VideoPoints

• ••• • •• • ••••• • •
GEOL7330 Potential Field Methods - Day3 01-27-2023
Help Tour
© Distribution of this video is restricted by its owner
Transcript ×
Auto highlight
Font-size
00:02 I'm the best student off of the . Okay, well then if you
00:10 questions then let's just um let's just get started with this evening lecture and
00:22 afternoon's lecture and that's gonna be on source estimation. And then on modeling
00:31 modeling, inverse modeling Of which there both two d. and three
00:37 versions. Alright, so deficit refers potential fields are typically mean basements.
00:50 ? Hello, did you have a ? No, I don't know what
00:56 was. Okay. So yeah, we were thinking of base in
01:11 So structures in the basin. if you think, I mean if
01:18 in an area where there might be some, you know, intrusions,
01:25 cells or dikes or you know, kind of lack a with some kind
01:31 volcanic intrusion, you might do do this work for that. And
01:40 couldn't do it. I guess if wanted to with gravity data and
01:44 but we'll talk more about that. Typically people use depth source, they're
01:52 about magnetic data. And the reason that is as I think we talked
02:00 uh sedimentary rocks are essentially not effectively not magnetic. And that means
02:08 um you know, in the basement are very magnetic comparably so in most
02:16 , almost all cases when you're looking magnetic anomalies over over a mapped
02:21 you are looking at anomalies produced by rocks, the rocks beneath the sedimentary
02:31 . And all of these methods, are several methods, they're all based
02:37 wavelength, in fact just like all long wavelengths mean deep sources,
02:45 You get reflection data. All your frequencies are generated, you know,
02:50 the shallow part. And then you don't have any energy. You
02:53 they get they get absorbed. Those frequencies get absorbed faster than longer low
03:00 . So what you end up with just you know, low frequencies in
03:04 deep part of the science section. with gravity data, you tend to
03:10 that long wavelengths are produced by deep . And the same with with magnetic
03:18 . Now there's there's a in a where rocks are homogeneous then you could
03:26 a shallow source that will produce a Waverly but in the real world they
03:30 do that. So the methods are graphical methods which date back to the
03:40 . And then there are uh profile that are automated um um that worked
03:51 profile data. So those are like D. Methods. You can think
03:56 it that way. And then there's methods, you can think of those
03:59 three D. Methods. And in cases you would you know, you
04:05 a window across your map of various to estimate source depths in that
04:12 And profile methods, automated one, pass different windows and two D.
04:19 , you know along the profiles. here's what I'm talking about. So
04:27 is just a little sketch. Um it illustrates illustrates very well what's going
04:36 . So for example here we have base in this yellow here to sediments
04:42 down here would be our basement Right? So we have two different
04:46 three different compositions. Actually, we this dark purple composition, then we
04:51 this sort of tan and this kind brown color. And here's a hypothetical
04:59 anomaly over there. So what you is this this sword. And this
05:08 be in the northern hemisphere, south on the left, north is on
05:12 right. So the inclination here would about 45° because the source is right
05:19 this this gradient. And so this be like a high low pair,
05:24 ? But even though this is a big amplitude anomaly, it's pretty deep
05:32 that's because of its wavelength is broader these other ones. Okay, and
05:41 this one here is about this contrast is about the same depth, but
05:47 producing actually a wavelength that's similar to , it just doesn't have as high
05:51 amplitude. So the contrast isn't as . And then these structures here,
05:57 producing these very low attitude anomalies. um short wavelengths. So, you
06:05 that what these depths are based on wavelength, not the amplitude. And
06:11 think I made a big deal about last week, but and I will
06:15 to um as we move along. as you move forward because this is
06:21 how you look at magnetic data. want to look at wavelengths, you
06:25 want to look at amplitudes are They're important for terrain boundaries. See
06:31 a here's a composition change here and producing this amount. So that's what's
06:37 . So this is the idea that of underpins all of these methods.
06:42 they're all searching to map source depths wavelengths. So for example, let's
06:51 remember we looked at some gulf of maps last week and here's a reduced
06:55 pole um of magnetic data. So could if you, you know,
07:04 you were so inclined you you could , Okay, this is a this
07:09 This is 2°. So that's 220 You could look at these things and
07:17 sort of like the half wavelength and could estimate its source depth or the
07:24 way. What's the rule of phone steps is four, is wavelengths are
07:33 times a source step or or Links are two times of source
07:38 Right? So when you do that of work, you want to look
07:42 anomalies that can be isolated. And where all these arrows is pointing
07:46 Just pointing out anomalies that you could those sort of estimates from where some
07:53 would be a little bit difficult. . So we can start the beginning
08:02 I think Peter's 1949. It might one of the original papers on these
08:07 methods and your family called a slope . And there's a bunch of
08:19 a good summary papers written by M- where he covers all of these
08:29 But the slope method is basically, your magnetic anomaly and you draw this
08:39 line through the gradient and where that that um where that straight line,
08:55 know, departs from the from the . You mark those lines here and
09:02 horizontal distance s that is proportional to source depth. And you you divided
09:12 um or or you scale it by they call a structural whatever an index
09:20 for. So for peters For the slope is 1.6. And I think
09:29 it's less than that for the slope . So for the half slope
09:33 you do the same thing, You this line. But then you calculate
09:39 of that slope and you find where slope is tangent to the profile and
09:46 horizontal distance is um uh is it to the source steps? So you
09:59 the slope line, then you figure what the half slope of that would
10:03 . And you draw the tangent of . And then you measure from that
10:08 point to that tangent point. And the Peters method and you would multiply
10:14 by 1.6. And I think as would multiply by two, probably.
10:22 that's the idea that that you measured distance of commonality. Now you have
10:31 make sure you're drawing on the right . So for example, back
10:36 you wouldn't want to do the slope on this side of the anomaly.
10:42 if you're working in the northern you know that you have a
10:45 low pair. So it is that in between a high low pair,
10:52 is what you're going to measure the from. So does all that make
10:58 ? Stephanie? Yes. So if were in the southern hemisphere would be
11:03 other side. That's exactly right. in the southern hemisphere, this gradient
11:09 be going the other direction and it be, it would be like right
11:15 . Exactly. Yeah. The highest of the source body in the southern
11:21 and the south of the source body the northern hemisphere. Just remember that
11:25 highest opposite the hemisphere. Right? the highest south of the source body
11:30 the where we're at in the northern . Okay, well shells, bob
11:43 um drew, he made several uh several graphs to help make further corrections
11:57 for estimating source steps. So in one, so on the, on
12:02 left is the distance between the half half maximum slope points. So you
12:10 that distance here and you plotted against distance between inflection points here and then
12:20 , so these are the with over ratios of source bodies and this is
12:27 parent inclination angles. And so where where your, you know this when
12:33 plot the half maximum slope distance versus half inflection point distance can fall somewhere
12:42 here and then you can make a , You can figure out what the
12:48 depth ratio was of your source. you see back in the day,
12:55 would spend a lot of time examining single profile to try to figure out
13:01 you know what what what what it , you know, what depth was
13:06 source that produced it. Okay. then he has this other chart here
13:13 that the width of the block. if you got to be your width
13:15 the block, you plotted here with black in depth units, right?
13:22 then this is the distance between half slope points. You can plot it
13:27 here. And then from here, are you measuring here? You're getting
13:33 I guess this is a dip this is uh feed. Yeah,
13:39 must be the must be their This must be the diff I guess
13:49 yeah. Anyways, um we nowadays we all this stuff is pretty much
13:56 computerized, so we don't have to around and do this kind of
13:59 but that's what people used to do . Um but you know, now
14:08 we have computers, there's several programs work on profiles that basically, you
14:14 , measure, you know, they the data at increments along some predetermined
14:22 , right? And typically what we is all these methods you start with
14:27 small window or a big window and either increase or decrease. So you
14:31 have you might make five or six over the profile with different sized
14:39 And then um Actually the very first that was done on this was done
14:45 using analytic signals. Hilbert transform by back in the 70s. But really
14:53 wasn't. But well Warner did this in 53 but a lot of this
14:59 was all developed in the 80s and . So you know, not a
15:06 of computers were just beginning of computer . So the three profile based methods
15:12 show you that have been used commercially Warner which is actually my favorite.
15:19 oiler and there's naughty naughty. Was is very rare. It was developed
15:27 a company owned by C. G. Called JIA Terex. And
15:32 were the only company to use They didn't let other people use their
15:37 , Warner was was uh developed was , you know first Was first developed
15:47 this guy named Warner back in He was German and there's probably the
15:53 papers that Hartman and others from I worked at Aero service and Aero
16:00 used this method and their interpretation Um and then Oiler method was developed
16:11 a guy named dan Thompson And our which is uh salsa oiler homogeneity equation
16:21 it was expanded to three D. by Alan Reed. So I want
16:28 recognize that the equation of the total produced by an infinite strike death.
16:32 other words, he has a it's called the thin sheet model.
16:39 . And It's samples in this case seven. It will sample across some
16:48 seven times. And what it does it solves for uh the location X
16:55 C. Of the source dip strike magnetic inclination. Well, well I'm
17:02 , I'll take it back if you into it, the magnetic declination declination
17:07 it finds X. Z. And susceptibility and um yeah and then so
17:20 are the four unknowns X, A and B A and B and
17:22 strike. Um So to solve exactly, you could just sample
17:30 you know, you have you have unknowns sample data four spots. So
17:35 can solve them explicitly but there's probably noise in there. So in practice
17:41 we do is we sample sample like times assuming some noise component. And
17:47 we have four unknowns and seven samples it's over determined. So you solve
17:52 by least squares and that's what it . So as this window moves along
17:58 profile, it will sample at seven solved this in some noise and it
18:03 have a solution and how it works practice is that we put limits on
18:12 many solutions, you know how if there's a cluster of solutions. If
18:18 close together in X and Z, there's enough of them within certain
18:24 then it will save that one. it will or it will save it
18:28 something else will save all of But it will like remember that
18:32 Right? So what's what's the thin model? The thin sheet model
18:40 let's start with a So if you a vertical sheet um Dich it will
18:47 an anomaly at a pole position that symmetric about that about that sheet.
18:56 ? Well, if you turn that a side so it's horizontal and it
19:02 produce a total fuel anomaly. Like , right? Where the center of
19:07 here is right in the inflection, is at the pole. Again,
19:12 , the horizontal gradient of that produces symmetric anomaly like this, which is
19:18 it's an edge detector, right? it's finding that edge which is just
19:22 the total field solution of the vertical while a block who produced the same
19:27 anomaly as a horizontal sheet. So water does is it makes a bunch
19:34 passes of the total field profile and bunch of passes under horizontal gradient
19:41 So the total field solutions are a bit deeper. And the gradient
19:46 the edge solutions are a little So it produces a set of two
19:52 of solutions and again, each one it the ones that generates that you
20:01 are based on, you know, criteria that you set up that where
20:08 says in some specific action Z It will it will plot those because
20:16 enough solutions in that range. So hope that makes sense. Let me
20:22 you how it works and then we go back if you want. So
20:27 is an example of a project that did. And what I do is
20:31 one head I used to machines So I have on one hand I
20:36 a map and in this case I'm gravity data. I'm plotting magnetic data
20:42 gravity data. So the little map one here is magnetic data and the
20:50 area is graduated. So I it's I have a high res survey here
20:57 I want to contextualize it in some . And then you see superimposed on
21:03 are some other feet other data and explain this in a second. But
21:09 over here I have my database and shows the total field which is this
21:15 profile and the horizontal gradient and then my depth solutions. Right. Well
21:22 on the other monitor I plot the section. So one of these lines
21:27 here is plotted here and in here imported the generic open file basement surfaces
21:36 line here. And then the top is the magnetic anomaly profile and I've
21:42 my little mag gravity software. This what we'll be using next week.
21:49 checked it to read in your gradient total horizontal gradient as the gravity.
21:56 he says gravity here but it's not horizontal gradient. It was let's just
22:03 at these separately. So here's what got on the left screen the map
22:08 so the procedures I look at cross and the map at the same
22:13 Always back and forth back and forth and forth because I I want to
22:19 at how this how these solutions are in the death panel. But I
22:25 want to think about them in terms what's around them. So on here
22:30 have control this plot. There's some that penetrate basement. So as I
22:35 close to those I need to pay to that. In fact what I
22:39 do is I will start interpreting the in and around where these well penetrations
22:47 and in fact that's how I tune Warner solutions. I because you can
22:52 around with the parameters and I do until I get solutions that are plotting
22:57 that are you know that that cluster hence are plotted in such a way
23:02 they are consistent with these source Then as I work work through this
23:07 it's a tedious and time consuming job kind of worked out from here but
23:15 can also put on this map. kind of interpretation. Someone might have
23:20 might have a plan view interpretation of . Um I think these contours are
23:25 file basement contours which is very smooth here and well I could put refraction
23:31 on here. I could put some line location if I have some reflection
23:36 on here. But yeah so you see this is the magnetic day.
