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GEOL 6390 3D Seismic Exploration - Day4 11-04-23 PM
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00:02 And is she on from far Ok, good. What kind of
00:08 do you guys far away have? they see the, and um,
00:13 , Jessica, I'm, I'm leaning uh Utah's laptop. Ok.
00:25 but now nothing for now. thanks. That was for you.
00:31 , good, good. How about ? You? All right out
00:37 I know how you. Ok. right. It's what one in the
00:42 ? What time is it? Um is sorry, you can hear my
00:45 . It is seven o'clock, seven . Yeah, that's not bad.
00:52 . Time to drink beer out of coffee cup. Good. All
00:57 Um So on the screen, uh , I think it was maybe Nathan
01:03 asked me this question because he was confused and the reason he was confused
01:08 marred was confused and I will uh this update to Utah and he'll give
01:14 to all of you folks. But the structure or in filtering um
01:22 what I wanted you to do is know in the exercise you ran it
01:26 Sigma X and Sigma Y equal to . And then you use the
01:32 you got one answer and you saw lot of stuff thrown away and then
01:38 I had you set it to a value, 0.5 vertically. Then I
01:43 you to cascade using the three by and a five by five filter.
01:46 , Patrol is not parameterized that That's the other software that I
01:52 So the to, to make that patrol speak, we would use
02:01 uh a window that's maybe 1.5 by and, and then 0.5 like we
02:09 , but then cascade it, do two times that way. So take
02:12 output of the first pass as input the second pass. OK. And
02:17 compare that to uh I still don't it right? But I didn't send
02:25 to you yet. I would probably this, I'm gonna take a
02:34 I'm gonna make a three just so see what it does? OK.
02:40 make it bigger. So the question , do we want one big filter
02:44 gonna be on a plane or do want two smaller filk? Now,
02:50 , I think I tried to get the idea that the smaller filters,
02:54 only are they gonna be tapered and structure better, but they're also more
03:04 . And that was just the numbers gave you was for an average
03:08 a mean filter. If you did median filter where you have to sort
03:15 , now it's even a bigger So to sort what the median is
03:21 of 25 is much harder than the out of nine. Right? And
03:27 get the exact numbers. I'll have go see how does a bubble sort
03:32 ? And you've forgotten about bubble Like you probably never learned bubble
03:37 Did you ever learn a bubble sort to sort data efficiently? And from
03:42 to smallest even UT is not in of bubble sword, but you can
03:48 bubble sword. So you know, so that's one clarification. So we'll
03:58 to the next lecture. Then there's be two more lectures today here we
04:18 . Who's that? The information that uh I'm glad. OK.
04:37 . So the next one then is attributes that map continuity and texture.
04:45 we're gonna have the coherence family of , amplitude gradients and something called gray
04:51 cour matrix textures. Um coherence Varian a type of coherence measures faults,
05:00 edges, cars dewatering, uh poor of the noise as well. Amplitude
05:07 are very sensitive to thin channels and fractures and uh textures are mapping more
05:15 versus smoother reflector patterns. So I'm skip the words and coherence is going
05:25 compare the waveforms of neighboring traces. the picture on the left I have
05:33 target trace and then I'm gonna compare waveform with the one to the right
05:40 the one cross line direction. And combine them. And this is
05:45 we started with coherence back in And then a little later on,
05:52 later in 1995 we realized, we'll get a more accurate result if
05:57 use five traces, nine traces, traces and come up with different measures
06:03 continuity. And I'll go through through . So the first one which is
06:08 easy to understand that you could program in Excel but that nobody uses
06:15 But it was where we started. gonna take my first trace. And
06:19 right here, I'm gonna, let's , look at the in line trace
06:22 to it. I'm gonna take a millisecond window and I'm gonna calculate the
06:27 correlation coefficient, the Pearson normal cross coefficient. OK. And I'll get
06:34 number between minus one and plus So here it is uh phase advanced
06:39 four milliseconds, 20 phase away by . And then I plot the cross
06:49 coefficient and find a ha its strongest now to get a little bit more
06:55 answer. It's not surprising that we don't want just phase away by
07:00 mill or two millisecond intervals. We wanna go with half millisecond per quarter
07:07 . But that's a, that's kind an implementation. Here is a um
07:14 from the uh Gulf of Mexico, they call a uh a spec
07:19 So Western Geophysical collected this survey processes the idea they'll sell it 1020
07:27 And if you're a uh interpreter, you all are now, you will
07:33 , oh, I got these onion kind of reflectivity patterns, peaks and
07:39 . So this is my uh kind a sedimentary layers and it's either an
07:47 or a thin cline. It'll turn it's a withdrawal salt, withdrawal
07:52 Then you haven't seen salt in this , but you've certainly seen volcanoes.
08:01 . So here I got no coherent kind of low amplitude. This is
08:07 a salt dome looks like. Then see that little pieces of channels,
08:13 part of the channel here, uh some bulbs, et cetera. So
08:21 go do this cross correlation thing. the image we got, OK.
08:26 it overnight on a big computer, computers. Uh 1995 weren't that
08:31 Your cell phones faster. Uh incoherent part of a channel, part of
08:38 channel, part of a channel, smaller channels. And then a lot
08:44 folks over here, right? And uh out of the salt, we
08:50 radio faults coming out of the We'll talk about radio faults next
08:55 Why do I not see the whole ? Well, remember the channels were
09:01 down in kind of sort of a environment. Ok. Might have been
09:07 little bit of a slope but kind sort of a flat environment on the
09:12 . And then as I built the , the the mini basins down the
09:18 came up. So now that at time flat horizon with the channel on
09:24 is now deformed. And when I a time slice through, I see
09:28 of the channel. OK? It's simple as that. OK. Let's
09:34 at this little channel I got in pink box and in 1995 an attribute
09:43 used and you'll see this in the of possible attributes in uh uh in
09:50 uh average absolute amplitude in a 40 window. Uh So probably you're all
09:58 comfortable with the idea of root mean amplitude. So I take if I
10:03 four millisecond data and I have a millisecond window that gives me 11
10:07 I take these value square, it them up divide by 11, take
10:13 square root. That's the R MS absolute absolute average absolute instead of being
10:21 squared norm mathematically called an L two , it's an absolute value norm called
10:27 L one norm. So we just the absolute values in average. So
10:33 we've got an anomaly here and another anomaly there, here's three trace coherent
10:39 I see more stuff. OK? see more stuff. I actually see
10:45 . Now let's go look at the a nine trace semblance algorithm. So
10:53 is now very similar to it is the same as Varian. OK.
10:59 this is a nine trace semblance algorithm we see these three channels very,
11:04 nicely. OK. So the difference the image on the bottom here and
11:09 image on the bottom, I'm using data using nine traces information in nine
11:16 instead of three traces. That's the difference. If I look at line
11:21 , a prime, I see a once, twice, three times,
11:26 , twice, three times. what's this guy? Oh, that's
11:31 channel down here. OK. And I had before was this area all
11:39 had with the uh absolute amplitude was part of the channel uh was maybe
11:48 with gas and thick enough that I see it without that. Now,
11:54 have to think like a geologist This channel was not flowing with
12:07 I don't want you to use the channel three conduits at the same
12:12 What we're seeing is what's preserved in seismic data. So, again,
12:18 a deep boy, what's preserved? . Geology. The boy thinks what's
12:27 . What's the other one? You're geologist? You're my geologist right at
12:31 hand. What do you say oh, what's the source of the
12:38 ? Oh, you got to say in a deep voice. You never
12:41 it in cocktail party conversation. What's the Providence? Right? You
12:48 that? Write it down. You to know it if you're gonna be
12:52 geologist, what's the provenance is? the provenance of the sediment? Is
12:57 gonna be? Are you gonna expect , you're gonna expect gravel,
13:03 You need to know where things are from. Ok. So that's a
13:07 thing in Strat gray and sentimental. . So I'm just gonna say this
13:15 was uh maybe done inside 100,000 years this channel. And this one was
13:25 years after this last channel. And three of them cut down into the
13:30 layer and they were all preserved. ? In other places, there was
13:35 channel and they all got eroded. . So what you see is what
13:40 preserved, OK. Now folks will up nicely on the seismic amplitude time
13:52 if the fall cuts the fabric of seismic reflection. So here this is
13:59 Texas um uh in the cotton valley . And yeah, I've got a
14:08 kind of doble feature over here and can say, oh there's a fall
14:12 there, there's a fall cut in , there's a fall cutting there.
14:16 , there's probably one here, probably here then over here, maybe something
14:24 . Here's the coherence image. And some of these folks I see like
14:30 two folks I could see on the amplitude and the ones down here.
14:38 one and this one I could see the seismic amplitude. But these like
14:46 here real hard to see hard to here. This one's real hard to
14:52 . I'll take it off. I see that ball. Why? Because
14:58 this time slice it's parallel to the . So the peak draw pattern I
15:03 , I can't differentiate it. And then there are a whole bunch
15:07 other f on the coherence that you see on the amplitude data.
