lot cheaper
40:50 having your expensive people at, who they might have came up with something
40:57 , maybe not, but you there's nothing good is gonna come of
41:01 data while it's sitting in, your gathering dust. But maybe we could
41:07 something good at the University of Houston you just give us access to the
41:12 . So as a matter of last week I made that exactly that
41:16 to a hess and they seem to receptive and so maybe we'll get some
41:23 from hess in the near future uh the sort that uh, they don't
41:28 to look at themselves, but they it in their archives and uh I
41:35 you'll share it with us. Now have a question about the long
41:42 So how do you define the survey , which has a long spring?
41:52 , depend on velocity of the frequent of the data you want,
41:58 it depends upon the national offset and depths of the reflection. So you
42:04 imagine that say you have a maximum in your data of say three
42:11 So uh the reason you have that of 17 kilometers is because you didn't
42:17 all those extra G. F you didn't pay the crew to put
42:22 in the ground because you know that maximum offsets you want to look at
42:29 to incident angles at the reflector of like 40 45 degrees maybe anymore,
42:36 last week. You know that you not want to look at these critical
42:42 . And so you don't have um far far offsets uh acquired in the
42:48 because that's expensive and you don't want do it if it's gonna cost you
42:52 . But now just so we have maximum offset three km and uh say
43:01 maximum all set up of six killer , depth to the reflector of three
43:07 . And so we figured that's gonna us angles, maximum angles around 40
43:13 50 degrees. And we think that's pretty critical if if it turns out
43:19 some critical angles uh included in those . That data, we might just
43:26 that because of the peculiar amplitude which we're gonna talk about charlotte and
43:32 probably just mute those out. So don't look at those at all.
43:36 now, in the same situation, maximum set six km. You
43:45 there's gonna be other reflectors shallower in subsurface, say, instead of three
43:51 depth in the subsurface, say it's one kilometer depth in that case,
43:58 our far offsets, we're gonna have wide angles of incidence, probably post
44:07 . So we already have those in data at shallow offsets because we've designed
44:15 acquisition geometry for the target depths, at all shallower depths we're gonna have
44:22 their offsets which are gonna probably be most critical and certainly going to be
44:28 non hyperbolic move out. And so smart thing to do, everybody thinks
44:34 smart thing to do is to just far off sets out. No,
44:40 anymore with the same argument maybe. there's some really interesting information in there
44:48 the subsurface of shallow that we're not ourselves to think about because we we
44:55 use those data. So let's uh we aren't gonna learn anything from those
45:04 far offsets, uh let's look at following analysis for post critical incidents.
45:14 gonna put myself into presentation mode and what we said about Snell's law.
45:23 the transmitted p way, the sign the, of the angle is equal
45:28 sine of the incident angle times this ratio where this is the incident
45:33 that's reflecting then for uh the case the lower medium is faster then for
45:41 large angles sign of 32 is going be greater than one. So this
45:48 , this is a real number. of theta one. Sine of theTA
45:51 is always going to be less than 45 degrees. But uh under uh
45:58 conditions, if the velocity ratio here enough, then we're gonna have sine
46:04 theTA two can be greater than one the point, the offset where it
46:10 begins to get weird is where X equal to one. And so we
46:15 that incident angle the critical angle that's by this philosophy ratio, which is
46:21 than one by assumption. This ratio greater than one under these circumstances.
46:27 is the inverse of that. This um ratio is less than one,
46:32 it should be for uh this angle is always a real angle and we
46:39 have Snell's law. And every quantity you see here is real. That's
46:44 , that's real, That's real. is real. But the co sign
46:50 not necessarily real under these circumstances. because it can happen that this thing
46:56 it's real, it's bigger than So when the square uh or maybe
47:02 bigger than -1, if that's a number, this is a negative number
47:06 the square of it's gonna be a number greater than one. So uh
47:10 co sine of this angle is gonna imaginary. This is bigger than one
47:17 sine dominates and we'll have a minus under the square root sign. So
47:25 gonna give an imaginary memory. So though this thing is real, if
47:31 bigger than one, the cosine of act is imaginary because it was there
47:39 critical reflectivity is complex. And so the same formula that we looked at
47:47 . So let's first consider the implications this for the post critical transmitted p
47:55 vector. So that's we call that two and as magnitude omega or a
48:02 . And uh this gives the two . And uh so putting in here
48:09 the Kassian is one minus the sine . And taking out the square root
48:13 minus one. Then here's the eye here. So this is now sine
48:18 minus one under the radicals. One these circumstances that positive number positive.
48:28 that's a real number right here. see an explicit I now let's put
48:36 understanding of the wave vector into this for the wave and here's K dot
48:44 . And so uh the kid dot has been multiply this quantity uh times
48:54 uh theater this X factor. It has magnitude offset X in the X
49:12 here, that's one. And so wow, what you see in the
49:20 bracken's is the dot product between K and X. And let's um you
49:32 have the minus. Uh still have eye out here. That's this
49:36 I have the mega T here, this mega T. And so now
49:41 separate out this part here uh that's what we have down here and
49:46 have this i times this. I some minus one and no more eyes
49:52 . Here's an eye. This thing going to oscillate. But this thing
49:56 gonna decrease with increasing death because of minus. Uh because we already decided
50:15 the cosine of theta two transmitted data imaginary. That's gonna make the amplitude
50:22 . So the transmitted wife is phase from that of the incident way the
50:31 is true of post critical reflected and a way of afternoon. But let's
50:35 on this transmitter as it travels along boundary beneath the interface with this apparent
50:46 . The transmitted P way forces the mediums oscillated at the same apparent
50:51 That's uh this is the same. is Snell's law insists that these apparent
50:58 . This one further lower media. one from the incident has to be
51:02 same. And that's gonna be a of which is bigger than V.
51:07 . One. Because we already decided uh Sine of theta one. Of
51:14 , that's uh um that is less one. This is a real uh
51:22 number. This one is also a number, but it's bigger than
51:27 this is less than one. uh current velocity is greater than the
51:33 philosophy. What happens then? What that do? This forces? This
51:40 a new way a plane wave radiates into the incident meeting. Now,
51:45 is this way? If the incident is plainer? This is just a
51:50 critical reflected P wave propagating up at angle incident angle. We already did
51:58 . But if the incident wave is , this is a new wave propagating
52:04 at the critical angle. So, gonna show you a diagram of that
52:09 . Just point out here that it happen that uh if you have a
52:15 fast medium down below, then the wave velocity down below is bigger than
52:20 p wave velocity up above. Maybe assault? Uh assault. But in
52:25 case there's a sheer critical angle uh um it's always gonna be a bigger
52:31 angle. That's a sign data for be the most critical awesome. So
52:38 can see here this is a calculation Sheriff and guild are of all the
52:44 behavior that can happen post critical. this complication is easy. This part
52:53 easy. This is transmitted here is reflected P way pre critical. So
52:59 the one we normally are looking at is the uh Mhm. Heard away
53:08 um laura Daniels, All kinds of behavior. Uh and uh that's all
53:20 for the model that they used That's all happening about 30° normally for
53:25 kinds of rocks. The critical angle happens further, it's uh they're here
53:32 most of the data that we look is. So before we get into
53:39 pictures of that most critical stuff, uh take your quiz. So uh
53:49 a statement and uh it's gonna be completed with all these things. Um
53:56 no in here we have uh all the above. So that's a possible
54:02 . And then there's another um uh here. And then again all of
54:07 above down here including this. So go through this from the top.
54:19 So Stephanie uh is this first one . No it I think I heard
54:29 say no. And so if that's then um we can't have all of
54:35 above here. So if this one false. Um We we better not
54:44 uh just we better not find more one of these answers is through.
54:50 let's keep this in mind. Go to number two, says number
54:54 the transmitted wave decreases in amplitude away the air face. Is that one
54:59 falls? That is true. that one is true and I'm gonna
55:11 back here. So now uh so we talked about that because this is
55:23 this is all positive and there's no hear anymore because this I got multiplied
55:29 this. I gave her -1. um wow sure. Uh this one
55:47 away as he increases the same Uh goes to zero. Eventually Z
55:55 big enough. Now let's look at rest of this. This shows an
55:59 solitary factor iomega of X. And that looks like a wave which is
56:06 in the X. Direction. It's propagating, it's not propagating down and
56:14 from the boundary. Like uh uh an ordinary transmitter way. This thing
56:20 trans is uh propagating parallel to the and away from the boundary. It's
56:27 an apple too. So now I to go back to the quiz and
56:34 you to reconsider your answer for a it would be parallel. Yeah because
56:50 only propagating in acts. It's not and Z at all. Oh I
56:55 . Okay okay now let's go. now we got to that part of
57:00 truth. So uh uh we expect find now probably either this answer is
57:09 or this answer is true. Let's our way down. Um uh point
57:14 the transmitted wave that has a shape from the incident wave. It's your
57:24 . Yeah, that's true because the coefficient is uh complex. And so
57:32 that multiplies times the way, what gonna make that it's gonna change the
57:37 of the wave. Good. So far we have all of the above
57:40 we're not done yet. So uh says here, the next one is
57:46 reflected wave as a shape different from incident. We didn't actually analyzed
57:53 We we didn't have to analyze. we didn't actually analyze the reflected wave
58:06 all. So this is a difficult here. Yeah. Um um here's
58:16 you might think in this case uh a member of the formula that we
58:26 for the reflected wave preferences. A formula that we got from uh and
58:33 . It has in there a bunch terms like co sign data to and
58:39 sign uh uh force. I'm I'm hearing an echo from uh from
58:54 here. I'm sorry I didn't I needed. So in that complicated expression
59:05 you can look back through your notes see that complicated expression. There are
59:09 numbers, there are some quantities for reflected wave which depend upon those other
59:15 , even though the reflected wave is uh not propagating at those ankles.
59:23 do see in their chosen data to cosign theta for etcetera. And so
59:28 things are gonna be um um complex imaginary uh in this context, post
59:37 . And so um I think uh that means is that the reflection
59:47 the p waves is gonna be complex though it didn't penetrate into the long
59:54 at all. And so it's also have, I'm gonna go with all
59:59 the above this. All of the F um includes everything. But so
60:08 uh if you were seeing this on on a uh final examination, you'd
60:15 to think about this for quite a . That's a question. If the
60:24 grave is a P wave in the critically reflected P wave propagates upwards at
60:30 critical angle, Not at the Is that true or false?