23:41 very beautiful survey and it's more more gravity. Okay now on the other
23:47 here I've got all the my little panel with the this is it says
23:53 but I've actually imported mag corals on gradient and I have the total field
23:58 here and these red solutions are total solutions and the blue ones are horizontal
24:06 and basically you get like a pear typically you're looking for the solution is
24:12 to be like basically between these you and how I would pick this is
24:18 look for where there's nice clusters of so you know whether it's just like
24:25 around kind of like randomly you know want to see him nice and
24:30 So here's a nice high low So I pick it there, I
24:34 it here and I pick it here here and so my basement surface I
24:38 is shaped something like this. And I picked these things I go back
24:46 I make a field in my database new channel and I put that depth
24:52 there and that's how how I do and I think everyone else does it
24:57 . And at the end of the for each one of these lines,
25:00 gonna be a bunch of depths that picked. That I will then spit
25:04 and interpret um maybe make a grid them but then interpret that. So
25:11 . So basically this is the concept this is true for all of these
25:15 these methods. And if you think it, it's the same way the
25:19 methods work that I was telling you . All right. So right.
25:30 it passes several windows of increasing or and it samples it so they can
25:37 know do a least squares and uh and strike and position. And it's
25:50 on this and this is how I shoot any questions on that.
25:58 it makes sense. Okay, Alright. So oiler is is very
26:07 the same except I use a structural instead of a thin sheet source.
26:15 and if what depending on you pick or three, it might represent some
26:24 meaning. Might be a line of , point, pole, line of
26:27 poles or appoint die pole. And is uh I think David Thompson,
26:34 Thompson. David, Thompson. David I think in any case he was
26:39 our co and then um yeah, it's the same idea. You picked
26:45 and this oilers based based on hoarders relationship which is partial differential equation with
26:53 degree of homogeneity. The structural Okay, is the structural index.
27:01 , that's what one of these look . So you can see you start
27:04 get the idea here that that these look kind of crazy. But what's
27:11 here is as as these various windows this thing, you can see they
27:17 to draw and then when it finds lot of them it starts drawing a
27:20 of them, then it disappears as goes away from it. And different
27:26 sizes show you that these are different . That's the whole thing and the
27:31 thing with with with here water. ? So in between here it's still
27:36 it's still solving for deaths but there's it's you know, they're sort
27:42 you know, because the algorithm has , you know, it's not going
27:46 fail, right? So but it's they start to cluster is where you
27:50 having confidence and you can really see in in in in the you
27:54 So here is this anomaly is right in the gradient there and so the
28:01 are right where there's minimum maximum, like you would imagine from some model
28:09 . Okay, so here is a case history. Um this is uh
28:18 of oiler in a study in in Sinai Peninsula um here's a regional geology
28:26 and on the on the right is magnetic anomalies. This is Milligan.
28:32 mean gammas rather nano Tesla. So a legend here, that explains what
28:38 these rock types are and they're all except black. That's pre Columbian
28:44 Everything else, there's sedimentary rocks of ages. And the red ID dash
28:53 is, you know, corresponds to this match Arrow Mag Survey. So
29:00 the next slide, I'm going to you this little cross section here through
29:05 gulf of Suez. So that's a geologic cross section. And then I'm
29:11 show you L. Two L. , right? Which goes through through
29:19 . And then this Mt magneto tularik which goes through right right through these
29:27 um pre Columbian where this pre Columbian rides. Okay, so we'll probably
29:34 to flip back and forth. But just look at L. Two.
29:37 . One. Okay, L 12 goes strikes to the northeast and just
29:43 of its center is the northern end the MT two Mt one which is
29:48 magnitude to look right. So that's on the left, L two.
29:55 1. Remember that goes from southwest northeast and right about here, strike
30:02 north to south this M. Line. So actually um yeah.
30:10 so they've interpreted just some vertical features . They're talking they think these are
30:15 . And then they're suggesting that these structures they could be. But basically
30:22 can see what they're picking in these oiler solutions. And then here's the
30:27 . T. M. T. then In the Gulf of Suez,
30:33 this geologic cross section that shows the of, this is the sort of
30:38 in geometries like they're expecting to And it's sort of guides what
30:42 how they're interpreting these things here. the way. This was a usgs
30:47 section from 1998. So very Not , but this paper is 2015.
30:54 it is evidently there's not a lot , you know, presuming that they
30:59 their research. Okay. So that cross section was here and then the
31:08 goes right through here, right? their basement. And I think there's
31:14 , there's a big compositional change And that's what they're saying that this
31:19 high is right there. So, know, you're going, everything is
31:24 negative and maybe, you know, little bit positive, but then you
31:29 this big anomaly here and that's a fair interpretation composition changes produce big
31:37 And then, um, right, this line doesn't, doesn't cross
31:43 This is this is this goes from to 250 gammas. So, you
31:49 , it's just going right right through part here. Okay. Um,
32:00 questions about that? No, Okay, good. So the last
32:08 one profile based, automated one is naughty, like I said, you
32:12 see this kind of rare in fact days. You might be surprised.
32:19 . You might be surprised if you people that actually know what you're talking
32:22 when you mentioned this, But this developed again in the 70s and here's
32:27 little case history in uh, over Lincoln in south Australia. And,
32:38 this is what his fellow name She. So here's the cross actually
32:43 from A to B from northwest of and here it is along here.
32:49 it's pretty flat actually. You there's some little amplitude anomalies here and
32:54 pretty flat because you got this really anomaly here at the, at the
32:59 end of it. And then here's depth solutions. Now this is
33:03 this is a little service. This only, this is only 50,800 m
33:08 even six km. This is only seven km. So it's a small
33:13 And zooming in on the cross You see it's, it only goes
33:17 0 to 150 m. So they're for shallow sources and here's their little
33:24 sources. Um, Yeah, There's a mining well, 33
33:37 Where's that? Oh, these oh, I'm sorry the wells are
33:43 black. All these lining walls are these black things and the depth solutions
33:48 from these blue X, I Yeah. So they found this one
33:55 and this one is, they didn't find it, but they found these
34:00 right here. Yeah, that's how works. Right. The Blue Xs
34:03 the oilers, I mean the, naughty solutions. Well, um in
34:12 , Alan Reed wrote this, it's a geophysics paper and it's like in
34:18 top five cited papers of all it's a very well read paper by
34:23 of people. Um So they calculate in X, Y. Z.
34:35 they, and it's based on a of square, you know, square
34:42 , square windows that pass over the the magnetic data and they saw before
34:49 , rock property etcetera. Using some that's defined in three D. Um
34:57 really good paper explains this is U to 2014 wasn T. L.
35:06 . And these figures are are from . So these shows kind of kind
35:10 a dyke and then an intrusion here then maybe a cell here that's still
35:16 bit deeper. And then here are examples of using three crustal three structural
35:25 over two different window sizes. So get you get a lot of things
35:30 play with with these these methods. yeah, you can spend a lifetime
35:36 around with it by the end of day, you have to, you
35:39 , make some decisions, but so think the discrete source bodies cannot
35:44 Yeah, so he's saying that using S. I the structural index of
35:51 for one kilometer window. So let's just one window, one kilometer and
35:57 three kilometers, the top half is kilometer windows, the bottom half of
36:02 kilometer windows And structural index goes 2, 3 vertically. So they're
36:09 using one kilometer window a structural index three C they're saying there's just too
36:16 , you just know, you they've they you know, they've allowed
36:22 many solutions to be posted such that all piling up on top of each
36:27 , you can't really see what's going . So one might like maybe maybe
36:34 window of three, you know, a structural index of one looks like
36:43 two are quite similar, so the doesn't really have much of effect on
36:49 , but you can see how you really limit the number of solutions based
36:57 , you know, the window size the structural index and you know,
37:04 me these folks that worry about this , you know, they get in
37:08 big time arguments about this stuff, know, so they talk about the
37:13 of the solutions and things like I have a question, yes,
37:18 does it mean by window? Like is a window? So like I
37:24 um we'll go back to the let's back to that figure. Yeah,
37:34 this is in two D. But in this window is the width of
37:39 , is this direction is this this is a two d window that
37:43 a width of this, you from X one to X, what
37:49 this, that from there to Right. And because of the size
37:54 the window, it's gonna solve all these points. So it will have
38:00 source step that's related to this So this window passing over this little
38:07 is not gonna adequately sample that So it's gonna produce spurious results.
38:15 ? So if a smaller window was then this could be resolved very well
38:21 it would have some solutions real shadow and it would be well defined Because
38:26 would have seven points which would define shape. Does that make sense?
38:32 , so in 3D you just do with a square window with a with
38:36 grid with a grid. So you every point within an X. Wise
38:46 . Let me see here. Um , so you would you would
38:55 you know, you would just pick , you know, it would pass
38:59 small grid over here, you in X and Y are window and
39:03 and y. But it would do same thing. It would try to
39:08 Orders homage in an equation in three for these solutions. So when we
39:14 at these kind of things, what's on here is there are different
39:21 These are colored by source depth, depth and color here. All these
39:25 circles are colored by source depth. greens are shallow reds are deep And
39:33 is the problem I have with three . oiler is that these solutions are
39:39 piling up on top of each How do you how do you decide
39:43 what when the reality is, it looks something like this. So if
39:48 were to take this view in depth plot all these things on top of
39:53 other on plan that it would you know, you'd be hard pressed
39:57 sort of make sense of them. that's what people do. In fact
40:02 grid these things. I mean it's nutty. I I don't think that's
40:06 really good way to examine these But you can see you can see
40:12 far we've come from the days of individual anomalies. Using bob bean's church
40:21 come up with source with thickness ratios things like that in this case they
40:26 just populate the map with a bunch these depth solutions and grid them.
40:33 so I think my my preference is because you're getting this detail but it's
40:41 profile and some of these things you really see what's clustering here in
40:46 It's difficult to see but they're looking this implant. I can tell you
40:52 don't need oiler for me to tell where the gradients are in his
40:58 I could just map with with a right and and you see these are
41:04 great, well that's I mean it's these sources ingredients which makes sense right
41:13 or or in this case of vertical , they're going to produce these
41:19 So you can start to visualize what is really doing. Its picking source
41:24 . Same thing with this one. picking source steps in this case,
41:31 the gradient in this case it's picking here. It's you know, does
41:40 answer your question or does it make worse? No, no makes
41:45 And then you see here they plotted solutions in three D. So they're
41:52 gonna exactly made a point that they're going to exactly trace the complete edge
41:57 the sources. But they're going to you an idea where things are.
42:04 . So in Allen's paper this his 1990 paper, their little case history
42:10 was in England. Alan's, Alan's he's from the coast, I think
42:15 from the coast down here somewhere. uh I visited him once, my
42:21 and I did in any case. then this study area is shown on
42:27 right and they're showing um they have ground gravity stations. They have some
42:33 death estimates. These X are all places here um There are some
42:40 all these open circles and then there's Bgs british Geological survey um seismic line
42:48 and show you what the dashed area . I don't think I have notes
42:54 this either. This is slide Okay, okay, so here's the
43:00 the uh geologic map. So uh Permian sub crop. And so they're
43:09 here this lower devonian Mississippi, middle upper Devonian. And there's I guess
43:16 a Westphalian section that they call And then here's their depth in kilometers
43:23 the pre Permian basement. So this one goes to 1 to 10 down
43:29 15 kilometers here. But it's pretty the order of zero, I guess
43:34 outcropping here and then it's uh pretty through here. So here again are
43:44 death solutions. And see one km steps are the small open circle two
43:50 four. So the bigger the the deeper the source. And
43:55 you see they're all just piled up top of each other. In
43:59 this is using a structural index of , which is a theoretical contact versus
44:05 index of a half, which is a cell or a contact is supposed
44:13 supposedly defines major faults. But I the idea is that the small circles
44:22 from the shallow part of the the fault and the big circles are
44:26 the deeper part, I guess. you can see where this would be
44:30 or challenging to interpret um, on own. But there's certainly get the
44:36 . You certainly get the idea that something going on here that is not
44:40 displayed in there, man. and, and then here's another structural
44:48 of one. So this is a Sylar day. So, and this
44:53 their their structural interpretation when they you know, they're following these things
44:58 you're saying these are, you some boundary faults and they're cashing some
45:04 to hear that they think might be . Okay, what they didn't do
45:12 , which is something that you death to source sort of, I
45:17 whenever I make a depth to source , I make a map of the
45:21 , I make a contour map of I think the basement depth is and
45:26 what most people want you to Okay. Right. So as I
45:35 earlier in the vision was the first that really worked on any of this
45:38 in the vision and he did the d stuff in 72 and 74.