15:16 what you need to keep in mind the coherence image on the left is
15:22 computed from the amplitude image on the . It is computed from the amplitude
15:29 on the left from on the right five slices above and five slices
15:38 So 11 samples in pare their default 15 samples of team. OK.
15:45 now if you were to look through 11 samples and animate, you'd see
15:51 kind of a difference and you might able to pick it out. But
15:54 think about oh man, it's already enough to pick faults. Now I
15:58 anime through every slice and then figure where things are and try to pick
16:02 . Oh OK. So the coherence that out and the reason is that
16:07 looks so nice is it's using more than you can look at it in
16:12 single slice. OK. So we five common ones out there cross
16:21 No one uses that anymore. Uh variance is one minus semblance. Manhattan
16:28 is the absolute value based semblance. then Eigen structure gradient structure tensor plane
16:36 destructor. OK. So let's look semblance. I've got five traces.
16:40 drawing it in two D because I draw two D. Usually you do
16:44 in 3d. By the way, does work perfectly well on two D
16:48 on two D grids and seismic I'm going a long structure. How
16:52 I know that? Well, I my dip thing as I did in
16:54 previous lecture. Then gonna calculate the of the input trace. First name
17:01 those 11 samples, I got 11 and five traces. I got 55
17:07 . I'm gonna gonna square their values add it up. That's the
17:12 And I'm gonna calculate the average trace summer along five samples divided by 55
17:22 divide by five. OK? There's average trace and I'm gonna say uh
17:27 coherent part of the data kind of by the average the smooth value.
17:33 I'm gonna calculate the energy of the traces. OK? So I've replaced
17:42 original traces with the average value kind a filter. And then the coherence
17:47 the sum of the, the ratio the those two energy measures.
17:53 That's what we have. Now, may not remember semblances this way,
17:58 might remember it as this formula where ? I gotta go on dip.
18:03 my P, there's my crossline But you might remember I take these
18:10 , I divide I sum them I divide by J which is maybe
18:15 or nine however many traces that's my , then they square it and then
18:22 is the squared value of each I add those up and I divide
18:31 by one or five or nine. however many traces I use, that's
18:36 average energy of all the traces. I'm gonna smooth vertically over, let's
18:44 11 samples and patrol 15 samples by . And that's gonna give me my
18:51 . That's the formula. Now. Manhattan distance. I used to live
19:02 . This is a city hall where get your driver's license. Uh
19:06 you show up for court if you're trouble. OK. That kind of
19:11 . And we have two distances. New York, we got the Manhattan
19:18 . So I walk along uh Fifth and then 100 and 10th street and
19:25 that's the Manhattan distance or you got Pythagorean distance. But in New
19:31 we didn't say Pythagorean. That's the words as the crow flies, the
19:37 , you know what a crow It's a Floyd the boy. So
19:43 crow flies in a straight line. ? That's the normal distance. We
19:47 X squared plus Y squared square rooted distance, absolute value of X absolute
19:52 value Y why in Manhattan can't walk the buildings they're in the way.
19:58 ? Landmark use this as a way get around the patent that AMCO
20:02 OK? And then um pare Varian said, well, we're not doing
20:09 , we're doing variant and then you the equations. Well, how do
20:13 calculate variant? And I in my , because I was involved in some
20:17 the patent things, John Castano was one who actually went to the
20:21 And I looked at my my she teaches nursing and on the back
20:26 her panel of basic statistics, how calculate variants fast. Ok. You
20:34 the energy and then minus the square the mean and there's the variant right
20:39 . So, and that shows that is one minus template. So why
20:44 we have these different things because of and copyright? So you got three
20:50 names of almost the same thing. here's the Manhattan district just take an
20:57 value instead of squares. Ok? , another thing we got to worry
21:03 is if you make the window too and in patrol, this is exactly
21:09 you would get. If I make window, let's say three samples instead
21:14 15. Then when I'm coming across zero crossing, my signal and the
21:21 ratio is going to be greatest at peaks and the troughs gonna be least
21:25 the zero crossing, especially if my is zero. And so you're gonna
21:30 these kind of stripes around there. yellow lines are vaults and the curvilinear
21:40 . Well, those are zero Well, you guys are pretty
21:43 you say, oh, we'll do , why don't we calculate the variant
21:48 the quadrature the Hilbert transform? And my zero crossing then becomes a peak
21:54 a trough and I'll have a better and noise and that's true. So
21:58 could do that, but then the in the truck would come back.
22:01 what you need to do is do of them. So you're gonna add
22:06 semblance of the data and a Tober and then you gotta normalize it.
22:12 in this picture, my buddy Chopra and Alberta, here's all this
22:19 As you go across the zero crossing of the real trace. Here's a
22:24 of the complex traits or the analytic the data and its over trans
22:31 So it gets rid of a lot those artifacts. Now, the next
22:37 is uh associated with eigenvalues and Again, Ali's best friend,
22:44 I have friends and eigenvalues are one them. OK? So we're gonna
22:50 the energy of the input trades going calculate the wavelength that best fits the
22:56 within the analysis window. We're gonna the coherent component of the traces.
23:04 are we gonna do that? We gonna do this with eigenvectors and
23:08 I have to go back a calculate the energy of the coherent component
23:14 the trace. Take the ratio right , seismic data. We used to
23:24 this data set in this lab. And here's time slice through the
23:30 There's some salt in here. Uh a Paleo Mississippi River coming right through
23:41 . OK? And then you see onion rings of the tipping reflectors about
23:45 salt. Let's calculate the energy of data. So nine traces 40
23:51 so 11 sample. Thanks. And uh I used a, a funny
24:00 bar to show very high energy, low energy. Then I'm gonna filter
24:04 data using this Eigen structure filter. I'll have to go back and explain
24:10 and see it's a little different and gonna take the ratio of these two
24:15 and they get coherent. OK. exactly what we're doing. So we
24:20 call it Eigen structure coherent. We call it Engen ratio. So mhm
24:33 Unless you ask me about, I structure coconut the details. I won't
24:37 into it if you ask me, go into some detail. Oh It
24:42 says hell no. All right. we've got three different algorithms. We've
24:52 a cross correlation algorithm based on three . These two were used, I
24:57 we used 11 traces because the spacing uh 100 and 10 ft by 220
25:05 . They were decimated. And so I see the sal film, a
25:10 of a blurry canyon. A couple folks, the semblance, I see
25:14 Soul film Canyon is a little better more continuous but a little thicker than
25:23 . Why? Because I'm using more and then I'm starting to see some
25:28 . And then here's the Eigen structure see these channels, they show up
25:32 nicely now and then my canyon is clean as well. OK. Next
25:44 we had this gradient structure tensor. gonna take the derivative of the day
25:48 the amplitude mhm in line cross line . I'm gonna cross correlate those derivatives
25:56 each other atom at a location. I'm gonna have at every location I'm
26:02 have a little three by three cross maker. I'm gonna average that over
26:08 traces by five traces by seven And get this gradient structure tenor.
26:15 gonna push a button. The first tells me the normal for the
26:23 the eigenvalue. So how much of data is represented by a plane I
26:35 use that to compute chaos, So they're gonna use all three
26:42 But anyhow, here is a vertical through amplitude in the in line direction
26:50 the cross line direction and the time then here's the gradient structure tensor
26:56 let's call it chaos because that's what is gonna call it. And then
27:00 is a dip scan coherence maybe using . So Baker doesn't say um the
27:07 thing is, well, this one higher resolution why using less traces probably
27:12 nine traces instead of 25 traces. you wanna compute coherence along structural dip
27:21 a couple of you used the default and uh patrol, their default is
27:27 the compute variant on structure di computationally longer, but you're gonna have a
27:33 of smearing artifacts in there. So I calculate on a time slice,
27:42 default and patrol, I am going correlate a drop with a zero crossing
27:49 a peak with a zero crossing with . I'm gonna have a low
27:54 OK. If I go along structure across 408 of peak with a peak
28:01 a peak with a peak with the , I have high co so that's
28:05 you wanna do. Here's an example Alberta with quite a bit of structure
28:12 it using along a time slice. what you see is something that looks
28:19 lot like contour and it does look contours. Because if you think of
28:24 onion pattern on when you cut seismic data, what you're doing is you're
28:30 those chops and peaks of the onion each other, you're not going a
28:34 structure. Here is a long Now, I have something that geologically
28:40 very reasonable. I have a bunch an echelon pa Hi. Now your
28:48 analysis window makes a difference and this uh from oh a low quality seismic
28:59 volume. So we're gonna look at window that's just one sample thick,
29:04 milliseconds thick and then there's steps and , now things are starting to come
29:18 18. Yeah, it looks pretty . Then if I go to 24
29:25 3036 they start to get washed I even go to 42.