60:36 that one is false because we decided that it's gonna be propagating upwards at
60:43 incident angle whether it's pre critical or critical. And we didn't assume anything
60:50 there about where they were most credit . Oh okay. So uh now
61:00 think about both curb ways and curb . So one more of these plane
61:11 and no more of these plan Now we're getting real. So the
61:18 where a friend is curved, the critical reflection coefficient is modified by a
61:25 which I haven't showed you but it's to be modified by a term which
61:29 proportional to this. And so this the wave uh the attitude of the
61:35 factor times the greatest of curvature, that? That uh concept of greatest
61:43 curvature. Uh So if the if have a source at the surface radiating
61:50 into a uniform hypertrophic media, it's be uh a spherical away from
61:58 and it's gonna have a curvature which going to be decreasing as it goes
62:05 because uh it's a tight sphere at beginning and then it gets uh bigger
62:10 bigger sphere. And so we called radius of curvature under that simple uh
62:17 is the distance back to the That's the radius of the expanding
62:25 Now, in the real earth is gonna be a sphere anymore because you
62:29 layers and refraction and all that but it'll be approximately equal to the
62:35 back to the source along the And so that's what we mean by
62:40 greatest encourager. And so you can through this algebra and you can see
62:46 in the end we we convert this wave vector amplitude to two pi divided
62:57 the wavelength, it's a two pi approximately equal to six. And so
63:03 this ratio is uh 1/6 Approximately 1/6 the of the wavelength divided by the
63:15 back to the origin back to the . So that after a propagation of
63:20 or two wavelengths is as soon as thing gets to be one or two
63:25 the wavelength this correction which is implied uh is negligible. And and that's
63:33 valid argument ex uh for it's a argument for what happens um uh to
63:41 expanding wave um pretty critical that near critical angle it's gonna be different.
63:48 here is a picture which is kind similar, isn't it, to the
63:56 movie that we just saw uh and me walk our way through this.
64:03 This is the incident wave front and one also in green is the incident
64:10 . So you can see that this front is perpendicular to the ray here
64:16 then it goes a circular away And you can tell from the radius
64:21 curvature here that the the origin of was somewhere around in here.
64:29 so that's the incident way, the way is this one? And it
64:34 a little kink right here because this is greater than this philosophy. That's
64:39 it makes a kink like this not kink in the other direction, but
64:44 like this. So this angle is angle than this one and the ray
64:52 ray vector for the refracted rays. this one? Now the reflected
64:59 here's the reflected uh wave vector equal opposite angles expect and has a corresponding
65:09 that looks like. So okay, that uh that will be familiar to
65:15 from the uh the movie. Now this case we don't show all the
65:21 ways. So uh so this in there's gonna be share ways but these
65:27 are complicated enough without share waves. we left the share waves out.
65:34 these this point of intersection right here along the uh interface with an apparent
65:42 given here, V one over sine one has got to be exactly equal
65:47 B two over sign sign 32. this one gets ahead or behind the
65:56 um Yeah. Uh Yes, way. Now that's all pretty
66:05 However, now if the incident angle post critical then something new happens.
66:14 it's post critical, then the uh . We have the velocity below is
66:23 than the velocity above. So this propagating horizontally, is gonna get ahead
66:29 anything that's happening here, but this velocity has to be the same,
66:37 it can be the same because this got ahead. So what that means
66:42 uh we're gonna have an additional This one right here. This is
66:49 we call a headway. We didn't that in the plane wave problem and
66:55 didn't see it in post critical. post here's pre critical and so post
67:00 . Uh that means that uh this the same incident, we can see
67:08 this uh incident wave is coming. Here's the here's the rate the incident
67:14 . Can you see this one is in at a greater angle than this
67:19 . So this one is coming in critical and it's incident wave front looks
67:28 this. So the fans middle wave down here and it's dash here because
67:35 didn't remember, we said that the is going away as you go
67:41 So this uh this is uh this is less than this amplitude. This
67:49 is even less. So the way was propagating in this direct parallel to
67:56 the interface and this apparent velocity is to the apparent velocity mm. So
68:37 , because the new wave which we see before, we didn't see it
68:40 critical and we didn't see it with waves. This happens because only because
68:47 waves are curved. Now, what the angle that happens here? So
68:53 this wave has obviously propagated upwards from uh in this direction with the P1
69:02 uh in a interval delta T. meanwhile the wave down here is propagated
69:11 in the lower media at the P two times the same time.
69:18 that means the angle of this triangle here. Anyway, angle is equal
69:25 uh sign of these two distances. deputy that's here, VP two,
69:34 T. is here and the right right in here. And so uh
69:42 angle is the angle whose sine is by this these delta T. Is
69:47 app. And now you see what's is V. P. One over
69:51 . Two. So that means that head wave angle is critical lying and
69:59 a plane uh it's a straight So of course you can imagine that
70:07 this is in three dimensions it will the point of a cone. So
70:14 imagine uh cone whose point is here uh intersects the figure right here.
70:22 it's uh on the behind the And in front of the screen it's
70:27 comical surface. And now there might other head waves associated with other outgoing
70:38 corresponding to other critical angles. So have a really nifty figure from sheriff
70:45 jail dark. And let's step our through this and you will see how
70:50 it can be. So uh first is the incident p wave wave front
70:58 here and you can see that it's circle whose whose origin is here.
71:05 now here is the reflected P wave its origin is uh um down here
71:17 that that we call that the virtual point or the mirror source point.
71:24 Real source point is here and this is the virtual source point or this
71:30 reflected p wear And here is the p way uh in this case where
71:38 lower medium is faster than the upper . So this one got way ahead
71:43 this um uh convergence here. So going to step forward one at a
71:50 and see what I was going So this is the head wave that
71:54 just talked about. Uh This is angle here. And this head wave
72:01 this point here, where the P in the lower media got this
72:08 it's way ahead of these because this is faster and there's a straight line
72:13 goes up here and I get to tangent up here. So now here
72:22 the reflected few wave also coming from uh mirror point. Yeah.
72:39 And now there's two more headways coming in here. Uh just number them
72:45 and three connecting uh different points down with Yeah, reflected your way.
72:57 of them uh connects all the way to here and one of them connects
73:02 to here. Here's 1/4 head wave goes from the uh transmitted p way
73:11 to the reflected s way here is refracted as appears to transmit it?
73:16 way. And here is head wave Headway five In here, this one
73:27 , and the sure way of critical is given in here and here's head
73:33 six from here back to here. can see how uh startlingly complicated this
73:41 and this example is a good one it shows uh the medium below is
73:47 lot faster than the medium above. all these things separate. You can
73:51 that if this thing is if this at this point is close to this
73:58 , then all this stuff gets on of each other. Now these head
74:07 are seeing wherever the incident angles are and there's a strong velocity increase,
74:12 example, um where we see a between sediment and salt, or maybe
74:20 sediment and carbonates, um plastic sediments carbonates, and maybe between sediments and
74:27 . If you have long enough offsets enough angles, you're going to see
74:32 . And like I say, it's . So maybe it's a good
74:36 we ignore it, but who Maybe we could learn something if we
74:40 at now. We also see it the time. So these are special
74:48 , but here we see it all time in uh more hard logging.
74:54 in fact, that's the basis for borehole logging. So uh you see
74:59 uh you know what? This is good spot to stop and take a
75:09 break because um been going on for hour and quarter, let's stop at
75:16 point. Uh pick up again at o'clock even and we'll go into the
75:25 Context wave propagation now in the So I'm gonna go back here and
75:32 here. So in 15 minutes I'm to uh Come back and in the
75:39 I'm gonna stop my video and uh myself and I'll see you all at
75:49 . Okay, so now let's talk sonic logging groups. This um isn't
75:57 . I'm gonna have to stop sharing uh now I'm going to start sharing
76:20 . No, I can't do I'm gonna do this, start sharing
76:31 . This works. Okay. Can see the cartoon or the borehole?
76:53 . Okay. So uh now so this is a cartoon um showing what
77:02 in a conventional sonic long. So we have the formation and this way
77:07 up of course, and we have bar a hole here in purple.
77:10 we have a tool down here. and the tool has two parts got
77:14 source and two receivers. And so source fires in all directions. That
77:20 p waves through the mud. Purple at all angles. And because the
77:30 is faster than the mud, these refract upwards like some and the one
77:37 comes over here refract downwards of But uh this one refracts upwards.
77:42 uh for this takeoff angle here, is the critical angle where it's critically
77:48 along the p wave uh along the wall. And this is in cylindrical
77:56 . Of course, this is a section. So that that's a difference
78:00 what I just showed you with the wave. But aside from that geometrical
78:05 , it's exactly the same as we before. So as this thing propagates
78:11 along the boundary, it ripples the boundary like this. and it puts
78:17 p waves back into the mud at mud velocity, of course, all
78:23 here. And so when it gets to here, it's gonna emit this
78:28 coming up this way. And the of of of this angle is the
78:33 as this angle, which is the angle. And so uh when it
78:39 to hear it emits critic at the angle back here and this one happens
78:42 get this receiver and then it goes a little bit further and when it
78:47 to hear it, um it's this . So you can see that these
78:52 are receiving signals which measure the velocity the formation. And a modern tool
79:02 have maybe a dozen receivers instead of two, but you get the
79:07 So um now let's think about shear . So, so here is the
79:15 situation in the same formation, and also want to record shear waves.
79:22 so the same tool will do So, here's our source down
79:26 And uh in addition to this wave , there is a refracted S waves
79:31 reflects out into the formation never comes . And this angle is uh closer
79:38 the um uh to the normal uh this one. So, the um
79:50 one is refracting away from the Hold not as much for the wave
79:57 travels through the mud at this You see this angle is a bigger
80:01 than this angle over here. So is the sheer way of critical angle
80:08 this point. Uh Refracted share This refracted shear wave. This one
80:15 propagating um exactly along the boundary. it's like this one except that it's
80:22 and it's propagating at the sheer velocity the mud and it's putting back sheer
80:29 in the formation and it's putting back the mud api way at this same
80:35 way of critical angle that. so then this shear wave, so
80:40 difference in arrival times between here and uh gives the shear wave velocity between
80:46 and here. You know. Also can measure the time delay between the
80:53 and the first receiver and that will you an average velocity in here that
80:58 lower resolution. Normally we don't look that. So this is the same
81:03 . This is the same tool as have here. And so the deal
81:07 that this because this one is slower this one. This arrival is happening
81:13 . And uh we have a dozen up. This pair. We can
81:18 this one moving out across this array a consecutive time delay. It will
81:24 a linear move out through the array receivers at the p wave velocity.
81:32 then the same on the same wiggles see this signal moving out at the
81:37 wave velocity. So you have a receivers here. And you can see
81:42 shear wave arrival moving out linearly with share with box. And then as
81:49 pulled up the two up the um pull the tool up the the
81:57 They do clever processing so they can and find the interval velocities in each
82:02 about uh highest resolution they can get about the distance between these two
82:11 Like I said, normally there'll be dozen or more receivers up here.