45:43 then he followed up with three D 84. So, you know ahead
45:48 this stuff. So there's a there's term that's that's tossed around called extended
45:55 and it actually could mean one of things um I can't say this guy's
46:01 , but they presented an extended algorithm magnetic data with the structural index of
46:11 . So I said the different susceptibility can be calculated in addition to source
46:18 . Now implied in their work is addition of a second oiler equation of
46:23 structural index. So right, so a lot of work has been done
46:30 not only estimate source steps, but figure out what the correct index is
46:37 of making it up the folks that this stuff now can they can actually
46:44 for the structure for the most optimal index. Mhm Helbert Transform. So
46:52 is the vision. This stuff goes to the 80s and 70s again But
46:58 wanted to unify oiler and Warner and they did that in 2001 paper.
47:07 and so it's an extension, it's three D. And and three
47:11 Extension of one Warner. So the is they want to combine, they
47:19 to make a three D Warner combined three D. Oiler and unify the
47:24 into one algorithm. And I think was a pretty big deal at the
47:29 . This paper just does this by way, you will hear people all
47:36 time talking about these methods as a convolution. Now, I'm not crazy
47:41 that, that moniker because well I I'm a little cynical but I think
47:53 use it because they just want to it sound seismic e you know,
47:58 but but in in reflection data you that the way for the way front
48:11 convey loved with the earth response. ? So you have some pulse of
48:18 and then that travels through the earth interacts with the earth and what you
48:23 is that pulse plus the earth And the idea is that that you
48:31 , if you know what the paul's is and there's like, you know
48:37 of literature where people examine, you , examine wave, let's, you
48:44 , sample close to the source, know, whether it's dynamite or vibrate
48:49 or whatever. And then they try best model what that source way that
48:56 . So that they can then involved the measured data, the time series
49:04 that you, you know, you out of the, of the
49:09 And the idea is when you do , you're you deacon involve, you
49:13 , you remove that pulse signature and left over is the earth response.
49:20 , I'm probably telling you stuff you already. Um, but the point
49:26 that reflection method is dynamic. You a source and receiver with potential
49:33 It's not dynamics. It's completely passive of the earth's field. I mean
49:40 idea that these solutions are somehow involved the the magnetic data that you're measuring
49:47 just, you know, but I that you can talk yourself into that
49:54 . But to me physically it just kind of kind of, you
49:59 kind of silly. So being a cynical, I think that they just
50:06 this this, you know, this place, you're calling the methods de
50:13 . So so that you know, sounds kind of seismic anyways, so
50:19 might run across that. But I interrupt people say, hey, it's
50:23 the convolution but I don't think it . Okay, so um yeah,
50:32 three D. Warner, this is , this is, I'm sorry,
50:35 2005 paper this is the paper on , three d Warner and he used
50:41 Tetra hedo source and then here's just computer locations from his from his model
50:48 on some actual data. So he really you know exceptionally good results.
50:54 Rick Richard died just a few years maybe like 10 years ago. He
50:59 a pretty nice guy. Really really really smart guy. Okay so now
51:08 are grid methods. Um We uh looked at tilt driven before and I
51:16 started this the other day and I look at this should be this because
51:21 c uh DF dX is right So it's not like redefining the
51:28 This should be D E F G . That should be an H.
51:31 there. Okay that's the fBh and where that comes from. But basically
51:37 you said you know that it's the tilt angle is the inverse tangent of
51:43 ratio of vertical to horizontal gradients. so it's defined by plus or minus
51:51 over two. And then solving for you have to use this triggered a
51:56 identity. Punch it into this Uh D. C. To
52:04 H. And z the source that out of it. And the paper
52:11 miller and saying this is geophysics paper we looked at these before I just
52:18 them back in here because it's uh pertinent here but so the estimates and
52:25 indices are calculated driven over. This Namibia and I think this cross section
52:32 shown in some places, but so the reducer pull, here's the tilt
52:36 so that's in radiance and then here the horizontal gradient of the tilt
52:42 So that's just You know, the of these things and then here's the
52:47 gradient of the 12th angle. Again up these things and here are the
52:52 steps. So they're going from 0-3 and again you see the different colors
52:58 they will just pile on top of other. I mean I would not
53:02 at this cross section. Maybe this in this cross section there. It
53:06 of course and you can see how solutions find the tops and that's always
53:12 it works. The source steps are around the tops of solutions but didn't
53:18 this deep one here, so it work that great. Um but
53:24 the source steps are typically around the of the solutions. Oh, these
53:32 calculated structural yeah, this is one the cases where they calculate the structural
53:37 . So here they're ranging from, know, from 0 to 1
53:44 So look at that, this is this is a model and you
53:50 I mean I think models should be . Is it a model?
53:54 it's the data, I'm sorry, is oh I see this is the
53:59 they made a little model here to see what they can do and and
54:04 uh yeah I mean I don't know don't think he's a really great result
54:11 yeah. Yeah. Anyways. Uh . I think it's just a few
54:20 slides in this depth to source estimate . Do you have any questions about
54:25 material? Not yet killing me. No it's okay. Um You know
54:38 I I've been I go through these and probably just blasting. I mean
54:48 I prepare and then I'm like but just like ramming through so yeah Okay
54:56 so why don't we why don't we a break for about 15? Is
55:00 okay? Okay. Alright okay. right so let's finish up the depth
55:15 source estimation. Well remember I said they all work on wavelength. So
55:23 means you can convert these things into spectrum and then estimate source depths by
55:35 you know by their spectrum by their spectrum. And Probably the landmark
55:44 The important reference to that is paper specter and grant 1970. And just
55:54 show you how how the power spectrum with source blocks. Source black
56:00 So if you start with a three . Block here you can look at
56:05 . And of course you can just off the top make a thin plate
56:10 from that you can get to a or die poles or just a point
56:18 ? Can reduce can reduce it this and then reduce that way and get
56:21 a point. You can also extend bottom of this prison. And then
56:28 the same same argument. You can you reduce it this way then you
56:34 have a vertical ribbon that's infinite. reducing it again this way you can
56:41 a you know a vertical rod. if you take this idea to the
56:49 spectrum in terms of the thickness. if you have an infinite thick block
56:56 will produce uh power spectrum like this the same or the top is at
57:04 same depth. If you limit that , well then you'll what happens is
57:08 lose the longer wavelengths right? Because you can think of you know there's
57:14 source coming from very deep. It's all shallow shallower. And then if
57:19 really make it a fence sheet it take away even more erode even more
57:26 wavelengths or low frequencies. But the specter and Grant make is that there's
57:34 a vertical line here. This slope tells you how deep the sources.
57:44 they did a little study here. is in this place called Petrie
57:50 And this is their own magnetic anomalies looking at. And then all these
57:54 , these are their flight path And is contoured at 20 Nana Tesla.
58:03 just looks like to be pretty good to me. I mean there's some
58:06 interesting gradients in here and then here's mean C. C. Okay.
58:16 then here is a power spectrum through . I mean of that data.
58:22 think it's that whole map. So this is this is the long
58:30 , so this is the regional And then you have some near surface
58:37 and you can draw a best fit through this. You can see there
58:41 definitely two different components um of source in here. And this is what
58:49 do. They just they plot power and then they try to you know
58:55 in. So you know it's the versus wave number and they try to
59:02 in some slopes that they then infer related to the source. Here's a
59:10 that was done in uh Saudi. They have data here in the red
59:17 as well as I'm land here. interesting things about this data. I
59:24 you can definitely see, you can see the train boundaries that they're
59:28 Or many of them. Um Maybe all of them. But you can
59:32 see some train boundaries in this data of the big amplitude changes. But
59:39 regardless wavelength, I mean there's a of chatter, a lot of short
59:44 up in here. This is all shallow basement. But then it gets
59:49 wavelengths up in here. Right? starting to get starting to get deeper
59:53 wavelengths here. So this is kind like you know shield area. Then
59:58 at the red sea. Look at . Look at these um linear
60:07 Well, these are sea floor spreading . Do you know what? Sea
60:09 spreading anomalies are? Stephanie? Uh , I don't think I do.
60:17 you ever heard of a magnetic polarity ? So as sea floor is being
60:25 at a spreading center as as new sphere, an oceanic crust is being
60:32 at sea floor spreading centers. Those are cooling to the curie point depth
60:39 the curie point temperature, which is 5 80. And when they cool
60:47 acquire the magnetic the uh the field of the present day magnetic field.
60:55 when the field reverses, then the batch of rocks that are creating the
61:02 floor will will cat will be, know, they will be magnetized according
61:08 the reversed field. So if you at the ocean basins magnetic data,
61:16 are about spreading centers. It's alternating and lows and those are called sea
61:21 spreading anomalies because those are there, are all about the same magnetization except
61:30 just reversed, alternating being reversed. that make sense? Yeah, that
61:36 actually really interesting. We're gonna look some of that. I mean that
61:43 revelation actually is one of the really like nails in the coffin of jesus
61:51 ism and acceptance of plate tectonic theory was only, you know in the
62:00 . So tectonics is a really young idea. Okay, so right,
62:06 these are sea floor spreading anomalies in the over the red sea here,
62:12 the way, I always say, talking about potential field that I typically
62:16 always say over. And I'm because data exists where you measure it and
62:24 always measuring it over land or over basin or you know, over
62:29 You're not measuring it in something unless like borehole gravity. So that's why
62:35 always say over because the data exists you measure it. Okay, so
62:44 on the, on the upper left their power spectrum analysis. Um,
62:50 I guess they had a power spectrum line and a scale power spectrum here
62:55 this red line. And in both , they're predicting some long wavelength
63:03 which which the I guess they filter data to that. Let me
63:07 Does that look like that? Maybe must be a polygon filter Carry deaths
63:13 estimated using 26 overlapping windows. So that's that's another key element of this
63:19 I haven't really spoken of. But really critical factor in doing these estimates
63:28 the size of the window. if I have a size of the
63:32 , that's this entire area is going come up with a single depth
63:37 You're only gonna be able to you might come up with two different
63:40 or whatever, but that's gonna be the whole whole area. But when
63:43 look at this, I think you know, I would use different
63:49 based on these wavelengths because you the character of the data is
63:56 So right, so they used km windows. Let's see. This
64:02 this is 400. So about that . So that is only gonna pull
64:08 what you see here. Yeah. that's up to 50 km to be
64:17 . Yeah. 25. That's about . Um the query isil term is
64:23 to be 10-20 km increasing. Ah they're trying to count. Oh I
64:31 . So what their what their map here is of the kiwi point
64:36 That's why they picked such long a big window because they're only interested
64:41 this longest wavelength. And they think that that's produced by the Kerry point
64:49 . So the key point is 550 580 Degrees. Did we talk about
64:57 before? I I think we go . Yeah, go ahead please.
65:07 , okay, the curie point is temperature at which rocks either gain or
65:12 magnetism depending if you're heating them or rocks are getting hotter or colder.
65:20 like when the magma cools when it the curie point temperature it will acquire
65:28 magnetic field that's you know uh controlled the present day inducing field orientation,
65:38 know, inclination declination. Um And is what think of it this way
65:52 you can map this thermal, this point uh temperature in depth. You
66:00 map that in depth. You could the, you know, this this
66:06 horizon. Well, the idea that have had for a long time is
66:11 the very longest magnetic anomaly wavelengths that measure are produced by morphology on this
66:19 . That's the idea that the Kerry depth, that temperature temperature horizon is
66:29 a horizon in depth. That can met from magnetic data. Because if
66:34 rocks above it are magnetic and the below it are not magnetic, then
66:39 is a surface there that has some , some, you know,
66:45 that's related to the that temperature. the idea. So what they've mapped
66:51 is it's shallow beneath the Red Right? And it's shallow here beneath
67:01 Red Sea, but it gets deeper the shield. Which intuitively makes
67:07 So yeah, that's what they've done . Let me just go up to
67:11 . Right. So they're only showing this part here. See this outline
67:17 . Is this outline right here. , the Red Sea is just right
67:24 here and that's what they did. fact they posted all their little points
67:31 for the source depth. So that's they're trying to map here. And
67:37 reason people do this is because they to do, You know, thermal
67:42 . And we'll talk about this in very final lecture. But but they
67:47 to do thermal basin modeling calculation. that's how they why they do this
67:51 . This is very prescient work. this is the 2016 paper but people
67:57 are doing this stuff a lot these . Okay so death estimation summary.