29:34 So the idea the question is so days, the sampling per was six
29:40 and it was one of the earlier ocean bottom cable acquisition in the Gulf
29:48 Mexico. OK. And they well, we don't have high
29:53 no ocean bottom nodes. Actually, ocean bottom nodes. We don't have
29:57 frequencies. We only have so much at the ocean bottom. Let me
30:04 every six milliseconds instead every two milliseconds I don't have greater than 90 Hertz
30:09 . OK. Well, that's what did. Now, a good rule
30:16 thumb, if you were to ask , what's the best window to use
30:20 coherent for variance? Never going to the default. OK. The
30:28 So if you ask me, which the best one, what you can
30:32 is look at your target, what's peak, the peak distance and
30:40 What's the dominant period in the And if the dominant period is 20
30:49 , that's the window you wanna use you build up. You're adding better
30:56 as you go from 2468, up 20 milliseconds, you're gonna build up
31:03 statistics, you're gonna get rid of stuff and look at more geological
31:09 And below that, you're already mixing reflectivity with the seismic wavelet with,
31:17 um now Anthony's favorite operation convolution. willing to share that with them,
31:31 ? OK. It was Zach's favorite week. He loves convolution.
31:37 So, convolution. So, you , I'm gonna, if I have
31:41 bunch of little reflectors and I'm doing copy paste operation, I'm already mixing
31:47 with my seismic wavelength, you So, yeah, I can,
31:51 be able to improve it a little by, by going bigger. And
31:56 I can go find her, maybe get a little more discrimination of thinner
32:01 channels and so forth. I I'd it if you've got good signal,
32:06 you're greater than the dominant frequency, what you're doing, you're mixing other
32:12 . OK. So you're not And that's why in this image.
32:17 here are the dominant periods uh probably 18 milliseconds. All right. And
32:25 I go a bigger window things, start to see other channels from shallower
32:31 deeper come in and just mixing And I think I'll have a,
32:35 another image of the same data volume some point though. Then the vertical
32:40 window comes into play as well. This one happens to be from,
32:46 Mexico. And uh here and this here's my wave list. So I
33:00 actually peak, drop peak. So it's gonna take this anomaly and
33:09 it here. This, this strong is gonna give me a vertical
33:16 And so is this one? So I cut it, I'm gonna see
33:23 orange fault is gonna be right on green slice and this magenta fault is
33:28 to be shifted to the side. what happens on the time slices through
33:34 or variant? It's kind of annoying the faults move a little bit and
33:40 has to do with which wavelength is the calculation of the wavelengths not centered
33:47 your time slide, it's gonna shift to right in and out as you
33:52 really deep and the ball becomes more . Well, now I see the
33:58 Paul three and four times and I total garbage. So the uh coherent
34:05 down for faults that become more and horizontal. OK. So in
34:13 coherence is an excellent tool for delineating boundaries in good false lateral stratigraphic
34:20 In your exercises, you're seeing you're saying edges of bright spots,
34:28 seeing turbos and all channels inside the , OK? It allows accelerated evaluation
34:37 large data ions just by animating through like you did. OK. You
34:41 a real good idea of what that um volcanic sequence looks like provides quantitative
34:48 of fault or fracture presence. If dark black, I'm real sure there's
34:53 fault there. If it's light well, maybe a fault there,
34:57 it's not. If you hand pick , you're saying it's there or it's
35:03 . I mean, if you pick or you don't pick it, it
35:07 Strat democratic inter information that's otherwise difficult extract. So we can see
35:14 it seems to be watering features, sees TSH collapse, all kinds of
35:18 that are pretty easy to visualize. hard to pick. You always want
35:24 calculate a more structural depth. They local balls that have dragged or poorly
35:31 or separate two similar reflectors don't appear to be discontinuous, won't show up
35:37 coherent form. So you gotta be of that. And in general,
35:42 want to use stratigraphic features are best on horizon slices structural best analyzed on
35:48 slices. OK. So that's coherence , that's family. The next part
35:59 amplitude gradients soble filters and second derivatives amplitude which I'll call amplitude curvature.
36:08 our wedge model again, high low impedance, high impedance, positive
36:15 on the base negative reflection on the peak chop peak trough, peak
36:23 OK. And then I'm here's my term resolved punning unresolved. So if
36:33 were to look at the draft heat and plot that, notice that here
36:42 it's unresolved, the trw peak, the thickness is near constant, we'll
36:48 to that next picture. OK. around a little bit near constant.
36:54 is it wiggling around? Oh the lobes are modifying the thickness a
36:59 OK. Then below resolution notice the gets by smaller and smaller and it
37:11 out that I have here's the uh my layer is capital delta T thick
37:22 I have a reflector that's capital delta over two above capital delta T over
37:28 below and one of them is one of them is negative. Then
37:35 recognize from first year calculus I take one to the right minus the one
37:41 the left divide by self fatigue. my derivative ex so that's my
37:52 So this thing here on the left by delta capital T is the definition
37:59 a derivative. So what happens is interference pattern is going to be instead
38:08 a uh a trough peak trough is to be a trough peak that's gonna
38:14 rotated 90 degrees. And the amplitude going to pay linearly with thickness.
38:24 . That's what we have. So linear decay with thickness. OK.
38:30 here's a Soble filter edge detector that's canvas, all the you know Photoshop
38:37 the different uh you know, graphics , photograph processing stuff. So uh
38:43 was a phd student here and he one to me because I was younger
38:49 . And here's my edges. I spider eyes and chicken legs like you
38:54 the river numerically and delta X goes zero. That's the definition of
39:01 And the Soble filter is I take derivative and in line and cross line
39:07 in this case, horizontally and vertically from each Adam a square root that's
39:14 filter common edge detector. Other ones picture three by three median five by
39:25 median North south gradient, East west in Boston, you know all those
39:30 filters that um these guys applied to . OK. So we looked at
39:37 difference between two traces instead of cross , let's calculate the square difference between
39:44 trace on the left and the target . And this is work that uh
39:48 at all when he was a Chevron done and but spot the minimum difference
39:58 then we got to normalize it. I'm gonna take the difference in line
40:02 cross line and I gotta normalize by end of this. So I get
40:05 between zero and one. Here's an using Chevron's algorithm that they call edge
40:14 . OK. And it's a sole . And then this image by a
40:18 called Aoba offshore Nigeria and I was shallow. He's got some mud
40:26 he's seeing some channels, some more , uh more channels over here.
40:33 got a mudslide uh except I don't any faults at this level.
40:42 So now what value should we use the soble filter? Well, normally
40:49 just calculate the one to the right one to the left, right.
40:53 I could have used one that's three the right and three to the left
40:57 five to the right and five to left and seven it to left,
41:01 to the right and seven to the and just take a nose derivative.
41:06 then here is a nice amplitude And here I'm using 57 away and
41:15 five away three away one way, ? And as I become closer and
41:25 , one of you mentioned, you the tangent. So here, I'm
41:29 chord Cho RD and here I approached tangent which is the definition of the
41:38 . OK. Well, how about ? Here's a longer wavelength event,
41:44 smoother. All of those are pretty . Let's add up an average.
41:52 And if I add up those oh, last week we talked about
41:57 Hilbert transform, what these guys are is taking the Hilbert form horizontally.
42:06 . And using that as an edge to OK. Well, they're gonna
42:14 it by smoothing it a little bit winning it the original and then they're
42:19 do it. And uh at Saudi they'll call OK. All right.
42:27 here's a example then of a cartoon zero, negative amplitude. Uh So
42:37 , I've got low amplitude and then strong negative amplitude here is my uh
42:43 part, here's my cut bank, the flood point. So I've got
42:47 two point operator and by the this is kind of the amplitude as
42:51 go along looking through. All So now I got a two point
42:57 and I'm gonna go across there. am. OK? Give me that
43:05 , right. So I got a sharp change here at the cut bank
43:09 kind of a more gentle smear change the point part. So they're gonna
43:14 this Hilbert transform, which is a out operator. It's actually a longer
43:22 operator and they're gonna take that guy cross Cory and now they balance it
43:33 bit. OK. So we then it a little more. So that's
43:39 they're doing. Here's an example from Arabia seismic amplitude times sliced kind of
43:49 . I can structure time slice. technique that I really like my
43:53 maybe three by three traces are just don't say here's the generalized Hilbert
44:00 So from where you are, I you can say yeah, pan show
44:03 this. OK. So now we to think well, why, why
44:08 the channel show a better on their pills of transform? Well, their
44:16 is bigger. OK. Might have traces in it instead of nine,
44:22 gonna get better statistics. OK. of all, I've got all these
44:29 problems and stuff my channel edges might smeared. So my response is going
44:36 be a smeared edge instead of a edge. So a long wavelength
44:43 it is going to enhance that a better than the other one is.
44:49 , I'm using Eigen structure coherence. structure coherence is gonna be sensitive to
44:56 wavel shape, not the amplitude. it may be that here I'm at
45:02 below tuning those channels have an amplitude below tuning. That will be the
45:09 with decay is one over the If you're below tuning the wavel,
45:14 is the same, that peak to distance was the same. So the
45:17 algorithm might, might fall apart when get very, very, they don't
45:22 to be really thin, they have be thin with respect to a
45:25 OK. So a couple of reasons to why, that's why. But
45:30 , a nice algorithm OK. Vertical window here plus or minus 24 milliseconds
45:41 and then Soble filter plus or minus milliseconds. A little better resolution plus
45:47 minus six. Not bad. Then look at here. I've got a
45:54 uh animation question M is zero milliseconds . Well 18. Yeah, maybe
46:05 or 18 works the best. Then start to mix again. So the
46:09 thing happened, happened with coherence that make too big a window. I
46:15 to mix, mix uh photography. . How we doing Stephanie is still
46:30 with us. That's good. All . Now don't throw your head
46:35 You look like you're being pummeled. . Got the seismic AM amplitude.