82:15 that's that allows them to do ray processing. Not great processing but a
82:21 process. And that they can usually uh these slower philosophies even in the
82:29 of these fashions. Okay, so is the standard um sonic tool and
82:35 one has been in uh in operation uh I think uh 80 or 90
82:44 and it gets better every few Uh the two companies make some kind
82:50 improvement and now that these things have worked well but there's a problem and
82:57 called the slow share problem. And happens if the formation slowness formation sheer
83:07 in here is less than the p velocity in the mud. In that
83:15 the refracted p wave is gonna refract from the bar hall access. Here's
83:23 refracted p wave of course this VP the formation is going to be bigger
83:29 VP in the mud but it could that V. S in the formation
83:33 great event is less than uh VP the mud. Let me say that
83:40 . Of course VP in the formation greater than V. P. In
83:44 mud. But it might happen that . S. In the formation less
83:49 VP in the mud. In which this thing refracts away from the borehole
83:54 . This is and that's also through and you're never gonna have in this
84:00 a critically refracted shear way like you here because in all cases it's refracting
84:08 from Warhol Access. So um to with this situation, they invented the
84:19 pole tool about four years ago. so what this tool does is it
84:26 the borehole wall with the positive Wave pulse this way and at the
84:30 time it sucks uh it sucks fluid the tool, making a negative p
84:41 pulse on this side. So it the borehole wall sideways and pulls the
84:46 heart full sideways, deforms the And so this Torsella wave travels up
84:52 bar hall and then it gets received di paul receivers up here which which
85:00 designed to to detect this kind of deformation. Personal wave travels up more
85:11 and vibrates sideways and it goes at distortion Allele mode travels with a velocity
85:20 is a little bit slower than the than the body wave velocity. Body
85:25 shear wave velocity in this and so know how to convert uh distortion wave
85:32 into the body wave velocity. And what they report by the way,
85:37 this uh torching away uh travels with it, which is frequency dependent because
85:48 the world, the borehole is this . So the um long wavelengths are
85:55 travel with a different philosophy in the run. Yeah, so you can
86:03 of take the inversion of these arguments apply, that's the case where plane
86:09 her incident upon a curved reflector. that in this case you don't necessarily
86:16 that the radius of curvature is Make radius of curvature might be small
86:21 you uh you know, just depending how curved that reflector is. And
86:29 , normally the reflector has two radius curvature, kind of like a
86:35 Uh You try you know that saddle in insurance saddle? Okay,
86:45 uh the specialized word, I wasn't if you knew that word, but
86:51 for a saddle you have one radius character uh crosswise to the horse and
86:57 one another radius of curvature along the . And so uh the same way
87:04 in general, you can expect that matter how complicated the curvature is and
87:10 curved deformed sedimentary interface can always be described as two orthogonal radius of
87:23 Uh Coming from this, we're gonna focusing or d focusing, which we're
87:31 to discuss further in less than Uh but before that um uh let's
87:38 a little quits. So back to problem of curve rations. It says
87:45 don't care if the incident wave is or not since an exploration geophysics plane
87:50 are an acceptable approximation. I'm gonna that false. Uh two reasons.
87:58 , uh, when we have the critical reflections that we just talked about
88:04 the break and then also in the sonic organ contact. That's also question
88:18 . Even if the incident wave is plane wave approximation to the reflectivity,
88:25 critical is usually sufficiently accurate if you're than a couple of wavelengths from the
88:31 Stephanie, is that one true or ? Um this one would be
88:42 Yeah, that's true. Matter of , I showed you the correction factor
88:46 the correction factor goes to one as as you get more than one or
88:51 wife away from this Question three For reflecting interface. The maximum offset which
89:01 having your data may allow for maximum ankles, which are beyond critical so
89:07 these post critical headways are recorded on shallower interfaces. Even if they're not
89:14 at deeper interfaces. Stephanie, is mature fonts. Okay, that's
89:20 Although we normally uh, ignore them they're in there, they're in the
89:25 , they're on our service and maybe could give us useful information if we
89:31 look at them with intention. Maybe could learn something about those shallow
89:37 Now, maybe we don't really but maybe we do. You
89:41 it might be that there is uh in the shallow uh overburden above what
89:49 thought was our target horizon. Uh designed our survey to properly image that
89:55 horizon, but who knows what's in overburden. It might be worth our
89:59 to think about it. In the these post critical reflection post critical reflects
90:10 an interface with the faster formation below slower information above blah blah. We've
90:16 uh three statements and then all of above. So uh Stephanie, let
90:21 hear you talk your way through B. And C. Um
90:31 So a contains reflected head waves not in three critical reflections. That's
90:42 Yeah, that's true for all the we see. So so now we've
90:47 a problem. If we find even more of these uh which is
90:52 then we're immediately gonna default to But let's go through it. Uh
90:57 with B. Let me hear you away here. You talk your way
91:01 B. Have wave forms which are shifted from the incident wave. That's
91:07 as well, isn't it? that's true as well. Of
91:09 Well done. So we're now suspecting answer Indeed, but let's uh let's
91:16 C. Just to make sure have decreased by the geometrical spreading associated with
91:22 longer path fleets? Yes. Ok. Number. Good question
91:29 These post critical reflections rarely occur in sonic sonic content France. Yeah,
91:38 false because they normally occur. okay. So um that brings us
91:44 the end of this uh part Uh So you know if you were
91:53 this course with this name from some professor, we might stop here and
91:59 might have spent a lot more time these previous um topics. We might
92:05 gone more into the practicalities. But got me instead of that guy.
92:11 uh what we're gonna do for the of our time is look at uh
92:19 from keeping these same assumptions and then we're gonna relax those assumptions and important
92:28 to deal with rocks to deal with elasticity and to deal with an
92:34 So as so what I'm gonna do stop sharing here and bring up my
92:57 around a little bit next style. we go. Alright here it
93:31 Okay now I am going to bring zoom and I'm gonna share the screen
93:44 show you this file. So you be able to see the um introductory
93:53 for less than seven. Yes, . A presentation. Okay, so
94:05 . So um you can imagine that lots of complicated issues that we haven't
94:11 yet. And so now we're going discuss a subset of them. I
94:15 we could go on forever but uh just gonna to discuss a substance so
94:23 gonna be able to understand and explain and uh furthermore they can either confuse
94:31 interpretation or improve it depending on how ideal, you're gonna know what a
94:41 is, you're gonna know what a zone is in particular, you're gonna
94:46 how to pronounce that. That's a name. And you know the french
94:51 things differently than us. And so pronounced without the S. So um
95:01 is always a big issue. Uh always tell us the physicist we need
95:07 resolution, we need more resolution. when we give it to them,
95:12 not happy because uh of the subsurface be really complicated. Uh But we
95:19 to talk about some important ideas about and then we're gonna do more about
95:25 reflectors. And so here is the time. So these are the direct
95:32 here. We talked about the direct arrival and then the direct arrival
95:38 Uh and I guess we call this . Never mind the fact that I'm
95:43 retracting here. This is just a . Now we also record multiple
95:49 So these are these are two different . But then also in this situation
95:55 is a multiple where the energy goes up, down, up and gets
96:00 here after three bounces instead of And this one is uh this um
96:08 what we call a surface related multiple the the uh the balance downward is
96:15 at the surface. And furthermore if happen to have, if we happen
96:20 have a receiver right here, we record this and we call that a
96:24 wouldn't have a receiver here when it's over here. It's multiple. Here's
96:30 internal internal multiple. Whereas the downward happening off of some interior interface and
96:37 never did record that. Now here a symmetric multiple and here is an
96:50 . So in both cases the reflection in the surface. This one uh
96:59 uh asymmetric for obviously asymmetric. Now have what we call long period multiples
97:13 it's called long period. That's not good name, but that's the name
97:17 used to that. And what it is there's a long delay between this
97:22 arrival and this multiple arrival because The selection happens a long ways away from
97:30 from the two upper here's a by is a short term multiple where this
97:38 the light is not too much and really should call it a long delay
97:44 long and short delay, but only of short. Yeah. So here
97:51 have uh the simplest way Of reducing multiples out of our data invented a
98:02 time ago, probably invented in the . And it's the normal move out
98:09 . So here is a common midpoint trying primary reflection with move out.
98:16 this wave look here uh in the is exactly the same as this and
98:24 is a multiple with a slower move philosophy. You can see here this
98:28 move out uh moves out, moves more than the primary, let's go
98:38 here is the primary has only changed uh arrival time by this, March
98:47 . This this mark move on. changed, it's ruled out more but
98:54 arrival time is earlier. So that first let me say so. So
99:03 is this slower has spent more of time than the primary did in the
99:08 formation where it's slower. And so why the uh the average loss is
99:15 . Here's both of them together. you see that I've made this diagram
99:20 that here's the multiple uh arriving earlier short offsets and at further offsets,
99:28 gets tangled up in the primary, superimposed linearly. And so right here
99:37 fully superimposed. So the wave front a lot different than this one
99:43 This is the same way we're here here. But uh this is by
99:49 way, do you know why the here has smaller amplitude? It's because
99:54 it's reflected twice more than this So each reflection makes a reduction in
100:02 . So that's why this one has applicant. So in the cartoon,
100:11 multiple interferes with the primary, this primary long offset but not startups.
100:20 , uh one of the clever ideas we had a long time ago is
100:25 correct the move out. Using the velocities in the surface subsurface. And
100:31 so now this uh gather has been and the primary has been flattened.
100:37 see the multiple didn't get flattened because multiple is traveling at a different philosophy
100:44 we flattened together with the right velocity line these all up. And so
100:49 we had them all together and divide seven whatever 246 divided by eight.
100:55 we get this one. And so can see that by that averaging
101:01 The uh primary looks good, primary like this here. No uh no
101:11 from the uh multiple. But the almost got wiped out. Why is
101:18 ? Because it was not flat. so these terms here, they sort
101:23 cancel each other out. Not but very well. So the primer
101:28 enhanced. They said that is the reason folks why we do acquisitions,
101:41 allows us to do to make common point gathers. We want to impact
101:48 reflectors multiple times with different angles of and then um move out correct the
101:58 so that all those add up the . And by the way you can
102:04 that in this uh diagram here, isn't any uh oh effect, all
102:10 amplitudes are the same and these amplitudes the same. So, uh amplitude
102:18 discussion that's not included. If there an Avio effect, that would maybe
102:26 one here, this one will be amplitude than this one. Maybe
102:32 maybe smaller depending on what kind of leo we have all those amplitude effects
102:38 are ignoring. Yeah that's why we it. Well look here and that's
102:45 good idea. But look here this uh another way to handle the same
102:51 center here. We've done exactly the process except that we we did the
103:00 out removal with the velocity uh suitable the for the multiple. So we
103:07 the multiple and we reduced the primary not eliminated completely. Number one because
103:13 bigger and number two because some of are still in there, these waves
103:18 not um exactly cancel each other but can see that if we wanted to
103:24 could uh good process today to enhance multiple instead of removing and if we
103:33 that we would gain different insights in uh so that's a good idea in
103:43 context. You should remember if you're data that removing multiples is a good
103:49 but also moving primary. Just a idea. And both of them lead
103:54 different under different insights concerning the So here's a quiz and so Stephanie
104:06 out here, there's no all of both. So um either all of
104:11 are true. Well um uh what hoping is that just one of those
104:16 true because they don't give me the of all of them. So I
104:20 to listen to you while you talk way through this, starting with a
104:28 not A is true. That's sort the definition in it. Okay so
104:33 go on to be if the subsurface literally even apply I mean not
104:43 Right. Yeah that's you are That's a special case where it uh
104:48 at the midpoint by symmetry. But is it uh where the uh the
104:56 multiples happen? Could be not Okay so that's good. It's going
105:01 see sees kind of the same as . It doesn't necessarily happen. Have
105:07 happen at the surface. Oh they they can just be whatever they
105:20 Really? Right. That's right. don't know about this little thing.