68:07 You know there's a broadly three groups hand calculation, no graphical method,
68:14 two D. And three D. calculations and there's two D. And
68:18 D. Frequency calculations, wavelength calculations the two D. The graphic ones
68:24 two D slope slope. And then course you can check out bob Bean's
68:33 . I met him once um a time ago but you can check out
68:38 Bean's papers his paper for you know by the pound. There's lots of
68:46 and graphs in there but all that can be animated now. And is
68:51 really good paper for a really excellent of all the different graphical techniques because
68:57 more than I said. There's so . There's yeah there's peters of course
69:03 the original one but there's slow path . Okay there's there's a lot of
69:09 then um really with computers and the know um the advent of these these
69:18 D. Methods that estimate source depth I said they're called convolutions but they're
69:23 , see I even said that here they you know they solved systems of
69:31 determined linear equations by passing a bunch different windows over your profiles. The
69:37 in practice. What we do is we we test different parameters play around
69:45 where we have control, where we like a basement or refraction station that
69:49 us what the horizon depths are and we and then we um you know
69:56 sort of tune tune the tune the so that they that the solutions that
70:04 clusters and producers are consistent with those depths and you can do that with
70:12 of them. I mean that's a thing to do with any of.
70:14 then of course there's frequency ones, know analytic signal, tilt,
70:18 power spectrum and those are all involved window. And it's important that you
70:23 the right window. So you would you would make not only would you
70:27 around the parameters in terms of clustering that you would also play around with
70:33 sides and see what it generates. might be some sweet spot where you
70:39 , certain window is really producing a of interesting results. And Kerry Kerry
70:47 5 80 is for magnetite but it be less. It typically can range
70:55 about 5 50 to 5 80. you know a little bit maybe a
71:06 . Okay, so that's that's that we can talk about forward and inverse
71:15 . We'll start with forward bonding but first I need to make this point
71:25 and that that is that there's no model or a geological model for this
71:33 can approach the true complexity of the . And so the question is what
71:39 why do we make these models? the point is to learn something.
71:44 . So when you're modeling when you your modeling what you you can always
71:51 into kind of like a a feedback where you just keep playing with
71:55 playing with it, play with But at some point you're not learning
71:58 ? When you first start making a you're learning a lot. There's a
72:03 of the learning curve is steep but some point you're you know you're not
72:11 improving on your knowledge. You just know you're just making things fit better
72:16 it doesn't really it doesn't really tell anything more. Right? So the
72:20 is to learn something. The point to make a mile that fits the
72:24 because You know it might fit the but it still might be it's still
72:29 wrong. So or it's probably not know an actual true 100 representation of
72:38 earth can't be it's impossible. And couple of important points. You should
72:43 model with residual data or filtered or . T. P. And the
72:49 is is that is that when you something from the measured data you you
72:58 know what the geological component that's that produce that signature you're removing in,
73:06 ? So you can so you can't you model residual data that means you
73:11 something and that means you you think know what the geology was that produce
73:17 component that you removed. You don't that. So you should never model
73:21 residual data or filtered or R. . P. Okay. Um And
73:32 the general method for modeling for ford is the approach is that you have
73:38 data. Then you build a model you you calculate the response from that
73:46 . You compare with the measured the observed data and then where they
73:52 match you change something right? You be the geometry or the density or
73:59 magnetic susceptibility. So it's kind of . If you go back you're going
74:03 and around. The general idea for modeling is is that you have a
74:13 have data, you have a model you tell and you tell the program
74:19 modify one aspect of your model based the data. So the data drives
74:26 thing it drives to change. You like adjust things yourself. The
74:30 The data does that. Okay. but but the problem is you can
74:38 have it, you only modify one of the model at a time.
74:44 one horizon or one layer. And um that can work great.
74:53 my experience is that inverse models work well when you're close to the
75:03 But if you far off the the results are never good. So
75:09 not really a fan of universe I do it a lot, I
75:12 it a lot, especially if I'm tuning something. Um but I like
75:18 fiddle with more than one thing at same time. But um so forward
75:24 is when you adjust the model and compare it's it's uh its response to
75:34 measure to the observed data. And inverse model is where you calculate is
75:40 the model model parameters are modified by data directly. Okay, so um
75:52 you say that last part? One time in verses what and versus what
75:58 model is changed? Uh is the is modified not by you but by
76:06 the program based on the data. the data controls the inversion. What
76:13 in the model. Now? You might select what is gonna what's gonna
76:18 , you might select horizon or a . But when you launch an inversion
76:25 does an intuitively squares modification of that or that horizon until it it does
76:34 best to fit the observed data. matching the it's matching the model response
76:40 the fit data internally. You're not that, does that make sense?
76:47 . Perfect. Yeah. So forward , I'll say it again. Just
76:52 so forward modeling is what you have model, you have observed data and
76:58 have a model with a calculated response you change the model yourself to try
77:05 make the curve, The two curves the two fields fit you observed and
77:11 . I mean the the observed versus calculator in the inverse model. You
77:19 you start with a model as well it's modified by the algorithm by the
77:25 . It tries to it adjust some of that model based on the misfit
77:32 the two the measured and calculated It's making those changes. You're not
77:38 them but it's only doing it selectively . You tell it what to modify
77:42 it's doing that. It's doing the modification. Is that clear? Yes
77:51 . Yeah. Yeah. One is I'd like to think of ford is
77:58 up to the data and versus data to the model that I like to
78:02 of it that way. So this sort of like your generic modeling case
78:10 anything. Um So if you two . And three D. But if
78:15 have a three D. Source down of arbitrary shape then there's some vertical
78:22 of gravity. D. Z. . D. G. Rather at
78:28 point up here. Right. And changing gravity is given by and this
78:35 this is not scary. It's just bio integral of some function of density
78:42 the distance between the 2? Over difference between Z parameter uh uh over
78:54 distance cube And okay so r is distance it's the root of the sound
79:01 the square. So this is our then um this is e this is
79:08 . Prime. Okay so this is for vertical line of gravity. So
79:16 is the density function as a function density. And and then this uh
79:23 I guess is universal gravitational concept which outside of here. So that's and
79:30 I was telling you this is you this is like this is like geophysics
79:37 that can be kind of like pulled and put into any geophysical application.
79:42 doing right? You have integral of function uh you know based on you
79:52 some distance between your measurement and the . Does that make sense? Does
79:59 look look familiar to you? Oh yes yeah. Okay, so
80:07 is this is all geophysical problems are . I think they all start with
80:11 like this. So, okay, two D. The term two dimensional
80:16 a body whose third dimension is infinite ? In and out of the plane
80:21 body has infinite length along the The horizontal axis perpendicular to the profile
80:27 is infinite. Right? The body is entirely defined by the shape of
80:32 cross section. So, So the magnetic response is much simpler to calculate
80:39 three d. obviously kind of simple see um um There is some debate
80:47 to what makes something two dimensional in words, is an anomaly two dimensional
80:55 a circular anomaly right? Is not dimensional, right? So as anomalies
81:03 more and more problem, they become two dimensional. So technically you wouldn't
81:09 to make a 2D cross sectional model a circular anomaly because an anomaly isn't
81:16 produced by a two dimensional source. the idea. So And then what
81:24 what this point is making that some say what what makes it two dimensional
81:30 2-1 3-1? Yeah, 20-1, know, I mean, I don't
81:36 , but frankly, I don't think even worries about it. They just
81:41 make two D. Models and you , there you go off with the
81:47 . But now the software we're gonna using a waste of montage has lim
81:54 you can make end corrections what they end corrections. In other words,
81:58 gonna limit The strike in and out the plane. You can say the
82:03 only goes 10 km or two km whatever you want. And and in
82:09 with the software reason you can what they call two and three quarter
82:15 next will be like two and 5/8 guess. But anyways, what they
82:20 two and three quarter, you couldn't have a source where were you?
82:25 end correction isn't symmetric and in fact can even have the source offline,
82:31 could put a block that's offline and can model its effect which is really
82:37 because say you have a salt Well, you can model a salt
82:44 even though you're not going a salt have a big anomaly over right and
82:48 might not be you might not have line that goes through the salt
82:51 but just just by its flag. you're feeling the effect of it because
82:55 the wavelength. You can actually build model with that salt dome offline and
83:01 can calculate the effect of that on two D model using the software.
83:05 that's pretty darn handy. I've used many times. So yeah, that's
83:11 good good one to know. so nearly all to de mining programs
83:16 based on the Taiwan mathematic Taiwan and still around. I saw him at
83:21 image conference, I think he's got be 90 years old. Um very
83:27 man. He developed this method and published it in 1959. If he
83:33 kept that to himself, you he'd be probably more more wealthy than
83:39 is now. He's pretty wealthy. lives in there, he lives in
83:42 condo right there in the in the the near the M. F.
83:49 . Herman Park area. You I mean it's pretty upscale in any
83:55 . Um basically what it does, assumes a polygon shape and it and
84:02 solves for contributions from inside polygons. it's like a solid angle between you
84:11 , R. N. And N plus one. This solid angle
84:15 so it approximates these sort of You know by some sort of
84:23 That's the idea and you can have lot of angles. I mean it
84:28 pretty fast. So the and in inverse two D. It's the same
84:35 of thing. Except for example if say you want to invert this
84:41 you know, Then what this two . Inversion would do would it would
84:47 move this point from here to here on the response over it. Or
84:53 could change the density of this that sort of idea. Okay so
85:06 to the red sea here this is is gravity data um on the left
85:15 again on the right. So here's sea floor spreading anomalies. And here's
85:20 that outcropping basement all that chatter from . And then in the gravity data
85:26 the red sea, you see that this big high through here. What
85:30 you think this big? Not only it's Stephanie. Um Could it be
85:40 some spreading? That's the spreading right? That's the mid mid ocean
85:48 . And yeah it's it's yeah and also there's a lot of salt in
85:56 basin. So um you may be some effect of that and these little
86:02 of stuff in here. So spreading anomalies. Yeah. In fact
86:10 can maybe see some fracture zones in . Okay, so here's their
86:17 Where did they say where this model . I think it's one of these
86:19 lines here. Um No, it's red line here. Is this red
86:25 here. So when it goes to spreading center goes from the coast to
86:29 spreading center uh to that, So this is bag on top and
86:40 is gravity on the bottom. So where the spreading center is. This
86:46 weird. This is a weird Is that right? This looks this
86:57 look right west southwest, northeast, coast here. It was past the
87:05 center. This looks like this looks with the spreading center is of
87:12 so 2.75. Yeah. So I all kinds of problems with this,
87:23 let's just let's just break it Okay, so the the upper panel
87:28 magnetic data. The red line is watch. This I pass observed.
87:41 , The red line is calculated and yellow is observed data. So the
87:48 data is yellow and the red line calculated and the same for gravity.
87:55 um it looks like they're modeling um think it's modeling. Well, this
88:05 like free air date to me. It's got to be free air
88:12 So the water dance is gonna be , that's blue. And have a
88:17 sheet here. A thin layer of density looks like Two point doesn't say
88:24 . Then it has 2.4 density in green. And then the salt.
88:30 density is two 2.29. It looks I have to get my 2.22,
88:41 fair enough. I mean I I a little higher but that's fine.
88:46 it's interesting that these anomalies salt wait a second. Oh, they
88:52 different densities for just 2.4 up 2.37 here. And I guess you
89:00 to have it. So it's just . I'm looking for a big low
89:05 produced by these the salt and They're . Um so the density contrast isn't
89:14 great? So that's why he's going 2.4 to 2.2 to 2.22, I
89:22 it's different everywhere, isn't it? . And then the salt sits on
89:29 layer here, which is not which only slightly more dense than the other
89:37 sentiment layer. And they've got some depths here as well. Look at
89:46 , they've got some oil depth So you start to get a sense
89:51 how that's a really good solution right . That's pretty good. Okay,
89:59 then they have the crystal and Right? So the more holes at
90:01 bottom 3.35, really in high density then they have what they're calling lower
90:10 here, 2.74 and 2.74 2.7 - . 2.8 - two points a really
90:24 density here. So, okay, this is a spreading center, this
90:41 should be coming up here, Or maybe a lower density mantle?