46:43 got an envelope. Let's take the of the envelope. This one,
46:47 approach is very easy to understand. why I'm gonna do it. The
46:51 art Barnes did. I'm gonna take in line derivative of the envelope divide
46:56 one over the envelope cross line derivative the envelope one over the envelope.
47:01 of doing it on a map. . Here it is uh crossline
47:09 So uh in this direction, he's a salt dome here, a salt
47:15 here. This is offshore in I start to see some channels.
47:19 doing it on time slices. So he crosses the onion cut of
47:25 he's got some anomalies there. So gonna filter it with a vertical median
47:29 and this is what he will Yeah, it looks pretty good.
47:36 ? And now I see some nice in here. So this was a
47:40 paper. It never really got deployed in landmark. So we can do
47:48 the same thing. We're gonna take structural in filter data, take the
47:53 line energy gradient cross line energy Got it eigenvectors. OK. So
48:01 going to be the principal component filtered of the data. And then I'm
48:05 to take it derivative in line through cross line, right? So what
48:15 did with the eigenvector analysis we can you hear me tell you what
48:28 asked to take a break and I'm go back when we come back in
48:33 minutes and cover four or five slides what I get and we got 200
48:41 three. OK. Let's take a minute break, come back and pretend
48:47 competing. All right, I uh had skipped this section figuring you guys
48:57 look at it on your own because had it voice over and because I've
49:06 talking about Eigen structure coherence and things this. Let me just spend a
49:12 of minutes to finding different filters in for structural or new smoothing. You
49:18 one filter and only one filter you've a mean filter to calculate the
49:23 they call it structural smoothing. There's other filters. So on
49:29 the mean filter, if I have samples, OK. A long
49:34 the mean it's just the average. I can sort those nine samples in
49:42 with the biggest sample amplitude to the amplitude value and they can be positives
49:47 negatives. That's fine. If I the middle one, that's the median
49:53 . Ok. Um then the and guys like uh I'm here works for
50:07 oil company. You know, they'll about, well, look at our
50:11 versus who's your big, who's your Exxon, let's say Exxon salaries.
50:18 . Look at our salaries versus Exxon . Here's, here's our mean salary
50:24 there's their mean salary and he's mean is higher. Well, hang on
50:30 is highly biased by how much money executives make. So the main,
50:37 main salary is, is doesn't mean getting more, it means the executives
50:42 getting more and skewing everything towards higher median is what you wanna look
50:46 Ok. Meum by median housing that's reasonable than having the big mansions
50:53 Ok. So that's the median Now the alpha trim me, we
50:58 this a lot in processing and we'll the same thing. We'll sort the
51:05 . But we're saying, yeah, if I have spikes in it,
51:09 know, I wanna get, I have some of the statistics of picking
51:13 average, but I wanna get rid outliers. So I'm gonna pick,
51:17 say 20%. So I'm gonna sort nine samples. I'll take the top
51:22 , throw them away, I'll take bottom two, throw them away.
51:26 take the remaining five and average That's the al paternity on the bottom
51:33 lower, upper middle filter. So got my data. They're, they're
51:39 a grid. OK? So in case, I'm thinking of a nine
51:42 grid. I got my analysis. , I've got my analysis point and
51:47 others put it that way. So I'm gonna sort them and I'm
51:53 , if that analysis point is greater the 80 percentile value of the sorted
52:04 , make it the 80 percentile. it's less than the 20 percentile
52:09 make it the twenties percentile if it's between, let it alone.
52:15 That's the uh lower, upper middle filter. So here's one that Antonio
52:23 at EN I uh did and you see the data are kind of
52:28 So he's not throwing away anything and he's got a 30% L UN
52:38 Much eas I think you'll agree. picking will work a lot easier on
52:42 and 40% and 50% turns out to immediate filter if I throw 50% upper
52:49 away and 50% lower ones away. always, I'm making it the
52:53 OK. OK. Yeah. Now principal component filter or the Khoon and
53:03 filter is looking more for patterns. back to my friend, Alicia,
53:12 don't always pick up, they don't pick on you. I am biased
53:15 the front row because I can look in the eyes and anyhow. All
53:20 . So I got my drone from drum. I'm flying over here campus
53:29 a picture. 7 a.m. 89 1011 , 123456. Ok. So I
53:38 12 pictures photographed from my draw. still up a battery. Great battery
53:43 12 P. Um people are walking and from classes, clouds are moving
53:51 , clouds are moving out. Uh are moving in cars moving out.
54:01 us, car got bowed. That's of the pictures. Ok. And
54:08 , you know, lots of different . Uh Oh, and it's,
54:13 bright at one o'clock, kind of at seven, getting darker at
54:17 So there's different intensities of the But if I look at those 12
54:23 with all this movement of people and and clouds and stuff like that,
54:28 the pattern best represents 0 12 the one well location, but give
54:42 something specific of this. We're all the same location. I'm taking a
54:46 from the same location. Down cars moving, people are moving clouds coming
54:51 . Now, what pattern in that is the same or can best
54:56 But, ok, so I'm taking picture when you just take one
55:06 What do you see? Ok. in the area? Show me the
55:11 , people, cars, what Street, what else? Buildings?
55:20 . So what's not changing or what's of the same for all those
55:26 Yes, on the stationary. So streets and the building. Ok.
55:29 that's pattern of the streets and the and fences. If she were to
55:37 , correlate it with those 12 you would get the best cross correlation
55:43 of any other pattern. We will that an Eiden picture. It is
55:50 friend. It best represents it. with like the one, the normal
55:55 represents the direction of most change. . Now we're taking pictures which one
56:03 represents those 12 pictures. That's the picture if we were picture faces and
56:11 can face another thing they use at courses. Uh So we're looking at
56:16 pattern, that's what we're doing. ? And then that if I were
56:21 leave square subtract, fit those data that picture and then we square subtract
56:29 and then fit it again. And would be the second Eigen phase and
56:33 would keep doing it until I had of them. And the last one
56:36 have very, very little information So on this slide, I've got
56:41 traces and I've got a pattern. use the, the mouse so that
56:49 far away can, can see. I got uh amplitude one,
56:56 one, amplitude, one, amplitude , amplitude two kind of store.
57:01 got a wavel got noise on Gonna take 55 samples. I'm gonna
57:08 11 samples in time five traces. ? And I'm gonna ask,
57:15 what's the pattern? Well, I 11122 um kind of minus one maybe
57:29 0.75 minus 0.75 minus 7.5 minus 1.5 1.5. Uh one half, one
57:40 , one half, 110, crossing . You see laterally, I have
57:48 same pattern. Now it can be down or positive but it's the same
57:54 of getting we three weak ones and strong ones. OK? That's what
58:00 eigenvector is gonna look like here or Eigen pattern or the Eigen map.
58:06 . So I get that pattern. we're gonna apply it to the five
58:12 . There are my five traces and red is the mean filter and in
58:22 is the median filter. Um in , I'm sorry, is the median
58:28 and in green is the principal component . So you see, I'll go
58:33 the next picture, see how the and the medium filter they overshoot.
58:41 not representing as well as the principal filter. Now, what we have
58:47 the main filter for this center point based on five samples. I take
58:55 average of those five samples. The filter of that center point, it's
59:01 on five samples. I take the of those five samples. The principal
59:08 filter is a little bit more I compute the pattern from 55
59:15 So I have more statistics. I a cross correlation matrix. We call
59:20 a covariance matrix. I calculate the . That's the pattern. I cross
59:26 that pattern with the data itself. five point pattern with the five point
59:33 get a cross correlation coefficient multiplied by multiply the pattern by the cross correlation
59:42 . That gives me the first principle . That's what it's called. You've
59:47 heard the word principal component here and . OK. So that's what we're
59:52 and that's why it gives a better . So if you have normal
59:58 the principal component or Cohoon and well after two people filter is the best
60:04 to use. If you got spikes the data, it's probably the worst
60:08 to use. Do you want to a median or alter being filter?
60:12 . And here's one using principal component from Antonio. So original data.
