GeoSci.xyz GWB Lectures, 5 Feb 2020

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From YouTube: 2020 02 05 Day3 Part1 ParametricInversion

Description

In this video, see use Jupyter notebooks to invert 1D DC resistivity data.

A

Mystics, how well to fit the data using at least squares. The.

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Aloha malihini under body formula and square.

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Let me ask the question: are our people familiar with a least squares, misspent criteria.

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At least square misfit.

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Statistics, it's do. They know statistics so this this thing they do these squares. How many people know these theories.

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Right me different shape.

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How many people have fit a straight line to a set of data.

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That got you gotta, make sure you can see this suppose. I've got data like this okay, and so this this is y, and that is X and I'm. Looking for an equation y is equal to a a X plus B, so I want to try to find parameters a and B such that I make a straight line that fits this.

B

Fermi, does it look like real me, yeah.

C

People done that.

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Straight line fit don't know, yes,.

A

B

Know it didn't have to be like that in.

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In in your high school in university, nobody.

C

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Asked you to fit a straight line to data.

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A

So here's here's Y, here's X and, let's suppose, I've got data that looks like this.

B

Okay, you cannot see another movie, I didn't even feel it I think you are denied in the alley of all the neon, yellow, yeah, yeah and.

A

A straight line: how do my, what is my equation for a straight line? You never.

B

Get my equation down there.

A

So here I need an equation for a straight line, so I could write. That y is equal to Britney.

A

So thanks yeah, so X, but if Y was equal to X, then that would be a straight line. That looks like that right. So for every value of x. If this is 0.5, then Y would be point one.

D

A

So that's that's an equation right, so Y is equal to X's is good, but what happens if I had if I had a line that was.

A

Yeah, let's suppose it's like this right, so this is y and this is X.

A

But if this is X, then the value up here is much less than the same length. This way right so y, equal to X means that I'd be up here, but it's not that right. So for this maybe it's y is equal to 1/2.

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Oh Jenna! Well not for me at all when you put extra. Why.

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Not History X cut it yep.

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Sorry together, they.

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May one day explain that one to day as I wrote, Nia.

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Salman it the part of my X, so.

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If I, but if I took this line a night, I did something that was parallel, but I shifted it up by. Let's say one point: zero, then now, what's the relationship between y and.

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You know I want have that, follow him attention, I think as a rock, so 1 1 0, then I get 1 so.

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1 equal to, why are you going to one cut one of those things yeah.

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So that would be this would be the equation for this one. So in general you know, Y is equal to ax plus B right, where a is the slope and B. Is this intercept? So yes,.

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The many on it yes slope so.

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A is the slope. B is the intercept so now. What I'm going to do here is to try to find a best fit line.

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Like we do at night, the line Jankel and these days are more but.

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The form Y is equal to ax, plus B.

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Honey, they equation that you know and.

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So my parameters are a and B I'm going to adjust my parameters until I have a line that goes through these data.

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In a bimini you know my line.

B

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So how do I, how do I decide if I'm doing a good job.

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Look at how many oh girl, I need.

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To have some way of deciding, and is this line that I've got here: okay, it's that doing a good job of fitting these points.

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B

The look is the line go on with you get points. You got I'd like a big tip the lava so.

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I can look at the distance here these guys here and.

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Find each of them since some are negative, so let us call this point why I observed and.

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This point here on the line of why I predicted, if the distance, that that's that difference between this and the straight line, is a misfit.

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Misfits them and we need a mini tamiya, let's eat the cake. Reality die at neon nae nae mam. Achievement in here is quite sizable right.

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And because sometimes they're positive and negative I can choose to square that.

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Negative in ma you know and I was weighted, then I gave up and.

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Because I want to work with all of the points I've got I've got. You know, look at the sum of these from one. However, many I've.

B

Got the panic away yeah, but yeah I have a bra pound below waiting like that. So.

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This line might have a very small misfit demands.

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Erupts all misfits early, they make welcome news read, but.

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This one here would have a really large misfit, because now my differences between my observed and the predicted- that's a really big number and if I Square guys to put again I'm going to make that really big. So.

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Don't know nothing.

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Together, like so anyhow- and we might not so.

E

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Get she did it teaching the points that are we gonna misfit at the RT, so.

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What is usually done is to say I'm, going to find a best parameters, a and B such that I fit these data as closely as possible.

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Afp, a paramedic on zone wahhhh, oh yeah, ahhhh meet. Oh, my I resemble phenomena.