90:47 mean, you know, maybe Or something like that. But um
90:53 definitely makes you think like this ridge like got some kind of So they
90:59 so have these high densities in But that's because they're trying to represent
91:07 I think natural material in here, won 45 was I have notes on
91:17 . Yeah, let's see what they . They say that the red CJ
91:20 marine land mag data down continued Mag , oh, I see a 24
91:28 refined using enhanced grabbed magnetic edges for susceptibility bodies. Three D gravity inversion
91:36 the Egyptian margin basement lows interpreted as correspond with thin crust, Short distances
91:45 approximately 30 km proximal to the coast . Reviews high density magmatic magmatic bodies
91:52 along the margin. That's what they're about right here. Um Some to
92:06 amount is high past. See the filtered data filter, R.
92:10 P. It's a bug a Um Okay, here's my comment.
92:15 model is flawed. The basic geometry assumed and then the right,
92:20 this is something people do it, is kind of like nails on the
92:25 for me, what they did was said this is the geometry they want
92:31 the crust and basin. And then just started sticking in densities until they
92:35 it fit. Well, you're not learning anything there, are you?
92:40 telling what you think you already So you know, oh now they
92:49 a point here. They okay. I say the models flood the basin
92:54 assumed in the rock properties were added high. And then I say
92:58 the first sentence of the abstract, is very correct rift and rift ID
93:03 margins are often associated with thick evaporates which challenge seismic reflection imaging.
93:10 so that's the point of this is is to help the seismic imaging.
93:17 they started with a model which was by the seismic image. That's I
93:22 and this was published in I don't what journalist was published in. But
93:29 uh that's criminal. That's just criminal a life. Uh Let me look
93:38 up. What is this what this ? Um Right. Lecture four.
93:52 gonna go to the bed. This published in Oh, interpretation. You
94:03 , interpretation journal. No. So general. It's a very new
94:11 So this is for example, this published in 21 And it was Volume
94:16 . Right? So it's only been for 11 years. And new journals
94:24 often have uh new new journals, know, they have they start
94:33 So quite often they don't really you know, the best stuff they
94:39 get first choice is right? Everyone's go to the established journals first.
94:45 yeah, says my system is I'm gonna turn my video off.
94:53 but right. So um they I mean they they say that they
95:01 to make this model to help the interpretation. But what they've done is
95:06 just mapping these geometries and then they slice everything up and they put it
95:11 a bunch of densities to make the fit to make these things fit.
95:15 I think that that's just that's not not learning anything when you do
95:19 are you? I mean if you it, if all you're doing is
95:22 want to go and run and tell excitement guys that their interpretation is
95:26 then you can do this. But mean, I don't think it really
95:29 anyone, you know? So I have lots of problems with this
95:33 . I think it's incorrect. so that makes sense to my criticism
95:37 sense. It does. I think used a program similar to that when
95:44 took reservoir. I took something with Wiley. It was think something
95:51 I don't remember. But we used model like that where we just like
95:54 with the densities to make things Oh so you you assume that you're
96:01 mean if you geometries are welcome then that's that's all you can
96:05 Don't get me wrong. I mean if, you know your geometries,
96:11 know, if it's like if you're if you're exploring in a little spot
96:15 around the salt dome and it's been by, you know, whatever 333
96:24 of three D surveys and you have these, you know, volumes of
96:33 and stuff. You ain't changing Then you're just looking at what's going
96:39 typically with the base of the salt you know, you might be inverting
96:44 only densities then because the japanese are defined. But in this case what
96:50 kills me is the very first sentence the abstract says, hey, you
96:56 , the solves the problem, we're to try to fix that. And
96:58 do they do? They just do ? I mean, I mean,
97:03 , you know, give me a . It's horrible. It's just really
97:07 science. So, yeah. All right. So, um
97:15 I think I have another one. think I have another one. So
97:24 is, yeah, this is um me ridge, which is this feature
97:32 in the Arabian sea. So India up to the north northeast.
97:38 And um, you know, Somali to the southwest and let me see
97:48 the region north of the lax me between Laxmi and in the gulf
97:55 So the golf basically this right it's composed of volcanic basaltic flows and
98:05 related to the deckhand traps. You of the deckhand traps. Right?
98:10 think so, yeah. So deckhand are flooded with salts that erupted.
98:17 uh in India and they lasted for long time. Flood assaults are often
98:28 traps. No, I should know that means, but I don't right
98:32 , I'll look it up. so they're suggesting that that uh they
98:42 this basin existed before the decade uh igneous province erupted. Uh and and
98:54 said in the region between Laxmi and bases between Laxmi ridge, which is
99:00 feature here in the bouquet gravity. this way, it's just it's a
99:05 of seamounts. Okay, and The Model three. The Model three Different
99:18 . Okay, this is profile three the dash line that's solid line.
99:24 this line right here. Is that ? This line, this black line
99:31 . So they wanted to model the ridge and this is magnetic data below
99:37 email too. And the satellite gravity here. So, and this is
99:45 the topography. So you had the high continental shell and then um water
99:52 getting deeper. So what's interesting to when I look at the gravity,
100:00 look at this broad high here and I see this low and this tells
100:08 that this is this is a line seamounts that these seamounts are rooted into
100:15 mantle because they're producing a low, the high density mantle material is being
100:21 by this low density gah bro, basaltic ridge and the high around it
100:32 sort of halo around it. That's chur, right. In other words
100:38 pushing down into the the crust is down into the mantle. But then
100:44 it's like it's also flexing you know of like around this feature. So
100:50 like going up and then down and . Does that make sense?
100:57 And then down here in the magnetic you can see that the feature does
101:02 a magnetic signature and an outboard. are some anomalies that look a lot
101:06 sea floor spreading anomalies. But then pair maybe they do as well.
101:13 know maybe this gulf basin sits on on oceanic floor because I mean you
101:19 have some of these features. These type features. Okay so let's see
101:26 happening. So here's our model. is their model profile three. The
101:33 data the dots are observed or The thin black line is calculated from
101:39 model. And the red line is difference. The program caused an
101:45 It's not an error. It's just difference because you don't know which is
101:51 measure this data and it might be or changed. Okay. Um And
101:57 bottom panel the middle panel is gravity . Data is dots again calculates a
102:03 black line and their differences. The line. So they've got a really
102:08 reasonable fit here I think. And look and see what they model.
102:13 they're saying they have lower crust Lower crust. Upper you see his
102:20 crust now in the industry, people say crust to mean crystal and
102:29 But just note that if you look a geology handbook dictionary, rather it
102:35 tell you everything about the mo hall crust that would mean the crystalline
102:42 sedimentary rock layers and even the sea . It's all mass above the
102:50 So which is why you'll always hear say crystal and crust when I'm talking
102:56 these things. But just so you , you'll often see upper lower crust
103:01 they're just talking about the crystalline So they have low densities um in
103:08 . Uh 2.4, And then um . Okay, so here's how it
103:18 . Oceanic crust, layer two is same as continental upper crust. Whether
103:25 to a or to be layer three lower crust for oceanic crust. So
103:32 they're saying here is that you have crust from here to the north to
103:42 north northeast and then lower. I , oceanic crust to the southwest.
103:52 magmatic under plating is a phenomenon where if you have a seamount,
103:57 It's being produced by some mantle mantle plume is right, Yes.
104:05 , So there's some deep magma sores erupting and making its way to the
104:13 and as it, when it approaches bottom, the base of the
104:18 it will sometimes spread out and accrete the bottom of the crust and this
104:25 called magmatic underplayed folks that worry about . They arm wrestle over whether it's
104:32 adding to it or it's replacing lower and there's no way to know now
104:39 planning is one of those things, of those reasons that cited, um
104:49 too much because it's just so Oh, magnetic underplayed because there's no
104:53 to really prove it. I mean they're looking at the velocities and that's
104:57 good sign. I mean, they have some some data that supports that
105:03 . They have velocities here. So Mojo is defined by 8.0, that's
105:10 definition in Bob Sheriff's Dictionary. Lower Is here 7.15 upper crust 6.3,
105:21 fairly typical. Um Oceanic 6.9 - . That's pretty high for layer
105:30 In fact 5.2 - 5.4 is a good layer two velocity. So,
105:42 I looked at sea mounts all over world. Um As part part of
105:49 dissertation work, I looked at all them, the velocity structure and c
105:55 are just basically thick ocean floor and really makes sense when you consider the
106:02 . Right? So they're just basically versions of oceanic crust, that's all
106:09 are. So this is kind of upper crust. Lower crust, it's
106:14 continental, but you know why they to make it continental, they want
106:19 make it continental because they want this be have radio genic heat flow so
106:25 it can be producing, you oil and gas. But yeah,
106:32 not how it works. In any . Look at the profile, the
106:36 profile dips down like this. This this is it's rooted sees three point
106:41 53 point oh five or 30 This is in kilograms for cubic meter
106:51 c c grams per CC three point five and 3.3. So, the
106:57 is really enormous here. And that's producing this big gravity low.
107:02 that's only 30 mg. It's not big, but yeah. And then
107:09 what's producing these magnetic anomalies? These are huge. Look at that.
107:14 700 gamma 700 nano tests. But that's being produced by my thinking is
107:22 sea floor spreading anomalies. But I'll you what looks really fishy here.
107:29 I mean if you were to split profile right here and flip this side
107:35 on this side. There's a lot symmetry in this in this data,
107:41 is interesting. Yeah. It's very . I think there's another profile
107:56 No, there's not. Okay. . Oh, I see. I'm
108:06 . I'll go back. They do their uh, it says here.
108:15 , there's okay, they have a . They have no bs.
108:17 That's good. Um It says all normal and reverse layers are black and
108:24 , volcanic. So black, black normal, gray is reversed,
108:32 Because it's kind of a low in . Right, okay. All
108:47 see here. Um So here's here's on that Laxmi Rich, isn't
108:54 Is that right? Yeah. So the Laxmi region here. Oh,
108:58 see. Okay. So, so I went ahead and and zoomed out
109:05 this area just to show you this the ship track coverage here. And
109:10 are geomagnetic crimes um identified. see they're saying it's going completely straight
109:19 25. 34. So this is is 80 million years ago And 25
109:27 I think 54 million years ago. you're going from 5054 to 80 over
109:34 range and 31 I guess will be and a half of that. So
109:40 are spreading anomalies. So this is this is probably 30-31. It says
109:49 . Yeah. And and then where this? How far up does it
109:57 ? Profile Okay, this is profile . It goes right there. I
110:03 put it on the stupid map. three goes see where's the topography
110:09 Right here it is. Profile Goes right through here I think or
110:15 here did I put that on this ? No, I didn't put it
110:19 on there. Okay, in any . So this is how it
110:26 To see the spreading ridge. The center is right here. Carlsberg ridge
110:33 right through here. This is five five and if it's not on this
110:38 but you go off the map it be 6 13 and 18 21
110:42 Just like it is here. So and five right here's the ridge.
110:45 it shifts along the transform down here then you have 6 13 18
110:54 Oh that's really interesting. So there's wow. So there's a big offset
111:06 . Mhm. There's a subduction zone here too, I think seductive to
111:12 north. Yeah. Alright. Um Yeah so gina there's so these
111:33 lines, you can get this data free, you can download it from
111:36 internet. It's called Jihad as data it's different combinations of track line
111:43 gravity marines, all marine data. then of course these this gravity is
111:52 over marine areas and then this G. M. Model from Palace
111:58 and then um Yeah. Okay so just to give you kind of contextualize
112:11 study because it's kind of zoomed it's kind of hard to see where
112:14 at. Oh here's more. Okay I talked about the magnetic data.
112:23 that's right and there's two different versions this email, they used the meg
112:29 this shape. Probably this panel information but it's email to is actually a
112:35 flawed database because what they did well the mag two was was an
112:44 supposedly over W. M. N. The world magnetic anomaly man
112:49 was this guy moss and others released oh seven and then they made me
112:56 two. But what they did was the the problem with go back to
113:00 track lines. The problem with this marine open file data is it's
113:06 a uniform coverage around the world. a big huge gaps in it.
113:12 ? So what what mouse did, is kind of insidious. What most
113:20 was they said, well, we this geomagnetic polarity reversal scale, uh
113:24 was developed by Mueller. I mean have the scale and then we have
113:29 ocean age grid that was developed by and it combined Geomagnetic polarity reversal
113:36 So those are, you know those those maps the pole reversals going back
113:46 time right there. Like, you , there's just like the sea floor
113:51 stripes. But they're like, They uh you know, they just map
113:57 time when the pull the field was and then it was when it was
114:03 and they do it using magnetic it's grad city and others as a
114:08 bunch of 2020, is the latest . And in that one, I
114:14 something's changed a little bit. But here's the ages for those crimes.
114:21 , 13, 18 up to So I said 80 it's 80.
114:27 84. My bad. Um I 2057 33 million years off anyways.