60:20 I don't know why I'm missing that data. Yeah, I know what
60:26 need to do. I need to animation of OK. So, so
60:41 , I probably had them on separate . After. Yeah, I it's
60:47 the way it really preserves amplitude quite . OK. All right. Oh
60:55 on. Here's your data quorum. . Before, after it gets rid
61:04 a lot of cross cutting. So you're gonna look at that this
61:20 . Pardon? That's a structure or . Yes, sir. Yeah,
61:24 a structure or filter. And um that, that, that version of
61:29 and filtering is not in control. . So now here's my data gonna
61:42 this principal component filtering or Khoon and filtering. And we're gonna represent the
61:48 curve by the the magenta curve. the magenta curve noticed got the same
61:56 but different amplitudes. So that's how different than semblance semblance. I'm using
62:01 mean replacing all five traces here, maintaining that pattern and amplitude. Then
62:09 can look at that pattern and I changes in amplitude from uh three stronger
62:16 to two weaker ones. I can a derivative of that. So I'm
62:20 do that. If I have three three, I can compute the derivative
62:28 this pattern, which is the first , the first Eigen map if you
62:35 . If we're a photograph, I it an Eigen photo and put first
62:38 map in the X direction in the direction. How much energy does it
62:44 ? Um first eigenvalue measures the OK. So here is uh data
62:53 gulf of Mexico happens to be depth . And here is the gradient of
63:01 eigenvector multiplied by the energy. And this this uh the west to east
63:07 . And I see this change uh change in amplitude. And I've been
63:12 this uh sand pan over here, the details of it. And then
63:18 I can, I can co render with the I can value if you
63:24 or the energy associated with it. then I kind of now it looks
63:28 shaded relief ball. OK? I you this picture earlier on coherence.
63:35 on a time slice here it is the horizon slice, it's the Paleo
63:40 River. We'll come back to that week and here is the amplified gradient
63:47 left to right. So what do see different? Well, I see
63:52 South acquisition footprint which is due to sale lines. Uh you know,
63:58 geophones, the hydrophones moving in and of the line because the currents,
64:02 cetera. OK. Then the things the yellow arrows. Well, I
64:08 this little guy wiggling here, don't see it on coherence. I see
64:16 little guy wiggling here. Don't really that incoherent. So when I fall
64:27 resolution tuning thickness, so the thinner are gonna be I'm sorry, the
64:33 channels will statistically be thinner. I my coherence Eigen structure coherence change,
64:41 I still have an amplitude change because the amplitude changes with respect to
64:46 So I can see those changes. one from uh West Texas Central Basin
64:56 . I see some pieces of channels here. Uh It's a Devonian 31
65:01 of church. And then I see of these channels you got meandering channel
65:07 this happened to be the targets, these targets show up very nicely on
65:12 amp gradient. They don't show up on coherent. There's one from South
65:18 Oklahoma, a coherence image. I see a little bit of it
65:22 now I can follow it better. follow this one, all these as
65:28 . And then uh one from South Island, I can look at the
65:33 of different angle that as I'm So it 45 uh 90 degrees.
65:41 of course, when I look at perpendicular charter, thanks, gonna skip
65:50 one just for historical reasons. I it in. Let's say you've got
65:57 horizon you've got most of you are um pretty well with the horizons.
66:02 I wanna say one thing I noticed with Zach here that unbeknownst to
66:11 he hit the auto picker and the picker. Damn, did a pretty
66:17 job on this horizon. And this not, I've used this one,
66:23 survey for eight years at least. this year I decided, let me
66:31 the structure in a filtering early in beginning because it's gonna sharpen up the
66:35 . It's gonna make the picking easier like, wow, his horizon was
66:41 . Your past, you got to it almost all by here. So
66:45 so this is good. Nothing, nothing wrong with things being easier,
66:51 ? You still got a quality control it, but nothing wrong with being
66:54 . So now you're gonna have this and then let's say you're gonna pick
67:00 MS amplitude on the, you're gonna R MS. Not. Well,
67:05 me take the derivative in the in direction of R MS amplitude. I
67:08 look at uh I think that Carlo he he's doing reservoir kind of
67:14 So he wants to look at a sub changes inside of his reservoir.
67:19 let me see. Well, what's change in R MS Ams or maybe
67:23 has a friend who did a plus ratio calculation? What's the change in
67:30 north direction of GUS ratio? The in the east direction of plus's ratio
67:34 his restaurant? That's the first derivative can take a second route or
67:39 OK? Just on a map get . So those are the kind of
67:44 here. The original amplitude, 1st derivative could be arms amplitude could be
67:50 could be plus ratio P MP OK. That means we can take
67:57 and compute second derivative biometrically. So I've got a coherence image carbonates
68:08 in Alberta got these little bagel shaped . So these Winnipeg Gsis age
68:16 I think they're sour in age. have a nice carbonate reef with a
68:21 of porosity in the middle and then gets crunched down in the middle.
68:25 , structurally, it looks like a and porosity wise, it looks like
68:29 bagel. Ok. So all your is in the ring so you can
68:35 them reasonably well. Here they all . Um, it's b itch.
68:44 when things come together, another power in geology with my, my
68:51 Hey, you're my geologist. When stick things together and they grow on
68:56 of each other, what might you that in geology? Ok. When
69:02 eat too much candy as a kid Halloween for 20 years and your teeth
69:09 apart and they keep putting fillings on of fillings. What do they call
69:14 kind of fillings? You don't have feeling. No, somebody here has
69:24 fills. No, they call them . Put the fillings on top of
69:27 fillings on top of the filling. . Go look up the word
69:31 Anyhow, amalgamate is the carbonates grow top of other carbonates or they grow
69:38 each other? Ok. So that's of the words we use a lot
69:41 the carbonate world who have amalgamated uh buildings they just build on top of
69:47 other. Why they build on top each other? They wanna be close
69:50 sunlight. They're gonna try to grow high as they can they're gonna step
69:54 top of each other as they OK. So here the in line
70:00 , I see a little bit cross dip. Here's the curvature.
70:06 I kind of see these little holes the, the structural curvature.
70:12 So here I've got structural dip and curvature. They're OK. But they're
70:19 , the coherence is better. Oh at the amplitude dip. Ah that
70:24 pretty good. It, that gradient the East West Korea looks pretty
70:30 Really stand out. Then I can the amplitude curvature and look at it
70:35 more. OK? Here's one chopra up in Alberta. Normally you don't
70:43 fractures sometimes you do. OK. here's amplitude and here most positive amplitude
70:53 short wavelength, long wavelength. So what what you have here is
71:00 carbonate and the carbonate has fractures in but those fractures for whatever reason have
71:08 significant seismic cross section. OK. they can scatter they're scattering data.
71:18 they're they might be filled with they might be digenetic altered. But
71:24 though they're probably pretty thin, you , like maybe as thick as my
71:29 , I can still see them Uh an example for Utah who is
71:37 local ground roll expert. OK. ground roll for seismic data at 20
71:46 , you're talking 220 ft and back 220. Where's my buddy who has
71:55 ? Why? Why? 2110, ? So 220 is a common number
72:00 that's common for ground roll, you , 5000 ft per 2nd and 20
72:08 . And you wanna have your geophones . So that stuff going sideways,
72:12 of the array is reading the the other half is reading a
72:15 It cancels out. Well, that roll, even though it's 220
72:21 When I stick a telephone pole in ground, I have a hole.
72:25 does two things. One, it the stress around it so it
72:32 even though the hole is maybe 1 , it's released stress for at least
72:38 or 20 ft around it. And two, it acts like a tuning
72:44 . So that wave comes there and bounces right off of those telephone
72:50 You can see it even though they're , you see them all the
72:53 They have a drill hole. You'll that on seismic data. Even though
72:57 the drill hole, eight inches, inches. It's, it's because it's
73:03 the stress around it. Well, the word we use is scattering cross
73:08 . Ok. And like bubbles in marine environment, they use that to
73:14 submarines when somebody's firing a torpedo at . Uh, airplanes either. Did
73:21 watch any of the suspense movies? always some buff president, you
73:26 in an airplane and he's releasing Jack that the heat seeking missile can't find
73:32 that improves this. Yeah. you're thinking 34 movies, right?
73:35 all the same. Anyhow. Uh cross section. Oh, and they're
73:41 old and buff like me, No. All right. Anyhow,
73:47 isn't even smi I give you a . OK. So, um that
73:54 cross section is what you're seeing even the those things are very, very
73:58 . OK. All right. The one in this lecture is texture
74:05 So that's like furniture. Do you an apartment with furniture in it?
74:20 it all IKEA? No. Oh, it's random. OK.