A

In a parametric inversion, that is, is our goal to adjust the parameters so that the predicted data say the black line is as close as possible to all of these points. Yeah.

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Going beyond kind of diamond Shinya points, they got a nice that so Nick babe stop on sweep. You know bar me, don't oh.

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Yeah, and so it's this is a least-squares fit because I'm squaring I'm squaring that number and I'm squaring it, because I've got positive and negative values, so I need to always be working with something that is going to be positive, so I'll.

B

Sit down the square like that, let's wait tonight.

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So that's our procedure, we're going to introduce a parametric representation of the earth and then we're going to forward model and look at the difference between the predicted data at the observations and we're going to square and sum and try to find the parameters of the model so that this is a minimum.

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And one yet Oh y'all get a point for the get-go. Look at a point: right: niku, hello, Emmanuel on the parameter yeah.

B

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That's our goal and we have an app that will allow you to play with this LT.

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Harvel, not equal 100, apps too cushy Ballymun.

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Yeah, so here is, is how we do. We have some observations, we're going to adjust the parameters and then we're going to model those and get the predictive data. And then we compare predictive data with the observations. If they're good, we will say. Yes, we have an acceptable solution, so.

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The diagram, your ally for my observations on.

C

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Did not get a house observation with your mana subjugator, how he'll adjust yeah drop me right hand enemy. Now she may be mono young Tommy come on 410, say man, hello, Pierre gross, don't EE I, look like you know the mall. There got that nice evening. Hydra come on. ah Yes, the know that yes, so I, not OPD, more iguana left-handed. You know.

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B

So I think you.

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The rest of which are so we have observations. We've got a bottle. We predict what the data should be. We compare.

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Fishing at the adjust adjustability like the honey yeah, daddy done it you're. Okay, shame you know 99 today or not an item or not: oh yeah, yeah tightly today, more than that I quantity, not cool the koozie groups. It is you know about.

A

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For EM, you know and.

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So it's if the misfit here is less than some target misfit bar is acceptable. We say good. If it's not, then we modify the parameters and try again misfit.

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Gun Danny that my talent know how young.

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But man is another.

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So, there's a number of ways that that you can do this, there's something called Monte Carlo in which you just specify the number of layers, the resistivities. You have the ability to predict the data and you just carry out many simulations and you could keep those that are a best fit. The.

B

Monte Carlo commonality that the nine alone on an island be right, number of layers layers in a very valid wa-da-tah PA. You know, resistivity lay stop Adobe day. No Yamamoto will a more area with an empty without pool at work. Tokine I never know which I don't know. The aikido 5000 account opt out of you know so we're now. Information, beatable.

A

When Kevin was here two years ago, he thought he trained you on using this of Monte Carlo software. So how many people remember this interface, the yes.

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I mean up, let me think begin the Nick wait. I've got Coptic Kevin Italy, oh.

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Yeah, that's good! That's good!

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So have you used this since to training.

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We're not going to go through the details button for those of you who remember this. There's many many attempts to adjust the parameters and to try to find out find those models that are acceptable fits and then you can type in constraints on model, thicknesses or number of models, or the number of layers software well decide how well you are actually fitting fitting the data model.

B

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Guac now take some words at work with your main information at a table. Oh ma cool, to get up, get a cool ball reading a blog, acceptable and I thought, that'd be Donna. So.

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This is also an example, then, that you might remember the red x's here or crosses. Are the field data so kind of like week weekend.

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So I'm out the neon bull then can I. Do that be be sending a great detail in your body and.

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So those are the data. The model was a four layer model for Liam Molony bunny. So it's got three layers: each has its own thickness and resistivity and then there's a resistivity of the bottom, both holy.

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Earth yet Oh Napoleon some orders work at their own, but I, don't we're a 2d. We are a resistivity me yeah me and the.

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Result of that is this, so there's a layered model which has got a low resistivity player here, a high resistivity and then followed by low resistivity.

B

Lilly, a woman turned resistive Demian and be they are due. Monday wanna read the Munich water gets out and you.

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Can see that the apparent resistivity curve has some indications of that it starts here at some value it goes low as a that goes high, and that goes down I'm.

B

On apparently received yeah, Lionel develoment down and then I take my obedient didn't get down.

D

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That's one piece of software I'm going to introduce you to an app that we have. That also will try to find layer thicknesses. The first part of that is actually going to allow you to experiment and try to fit the results by hand, not.

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Being receptive.