105:25 that one is wrong. So you right. Uh The answer is a
105:32 two. Let me hear your You let me hear you talk your
105:36 through this one multiples arrived. This false because they arrive after because they're
105:48 . Mhm. Be the multiples usually out faster. So know that ties
105:55 with a. Okay, how about . See the multiples usually move out
106:04 . Yes. So that means So we're hoping that d turns out
106:09 be false. What do you think muscles usually have larger amplitudes than
106:17 No. Yeah. Usually have smaller because they have more reflections in their
106:23 . Okay that's good. Um Number . Let me hear you talk your
106:28 through this one. The multiples are overcorrected. They're not overcorrected because they're
106:39 . Just like the other ones right Under corrected because we corrected with the
106:45 of the primary. Yeah. Okay go on. The number to
106:51 the characteristics of the primary then uncontaminated the multiple. Yes. Well to
107:05 I'm thinking that that might be true depending on whether the multiple is still
107:14 with the primary or not. Uh haven't guaranteed that we remove that interference
107:21 we flatten with the primaries. So gonna call that one um uh provisionally
107:27 . And I'm going to a better down below. So just for like
107:33 visual on being like just so I see it. That's kind of like
107:36 cartoon we were just looking at Exactly. Okay. Yeah that's exactly
107:43 the cartoon the after correction with after the primary. The multiple was still
107:51 at far often so it's gonna affect behavior. Okay. Yeah. And
107:58 the way uh the reason why the or term in the Avio um uh
108:08 equation that we talked about earlier. reason why that's so hard to determine
108:13 in my view it's because of uh interference with the buy multiples which we
108:21 not sufficiently uh got rid of. so uh you know that makes uh
108:31 interesting possibility. It means that if did a better job of multiple elimination
108:37 we could actually use that curvature term our analysis. Uh I am not
108:43 of anybody taking that approach of connecting view behavior with multiple removal. And
108:53 think that's a very far missing avenue research anyway. Go on. A
108:59 . See um they're not eliminated. they're eliminated if you're lucky. But
109:12 you uh if you don't if you if you're the normal geophysicist, you're
109:22 lucky enough to get the perfect And there's a whole subclass of us
109:29 are specialists in the multiple elimination. not one of them, but I
109:35 a number, a number of those among my friends guys and and women
109:42 they have much more clever ways of or reducing multiples than what we just
109:50 through here. But that's uh the of a more advanced course.
109:58 now there is one class of multiples has received special attention and those are
110:05 ones that have their their downward bouncing at the surface. So here is
110:15 marine uh cartoon where we have receivers along here and we're receiving a primary
110:21 this uh on this event. We're uh and uh we're also receiving multiple
110:30 this event. But look, we that multiple right here. Uh and
110:37 we didn't put this receiver here to the multiple. We put it there
110:42 record the primary from a shorter But look what we got the multiple
110:48 in here. And so uh the thing here is that uh we can
110:58 the surface weighted multiples without even knowing is the velocity structure in the and
111:04 overburden. We don't know how to what is the velocity structure in
111:09 Um And we can still eliminate, can at least reduce it uh Anyway
111:17 this is uh uh due to a of ideas uh promoted most vigorously by
111:26 . U. H. Colleague Arthur . And you might be uh confused
111:32 has not seen his name on the list. Uh And uh the geology
111:38 , he's in the physics department. , so this technique is called surface
111:45 multiple elimination because in in a instance can actually eliminate them S.
111:52 M. E. It requires that record the balance everywhere. Well we
111:57 afford everywhere but we do a pretty job in for two D.
112:03 Like you say, we don't have uh in the marine environment, we
112:07 have receivers everywhere, but we have spaced every 50 m apart or so
112:13 that's pretty close to everywhere, but think about it in uh in a
112:19 D. Survey uh we have the line spacing is less dense. So
112:25 imagine uh Simple Marine Survey with one and one source behind the boat and
112:36 streamers. So you know, they clever ways to mhm directly behind.
112:48 might be ways so that it might 100 m or 200 m between streamers
112:58 and then they might be 10 km . And so they drag this whole
113:04 stream of receivers through the water. the cross line separation off line spacing
113:13 always less less dense spacing cross line in line because if you try to
113:22 it uh you know spacing cross line of only 50 m, you're probably
113:29 get the screamers tangled with each So uh normally the cross line spacing
113:35 much bigger. So that makes problems three D. Um implementation.
113:45 so now S army uses a nonlinear of scattering theory, which does not
113:53 knowledge of the service service velocity That is when you record those
113:59 that gives you enough information to eliminate , even if you don't know the
114:08 . So usually starts from the wave . Here's our wave equation does not
114:14 from the equation of motion. Under equation of motion uh has this additional
114:21 . And that comes from the fact in the subsurface, this um um
114:28 cancer does in fact depend on position the subsurface is in in homogeneous,
114:36 there's always a term here. And that term is not included uh in
114:42 S army algorithm. So the S is not completely general and in practice
114:51 um they are mhm. But it's standard way i there's a standard way
114:58 uh funding reducing sometimes even eliminating surface most. So why is this
115:10 We've got three answers plus all of above. Uh So Stephanie talk your
115:15 through this. Um Okay so their are usually stronger. So that would
115:27 true. Yeah that is true because free surface is the strongest reflect going
115:37 be and then we have special techniques deal with them. So that's
115:43 And one of the special techniques is . Right. Yeah. Right,
115:47 good, that's good. Okay um let's now think about ghosts. So
115:55 is um cartoon showing the up uh of marine acquisition. And so from
116:08 source you see some of the energy down but also some goes up comes
116:13 and reaches the receivers a little bit this one. So if we could
116:21 it a shadow but they call it ghost and uh that's going to be
116:26 and it's gonna depend upon this towing , this going depth. So if
116:32 tow depth is 20 m, that's be a longer delay. Then if
116:37 towing depth is 10 m or five . And so um that in mind
116:47 gonna be in our marine data. also we have this receiver ghost now
116:52 uh you know, exactly symmetrical Now it's common that the streamers are
117:02 so with a different depth than the . So that means the time delay
117:08 is going to be different than the away here, I think I probably
117:12 um just this senior to show that Now the reflection coefficient of the free
117:23 is always a -1 for all So now um at a certain frequency
117:31 we're gonna determine just now at a frequency, the extra path length of
117:36 ghost is exactly one wavelength. So because of the opposite polarity given
117:42 it cancels the primary making a notch the spectrum at that certain frequency.
117:48 when you look at the, when look at marine data and take uh
117:52 spectrum of marine data, you always a notch in the uh in the
117:59 that is hardly any energy coming at special frequency. Middle of the notch
118:06 of that special frequency uh the ghost the parliament. So you can adjust
118:17 uh the frequency at which this notch by adjusting the depth of going.
118:24 if you have uh greater depth of means a longer time delay for the
118:34 and a lower frequency for the That's what it says in the depths
118:42 the source and the receiver are The corresponding ghost period is longer as
118:52 uh if time delay is very Uh as in an ocean bottom seismic
118:58 , that's handled differently because that multiple is not just a simple phase of
119:05 , but many cycles of uh uh wave ones in a deep water ocean
119:14 sandals. So definitely let me hear talk your way through this and notice
119:23 we got none of the above down . So read the, read a
119:33 , then we've got these continuations. in a towed streamer Marine survey assuming
119:39 the down going and upcoming rays have same angle of incidents. A the
119:45 ghost has the same delay as the ghost. That's false. Yeah,
119:50 the receiver ghost might be different depending how they might tell the receivers um
120:01 a different depth than the source. that was false or be a notch
120:07 the spectrum occurs at a frequency where depth of the receiver is able to
120:11 half of the wavelength at that That's false. Let's think here.
120:23 Yeah, that's clearly false because uh normal incidents that uh ghost is gonna
120:34 going not straight up and straight back but it's gonna be going at an
120:40 . So um uh and furthermore it's to be in a different angle depending
120:47 the offset to the receiver. So clearly false. But let's um
120:55 let's, I think this is through and specialized to um uh normal
121:08 Okay, so the normal engines goes up, half a wavelength up and
121:14 down. So it's one wavelength behind primary but it's got an opposite polarity
121:23 of the reflection coefficient at the service -1. So that sounds to me
121:30 for normal incidence. That would be . But your answer is um um
121:37 answer is technically for it. Well go on to make sure that that
121:42 is also false. Um If the to deeper the receiver goes, has
121:50 notch at a lower frequency. Wouldn't be true? Since that's always
121:57 So so the answer is C. and and maybe be with that
122:05 Okay. So now uh of course a question about how to eliminate this
122:14 of multiples. So if the what not late. So you see it
122:22 a lot of on this technique. . So the question is suppose that
122:29 the water surface is rough so that waves on the water that can happen
122:35 ? And now the question is, does that do to the S army
122:41 ? I'm thinking about that. I thinking so that's a really good
122:48 Never been asked me before. This not something that I'm very knowledgeable
122:52 What I'm thinking is if the surface rough, but it's everywhere rough in
122:59 same way. Um that uh that's . I don't think that we assume
123:10 the surface is a perfect marriage. think that uh I think that when
123:15 Wig line does his um analysis, doesn't care whether the surface is rough
123:22 smooth And furthermore, he doesn't care there's a big wave passing by the
123:32 and not at the midpoint. I think he cares about any of
123:36 Uh That's it. That's a good . The next time I uh talked
123:41 him. I'm gonna ask him that by the way you've been around for
123:48 years, do you know? Professional . So the next time you passed
123:56 in the hallway ask him about that I think that he's probably gonna confirm
124:02 guest. But he is what I say way more knowledgeable than me about
124:07 topic. It happens following question is because we can decide the death of
124:15 receiver and the shot source. So will we can control the notch filter
124:26 the frequency spectra. Right? So will prefer to uh uh place the
124:36 filter at low, bring low frequency the high frequency. Um Yes.