74:25 can you name any of this any of them? Oh, you
74:31 on your screen? OK. You're . All right. So these are
74:34 woods in North America. All So, um black walnut,
74:44 I think this is faithful. This oak cedar. That's the boss's desk
74:55 . It's a tropical wood. So , you can see wood, you
75:00 recognize wood by the pattern of the . OK. Like this is the
75:08 of thing you see in ski OK. The on the, on
75:11 lower right. Uh at my house got wood for, so I got
75:17 oak wood for. So, you know, I can see these
75:19 then, you know, I build houses out of pine and stuff like
75:24 . Ok. So that's got a . So texture analysis defined by and
75:29 have a reference in there go up the University of Calgary. Uh She
75:34 take your finger and rub it on surface. So kind of a little
75:42 . I'm rubbing it on the Oh, that's very rough on my
75:47 . Uh, a little smoother. . Put my f uh, Jessica
75:54 . She doesn't know. I got really good shave. There's more like
75:57 a baby butt, really, really shave. Ok. So you're measuring
76:03 asperities in a window? We're gonna the same thing seismically. You gonna
76:09 a window, let's say five by samples. A long structure. How
76:13 that amplitude change? Ok. How it change? Now, I showed
76:18 two measures I could take that soble and I could take a directional
76:23 but there's other measures you can make well. And uh yeah, here's
76:29 uh it's really commonly used in remote . OK? If you wanna fly
76:36 an area and see what's the health a tree, you might look at
76:42 color. If you wanna look at age of a tree, you're gonna
76:44 at the texture. If you wanna is the farmer growing corn, soy
76:52 , uh sorghum, medicinal marijuana. things you can tell by the
77:01 Ok. So it's used really commonly forestry and agriculture or taxation. So
77:07 of Indiana, a lot of taxes corn and soybean. How many acres
77:11 soybean this year? How many acres corn? Let's go figure out how
77:14 money we have to spend. So this one from Russia and they
77:20 worried about uh people um just going the forest and building a dacha,
77:27 know, a nice little home in . So, satellite imagery then they
77:33 compute textures from the satellite data. then they're even gonna do something
77:38 They're gonna uh cluster it and to what it is, they're gonna go
77:44 and have ground truth. So they somebody on a U TV out there
77:48 say, oh this is forest. This is wetland, this is agricultural
77:53 . Uh This is the river, cetera. OK. So in seismic
78:02 , we've got one texture up another texture down there, another texture
78:07 here. So we're gonna generate these matrices. I'll define them here in
78:14 second to better understand it. We're comfortable with 32 bit data.
78:22 know what eight bit data are. , we know it's dangerous but we
78:25 what eight bit data are. in this picture, I'm gonna use
78:31 a little over three bit data. gonna go from 1 to 9,
78:37 . Three bit would be eight. gonna go from 1 to 9 and
78:42 is gonna be a trough and nine be a peak and uh five will
78:46 a zero crossing, right? So I'm gonna look at a little pattern
78:52 uh traces here. We are, got five by five. So I
78:57 a pattern of fours, sixes fours and fours and I might call that
79:03 stripy pack. Ok. It's gonna Stripe North. South. Stripe.
79:08 what I do is I take each and say how often does the number
79:13 lie to the right? And the four and I go once twice.
79:18 , 80. Ok. Eight And I'm gonna put the number eight
79:27 actually, this is just right 10 . And then I'm gonna say how
79:32 to the upper right? Once, , 3456788 times about four to the
79:44 left of uh or four to the to the right of six.
79:49 Well, I've got eight there and there and then in the upper left
79:52 gonna be eight. So how often it, how often does the number
79:59 R to the level of number No time? So I have a
80:03 of here. Ok. And I a 12 in here. How often
80:09 the number four lie above the number ? Well, 123456789, 1011 12
80:24 the 12 there. And here I've four times. The number of six
80:27 above six. Thank you. So that's what we're doing. All right
80:32 for every box. So if we a matrix that's nine by nine,
80:37 a lot. Normally we're gonna use 33 by 33. So too much
80:42 we need some statistics. So we've a couple of mes measures out
80:47 Uh We got a contrast measure, got a dissimilarity measure. We have
80:52 homogeneity measure uh correlation entropy. So ones that are most useful as attributes
81:00 you're gonna have these in the OK. They're in the tr the
81:04 that are most useful are going to homogeneity. How smooth is the horizon
81:11 entropy? How chaotic is a horizon ? Yeah, they're gonna be correlated
81:18 . If it's really smooth, it's gonna be chaotic. And if it's
81:21 chaotic, it's not gonna be but they're a little different. And
81:26 one, the energy, the name unfortunate but it's a basically measuring how
81:32 is the is the measure, the ones are out there. But variance
81:40 gonna be superior for measuring contrast and a picture of a rock and the
81:49 on your camera. It's going to 0 to 255 for each color.
81:55 . So here are the values. we're gonna look at a little five
81:58 five window and we're gonna look at gray level co occurrence to the
82:05 to the upper right, to the , to the upper left. And
82:10 we're gonna have five pixels, 256 levels, four attributes. Here's contrast
82:19 energy homogeneity. So that little catch that picture, right? And then
82:23 can go and move it around everywhere and then here's my photo, here
82:35 the contrast at 90 degrees. Here come between 8090 degrees. Now,
82:40 don't mean much to most people. just like measuring patterns where it,
82:47 most common use is you're gonna put into a clustering algorithm. A machine
82:53 algorithm. OK. So think of , we use these as interpreters.
83:00 probably use these words to each other you're saying, OK. You see
83:07 ugly P Os. That's what you be picking, right? The
83:15 You got this P Os. You use that word P OS. That's
83:20 technical term I learned from my Anyway, like that car you have
83:24 drive pop at the P OS. of figure it out. OK.
83:30 you're going along and you're picking and saying at Amaco, we would say
83:35 would use animal nature and say this ratty pick that ratty reflector. That's
83:41 tarp of the top of the Uh uh this wormy area. Oh
83:48 inside basement. Uh this area. ma oh That making fun. You
83:54 , so we would use pejorative a dog's breakfast. That dogs be
84:02 , horizon pick that and to each , that would mean something. I
84:07 , you can pick stuff like Now how do we quantify it?
84:12 we can put it in the clustering ? So yesterday in the exam you
84:19 , oh let's pick what we don't . All right. So maybe what
84:24 most representative of a dolemite is not strong reflector. It's some ratty looking
84:32 in an otherwise nice clean carbonate. we wanna quantify it so we can
84:40 visualize it. OK, either through plotting or whatever. So this one
84:46 to be from machine learning using a called self organizing maps. And we
84:52 that kind of four clusters. We for 255 it comes up with
84:56 And if you look at the OK? I got solid rock,
84:59 got broken rock. I got some , I got some cracks. That's
85:05 it found, you know, green, red, yellow,
85:10 Energy ratio coherence using eigenvectors. Got nice picture of uh very complicated uh
85:23 and some faulting nice smooth shelf And here's homogeneity, OK. High
85:32 on the shelf edge, high homogeneity the fault box, low homogeneity along
85:39 bulk, low homogeneity in the cus and some parts of the shelf.
85:48 . Let's look at uh energy how , very constant on the shelf in
85:54 of the fault blocks. Definitely not . He let's look at entropy,
86:02 entropy in the CSIS, high entropy the shelf for some reason here,
86:08 entropy along the wall. So you see what they're measuring what it's
86:12 OK. Now, uh Deng Leon , uh he worked at Marathon
86:21 Now, he's at University of West and he has one of these GLCM
86:27 volumes how constant it is. And then went into Voxel Geo picked the
86:32 point and said, hey, go pick everything that looks like that kind
86:36 energy level auto pick this up Pretty cool, like 21 years
86:43 Here's another one the way he he's a geologist. So he describes
86:50 different faces. So he'll let's look number C A chaotic hummocky moderate
86:58 low continuity. To me, this , looks like a mass transport
87:03 OK. And then um you low moderate amplitude who have moderate
87:10 high amplitude, high continuity. So interpretation, uh we'll use these kind
87:18 descriptive words to define the geology. , can we put a number on
87:24 ? That's what we're gonna do. here, the same fellow working in
87:28 Africa, offshore West Africa, an volume homogeneity contrast randomness. When I
87:40 at this, I say, oh at the TH function and oh point
87:45 is lighting up point bar is lighting , point bar is lighting up.
87:49 one point bar is lighted up, bar is lighting up. I can
87:53 to make sense out of this. measuring things in the data.
88:00 Well, control helps a lot. more textures, a salt texture,
88:06 gas sand texture, marine shale a slump mass transport texture overbank deposit
88:15 . So how does he know how define those we've got well controlled?
88:19 he knows what the textures mean geologically you can go in and start to
88:26 volumetric geo bodies by using those OK. So that's where we were
88:33 . We're still going this way OK. We still got a long
88:36 to go. So, uh lateral and coherent amplitude, they're mathematically independent
88:44 EIG instructure coherence di aus and OK. So those latter three attributes
88:51 sensitive to amplitude at all. Lateral in the total energy is measured by
88:56 soble filter. They're sensitive to thin pruning and changes in the waveform.
89:02 And then the thin bed tuning thickness us see channels and paleo topographic features
89:12 the tuning thickness. So uh a of places in the world were looking
89:16 paleo topography and then that paleo topography represent where the accommodation space is
89:26 for sand, right? And then attributes, quantify lateral patterns in the
89:33 hard to describe but can be used subsequent machine learning based basic classing.
89:41 you'll see this quite a bit. I'm worried. Ah I test
89:50 don't look at the answer. you already look. All right.
89:55 the answer? Uh Loyal theorem. , good, good. OK.
90:02 what's the answer to that? He's on the computer all? Hey,
90:19 remember Loyal theorem. Uh the the local, what's the answer infinity?
90:35 Roy Tower. But now you guys geoscientists, geologists in particular, we're
90:40 about pattern recognition. There's two answers be that could be that. All
90:54 now. He's got it now. right. So let's, um,
90:59 do another lecture about 430. And then we'll work on the
91:04 I'll walk around. Veteran. San. Um, no, the
94:40 topic uh, we wanna cover is decomposition and let's make sure it's
94:48 it's on the right channel. Number . Ok. Is that working?