114:35 was in the ballpark um in any um But what they did is that
114:45 took the age of the ocean And they combined it they integrated it
114:58 the sea floor magnetic polarity. I the Earth's magnetic polarity reversal scale and
115:05 . And then they created what they synthetic magnetic analogies or or what I
115:13 call fake anomalies. And that's why looks like this. I mean it
115:18 beautiful right? But it's not but not it's not true. This is
115:23 the real data looks like. This So after a bunch of us complained
115:27 these guys about this thing because you will go into people's offices and they
115:33 have these global maps with all these anomalies over the ocean basis and none
115:39 it was real. And but they that you know all this was all
115:46 real stuff. And in any case What's that mouse did this in oh
115:54 And Meyer came out in 16. in the paper at the age of
115:58 and the 16 they had V. V. Three. And now this
116:03 here. So yeah just to know these are open file but what you
116:09 want is you want the latest one though it's not as pretty as this
116:13 . It doesn't have any fake Alright so let's see it's 3
116:24 We'll go let me just finish this up here I guess this two
116:28 Modeling stuff. So the canning basin in the north is the northern Australia
116:34 it's inside the Cannon. There's a a rift basin over here called the
116:39 trough. It's a big fat basin then down here is the Amadeus in
116:46 Officer. These are little coastal Sag . But this is a study,
116:52 see. Yeah. Um yeah this a study done um in whatever
117:08 I can't pronounce the name. My . This is county basin is the
117:16 home to a Devonian fossil which is quote from the paper to a fossil
117:22 fossil reef complex that stretches 350 kilometers the northern edge of the basis.
117:28 there's a fossil reef complex up The fossil reef is very well preserved
117:33 is cut by several modern day canyons the something something gorge this name
117:39 Where's it at? This is do I have it in here?
117:47 E I J I geeky geeky and Win gina gorge. So I don't
118:02 these gorgeous anything. Maybe they're in next band gorge. No, they're
118:10 out here. Okay. Uh the reef system extended about 1000 kilometers along
118:19 is now known as the northwest show of Australian continent. So so this
118:26 this reef cut system. And then guys say extensions occurred in the middle
118:33 early. So it's paleozoic basin and Officer basis of Lake Petani is a
118:41 Sag and this is very let's say pro nia protocol to carboniferous. So
118:48 saying this thing is catching said sediments 200 million years. That's that's what
118:55 saying. Okay so this is topography showing you the you know the where
119:01 basin is deep. This is on partition the basin I believe. And
119:06 is the the plus sign. That's the basement that crystal rocks are
119:14 Now this is some data from Um And they have gravity gradient data
119:23 we'll learn more about in the last and then they have regional gravity.
119:28 regional gravity just smooth data. And the grade geometry data is this in
119:36 white outlined. So very very Obviously lots more fidelity in the
119:43 And then of course it gets really . This is regional gravity -87 and
119:50 . Um And then A. This is this is dana. There's
119:59 Grady entre systems out there that are used. There's F. T.
120:02 . And A G. A. . G. Was developed by
120:06 H. B. B. H. P. Billiton. This
120:12 company and F. T. Was developed by Lockheed. Um Alright
120:19 and this is this is magnetic So what I think when I look
120:32 this. Okay I mean the magnetic it. Okay, basements shallow.
120:39 this steeple stuff that makes sense. all these short wavelengths up here.
120:43 fact really short wavelengths up here. broadway links through here, through the
120:49 trough. And then it looks like stepping up a little bit. But
120:55 it looks like this is also a bit deeper. So you have what
121:01 like to be a high going through . What's that look like in this
121:06 ? Yeah, yeah, So gradients kind of a little interesting, aren't
121:15 ? So this is showing really uplifted on the southern, the south
121:23 southwestern flag of the Fitzroy stepping Maybe stepping down here, stepping down
121:30 . That's what these kids are all faults. Stepping down to the
121:36 Same thing over here. This mag again. Well, I can see
121:43 . I mean there's really no difference in the magnate, but it certainly
121:47 shorter wavelengths stepping down into longer So that makes sense. Here's the
121:58 section. Where is this at? is see So this is going from
122:03 here to here. A cross C. Is it shown in here
122:07 well? Okay, so it's a , it's going up too high,
122:11 little bit low. High and it off to a big low and then
122:17 high. Another high. So it be should be things getting shallower here
122:20 deeper on both sides of it. it's not showing and getting deeper to
122:26 north, but it does have it getting deeper to the south. Look
122:30 that. I mean this is just enormous throw. This is two
122:36 It's over a km, Jeez. obviously these are all horizons that were
122:45 and put in here from, from and the and the profile is is
122:53 great amateur profile. It's it's the component, I'm sure. And uh
123:01 , you know What it is is , balls. Um, yeah,
123:11 don't know, you know, if mild this data, these data are
123:17 hypersensitive. Um, but they have lot of control in here I guess
123:24 , yes, it looks okay. . Oh, here it is with
123:34 reflection data. So here's these, geometries are inferred from this inferred from
123:44 . So here's the Fitzroy trough dropping and then you have these short wavelengths
123:50 great. And you know, here's gravity, there's no Magnetics at
123:56 This is the F T. Mat view up here. So that's
123:59 this one. So this is the . Alright, so this is the
124:05 gradient. So this is the this just measured D. G. But
124:09 should be of this and you can it. It does make some sense
124:14 are lining up, aren't they? , Okay. It's okay then I
124:24 . And then this is this is is in time. It's 28
124:27 So we don't really know what the function is here. Mm hmm.
124:38 there is some, you know, is some some character the data
124:44 Wonder why? What is this This is B. So that's where
124:50 B. At B. Is this here? So it's crossing right over
124:55 , you know, the trough is stepping down into the trough. And
125:00 a big gradient low in the middle the two hides. Yeah. This
125:07 the great world with these highs in . Yeah. So they didn't model
125:12 . So they don't know what these model because they didn't fit the seismic
125:20 . But I mean, you these there may be some inverted features
125:25 here. Maybe this guy's inverted. there's some, you know, there's
125:30 structure there there and there maybe there's like that corner. This is fairly
125:41 though. It's really shown that You know, there's something deeper in
125:50 model that they're not showing us Because there's some regional stuff in
125:54 That I am not saying that you , they did A as well.
125:58 . A. So a let's look the bag on a. Okay,
126:03 it's very, very deep here getting shallower destruction, slightly shallower. But
126:08 only the very very end words where um Or it's coming up right
126:15 The very, very end look at . They it's even, you
126:19 too much. So very, very . Yeah. Okay. And we
126:32 know what rock property assigned these things . Well, they're probably in
126:36 But there's no I don't. There's there's only density information here. They're
126:41 really no magnetic anomaly information but they're while they're not modeling Magnetics. But
126:48 , that's fair. Fair enough. . So why don't we take a
126:56 And then we'll look at three Forward and Inverse. Okay.
127:05 So um All right, let's just now we're gonna look at three
127:12 For the inverse modeling, which you know, it's just like two
127:16 . But more complicated still using, know uh two d. Slices and
127:25 know, lines were now we're talking grids. So let me get
127:34 Okay. So yeah, same, general case, the same slide.
127:42 um so three D. Forward gravity . There are many ways to approximate
127:50 three D. Geometries. You can it with rectangular prisms. You can
127:56 it with stacked laminar or triangular So at the bottom is modeling of
128:08 three D. Using rectangular prisons. so you could, you know,
128:11 kind of build up these little 21 to you know, to best
128:18 represent the shapes that you that you are happening in the subsurface. And
128:26 though this formula is really complicated, just like all the other stuff.
128:31 you know, it's it's a summation X. Y. And Z.
128:35 it's calculating the effect of all the angles. Kind of like Taiwanese method
128:41 two D. But in three So now I'm not working through any
128:48 this stuff and I don't think I have to because I think prerequisites to
128:53 class is that you have had calculus partial differential equations and complex variables and
129:02 algebra and all that good stuff. I right? Unfortunately? Yes.
129:09 we we've all suffered through that and no reason to suffer anymore other than
129:17 just post to post a solution, it exists and we can live with
129:23 because someone else can worry about doing math. Um So stack laminar,
129:30 is that? That's just basically another is if you have a three dimensional
129:35 arbitrary shape, you can define it the contours of the you know,
129:40 the of its boundary and then just it up into different sizes shapes which
129:48 can then much like our Taiwanese you can break that into a bunch
129:52 little straight segments even if it you know if this is a volume
130:00 cubic volume, it's gonna have at point little straight segments, right?
130:06 then you can just calculate the the response to that. Doing it that
130:16 , triangular methods, as you can one of these sort of mesh diagrams
130:22 the tops and bottoms of the a layer is represented by a triangular
130:31 So you can use you know, . E. M. S.
130:36 any kind of grid that you want you make and you can do it
130:41 a triangular mesh or again you can it as acuteness. Right? So
130:45 does that work? Well, basically the the the difference, I mean
130:52 the gravitational attraction. So there's nothing the sides, The sides could be
130:57 because they all cancel each other And so it ends up being,
131:06 know, some function of the top bottom surfaces there. Right. And
131:12 outward of the normal service unit vector . Is always vertically downward in the
131:18 direction. Yeah, Yeah. So are equal zero. And it's just
131:26 just, you know, attraction based the difference between the top and
131:35 So. Right. So for so for triangular elements the closed surface
131:41 . Is the top bottom and the sides sides go away and you ended
131:49 with the verticals go away. And the method reduces to revive the integral
131:57 the upper and lower surfaces. And what that's what that looks like.
132:00 I what I was just saying, , as you can imagine, is
132:07 complicated because you have to account for the direction of magnetization, the earth
132:13 declination. And then and if there's it's even more complicated. So in
132:21 forward model we um the magnitude and direction of magnetization is specified. That's
132:30 inducing field. So by the way inducing for two D. Models in
132:39 forward modeling or inverse, two you have to specify the inclination declination
132:46 field strength as well. So in day it actually accounts for the strike
132:50 the model in that, in that orientation. So you don't have to
132:55 about any of that. And we're we're gonna go through that when we
133:00 our modeling exercise. Um So so you can do rectangular prisons.
133:08 , you can do ribbons and poly . And but first let's look at
133:16 of magnetization. So there's, we think of magnetization in terms of volume
133:26 where the source has a mechanization associated it's too similar to the density for
133:33 , reminds us of pseudo gravity. can also look at as an assembly
133:39 electrical charges or magnetic magnetic charge poles die pulled distributed in space. So
133:48 our volume mechanization. There's a little representation. You can also think of
133:57 in terms of electric currents. So current density and or the poisons
134:05 Remember this is how we get this is how we get to pseudo
134:10 . So there's lots of different ways think about it. But if we
134:14 at prisons again, we're doing the thing. We have prisons with infinite
134:20 that can be defined in the total anomaly due to the prison. Uh
134:26 be calculated. So here's our here's , you know, our measurement on
134:32 surface here and here's our source body an infinite things. So if it's
134:39 from Z one to Z. Z one, Z two. And
134:46 the uh calculate the field for prison Z one to plus infinity. With
134:54 magnetization of M zero M. Not to calculate the field from Z
135:00 So you calculate it to infinity and calculate it from the Z two to
135:08 , then you add those two or ? And then you get I guess
135:18 the infinity part cancels out. Maybe them in any case. Yeah,
135:24 how you do it. Um the of ribbons that represent sides of an
135:36 polygon. In other words, this another one. This is like Taiwan
135:40 polygon except now it's ribbons of infinite right? Or at least?
135:47 And assume a uniform organization of the . So the surface charge approach,
135:55 can use that to calculate the forward . The gravity signature. Ribbon is
136:02 in the xy plane. Such as gravitational attraction is both in the horizontal
136:09 wide directions. So the resulting equation be generalized to an inclined ribbon.
136:18 it's no longer simply in the xy . And to convert them to
136:24 You just substitute for magnetization and the . Yeah, this this is all
136:31 little mysterious to me. Oh and Hadrian's. Again, we can sort
136:41 extrapolate dimensions. This reminds you of whole polygon calculation from the Taiwanese method
136:50 instead now you have little three dimensional that you can calculate all the solid
136:56 as you move around and your, know, your xy playing all solid
137:03 between all these three dimensional sources. so forward mining can be thought of
137:15 indirect method to learn about pragmatic data the geometry and density or mechanization are
137:25 and then calculate. Okay, this what I was saying. You you
137:30 indirect because you have to start with model and you and you you adjust
137:36 model then calculate and compare. Inversion opposite. So it's the direct approach
137:44 because the data are inverted to obtain desired information. But the drawbacks as
137:51 said, is because you can only can only select certain parameters or one
137:57 a time, one horizon or one , you can only select one at
138:01 time. So so uh Yeah. . So it's it's not as
138:13 So with regard to inversion just inverting layer to change to change its density
138:25 magnet or magnetic susceptibility. That's a inversion. Mathematically it's a linear But
138:34 you change, if you want to the source, the geometry of the
138:38 the horizons or the layer boundaries, that's nonlinear. Right? Because what
138:45 is there's two calculations because when you're that, when you change the boundary
138:51 not only changing that but you're also the distribution of density or magnetization.