124:43 we wanted to either uh put that at a high frequency uh short period
124:52 long period depending on um our objectives further at the receiver. And so
125:01 down further at the reflector. So would say that in these days we
125:10 more concerned. Well so if we're about uh resolution then we want to
125:19 the notch uh longer periods uh so we preserve the high frequencies. But
125:26 we're concerned about image making, we a new appreciation which we didn't have
125:33 most of my career, we have new appreciation of the value of low
125:40 in making images. And so if uh if we have that foremost in
125:49 mind making good images, then maybe want to move the launch too short
125:56 shorter periods. So as to preserve long period, um, long
126:04 both frequencies in the data. I would say that the thing to
126:10 is to uh, have, um, at the beginning of a
126:18 , you want to think about what your objectives are and think about
126:24 , um, uh, whether you to have a long period notch or
126:32 short period. And I think it depend well the circumstances you might
126:38 you might decide one way for this and another way for the next
126:43 And you know, this kind of is uh, one where two physicists
126:51 been keen keenly to understand this for . And so there's a lot of
126:57 , accumulated knowledge and uh, the on the acquisition company, we're gonna
127:07 running the uh, acquisition. They'll something like, oh, we always
127:13 the sources that seven m debt. what we have learned from our
127:19 And of course these guys have a of experience, a lot more than
127:23 in the oil companies. When I us speaking from my history at an
127:28 and BP, uh, uh, and service companies look at a lot
127:33 data than guys in all companies. the service company guy is gonna
127:38 well, this is the way we it. And so, uh,
127:42 that point earlier in the project, a good idea to sit down with
127:46 guy and say, well, explain to me why you do it
127:50 way and why. Um, it's a good idea for this case to
127:55 something different. And normally they love kind of a discussion because they want
128:01 have a smart customer. It's awfully the issues with them. And so
128:08 a good thing to talk about. maybe for this project you'll decide,
128:13 it shouldn't be at seven m, be at 15 m or it should
128:17 at three m or whatever. You decide that this particular survey because of
128:25 we're expecting in this environment, we want to do something differently than they
128:31 do. And uh, here's another a few years ago, I think
128:38 was PGS invented a different kind of acquisition is off where they had to
128:49 one above and one below. So called that the over under.
128:53 and the reason for that was to in the notch and maybe they have
128:58 over and under source to, to in uh, the source notes.
129:06 uh, all kinds of ideas are it's an important problem. This,
129:12 , this issue puts a severe limitation the resolution that we can expect because
129:22 these Golf so much for the, much for the service. Let's talk
129:29 internal most. So here's an intern and we can't eliminate that in a
129:36 way as we do with S. . M. E. Because we
129:41 record this what give up yeah because can use the wave equation to downward
129:50 the wave field so we record up and so if we know the velocity
129:54 here we can deduce and we know wave equation and everything so we can
129:59 what the uh what the data would like if we had receivers down
130:09 It's not perfect because we never know velocity here perfectly. For example we
130:17 know uh the velocity in all the here perfectly. We're limited by resolution
130:23 so on and furthermore we don't know anti socks. Be up here.
130:30 uh probably and I said topic but probably don't know that perfectly well so
130:37 we downward propagate we're going to not . Exactly. But let's um um
130:44 that possibility for now. And uh um assume that we can do
130:54 So we can compute the data that would have received down here and so
131:00 we can apply s army and also we we also have to know which
131:07 deep do we want to go do uh when we do this we're gonna
131:11 able to eliminate this one but still others that we did not eliminate by
131:15 technique. And so it will be for every surface and we're obviously not
131:21 do it for every surface. Um so uh now when we if we
131:31 this internal multiple here there's gonna be internal multiples from other interfaces which we
131:37 eliminate. And so it's not an problem means. So uh Stephanie,
131:49 let me hear you talk your way this. We got a B.
131:54 of the above and D. So me hear your Okay. Um Which
132:05 these statements are true. A salt interfaces are usually strong generators of internal
132:13 . Yes. Yeah. So now didn't teach you that, did
132:17 But because you are smart, you out from your common sense uh that
132:24 there's a big inner a big contrast uh uh an interface uh internal interface
132:33 gonna make multiples. And so this a good case where there's a salt
132:39 interface. And so it's gonna make multiples and we're frequently going to have
132:45 deal with. So good on you on. Number B. Internal multiples
132:51 always symmetrical. As shown in the . I feel like always is a
132:56 word. Yeah, always is a word. Right? So uh and
133:00 always a strong word. So uh that was going to be false because
133:05 going to be false. Uh And how about Dean? I would say
133:15 . Yeah, so they can be in many cases following the arguments that
133:21 gave back here, they're probably gonna be eliminated, but uh this one
133:27 we did find that this one is . So yes, okay, now
133:33 is interesting, this is friendly So all of the multiples that we've
133:38 about before we can say they're unfriendly they don't, they make troubles.
133:46 is possible that if you adjust your so that you reliance the so that
133:53 amplifier so that you enhance the multiples can that can be a friendly thing
133:59 do. Um wow normally multiples are as a nuisance and we want to
134:10 rid of but here are some friendly . How about this? Yeah.
134:17 off here in normal sub sequences there many interfaces closely spaced. Each
134:25 every one of them reflects some energy . And this the scattered wave field
134:32 upwards is partially scattered back gallons by near back interfaces above this twice scattered
134:43 has on average the same polarity as primary so they reinforce each other with
134:49 small delay. Hence they're called Friendly Nous. This concept was uh given
134:57 Nigel Anstey, one of the great of the previous generation. Still alive
135:04 well retired by now and you I do not know majority. Um
135:11 is the only important paper he ever and I think he was probably a
135:17 all company geophysicist and Anthony was a and they worked together on this but
135:22 sure the brains behind it was answered one of these uh multiples has a
135:31 attitude because it's been scattered twice once here once here and it follows along
135:39 the primary with a small delay. but it has a small aptitude.
135:43 when thousands of these reinforced together they most of the energy out of the
135:50 . And what you see on your are the multiples. How about
135:54 So I have here a diagram. this picture is oversimplified and lots of
136:01 . For example, there's no refraction , no conversions or nothing, but
136:06 want to talk about this. So this thing is going down, some
136:11 the energy gets reflected back up here then back down here follows along the
136:17 the uh primary with the smaller attitude a little delay coming from this two
136:26 travel here. And the same thing happening here and the same thing is
136:29 here. And if thousands of these , they superimpose constructively because they have
136:35 same um uh they have the same polarity and they just have a little
136:46 . That's what it says is supposed but delayed and the same thing happens
136:52 the way up. But look this is the primary without those friendly
137:04 . When it gets stopped here, doesn't have very much attitude because
137:08 most of the amplitude has been taken of it bled out of it by
137:13 with these interfaces. And so these um propagating along behind the primary uh
137:22 super posing not exactly, but each has its own delay. So they're
137:27 broaden the waves and that's what you on your workstation. Look at
137:34 there's Nigel Anstey himself a few years when he was honored by the E
137:39 G in Amsterdam. And I made my business to get in this picture
137:45 these famous guys, here's Nigel here's Anders Robinson, you've heard his
137:50 , He was uh one of the of digital seismic processing back in the
137:55 . Here is Claus Helberg, another previous generation, about 90.
138:02 um uh Nigel was about 90 of . Nice beard, don't you
138:08 And this guy is somewhat younger, guy is named Zhukovsky, Famous guy
138:12 uh del from uh University of Edinburgh in Edinburgh. And I saw him
138:22 this week in uh in Houston and asked him how is Nigel getting
138:26 And he said uh as of he was in good health. So
138:31 two correspond exchange. So uh I this opportunity with all these great
138:38 I just stuck myself into the picture I had my wife take pictures.
138:42 there it is and this is sort a Ray theory explanation of what goes
138:48 and that's the way Nigel did He was very good at explaining complicated
138:56 in terms of of pictures, like one I just grew a better way
139:04 describe that is in the wave theory in this case we want to use
139:10 equation of motion for in homogeneous Just like we showed this formula a
139:15 minutes ago. So uh if this varies with uh with position, like
139:24 says here, then this derivative is make a term like this. So
139:31 part of it gives the wave equation this part gives uh an additional term
139:36 we should not we should not neglect term because of the many, many
139:45 sedimentary interfaces in the sub surface. there's more discussion about this in less
139:51 nine. So we're here on less seven. So we still have a
139:55 to go. Let me show you data. This is from A
140:01 And in the VSP you have a of receivers in the borehole source on
140:08 surface. And you can actually record down going wave field. This is
140:13 director rifle is going down. Um as it's going down uh Spectrum is
140:26 look like this. So the first , this is uh at a shallow
140:33 and this is a deeper and deeper deeper receiver. Okay, and so
140:38 is uh this shallow receiver is at certain depth. So this um trace
140:45 at 7/10 of a second. So it goes down twice as far to
140:51 how the traces look very different. you can see that this one here
140:57 a lot less high frequency in it this one. Here's uh down after
141:05 seconds. And it has broadened out lot. And after 3.5 seconds,
141:10 5.5 seconds. It's broadened way out , so make uh so this is
141:17 100 milliseconds here. So this is a broad waves and you can see
141:23 we lose the high frequency information as go down. And the reason is
141:28 all of these friendly multiples to propose each other with different delays and that
141:36 destroys the high frequencies as you can right here with your eyeball. So
141:47 take the spectrum here. So we 123 spectrum. So here is
141:53 the spectra from the shallow receivers and is the deepest one in the solid
142:00 not the deepest one, but 2.7 . It didn't show even show the
142:05 one, but the 2.7 seconds um the spectrum is here and you can
142:11 that that we've lost a lot of frequencies from the shallow receivers down to
142:18 evening. Of course, all of are normal, that they have the
142:23 amplitude here at this frequency. following this argument, the primary eventually
142:33 most of its energy to these friendly . That's free, is friendly.
142:40 uh given by Nigel Anstey and they them friendly because they do reinforce each
142:49 . What we actually detected what we on our on our workstations is uh
142:57 we call the primaries are really the superposition of all the friendly most of
143:04 . And the true primary is just first initial, the the very initial
143:12 uh emergence of the of the So if you if you see a
143:18 separated arrival, yeah. First very part as it deviates from zero,
143:26 the primary and welcome. The Is these friendly mountains. Now,
143:33 is the velocity of that? Um Finally multiple package travels with a velocity
143:43 by the back of average. Now me think here. I don't
143:54 Yes, I think it's true. we talk about the back of average
143:59 the first or second lecture. Did do that? Let me I don't
144:10 so. Oh no we did So we're gonna do that directly.
144:16 . Okay. So uh so we ourselves what is the velocity of uh
144:28 package of friendly and multiple super posed , which we call the primary.
144:33 really it's it's a superposition of all friendly most. It's going to be
144:38 than the rain theory average of the of losses. So here's the
144:42 Uh Consider the vertical velocity is a period waves. So here's a cartoon
144:47 sedimentary layers. And uh here we the velocity law. It's got alternating
144:54 of high and low high and low and all this of course bedded sedimentary
145:00 . And why is of course because gonna hit this from below with a
145:05 frequency wave, how to announce high because these are successive wave fronts.