94:55 ? Hello. I can't hear it now or? That's what I'm waning
95:07 . Maybe I need to go. . Mhm. Ok. I'll try
95:24 say something. Is that working? . Didn't work. I can turn
95:36 off and turn it on again. my side on one, going on
95:48 , turn it on now it's Ok. Had to reboot. Do
95:57 ever have a problem with the Everything defrosting. So it'll happen.
96:04 call up the company, what do do? It says unplug your
96:11 plug it back in. So what do you mean you got to
96:16 it? So in the refrigerator is modern refrigerator. You know how you
96:20 into the appliance store and you can open the light, turn on the
96:25 , come on. They have something display mode. So that in the
96:30 appliance store, like Home Depot, it's not using all that electricity to
96:36 things cold so that can happen to refrigerator, that's what happened to my
96:42 microphone. Had to reboot it. . That and Kim Yi is watching
96:51 through my microwave. So the last is uh spectral decomposition. Thin bed
97:00 . Usually you're gonna look at spectra in the context that the bed
97:04 Yeah, you if they're also gonna sensitive to the presence of gas instead
97:08 other pain like this is. So Victor era used to be the guy
97:18 the trial. He was tired of no oh September and you take this
97:25 wavel here and I've got spectral components from uh maybe fiber fibers. If
97:34 look where the peak, I just I have all the peaks of the
97:42 uh cosine lining up. So he's a cosine transport. And then over
97:49 where there's a trough, well, lot of the troughs line up,
97:54 all of them. So it's a weaker than the pain. And then
97:57 here um I get destructive experience all peaks and troughs. OK. So
98:04 got amplitudes and phases and one way looking at 48 components is uh putting
98:14 through trees and breaking it into a frequency, middle frequency, high
98:22 There's our thin bed tuning problem resolved, turning unresolved. So we
98:32 about this uh last week, about uh limits to resolution about order wavelength
98:43 half a wavelength if it's a depth volume, if it's two way travel
98:48 , order wavelength. And uh if thinner than that, it's unresolved.
98:54 what happens is the amplitude still changes though we're unresolved. So we're sensitive
99:02 the thickness, but we can't tell thick it is. We can't separate
99:08 top from the bottom, but we map lateral changes the thickness. So
99:15 a little bit of irritant you showed before reflection on the bottom 28 delta
99:23 reflection on the top by a sign front of its negative advanced delta T
99:29 two. And this is the amplitude gonna have OK. So it's gonna
99:36 with respect to the thickness when you're drink components. And in the time
99:47 , my seismic wave width has a spectrum view of omega. The riveted
100:00 a spectrum, same spectrum, you omega but now times high omega.
100:06 we rotate each frequency by 90 degrees you increase the high frequencies and decrease
100:12 low frequencies. And now it turns then even though we can't tell the
100:22 between the top and the bottle, we're less than a quarter wavelength,
100:27 can still see the amplitude change. if I have a horizon slice,
100:34 pick the horizon and there's a channel that horizon and it's meandering or it's
100:45 , it's a channel. Even though can't, I can still see that
100:49 on the seismic amplitude response, I can't tell you how thick it is
100:54 well control. OK. So there's difference between detecting and resolving. So
101:01 means I can see it, I can't tell you how thick it
101:04 OK? All right. So we've like all these things. We've got
101:10 ways of skinning the cat. So the one that is uh most
101:18 to seismic processors is called a short for a transplant. And in
101:26 what we do is we come with cosine waves in blue or sine waves
101:34 orange and then I put a little on. OK. So here I'm
101:39 for, I'm gonna have 100 millisecond wake up. So I go from
101:44 0.5 to plus uh minus zero 0.05 plus 0.05. So here's my little
101:54 and, and then for 20 I have a 20 Hertz carrier frequency
102:01 a window. And for 40 I have a 40 Hertz carrier frequency
102:06 , and a window. So what do then is in the time
102:11 we take the blue and the orange and we slide down the wavelet slide
102:19 the seismic trace and we cross What's the cross correlation coefficient? And
102:25 plot it sometimes it's a positive sometimes it's then a negative number.
102:30 that tells me what the spectral components for that little wavelength in the frequency
102:39 . I'm going from 0 to 100 . This one is centered at 10
102:45 , this one's centered to 20 this centered at 40 then the same width
102:51 in 48 theory. If my analysis is the same size, the frequency
103:00 is the same. OK. That's of the things you're ordering a signal
103:06 . So here's how uh we do decomposition. Wow. For how we
103:15 uh how much possible, how we spectra balancing in a processing shop.
103:21 we do, we're gonna just look different frequencies. So now I've got
103:26 reflexivity from, let's say a whale we kind of assume or it's a
103:36 assumption to say I have a random of reflectors of random amplitudes.
103:54 Some positive, some negative and therefore magnitude spectrum would be white and by
104:04 , we mean all the colors of light rays coming from the ceiling lights
104:09 this room are the same. So have a red light and a
104:13 red, green and blue light. they're all equal, I'm gonna get
104:17 light. So when we say we a white spectrum, we're saying,
104:21 , all the frequencies are gonna be same because I don't know much
104:25 Now, can we have a colored ? Yeah, sometimes on a big
104:32 , we can have it but it's rare. A co a common colored
104:38 are cyclo and like with that. you ever hear of a cyclo
104:54 So anybody so sea level rises, rises, fall rises, fall
105:00 fall, coal forms, buried, forms, buried, coal forms,
105:05 coal forms, buried. So in Europe, like Great Britain. Eastern
105:13 States, we have cold shell, shell, cold shell, cold shell
105:19 they're kind of periodic. It has to do with melanated cycles and things
105:23 that nature. So that, so do have some s sometimes we will
105:28 cyclic uh patterns in the seismic, the, in the geologic record.
105:38 this special, OK. Since nobody ever heard the word psych with them
105:44 before, I mean that's how common are. OK? But, but
105:48 do. So we're gonna assume that random. Uh and white spectrum we're
105:55 to assume for now my sore spectrum white or flat but band limited.
106:02 I go 10 to 80 Hertz. I got some noise in the time
106:10 . I take my little spikes, my wavelet and I couldn't b it
106:19 pare and not pare powerpoint every time have a spike, I'm gonna copy
106:24 little wave with paste and copy, it up and paste it up and
106:28 and I get my seismic threes in complex frequency domain. I have a
106:34 spectrum. I have a phase I've got a zero phase source.
106:38 with it turns out you don't have convolve in the like you do in
106:44 tango man, you multiply in the Ch lane. OK. So I
106:49 this by this spectrum and I get band up at the white spectrum.
106:55 ? So this is what we do a processing chunk once we make
107:01 Now, also in a processing our seismic data don't have this wide
107:10 . They simply, we don't, might have more 20 Hertz data in
107:15 ground than 30 40 50 60 We've got attenuation in the shallow surface
107:21 the weathering zone. A lot of going on the weathering zone, we
107:25 to, we have to deal with . So here's my power spectrum in
107:31 . So P is the magnitude power magnitude square. And one way of
107:36 balancing which I went through in in the one recorded lectures is I'm
107:43 to take my average spectrum for the at a particular time and I'm gonna
107:50 at it in th and the noise might be the cars and trucks on
108:00 45. OK? Or the wind the waves. So I'm gonna calculate
108:06 times the maximum and then I'm gonna it in this little bitty formula and
108:10 it does, everything that's above this is gonna move up, everything below
108:15 is gonna move down. And I a spectrum that's a little flatter,
108:23 ? So for a survey within this is how we would compute
108:29 That's just the formula we use in balance. Now, we've done
108:34 we've taken care of our spectrum. it's a little flatter and we're gonna
108:38 at parts of the spectrum that have do with geology, not with the
108:45 wavelength because the source wavelength doesn't tell anything about the subsurface. So if
108:53 just take a little window 100 millisecond reflectivity is no longer gonna have a
109:00 specter. A there's the uh reflectivity the entire survey. I've got 4000
109:12 of data and a sample every two . So I've got maybe 2000 reflection
109:18 . 2000 is a big number uh I might have a wide spectrum.
109:24 if I only have four little reflectors there, it's kind of like taking
109:27 coins out of my pocket and throwing on the ground. Well, I
109:32 have four heads, I could have tails. I don't have to have
109:37 and two all the time. So I have these different uh
109:44 So any particular realization, any particular is not gonna be white, the
109:50 will be colored. So it's gonna like this. Now through spectral
109:57 I've taken care of my source It is indeed flat. And then
110:03 is my uh spectrum that I would . So I could do this in
110:10 time domain. Take these little guys the wavel, get this little piece
110:16 a wavel or I could go into frequency domain and compute this window
110:23 Now how are we gonna analyze the of these, these little wavelengths or
110:28 look at a magnitude at 1020 30 50 6080 Hertz just gonna animate through
110:36 . OK. So here we we've picked the horizon, then we're
110:41 add 100 milliseconds to it. I've got, so I've windowed the
110:49 typically along a horizon of interest and I'm going to cross correlate with sines
110:55 cosines. And I'm gonna have, it's 100 millisecond window, I have
111:00 be careful with how I cross, gonna be truncated. OK? So
111:06 just cross correlate them and find out the cross correlation coefficient is. So
111:11 take that signs and cosines cross correlated each trace just like you folks are
111:17 uh comfortable cross correlating a resistivity log a self potential log. OK.