138:58 that's why it's nonlinear. It's changing things at once. Does that make
139:02 ? I mean if you have a density layer above a high density
139:10 And you raise, you know, you push that horizon up between those
139:17 layers then that the gap, The added area, that added volume
139:25 it. Now it's gonna have to more density added in the, in
139:30 area above the horizon is going to to have less density taken away or
139:35 difference of the two added whatever you do. But so that's why it's
139:40 linear. So in verse problems with and construction. So solutions to the
139:54 suffer from instability. The functions have there are singularities and this happens with
140:01 a lot. Is that if you're remember I said if you're close to
140:05 answer, they work really well. you're not close the answer and you
140:10 to invert safer for the for a horizon, you want to push it
140:16 and push it up. What happens three D inversions, they often get
140:23 in what are called local minimum. This is my getting ahead of
140:30 I am okay. Uh let me back up a little So solution its
140:40 anomaly field value at any point. ? It's been it is, it
140:46 um has contributions from the entire It all layers in all parts of
140:50 . Right. And so the sensitivity the bottle changes uh depending on the
140:57 the distance from the, from the point to whatever part of the
141:03 The calculations be being done. So four calculations, the distant contributions are
141:11 and the mom was incentive. But for lenny but for inverse it
141:18 be problematic. And I'm going to about that. I started talking about
141:22 but I'll do it on the next . So in verse and I said
141:27 for death. You mechanization is a version. So it just requires a
141:33 of the model. But the choice geometry is well, it says here
141:38 impose a bias on the solution Because it might be, you
141:44 slabs or prisons or spirits. If solution is robust then different geometrical geometrical
141:53 will give similar results. Yeah, mean right. So another way of
142:01 that is regardless of whether your your is um the sort of whatever sort
142:12 elements are involved, whether they're cubes tetra hydra or spears or whatever.
142:20 if the model is not too complicated it will probably be fine. But
142:26 it's very complicated then you know, source geometry might what you choose for
142:38 geometry. You might have a big on the result but linear inversion but
142:45 inversion is very simple and so is susceptibility. So, oh, I've
142:52 had problems with those, you only with structural inversions. The nonlinear
142:59 and that's where you're changing the geometry the model. So some aspect is
143:07 specified to constrain them out. And for example, yeah, the term
143:15 upper surface type of salt and the distribution. But there um there are
143:22 approaches to nonlinear version three of these are described by blakely in blakely's textbooks
143:29 iterative, compact body or linear linear . I think I'm going to go
143:36 those. Yeah, so nonlinear version for example, given a source geology
143:47 n rectangular blocks like the figure below in observations. Then the first restriction
143:55 which is the first restriction imposed on model. The second restriction is that
144:01 depth of the top is fixed? so now all you have to do
144:05 just find out how thick all the are. And initially the signal from
144:15 block is assumed to be produced by simple bouquet type infinite slab. And
144:20 forward response to the models, calculate inversion algorithm then figures out the difference
144:27 this initial calculations in the measured data then the base of the models moved
144:34 or down. That's how inverse it . And the second one is calculated
144:38 then the differences are figured out again so on. And then in practice
144:45 we do is we assign some convergence like you say you want and typically
144:53 like whatever the noise level on your is. So if your if your
144:58 level is one mg then you you know Iterate through this until you
145:06 to one mill gal. Some people go to a test of the middle
145:10 and the thing will run for 10 and it will resolve to test the
145:15 gal. But you know you're not anything because anything anything finer than one
145:23 . What your noise level is is know it's just it's just uh it's
145:29 making it look pretty but it's not helping or making it look different but
145:33 not really helping. Now for a inversion for the compact body it requires
145:42 the volume of the body be as as possible for some gmo geological
145:48 This takes makes sense for details. . The volume of the body in
145:55 words these little the little blocks I the geometry of the body can be
146:01 in various ways but the simplest is use elements or cells of uniform
146:05 I'm sorry never mind requires that the volume of the body be as small
146:10 possible. I'm not sure what that . In any case you divide it
146:14 into little cute and the inversion tries minimize the number of cells with mass
146:21 fitting the calculated data to the observed . So for l observations and end
146:28 . There's three situations if you have observations than blocks then it's over
146:32 So you do at least square. the same. Then you can then
146:37 can you can calculate an exact solution if it's less than it's under determined
146:44 you need to have some criteria to the possible solutions. So yeah,
146:52 need to you need to impose some limiting limiting aspect of it, such
147:00 a minimum vibe. And then the realization. So, so as with
147:11 nonlinear problems, some approaches attempt to lies the problem by using small
147:18 Right? So you look at a enough area, then it can be
147:22 trick that physicists use a lot. example, assume a two D.
147:27 of wise, infinite of unknown cross damaging can be expressed by an inside
147:33 polygon. So for l observations of field, um it can be expressed
147:41 terms of source geometry, assuming the is constant. So they have some
147:48 of a eyes from Eagle 1 to where w is a two N dimensional
147:57 I see containing X and z's of polygon corners. And then using least
148:04 approach, we can define a function can be minimized with respect to the
148:09 corner coordinates. So yeah, so basically they're basically um uh developing a
148:22 expression based on the number of coordinates the polygons in the in the in
148:29 in the horizon. And then they're solving the equation for that. So
148:41 our friend the canning basin again, Australia fitzroy trough going through here.
148:49 have a larger basin. I think was the browse basin down here.
148:53 remember the Amadeus was down here. the Amadeus this is the Amadeus right
149:03 . Um Right and then uh deaths from over four km 4 km Down
149:14 -10 km. Yeah. And then is the gravity gradient data on top
149:26 the magnetic data on the bottom Where is this at? This is
149:30 little blocks right here called the king and it sits on the Leonard right
149:35 to I guess the Leonard shell for it. And then this is this
149:45 observed gravity gradient, calculated response and residual. So it's pretty flat.
149:56 then but I mean these days they look so noisy to me. Um
150:02 I guess it's just a cross grab great jesus said with the vertical component
150:08 total total field anomaly. In the three D. Model results the observed
150:17 calculate it. And the difference. when you do models, you have
150:21 especially three D. Um Ology typically to show the comparison of observed versus
150:28 and then the difference And here's the d. model of that thing.
150:36 solicit classics and just base and fill A. And then be our
150:43 So you don't see those still down and then there's carbonate C. Those
150:50 beneath the surface there right here. they're slicing down through it, Kermit
150:55 is D. That's over here basin plastics. E. That's all over
151:02 . That's all this, this you see everywhere and in the basement
151:06 the green is the F. So And I'm assuming they mean crystalline
151:11 So this is the three D. . Which is pretty pretty. I
151:16 I mean it's very you know, friendly. Mhm. Another example here's
151:31 salt salt example in the offshore abu . So abu Dhabi sits in the
151:37 East that sits here in the southern of the Persian gulf. And um
151:43 see what's what is going on These are all salt homes. I
151:46 all these outline features. This is little survey area. Um Let me
151:52 my notes. I say dear protocol and in for Cambrian hormones salts.
152:01 not imaged or penetrated by seismic and dated. three d. Constraint inversion
152:07 aero gravity and aero magnetic data and and well and seismic data. In
152:14 magnetic inversion of the basement model, basin is 8 to 10 kilometers with
152:19 highs at highs at eight and 8.5 gravity inversion model does not delineate very
152:25 the basement and morphology possibly due to density salt bodies. By calculating and
152:32 the gravity response of the magnetic basement from the observed granite we recovered.
152:39 is what they're saying. This is quote. We recovered the residual gravity
152:43 of the horror Moon salt three gravity version of the residual show of
152:47 residual shows that the harmless salt are widespread and thicker than previously thought was
152:55 to top of the salt bearing 5.5 kilometers salt model suggests that the giant
153:02 fields in the offshore abu Dhabi such um Shave Nasser Abu Al Zakum Sarabande
153:11 occur exactly above crust of salt So all those these are the fields
153:21 these are the oil fields. Okay they say that those sit right above
153:25 salt. In addition a series of oil fields were found located at the
153:33 of the northern basement high. Yes here and three structural liniment trends the
153:46 , southwest north west, south east north south. So X. And
153:52 . Right. Alright. So let's at some data here. So on
153:57 left are reduced to pull magnetic And on the right are are gravity
154:05 . So. Okay let me see there anything else in here? There's
154:12 there's more. Okay I'll go back now. Yeah, magnetic data just
154:25 to me to be pretty regional Um It's just like four anomalies.
154:31 mean it's you know so but when look at these, where is it
154:37 deeper? I mean it's actually deeper . I think that's really broad and
154:43 here is like two anomalies are shorter . This one here is even more
154:50 . S. one s. 2 s. three S one S 12
154:57 three. Okay. Same thing. and three now gravity anomaly. So
155:02 what's the range on this. It's about 16 million gallons rage over
155:08 And I think that this gravity I mean, I don't think it
155:15 whether it's free or bouquet. Why that? Why am I saying
155:26 No guesses make a guess. Come . Um What is gravity? What
155:37 we do boo gay for? What's point of it? The point of
155:43 in two. Hold on, minimize . Yes minimized. I'm sorry.
155:55 fine. So if I say it matter whether this is free era
156:02 How can I say something like Because let's see really feeling because it's
156:15 very topographic. Exactly. It's Yes. So it's just no
156:28 There's nothing to minimize. And continental are typically pretty flat and they're almost
156:41 . So big shelf like the gulf Mexico. We're here in the Persian
156:50 . You could do a bouquet correction it would look just like the free
156:53 day. I mean it would it look it might look a little bit
156:57 but it's going to be essentially the because the topography is flat. There's
157:01 to correct for. And also, mean this is only 16 mg so
157:08 is not a lie, but it's high, it's interesting that it's
157:13 right here. Right. Between these . I don't know. I don't
157:16 how if they're related. It's interesting . Okay. So what's next
157:23 So this is basement interpretations. So did that's right. They did here
157:30 Did they did uh um interpretations basement depth estimates from both gravity and
157:43 Which is pretty interesting really. But mean you know it looks a little
157:51 to me because these magnetic anomalies highs basement highs kind of correlate with magnetic
158:00 and it really should be about So I'm not sure how they did
158:04 . And then the gravity. See gravity is more intuitive. But I
158:11 look at this, look at where anomalies are gravity magnetic anomalies and look
158:15 their basement. So I don't I'm suspicious. I'm suspicious you see
158:27 having gravity low here with a longer like magnetic anomaly. So that that
158:32 sense. And remember I said it's here and higher here. So I
158:38 is more intuitive. I think that's . Man is better the basement from
158:43 . However they did it is better this one. And then here's their
158:49 . So that's one of these magic three D. Salt maps. So
158:54 the plan and I guess this is death. So most of these guys
159:00 this range here I guess in the to 7 com and 6.5 to whatever
159:10 to 6.5 range I guess something like . And then here's their final
159:18 So they have have basement trends and trends and they have volcano volcanic magmatic
159:27 . This is just where they're anomalies just 123 and three and it's and
159:33 um the salt dome crust. Okay I like that. Oil fields nice
159:41 Salt islands. Oh so there's actually is breached has breached the sea
159:47 That's nice. That's nice. Um can't tell you like this idea.
159:54 event is something that is kind of old idea I think. I mean
159:59 not crazy about it. If I a line on a map I say
160:03 it is something geologic that it represents contact between two kinds of mythologies or
160:11 boundaries or it's an axis of a line or antique line or or it's
160:17 fault you know whatever kind of false whatever or undescribed fault. But I
160:27 liniment is so is such it's such , well it's it's happening it's overused
160:36 it's just amorphous. I mean what it mean? Well there's a little
160:39 over there. I mean I don't I think it's just yeah I think
160:44 so I mean and also you know no there's no straight features on the
160:52 the earth that looked like that. I do draw a line it's usually
160:57 . It has some sort of curvature something that files the anomalies. So
161:05 I think that that's something that could improved. I mean you can do
161:08 but I think you should you should the data. You should follow the
161:11 and if they say those limits are from the magnetic data, you
161:17 um I don't see any straight lines I don't see a single straight
161:23 I mean, why not make this if you're going to trace this gradient
161:28 trace the gradient? I mean, that I mean it's produced by
161:32 right? If this is, you , if you think that, I
161:35 this is structural, then draw I don't think it's a structure.