145:10 so these wave, let's these this here is less than the player
145:19 So we call it a short period . And here's our receivers up here
145:22 we ask yourself the question when we the transmitted wave, what was the
145:27 of this wave? Okay, so work it out. Uh So we're
145:35 define the velocity as the total thickness by the total travel time. Pretty
145:40 . And then we're going to uh the total thickness as the sum of
145:45 the layer thicknesses and the total travel is the sum of all the travel
145:49 . Pretty obvious. And now we're to eliminate the times in favor of
145:56 thickness divided by the velocity in each . Okay now we're gonna invert the
146:03 thing at the universe of this. now on the right hand side we
146:08 the sum over layers of the layer divided by the slowness, at times
146:14 layer velocity times the slowness which is same as divided by the velocity in
146:20 layer. So and then we're dividing by the sum of the layer thickness
146:27 this one. And this is the of this. And so that looks
146:32 a weighted average, a weighted And what are the weights, the
146:37 of the layer thicknesses. And so are the sum of the weights.
146:41 that's just a weighted average and we're uh you know that with angle brackets
146:46 that and what is being uh what being averaged? It's the slowness in
146:52 layer, that's what's being average, what uh that's uh rotation.
147:02 now that's all pretty obvious. So, uh so now, how
147:07 the vertical velocities for long period This is the seismic problem. It's
147:13 same um layered sequence, same And now we're hitting it from below
147:19 a long period waves. How do know this is a long period because
147:23 period of this distance between successive wave is longer than the layer things.
147:33 so it's gonna be emerging here and looks like a different maybe like
147:38 that's gonna come out out of the to then we're gonna um detective that
147:49 velocity in this case there's a thin case. So this is all the
147:57 layer case because the wavelength is long to the thin beds. So this
148:02 layer case. This is given by what we now call the backers
148:08 And uh um that's a bit of a disservice to the guy who really
148:17 this for the first time, who a guy named Brueggemann living in Germany
148:22 he had the poor judgment to uh this in german just before the
148:28 so nobody remembers Brueggemann. And when uh discovered it independently, 25 years
148:36 , he gets all the credit. in our business there are two Baptists
148:41 brothers. So there's George Baptist and backers. This is George Bacchus and
148:47 was a very mathematical guy who worked slumber. Uh and uh very mathematical
148:54 my old baptist was a very intruded and he was a professor at the
148:59 of texas and he just died a of years ago and I think George
149:04 still alive. But George was not accused. George was really a
149:13 Uh and he was he was quite guy. I knew him well.
149:18 was a former president of the scg professor at the University of texas and
149:25 died Apple music. So now let's at the formula. It's a terrible
149:30 formula. You see we have in upon in verses, we got square
149:34 and we've got squares and we got density appearing explicitly. So this is
149:42 real mess. That's what bank has it for me. You can look
149:47 this paper famous paper and we want compare that with the coarse layer of
149:53 which we just uh looked at previous . Very simple intuitive. So the
150:00 our velocity is the inverse of the of the Florence. Yeah. Um
150:13 do we call this rate there? remember rate, there is the high
150:17 approximation. So of course the problem that layers of coarser than the
150:24 So that must mean high frequency. what is the relationship between these two
150:32 when you just look at it are to see a relationship. So before
150:37 talk about that difference let's go back uh the derivation of the course
150:43 Uh of course layer problem and exactly we showed before. And I'm going
150:54 ask you is where in this which I know looked very straightforward and
151:01 obvious. Every step was an easy . We've got all the steps out
151:05 . Where did we assume? How ? So I'm gonna stop here and
151:11 me think about that both of This is not obvious. So think
151:16 that a while and then I'm gonna you, where did we assume in
151:20 derivation? Where did we assume? frequency. So you tie tell me
151:35 did we assume how frequency? Um would say that the jab, I
151:49 see depth in here. Okay, so when we express the thickness as
151:56 sum of larry thicknesses, is that high frequency? That seems to me
152:03 just the geometrical argument. If we the frequency, the death will not
152:16 just a value range. So tell precisely on this slide where we um
152:28 we made a mistake is it? is it here is it here where
152:33 is it? No any hint I . Okay so this is where it
152:45 right there. So when we say the total travel time is just the
152:51 of the individual travel time. That that assumes that the way it goes
152:56 it's coming up, it goes through it goes through layer one and then
153:01 goes through layer two and then it through layer three and this animal all
153:06 and you get the total travel But if the wavelength is a long
153:13 , when the when the when the of the wave gets up into layer
153:21 , The body of the wave is in layer one and when the front
153:26 up to layer three, some of in layer two and some of it's
153:29 layer one. So what it does it compresses them all together And we
153:35 say that the total travel time is sum of individual times because that's not
153:41 way it works, it doesn't go one and then the other and the
153:45 it goes through them all together. so that's what uh back is.
153:54 uh it's not a hard paper to . I encourage you to look it
153:58 . And if you need to you ask me and I'll give you the
154:02 reference that you'll probably be able to it for yourself. And so uh
154:08 I'm gonna ask what is that? the relationship between this uh is this
154:13 bigger or this one bigger or And so to answer that question,
154:18 know, we can't answer it in direct way because it depends upon density
154:23 example. You see the density density here at all. So what
154:27 going to have to do is assume things. We're going to assume the
154:32 among the layers is small. And we're gonna do a taylor expansion of
154:37 . And then we're going to assume statistical relationship between density and velocity,
154:43 . We're going to assume the uh correlation between density and velocity, which
154:49 given by gardening, who was a professor at your age at price and
154:58 years ago. So when you do , what I just said, you
155:04 that the long wavelength philosophy, that's one is given by the short wave
155:10 times one plus a correction factor. the correction factor involves an average.
155:16 what these brackets mean. And what's averaged is the local uh local velocity
155:23 . Uh This is layer by layer variation and this is the average velocity
155:28 the whole stack. So we had non dimensional relation here. Now some
155:35 those individual layer philosophies are bigger than average and some are smaller. And
155:42 each one we take uh general velocity average walls. That's right. And
155:50 some of them are gonna be faster some are gonna be slower than the
155:54 . So some of these members are be positive, some are going to
155:57 negative, but we're spurring them So this is all positive,
156:04 And because of this minus son means the long way going to velocity is
156:10 than shortwave lost. So you um that's uh wave theory analysis yielding
156:23 same results as Angela Anstey Doherty and discussion of friendly multiples. So
156:34 you can think of this as sonic . And these are the seismic velocities
156:41 see from a circumcise mint. Now you have sonic logs and you have
156:51 band velocities from a surface seismic survey the same area, you might want
156:56 compare them. And so to calculate sonics with the sizing band, you
157:01 an extra step. You've got to perform this uh calculation. So this
157:08 what you need for size mix. is what you can calculate from a
157:13 log. Just doing that uh sonic averaging like I should before. And
157:18 can also calculate this from the sonic . And this is the friendly multiple
157:24 coming from the wave equation are coming the equation of motion. So to
157:31 so back us. When you derive equation of motion. When he arrived
157:37 baptist average loss started from the equation motion, which I showed you a
157:42 times all slides back and discussion more less and more so we can do
157:55 . But there are other issues to uh for example, uh the seismic
158:01 and the sonic waves sample different parts the earth. The sonic waves only
158:07 , sample near the bar hole in seismic wave was going down some distance
158:14 from the borough. And it's maybe to think that uh walks in that
158:23 in the two parts of the earth the same velocity. Furthermore, the
158:29 ways uh, maybe aren't giving me right answer, but maybe you need
158:34 do some sort of correction to deal borehole damage. I suppose when the
158:41 is when the drill bit, it's down through the rocks, suppose it's
158:46 . It's chewing up some of the and spitting them out. That makes
158:51 what it does to make an empty . And in the process, it
158:55 be putting cracks into the uh rocks the formation wall and those cracks are
159:02 there, um affecting the sign of . When you come back with us
159:09 logging tool, you might be sending sonic waves to damage formation, depending
159:16 the formation. Furthermore, the rock might be intrinsically different from uh,
159:25 uh, the sighting from the low frequencies in size in place.
159:30 you can have exactly the right the rock in the laboratory and measured at
159:35 frequency and low frequency, you might a difference. Should not assume that
159:43 is you. And so, here's another important point. If the
159:51 velocities come from, move out as to from the same vertical bsp.
159:55 might be affected by an because, know, uh for financial social see
160:03 that the rays are going through the and a weak angle sonic tool,
160:09 gone vertically. And so those might different velocities and so well more learn
160:15 about that unless Okay, so let me hear you talk your way
160:25 this. Okay. Individual friendly multiples have very small amplitudes since they are
160:34 . That's true. Be many, internal multiples super posed constructively to make
160:43 amplitude. Yes. Yeah, that also true from why? Going to
160:54 , oh that's what you said, um the friendly multiple arrival has a
160:59 velocity given approximately by the back is of the individual. Yes.
161:08 so that brings us to diffraction. me see here how we're doing with
161:14 . Okay, so it's 4:30 so us uh take a break here and
161:21 will come back to the fractions at . So see you in 15 minutes
161:29 4:45 and I think what I'm gonna is to stop sharing and video.
161:48 don't know what I am doing wrong that when I first bring this
161:53 it does not um respond to the . So uh what I'm gonna have
162:02 do is like this. Um And , okay, now this works
162:23 so uh this is a really good taken from Sheriff and gil dark uh
162:30 shows about um uh what the fractions . So it's uh duty situation.
162:39 here we have uh soon to be variant in and out of the
162:42 And here we have a wedge in otherwise uniform body. And we got
162:49 coming in from the northwest like And so these waves which are way
162:55 board from the uh from the tip from the point, uh they are
163:02 by the point. And so you see here uh this is what the
163:06 looks like. Okay, now let's , let's look at various parts of
163:12 , there's the unaffected wave and here normal reflections. These are coming in
163:18 from here and reflecting off of Uh These wave forms look just like
163:26 wave forms and these are diffraction is at all this other energy. Uh
163:35 know, from here, around to in here, all these other,
163:40 are uh diffraction waves and you can that the wave forms look different from
163:48 incident wave forms. Uh and the gets changed, the amplitude sort of
163:55 , but it's not true that you a complete shadow. So you might
163:59 that there's a complete shadow, nothing all from here to here. Uh
164:05 of that's in the shadow, but not true, plenty of energy in
164:13 . And uh similarly from this point here, we get reflections in all
164:20 , not just back in the uh with these are reflections here off the
164:25 of this surface uh angle of reflection angle of incidence, but look at
164:32 these different angles here coming off of point. And with various aptitudes and
164:38 way for those are the fractions backwards all angles forwards at all angles,
164:49 the these defections smooth, smooth, smoothly where the undistracted way as you
164:55 more and more output. Okay, we want to apply that same idea
165:04 this context of imaging. So here have um A block sitting on top
165:13 a reflector and we're gonna show two of normal incidents acquisition Over here.