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Cheap I'm on the body. Excuse me nighttime event. They see three layer, inversion, dot box of erotic jihadi, no I'm gonna go.

B

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You've got three resistivities and two players and you're going to be able to adjust the sliding bars to fit the data. But.

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They donate me now the body was young. We ought to die yet, no Brendan. Would you go straight like it oh yeah in there, but that's lower yeah. So.

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Before I show you the app I'm ready to give you a couple of pictures from it, so here's the three layer inversion app. So one of the examples that your work with is a layered earth like this. So it's a conductive layer, mr. O'doul.

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Okay, my Bonavena Munna yeah hi leo TT, but alluminium you shimmy, porno away matter, are conducted with yes, Tita, the don't wanna they are. She may resist available for.

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The hundreds.

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Are all resist is demeaning, they oppose and you so.

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This is five thousand five hundred and five dollars so.

B

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Weather irate in red and the Trumper J in blue shows this sort of characteristic drop in the resistivity, and then it's going up, such as an indication of what's happening after death. When.

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Rotational rates they might just never Joe Gatto yeah I'll we're not ready young, but the way I pulled on it. Cindy went on down water. You might get that everybody.

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Xo, the three layer app well actually I think.

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Yeah so I think will terminate this and I'll. Allow you to use the 3d inversion app and that would probably be in backward for the afternoon unless.

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C

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Stuff that you wanted to talk.

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So the the notebook is called the 3d layer in inversion and.

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When you download it, it's going to look something like this, so, let's first of all see if you can access the.

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Three layer inversion.

D

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Just now there there's there's no questions, but they think and download a synthetic. They can use the synthetic result, layer, okay and then try to see if they can.

D

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It should be all with the rest of the apps, so death or so maybe, let's just circulate to see how many people were.

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Yeah, so what it tell them.

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Like this I know,.

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For anybody who can use your phone as a hotspot, could you do that? It seems as if the Wi-Fi that we have here only allows a certain number of people to be to be accessing it.

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Don't say y'all say I'm up in.

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Girona for my hot spot,.

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Some are, but we need to change.

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This is no book, and so they have to.

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Yeah, what was the name of the file.

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D

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We get them so that they can load on the synthetic data set and so that we can take them through the synthetic data.

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Whatever the name of the fire was.

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E

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So, can you go back to the three layer inversion.

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This is a little bit different than the other apps that you've got. This is actually much more. A notebook feel.

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Notebook you see things that look like this, so they've got in and there's a bracket. It's it's got some stuff in here. That's called a cell, so.

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Sell a c e ll together self.

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Okay- and that requires that we- that requires that you initiate well this. This does something that is required to run the program, but you actually have to make it fun and the way you do that is you go on to this cell and you do shift enter the.

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Cell with other shift and.

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And when you do shift enter, then this highlighted blue goes down to the next cell.

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So, can everybody go to the very first cell and press shift enter.

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What I'm a sheep that a black keyboard.

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D

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Okay, how many people everybody enter.

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When the auto-ship.

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Ship enter so now the Box moves down to here again, you can do shift enter the.

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Domain, not the box without.

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Bobby step.

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One Bobby and.

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Then it comes down to step, one load observe data and you press shift enter again much. It ends up that they may okay. Now here, I want you to click in this box.

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I folks, the video click lollipop yeah.

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Going to you're going to delete, see how.

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Not sure what you've got but.

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Press the button.

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Okay, so you have to load a new file in here. So if you click in here, you.

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Know strangle ma, there'll.

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Be another name that MSU.

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Buechele, a meadow Comstock.

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And you want to click in there and retype in so you get assets and that's fine, so assets slash and then three so get rid of everything back to assets.

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Access, so that you, okay about it.

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We look closer at this anomaly and click yes and then cap.

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Off I would say: manatee.

D

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I quickness they go ahead and change the file back to three players: synthetic data, dot, CSV.

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Yeah there was, there will be something there there's another file and there it's it's the DRD data, but we'll work with a simpler dataset.

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They will like delete after access again. This is that yeah.

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But we need up to assets. Let's.

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Do the little man and go.

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On yeah and then type three underscored layer underscore synthetic underscored, data dot, c-- at speed.

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Come on layer, 3, late, three layer on the core.

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So III with my under storm in three in guard three underscore the my nper photo Suri, sir Sir sir. You.

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Can write on the.

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Top on the top.

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Three and spawn layer on the score.

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Don't see SP.

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Saves on the integration there.

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We later synthetic dick.

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So right now most of our working.

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Slow, I heard they.