161:39 think this is a composition. I it's the biggest anomaly on here.
161:43 mean it's it's Whatever, it's cameras. I mean, that's,
161:51 know, It's not structural. I this is this is an intrusion.
161:57 think these guys can absolutely be structural they're going, you know, from
162:02 whatever zero, they're just about even 40. That's a big
162:07 But still Yeah. Uh so that's tearing apart people's people's work anyway.
162:17 I'm trying to look at these things , Right? I mean, and
162:20 and you should too, I mean lines drawn through data, they just
162:28 evoke geology to me. You they just straight lines through data.
162:33 mean, they think they say if idea is it's supposed to infer
162:38 but we're not exactly sure whatever. , you know, you've got that
162:42 because you've made dash lines or you know, I don't know
162:49 Okay, so full fit reconstruction. gonna show you some work that one
162:56 my students did, Nyla Dowel, dolla dolla, dolla dolla dolla and
163:06 she did, she did this what's a full fit reconstruction. In other
163:10 , When two continents break apart as know, plate tectonics, they break
163:16 the rift in the form of passive . An ocean basin forms. If
163:22 look at that margin, right? part of it that's unstrap etched and
163:28 there's a part of it that's stretched deformed and extended. And then finally
163:33 start producing ocean floor and plate tectonics that the Earth tectonic plates, their
163:45 spherical plates, they are in relative to one another and they are deformed
163:52 their margins. Right? So the of full fit is that you can
163:58 the ocean basin. See that's a reconstruction because once you start producing ocean
164:06 rifting ends and the motion between the is accommodated by the production, you
164:13 , the creation of new life, fear news ocean and cross. So
164:19 the rigid reconstruction. Then you can we call a non rigid reconstruction where
164:26 close this extended part and the way do that. If you try to
164:31 out where the free rift boundary And then of course the ocean continent
164:37 . So you know what these two are then if you can figure out
164:41 volume of this bit of continental then you can just squeeze it
164:49 That's the idea this has been done stuff, there's a lot of words
164:54 . But basically the very first one done by uh dale Sawyer who was
164:58 Rice University. He was on my committee and he called tectonic substance.
165:06 then a couple years later he and did the same thing in the Labrador
165:12 . But it wasn't until after this of this important paper by Chappelle Locos
165:18 you know 08 that a bunch of started doing these full fit reconstructions all
165:24 the world. Australia Antarctica Labrador of China Sea Central Atlantic. Now remember
165:32 is a group of guys at they did the central atlantic and Nylon
165:36 it as well. But I think is better. Of course I think
165:39 but she just used better, better data than they did. So here's
165:47 work and she makes some beautiful maps . But what you're looking at is
165:58 Different colors. So this is these different terrain uh what are called Paragon
166:05 and terrain which were created on to America when Pangea formed right? And
166:13 grandi all these different strips of uh of you know cra tonic blocks that
166:21 captured and switch it on to uh north America and over here on africa
166:29 the west africa. Creighton, there's shields and then some of these guys
166:35 also to reigns our team basement and this is so she's identified some uh
166:49 floor spreading anomalies. They're magnetic magnetic . They're not see some people.
166:55 it's debatable but they are they are magnetic anomalies. There's the uh
167:02 the East Coast magnetic anomaly. This one which produces a huge anomaly.
167:08 is a huge anomaly. And there's blank sperm. And economically this yellow
167:12 On the other side. There's S Which is this one here As this
167:20 one and S. three. Which this outboard one. And then there's
167:24 West West african coast magnetic anomaly. I think that's also um I think
167:33 S. three as well. So differ on that one. And here
167:40 is um uh the gravity anomalies with same gravity skills. This is free
167:48 gravity uh over the oceans and then uh this is modeled gravity over africa
167:58 then deny gravity over north America. thing you see right away you see
168:04 these linear features. Those are not . Giant strike slip faults.
168:09 Those are called oceanic fracture zones. talk about those in more detail when
168:13 look at ocean basins. I'll explain . But this is her gravity
168:19 This is the uh total horizontal gradient the gravity data. So this is
168:25 edge detector remember. And sure enough just seeing all sorts of high so
168:31 highs would lie in the gradient of anomalies. Right? So this would
168:37 two of them on both sides. it does you see? So it's
168:44 enhancing the gradient and that supposedly lies over the edges of sources, whether
168:51 density sources or structural. They sit the edges of them. Here's a
168:59 anomaly. So here are the sea spreading anomalies here. This is a
169:03 database. And over here this this M. A. To version three
169:09 . This is North called Dean. decade of north american geology. The
169:14 thing with the gravity before. And is the east coast magnetic anomaly.
169:19 just banging through here and then there's there's blake spur, right? They're
169:24 nearly as prominent but extra is just . And then um yeah, so
169:33 are sea floor spreading anomalies out here well. There's actually something here.
169:39 the S anomaly. Is this guy through here. Down through here?
169:47 she broke her area up into five that you can compare. Okay,
169:53 north, north, central, south, central and south here they
169:59 now on the left is her. I think these are both these are
170:06 is the full fit. This is think, oh wait a second.
170:17 , this is the full fit So there's overlaps and gaps. This
170:21 actually she did the whole closing of . Oh wait no the left is
170:27 rigid reconstruction and the right is the fit. Yeah, because so the
170:36 county boundary hit the blue line and for africa and the green line is
170:45 ocean county body for north America. this is the rigid reconstruction. So
170:53 this is done is because if if you think of the earth as kept
171:00 these plates, then that means you define any motion between two plates by
171:07 rotation pole through the center of the and some angle. Right? Any
171:14 plates can be described by a rotation and an angle. I think we
171:19 about that with the two polar wander . Okay, so this is
171:28 this is showing um the beta Now beta factor is basically it is
171:36 um amount of uh it's it's how the crust is. It's the ratio
171:45 thin thin crust over normal crust. ? So as it thins, I'm
171:53 , it's the it's the other way because high beta factors. Right?
171:58 . No one, you know, had it right the first time it's
172:02 amount of thin to thick. so smaller, smaller values are thinner
172:20 . Our blues. So this is shows you how, so the inboard
172:28 here, that's the pre rift That's the that's the the the,
172:35 know, the unstrap etched the under , you know, pre rift thicknesses
172:45 the ocean county boundary is the outboard of this. And then everything in
172:48 here is the deformed part according to cross sectional figure I showed you.
172:56 , where is this? This is cross section, yeah, that goes
173:01 Tennessee. And then along the border Georgia and south Carolina. And
173:06 you know, outboard outboard to um the just past the platform and she's
173:15 this gravity model, it fits She works for a long time on
173:22 . But here you have the different of terrain that are, that have
173:28 , that are that are outcropping. just modeling those dipping down into the
173:34 of the crop, into the, know, and then here here everything
173:38 spinning. And she has some a like crustal group. And there's there's
173:45 reason for that. Um Yeah. then on the other side, another
173:52 through the thin crust. And she's showing how that things over the
174:02 And then um now she's classified in of high intermediate and and minimal vertical
174:15 , basically, the thinnest parts are the and the thickest parts are purple
174:23 in between is this sort of brownish here. And here's a little structural
174:31 of the opening. So basically this this part of africa Mauritanian in Senegal
174:43 . This is all sort of like we extended kind of like the Great
174:47 , you know, like Nevada, the basic range, That's the idea
174:51 that because up here, I mean deformation zone is pretty normal, 2
174:56 300 kilometers across. But down it's like on the order of 500
175:01 . That's 5 64. So you're 700 kilometers. That's, that's the
175:07 of the great basin, that's the of whatever the borders of Nevada and
175:13 know, so that's the, that's we think might be happening here.
175:19 , where am I at here? at, I'm at 4:39. So
175:27 to show you some application of uh, For this full fit,
175:34 full foot is a 3D model awesome this 3D to get to this
175:40 the debate a factor and to close ocean basin is also, you
175:48 modeling. So yeah, any questions this stuff. Um, I don't
176:01 now, it was pretty heavy there the middle. So I just kinda
176:05 go, no, this part was . Like this is good. I'm
176:10 about like in the beginning we were about like all the math stuff of
176:14 third section. Uh um let me back like literally, yeah, stuff
176:24 that. So I just gotta go that again cause I don't really have
176:27 question right now because I don't know if you want just, you
176:33 you can please email me because it force me to, to explain it
176:39 . So yeah, I mean, be happy to answer any, any
176:43 like that. I mean this, mean this rib, I mean,
176:46 mean this stuff is really because I I'm a big time user because it's
176:54 like legible like I understand it. threw it again so I fully understand
177:00 . But it makes sense. Yeah. No, no it's I
177:06 yeah. Right. So here's your thing. So okay. Um I
177:14 the instructions already to send to you . I mean, I don't know
177:20 you wanna if you wanna play around software either you tie, but you're
177:25 welcome to um uh Let's see Uh Okay. I just yeah,
177:37 just said he sent me a Uh yeah 2:41. He said we
177:42 be good. And then um he I'll copy him and then I'll so
177:47 send a note to you this evening um Yeah. Okay. Yeah.
177:58 um right, I'll send that out then it will have instructions for downloading
178:06 installing. And then for I've made comments at the bottom of my email
178:13 how to set things up, basically exercise folder that you um that you
178:23 . I want you to set up project in that folder. So when
178:28 open montage for the first time Oasis the software package, it's it's owned
178:35 this company called sequence. But when open montage and you try to like
178:42 a project, the default is is software bin folder where all where all
178:52 DLL E X. Execute doubles Which is like the craziest thing in
178:57 world to me, why would you the default be like the, I
179:01 why not have it be your desktop crying out loud anyways. Um,
179:07 you, the critical thing is when create a project, navigate to that
179:13 And create the project in there, you want to call it. And
179:17 way when you go to open a , the model that's in the exercise
179:22 , there's like 11 files but it's one model. That's how they're
179:26 It's like tons of files. In case when you go to do
179:32 it will, it will go your will be right there. You won't
179:37 to navigate to find that model. the only tricky part. But uh
179:45 josh sellers is the guy with with and I'll be copying him on the
179:53 the note. And so um uh . So uh just just he says
180:02 out if you have a question and just answer right away for you or
180:07 can ask me first. I mean don't personally, I don't like to
180:10 those guys unless, so he's just really nice. You can ask me
180:15 and then if I don't know when can ask josh, can I download
180:19 on a Mac or Windows only. Windows only. Do you have a
180:24 program. Um, I'll have I know my husband did that for
180:30 one time. I'll have to ask to do it again? Yeah.
180:33 sorry. It's not Mac. It's Yeah. What are you doing with
180:37 McEntire's? Aren't you a geophysicist? realized early on in my undergrad that
180:43 should have gotten a Windows because every , every time we do something with
180:48 , nothing is compatible with Mac. I don't know why I still have
180:52 computer. Yeah. I mean that's . That's yeah. I mean I
180:58 I had him ipad and I hate because you gotta do all that sinking
181:04 everything. I mean I have an and I just plug in a
181:10 right? And it's as a file . Just like anyways, whatever.
181:14 sorry. Anyways. Right. So you can't find a shell, do
181:18 have another way of doing it? don't have a pc at all?
181:24 don't but I can I'll figure I'll you know. I think my mom
181:28 have like a laptop. I don't if I can do Chromebook, I'll
181:32 what I can do. I'll let know if you can borrow one if
181:34 can't. I mean because Yeah, or or I mean one of those
181:41 programs works. I know they were have done it. No.
181:45 My husband did it for me one when I took remote sensing because I
181:48 used the N. V. Um So I'll talk to him and
181:51 see if he can do it for again. Okay. Alright. So
181:56 why I mean you might be able get everything set up by tomorrow but
182:00 already changed the schedule and I think just to be safe to make sure
182:06 have time to get everything organized. know the downloaded get the shell
182:11 get it installed blah blah blah. know that way because I mean you
182:16 we're gonna be starting at eight o'clock the morning. I mean 8 30
182:20 the morning and and it's a little in the day to try to do
182:25 . But I mean it's a yeah don't want to go into the details
182:31 what the problem was but anyways um it's it's resolved and I told Don
182:38 is happy. So I just I his note just now too so it
182:44 like it looks like the you know can breathe a sigh of relief now
182:50 I fixed it. I fixed the and I also and then you've got
182:57 slides that you know what we went this. I didn't have to fix
183:00 . Maybe I will later after you questions. So. Okay so alright
183:06 then I guess we're good until um tomorrow morning at 8 30 then.
183:13 good. I'll be on time I . Okay. Alright see you
183:20 Good
-
+