165:22 this one goes through the middle of block and this one is outboard of
165:26 block at some distance and this is 150 m outboard of the block.
165:33 so these are zero offset traces along center line and so right over here
165:39 see a reflection from the base layer and the same thing over here and
165:46 is a reflection from the top of block. But look right here,
165:51 are other energy coming off of this being reflected back this way. So
165:58 is a normal incidence trace taken right . Source and receiver at the same
166:03 just outboard here, right about here it's receiving energy not only reflected energy
166:10 the base, also deflected energy off this edge and over here is the
166:16 sort of thing. Maybe I can that better. So so here is
166:20 is a receiver. This is a from a receiver which is just above
166:25 point. It's up here some and can see that it's getting re fractions
166:31 that edge. Now, here's something to look at down here is the
166:41 of the block. So uh evidently velocity in the block is different than
166:48 velocity in the base down here. there's an impedance difference uh right at
166:54 base of this block. And so can see that right here. It's
167:01 simple because you see what the waveform like, it looks like uh trough
167:07 , you know, peak trough, , that's not exactly what we see
167:12 , but maybe it's uh here we peak trough, no peak down
167:19 So these wave forms are somehow I don't know what accounts for that
167:25 . Uh Yeah. Now, let's at similar traces taken along this
167:34 which is outboard of the block. here is the uh reflection from the
167:42 all along here. And notice right here, those are the fractions coming
167:49 of this edge, even though it's away from the line of acquisition.
167:55 Some of the because this is uh raised, see uh the waves are
168:02 from sources above here somewhere. Uh looks like it's approximately drawn to
168:09 So the sources are up here. uh they're radiating in three dimensions and
168:16 of them are going out of the plane, hitting this uh corner and
168:23 back to a receiver on this vertical uh with zero offset. And so
168:30 see that that diffraction right there. , this is a portrait of
168:47 that's how this this name is pronounced . And uh that's his name,
168:52 an S on the end dutch And he thought of of reflections like
169:00 , he said that if you have incident wave like this, uh it
169:07 a reflection at every point along this along this reflecting plane acts like different
169:16 like we just said. So there's here, one here, one
169:19 one here etcetera. And each one those puts uh refracted way back
169:26 Uh not only in the uh the direction, but in all these
169:34 So, so uh so if there's diffract around here, it's putting some
169:38 over here, some here and some and some back here. And Hagan
169:45 that if you uh take a So all of these circles here,
169:50 comes up to the reflected waves from summation of all these diffraction points.
169:57 the mathematics for this turns out to just exactly what we talked about
170:03 Alternative way of looking at reflections. , um uh there there are certain
170:12 here. For example, if this a D factor, it's also distracting
170:16 the other way, it's also distracting . So what about that? Mr
170:21 . Well uh I am not familiar why that doesn't work out, that's
170:29 a fatal objection, but I don't exactly why this is got the factors
170:39 . These two factors they should be in all directions. Now, this
170:43 an important point in um um in imaging, because there's a technique of
170:55 called turk off imaging, where uh Kirk off another german name, assumed
171:04 every single point in the subsurface might a diffract every single point. And
171:10 he uh added up the uh energy from every single point. And in
171:20 places they they superimpose constructively making for coherent arrival in other places they interfere
171:30 and wipe each other out and you nothing. And that is a way
171:36 uh produce an image out of um direct David. And so that's a
171:45 good idea actually, assuming that everywhere the surface there's a factor just like
171:50 talked about here, and uh where uh imaginary the factors result in a
171:59 event, that is actually a And there's another diffraction point just nearby
172:06 here, which reinforces that, and one reinforces that. And so that's
172:12 gives us reflections, awful minor Another way of formulating so um about
172:27 quiz, which of these are So we got three and then all
172:33 then just two of them are So um uh Stephanie was here,
172:39 talk your way through this all pd are caused by discontinuities of p velocity
172:46 the subsurface. I don't like the all in the front of it.
172:53 . Good for you, you're uh alert to uh exceptions. Uh So
173:00 . So how about uh how about where uh the velocity is the same
173:08 but there's a density discontinuity in the . That sure that we're good.
173:14 you are correct to be suspicious Okay. Uh Let's go on to
173:22 an elastic discontinuity acts like a source activated by an incident wave, radiating
173:28 in all directions with different amplitudes and that be true. Yeah.
173:35 I'll call that one true good. we got one false and one
173:38 So see better be false. So read it through and verify. Go
173:45 A ray which misses the pinch out a sedimentary wedge by more than 1/4
173:50 is not affected by that pinch Well, we never said that.
173:55 , we we we never said And in fact if you look back
173:59 the at the figure which I started section with at that point. So
174:06 that was false. And so all have is being good. Okay,
174:13 funnel zones. Okay, suppose just that the reflecting plan is not
174:22 If it were perfect, you would um a reflection like this which we
174:27 spectacular reflection. But suppose that this down here is not uh polished in
174:37 laboratory, but suppose it's the result a sedimentary process. So in that
174:42 it might not be a perfect mirror it might uh energy from this uh
174:51 this mhm reflecting point might go back other directions in addition to this
175:02 So for an imperfect mirror you might um energy coming back made, may
175:12 different in energy coming back in all , including back towards the source
175:19 Okay. And that's what it says . If the reflector is import is
175:25 radiating wavefront sources right over here receives arrivals back in all directions included back
175:33 the source. Each of these articles delayed according to its path link of
175:38 . So the velocity is the same . But uh this uh wavelength,
175:43 path link is longer than this path . So there's gonna be a
175:49 So, now what that means is realistically seismic waves do not really respect
175:55 a point, but from an And so imagine here that you've got
176:00 imperfect mirror and a source point here we're gonna look at reception back at
176:08 cet reception. So it's a perfect , you only get uh energy reflected
176:15 from a but if it's imperfect then will be a zone around here of
176:21 certain radius, which we're going to out where uh reflections from inside
176:29 all add up constructively when they come here, even though it's not a
176:35 mirror. So that's called the first zone. And it's defined to be
176:40 circular area of which we see here uh the cross section uh and half
176:47 it obviously going to be another half here, and then in two dimensions
176:52 gonna be a circle in this but it's more fun to do this
176:58 two dimensions. Um uh So it's be a circular area around the speculator
177:05 point, which is here, it's have this radius and within which the
177:10 czar delayed uh are delayed Uh from one by less than 1/4 of a
177:21 . So um where does that 1/4 ? Well if if it's delayed by
177:27 half of a period then it Right? So so this 1/4 is
177:34 towards uh cancelation. So uh let's at some formula. So because I
177:44 said in the in the definition of first funnel zone, if the velocity
177:49 uniform, then it's just simple So this adept is Z. And
177:56 uh uh links here is Z plus over eight. And why is
178:05 Because if it's uh two way travel , it goes uh It's gonna be
178:13 over four Way with the report longer this one. And so what what
178:20 the length of this segment here? is the radius of the funnel zone
178:26 the other half of it is over for us. And just by a
178:30 uh that uh length of this is square root of uh my partners provided
178:43 the square root of the uh the side. So it's uh spanning this
178:53 . We have a length of uh is the first from Wellesone is given
179:01 Z times lambda Or four divided by over eight square. So uh it
179:11 comes from this from over here. so you can see that um Normally
179:17 have the depth is a lot bigger the wavelength. So normally we can
179:23 uh personnel zone by this first I just want to uh recapitulate
179:32 Why do we say we went over ? So uh wavelength over eight that
179:40 delay time, total uh total extra of uh wavelength number four. And
179:48 instead of wave went over to then would have opposite polarity and would have
179:52 . So for waves further out here began to uh interfere destructively. So
180:04 um all of these waves then, we have our source up here at
180:11 surface there. And what we just is that if this is not a
180:15 mirror, then we're gonna get um from all these various places back here
180:24 the surface, arriving with a little . But we're gonna arrive constructively and
180:30 gonna to propose constructively. And uh a little delay. And so of
180:36 that's going to broaden the wave Uh and this has nothing to do
180:43 friendly multiples that we just talked This is a new effect which broadens
180:51 the way of that. Now the says, what does this imply for
180:55 aptitude? So you can see right that oops, that's probably gonna affect
181:03 attitude that we that we receive up at normal incidence. Now, next
181:09 is, is this going to affect A. B. O.
181:13 um you can directly um extend these to finite social seaver offsets, which
181:22 what we normally are interested in. then you're gonna be thinking that from
181:27 from a a a circle, the of this uh with a source here
181:34 a receiver here, we're going to receiving distracted arrivals uh from everywhere in
181:41 , not just from the speculator reflection , and that's going to affect our
181:47 as a function of of offset. this is a complication to a
181:58 O. That depends upon just how this mirror is. Uh If we
182:08 a little uh suppose this interface represents difference between sand and shale in the
182:18 process millions of years ago. And supposed so, uh when that
182:26 it goes from sandy to Shelly. that means is the water has gotten
182:31 because of the shales are deposited in water and the sands are deposited in
182:40 water. And as uh water level and falls with geologic history. That's
182:48 causes the alternation between shales and So now this sends down here in
182:55 lower bottom when that was laid down , uh The water was shallow.
183:02 there might be ripples on this Sand, sand ripples. When you
183:09 to the ocean, you can see in the very shallow water, you
183:13 see them right away, I can them with your feet and so
183:17 And such things might get fossilized into rocks as the water level changes and
183:25 whole thing gets covered with shale. there's sand ripples down here and you
183:35 a right to ask, well, what's the what's the separation between these
183:41 marks? What's the that this is wonderful marks. You can see these
183:47 just examples of what sedimentary processes quite and do to make this a non
183:57 mirror. And you can see that the imperfections could be minor or they
184:04 be more significant. You just don't . So, if you were trying
184:08 model this, you would model this a foot with variable uh imperfections.
184:17 has some sort of parameter in here would measure the amount of imperfection of
184:22 mirror. And that would depend, example on the characteristics of the ripple
184:30 . Or you might have some something in mind, but you would have
184:34 sort of parameter to describe the imperfection this mirror. And when that Parameter
184:41 is a perfect mirror and when it's than that, it's more uh it's
184:48 . So you can you can sort imagine modeling this if you had this
184:53 a PhD thesis to analyze this kind stuff, you can imagine that with
184:59 unknown parameter in there. So the the question, the answer to this
185:06 is obviously this is going to depend that parameter, so maybe it's significant
185:11 maybe it's not. So let's keep in mind as we uh go through
185:18 course because we are gonna find cases maybe it's important as a matter of
185:28 , one of them is right So this is real data from my
185:34 days and this is a converted A sea wave split spread gather.
185:43 . Uh this is not a common point gather, but because as we
185:47 about a converted wave has uh image which various as a function of offset
186:01 it's never in the middle. So this is gonna have a split spring
186:08 . And uh let's see here, is this is not a common midpoint
186:15 . It's a common image point gather split with split spread. And I
186:24 you before that because of the uh characteristics of the sea wave reflect a
186:34 coefficient, it should be a anti . So it should be every positive
186:40 here ought to look like a negative over here. So uh it obviously
186:46 , so somebody has multiplied one side the other by a minus one,
186:50 that it looks to be symmetric. okay, that's just uh for
186:57 if you're looking at it with your , now look at this here at
187:02 incidents and zero offset normal incidents, of energy here. So according to
187:11 formula that we just looked at earlier , that's got to be a
187:17 we've got to have zero converted energy normal incidence because as a p wave
187:23 straight down, it can't send a wave back up because it doesn't know
187:28 way the shear wave should be right or left. It's got to
187:32 zero here at this normal incidence, it's clearly not. So one thing
187:40 do is to uh deny the reality what we're looking at. So this
187:48 me of a story um you know you know the story about Galileo and
187:56 was persecuted by the church. He prosecuted by the church lawyers for making
188:04 heretical statement that the earth is not the center of the universe. And
188:11 that was uh obviously a criminal statement he was under house arrest for many
188:19 . I think he died in a in the house arrest. He wasn't
188:25 in prison and a dungeon and he executed. I think she lived out
188:32 final years under house arrest. And uh so while he was being
188:44 he I think he had a judge he didn't have a jury but he
188:50 uh an interrogator. It was called Inquisition. And so he had an
188:56 questioning him about this heretical belief. had the earth was not the center
189:02 the universe. I mean obviously the is at the center of the universe
189:07 God made us and he made the for us to live in. So
189:11 he made us at the center of universe. But here was Galileo saying
189:17 not true. So Galileo had with in the courtroom homemade telescope, he
189:26 a number of telescopes in his Uh And uh I had the privilege
189:35 look through one of them. It it was in uh the italian city
189:45 forenza which in english we call Florence there's lots of very interesting places in
189:53 including cathedrals and museums and one of is the Museum of the history of
190:00 and in that museum there is uh a number of telescopes made by the
190:08 of Galileo and his assistants. And was before he was in house
190:14 And um uh they haven't that the booths a range so that you can
190:22 your eyeball to the viewing piece to eyepiece of the telescope and looked down
190:30 very same look up the very same where Galileo looked hundreds of years ago
190:36 he pointed it at jupiter and he well of course of course. The
190:43 thing he pointed out was the moon found out a lot of interesting things
190:47 the moon. Um while we're talking the moon um do you know why
190:59 moon always presents the same face to Earth? Uh There's always the same
191:07 you look at the moon and there's good clear here of the moon always
191:10 the same. You can see with naked eye, you can see a
191:15 areas and dark areas, you can't much more with your naked eye,
191:19 just with a good pair of binoculars you might use for bird watching if
191:24 look at the moon, you can lots of detail, isn't it?
191:32 that it's because like um it's thicker that side, so the gravity is
191:43 , you're close and so we're gonna to the answer to that question
191:47 But uh it was a question that didn't really know in Galileo's time.
191:53 knew that the moon went around the , but they didn't know why it
191:58 show it's same face to the Now you think well it's it's spinning
192:04 its own axis just like Gareth is . And it must be that the
192:08 of the rate of spin is exactly same as the orbital right. So
192:13 it orbits it spins with exactly the period that shows exactly the same face
192:20 the Earth at all times Now you told us part of the answer,
192:26 talk about more of the answer uh what's your name? So that's one
192:33 the facts that Galileo pointed out is uh the moon in fact does orbit
192:40 Earth, it doesn't slide across the excuse me uh in Galileo's time.
192:47 did not know that the Earth was . No I think they didn't know
192:51 take it back, they didn't know the Earth was round because columbus had
192:55 that uh century before. So um didn't think of the moon as sliding
193:01 the night sky. He thought of moon as rotating around the Earth and
193:08 pointing the uh face of the moon the same direction of the earth.
193:13 he didn't um I didn't know why he could prove that in some detail
193:21 his telescope. Then he pointed his at the next brightest object in the
193:26 which is jupiter and by golly he see it was telescope, the moons
193:35 jupiter orbiting jupiter, They weren't orbiting Earth. So it's you know it's
193:42 in his name that jupiter was orbiting earth but here were some moons orbiting
193:48 which uh definitely established that the Earth not the center of the universe.
193:55 here is Galileo in the courtroom with telescope and the inquisitor and he says
194:02 you know you can just look through telescope and see for yourself that the
194:08 of jupiter orbiting jupiter, uh not Earth so right there that proves that
194:14 Earth is not the uh center of universe. So please declare me innocent
194:20 let me go about my life. that's not what happened. What happened
194:25 the inquisitor reply to Galileo saying I to witness the obscene spectacle of nature
194:36 reason. So he wouldn't look through telescope and perhaps he suspected that if
194:42 did a doubt might call into his about the Earth being uh the center
194:50 the universe. So in order to that doubt out of his mind,
194:54 refused to acquire the data. He to look through the telescope. Well
195:02 right there you see he had a and Galileo was saying well here's some
195:10 to check your theory. And he denied he was refusing to look at
195:14 data because he liked his theory and wanted to keep his theory. Now
195:20 that discussion about the moon back to figure that you're looking at here.
195:27 have theory that says that the amplitudes at zero offset should be zero should
195:36 known that you can see there's lots amplitude here. So we can either
195:41 what the inquisitor did and deny the to keep our theory intact or we
195:48 say there must be something wrong with theory. That's the scientific group.
195:56 must be something wrong with the theory the data always has primacy over the
196:04 . Now, the data could be . Somebody might have screwed up here
196:08 the data could be wrong. But know, we can investigate that and
196:13 have and this kind of data is uh it says it's common. It's
196:21 It occurs in cases like 10% or of the cases where you look at
196:27 uh it's not very common, but not very rare either. And it's
196:35 at odds with the theory. The definitely says we should have zero.
196:42 what could be causing these uh finite at normal incidents? So one explanation
196:51 imperfect reflections. So this energy is not from the expected reflection point,
196:59 from the funnel zone uh surrounding the reflection point. Maybe for these uh
197:07 and most layers are like that. see uh right in here, there's
197:15 uh that's a reflection event which is small and normal. So maybe this
197:21 doesn't have an imperfect mirror, but of these do have imperfect reflected.
197:29 you see what we needed to um we needed to have, we need
197:37 have this kind of data to see if this if this had been p
197:42 data with the same kind of imperfect down there, we would interpret these
197:49 that complication and we would interpret it by adjusting our the parameter delta Z
197:56 Z. But since we, the says this should be a hard
198:02 we are forced to to the conclusion our theory that we spent so much
198:08 and effort developing In the past two . Uh That's wrong somehow. That's
198:16 we made an approximation which we And this is a very good,
198:22 very good way to say, we need to go back and uh
198:27 what happens in imperfect reflectors. And we can see already intuitively that if
198:33 if the reflector is imperfect, then gonna have uh non zero conversion at
198:42 incidence anyway. And the strength of are going to depend upon the amount
198:46 imperfections. And we can we now a more elaborate theory with another unknown
198:53 in there, which is, you , the the imperfections in the theory
198:57 the imperfections in the mirror and we adjust that unknown parameter to match this
199:03 . But there's there is a problem problem that this explanation is implying that
199:10 all of these reflection events has that of imperfection all the way down.
199:16 maybe that's a bit of a you would think that uh if that
199:20 happening uh if it happens at all here would be very common in our
199:27 instead of partly common in our So I would say that most converted
199:32 data sets don't look like this. of them have zero or very minimal
199:37 here, normal lawsuits and this one uh any of them. So this
199:45 be part of the answer, but not convinced that's the whole answer.
199:49 I would say that our community of geophysicist has not uh coped with this
199:58 . Who really cares? I mean of the data we look at 99%
200:02 our data is not converted wave So do we really care about
200:10 Or is this just uh an academic here? Well let's think about
200:19 If um uh if these reflections are and if we're gonna have significant energy
200:29 from everywhere in the funnel zone, that gonna affect our ideas about Avio
200:36 we um we developed a B. . For p ways assuming perfect
200:43 But if they're not perfect, doesn't mean that our our Avio analysis is
200:50 ? Of course it does. Because know this additional convert a way of
200:55 that you can see right here. got to come from the other
201:00 We've got to have conversion of uh energy between the incoming and the outgoing
201:06 , all the energy has to add the same. Otherwise the reflective boundaries
201:12 gonna get hot down there. They get hot down there. So the
201:17 energy that you can see with your right here has got to come from
201:22 other outgoing waves and it would be miracle if none of this excess convertir
201:28 of energy came from reflected p It's just almost I worked through the
201:35 completely. But even even in the but I can think automatically it must
201:43 would be amazing if none of this energy here came at the expense of
201:48 reflected P wave which is our primary source and exploration. So this is
201:54 really important result that shows that are about the reflection process which is universal
202:02 our business is maybe oversimplified in a way. So solving this problem is
202:10 solve is gonna have big implications about leo analysis and it's another great um
202:20 for PhD thesis. So we have a few minutes late here. Uh
202:30 talk talk our way through all these it here in the bottom and since
202:34 of the above so be alert to . Which of these statements is
202:37 Go on. A in the That is unrealistic to believe that seismic
202:42 are perfect in our elastic discontinuities. true because the results are the results
202:48 a sedimentary process. Nobody has been there making a perfect plane. So
202:55 course that's true. Go on. actually every point on a reflector.
203:00 energy in all directions. Not just the angle of incidence. True,
203:06 true, go on. So we two that are true. So we're
203:09 for easy but we got to verify C and D. Are also going
203:13 see those distractions from within the first zone arrive at each receiver only slightly
203:19 . Yes. Okay but you you the name of monsieur. So don't
203:25 that s okay for now otherwise people think poorly of you. Just like
203:32 you pronounce the word if you say poison. Uh people will think badly
203:38 so I don't want your your your if people think badly of you they're
203:46 be badly of of the geology department U. Of H. So you
203:53 know gotta know how to pronounce croissant you have to know how to pronounce
203:58 . Go on to D. They received amplitudes to a degree that depends
204:04 the imperfections in the reflector. That's . Yeah so we got E.
204:08 all of the above good. Okay that brings us to the end of
204:11 and we'll take up on next um next friday at 1 30 Pick up
204:21 uh at this point. So now uh let's talk a little bit uh
204:26 that okay to start at 1 30 friday? Okay um Should we be
204:33 in person or uh remote? I'm with friday being in person. Just
204:41 my job is like not even 20 from the U. Of H.
204:47 so so let's let's do that. uh let's meet at room 2 13
204:55 Friday. And then we'll play it ear for Saturday just like we did
205:01 . I think the rains are gonna still with us right next Saturday.
205:05 not sure anyway, so that's So and we'll take up some next
205:10 at 1:30 on campus at this so I'm gonna stop sharing.
-
+