111:24 you're gonna cross correlate and you're gonna the cross correlation coefficient. Here's the
111:29 correlation coefficients. We're gonna look at . OK. So we're gonna animate
111:35 what's the cross correlation coefficient at 10 1520 25. So here's a cartoon
111:43 uh folks at Landmark Kenny A and , a cartoon of a vertical slice
111:51 a channel. I've got the channel and then I have a flank of
111:57 channel, another flank on the other . And let's call it a longitudinal
112:02 in the middle. It has tuning the green for these thin parts of
112:10 channel at 30 Hertz and for the parts uh at 15 Hertz where it's
112:18 . OK. So we map So here's my line a a prime
112:23 vertical view. Here's line a, prime on map view and here's my
112:30 axis that I'm mapping here. And the channel axis. I'm ma over
112:34 . If I look at the green , the 30 Hertz magnitude component,
112:40 see the flank on the left, see the flank on the right and
112:44 see a little bit of this longitudinal in the middle. That's kind of
112:48 we'll do. OK. Here's a or not a cartoon but data from
112:55 I think it's Gulf of Mexico and got a little channel. We have
112:59 10 Hertz component, a 30 Hertz component, a 50 Hertz magnitude
113:06 So again, these are just take data cross correlate with the 10 Hertz
113:12 width, 30 Hertz way with 50 W with signs and co sign.
113:16 more fancy than that. I'm going put these pictures together in a little
113:24 . Here's the 10 Hertz component and is showing me geologist will call this
113:31 TV or the channel re access. is possible to with the, with
113:49 wait number. Yeah, so I you that's, that's in question.
113:54 all of the were just the oh I was waving my arm,
114:05 , all of the attributes work just well in the depth domain as in
114:11 time domain. There are a couple differences. Obviously, if your data
114:19 , let's say in kilometers in we're not gonna have cycles per
114:23 we'll have cycles per kilometer. And then um there's some headaches with
114:33 sometimes if your data are in meters depth, that's not that common.
114:37 if they are in meters per then you have cycles per meter.
114:41 I might have like 0.0001 cycles per and then 0.002 cycles per meter.
114:48 everything reads out as zero and that bad. OK. But most of
114:54 data are going to be in kilometers kilo feet. And uh so it
115:00 works just fine. Yeah. So in this one, we're looking
115:08 the channel axis, the fancy word a TV channel way and the longest
115:15 two is where it's uh orange. then at 30 Hertz, we're gonna
115:21 for a little thinner. The tuning gonna be at a little thinner um
115:26 of the channel. So it's moving towards the flanks. See here is
115:30 axis more towards the flanks and then Hertz, you're very much towards the
115:36 . So you see this qualitatively telling thickness. So here's the thin bed
115:44 model. I've got a reflection at top reflection at the bottom. I've
115:51 a thickness and here's my time axis I got a wave coming down,
115:59 coming up. I'll tell you it's first, followed by a trough,
116:06 the next reflector coming up. And this case, I'm saying the second
116:15 is equal and opposite to the top . So this would happen if I
116:20 a sand inside in a shale So you see how the delay time
116:29 is such that the second reflector overlaps the first reflector and when I add
116:38 up, I get a stronger So that's what the tuning frequency
116:44 OK. So when the tuning, the thickness of the layer is quarter
116:51 length of the, the uh I'm gonna have this kind of constructive
116:59 . OK? So we've got different of tuning patterns. If I have
117:06 negative and a positive reflection coefficient, actually have notches in the spectrum.
117:12 go to zero at zero frequency. sorry. Yeah. At uh zero
117:17 , it'll go to zero at zero if I have a plus and minus
117:23 and then I'll have destructive interference is I have a, a half period
117:28 of a quarter period, instead of interference, I'll have destructive interference.
117:34 then for, if I have two reflectors in bed, well, if
117:39 put them together that just gives me reflector that's two times stronger.
117:46 Instead of one reflection coefficient, I'll two of them occurring at the same
117:52 . And at quarter wavelength thickness, have destructive interference instead of constructive if
117:57 both positive reflectors. OK. Here's little cartoon uh not a cartoon data
118:09 Gulf of Mexico. Uh Here's what Paleo Mississippi River looks like on
118:16 a prime and here it appear on prime. And what I did is
118:25 picked the top and I picked the and I convolve them with a little
118:33 to generate a synthetic. I plotted thickness of the picked top and
118:42 And then I uh computed spectra magnitude of the synthetic. OK. So
118:57 picture shows me the thickness, so thickness uh is in red and thick
119:06 is in blue. And now I'm show you. So this is just
119:11 picks and then I'm going to uh the spectral decomposition compute the spectrum.
119:20 I'm gonna pick the peak of the , the frequency where the spectrum is
119:24 . So where the tuning thickness is I'm gonna plot that with the low
119:31 in blue and the high frequencies in . And you can see, oh
119:36 got a low frequency tuning thickness here I got a higher frequency tuning thickness
119:43 higher over there. And let me at my thickness. Yeah.
119:47 they were inverted to each other. the tuning thickness um the the the
119:58 the thicker, the wearer, the the tuning thick. OK. And
120:06 , so this picture here of spectral frequency gives me a pretty good image
120:14 what that channel thickness is. So here's one of the first applications
120:23 from uh kind of Central Oklahoma and a red pork channel. So uh
120:30 age channels, three surveys were then merged and inside the channels or
120:40 a bunch of stuff. Ok. the channel is not filled with one
120:44 . Like a geophysicist would like to of it as filled with just
120:48 Well, like stage four has a of coal in it. Stage five
120:54 pure shale. Uh Stage uh one two have a lot of gravels and
121:00 . OK. So they're, they're . Then we have a datum down
121:05 and this, we're gonna pick this of the, the nova formation.
121:11 uh it's a, a limestone. do we pick that? Because it's
121:16 to pick? Right. So here the nova, everything's flattened on it
121:24 then we can go compute a window of the uh of analysis where we're
121:33 do our spectral decomposition. So there's analysis window and we actually have a
121:41 of channels in here which we know the well control. Here's two of
121:45 wells. Uh This is stage stage three, stage five. And
121:51 , we don't really know what was there because it was no.
121:54 if you look at the dating, see, you see stuff.
121:59 That doesn't look like a clean It's not as pretty as the data
122:03 working with in the web here and a little ugly. OK. So
122:09 gonna do, just cross, correlate with sines and cosines between those two
122:14 lines OK? Or blue magenta. the 36 Hertz spectral component on the
122:22 board. And I see channels. . I see a channel here,
122:28 channel here, a channel there, some stuff going on here, not
122:34 from this picture. And the um channels that incise wasn't necessarily there filled
122:47 water at one time. What we is what's preserved. So we have
122:53 where the channels move during flood et cetera. And uh that's what
122:58 , that's what we see in the data. Now, here's a modern
123:04 from uh Alberta Calgary, Alberta. I've got here a the bow river
123:12 if you go to Alberta, um maybe 25 m cliff going into the
123:20 Valley. So it's really in And then here is the current channel
123:25 the time of this photograph going through around, et cetera. So here's
123:29 Meander Valley. That's what we're seeing the seismic data. Here's some architectural
123:35 , point bars, et cetera in Meander Valley. So this is the
123:41 of the thing we're seeing on this , right? And then we have
123:46 lot of well control. So what Payton did uh I said,
123:51 well, if the whales uh see five and I can map a nice
124:00 channels on the seismic data using spectral . I'm happy to say this is
124:06 stage five and this is stage five these are shale filled. So these
124:11 very, they're not good targets. one and two. Uh they're the
124:18 targets. OK. So we got and here. Uh and here's a
124:22 . She didn't, she didn't know it was because there wasn't any.
124:26 , so again, remember uh what see is what's preserved. So it
124:31 be kind of complicated. Here is coherence image he ran and the,
124:39 , she has, there's a lot well control here, but they drill
124:42 wells without seismic data, they just , you know, we don't need
124:47 stinking geophysicist. We're just gonna drill . And the wells pictured here are
124:55 that saw a slump in the well . So they're seeing the edges of
125:00 Meander valley where the cliff has, come down and that gives a nice
125:06 in novel. Oh You might imagine kind of overbank deposit up here.
125:14 . When spectral decomposition came out, were surprised that such a simple algorithm
125:20 show so much. And the technique we used at Amaco at the time
125:25 1995 96 we would pick the top the base of good reflectors. In
125:33 case, a limestone and a limestone and below the channel features. And
125:39 would look for differential compaction. So come up with the thickness. Here's
125:43 thickness map. We use shaded relief I see this channel and this
125:50 And if I were to go That's stage five, which is filled
125:56 shale. And that's exactly what I'm interested in mapping. I don't want
126:00 map stuff that's filled with shale. not a good target. Thanks.
126:06 , the reason that the thickness maps look as good as spectral decomposition and
126:12 good as coherence is because we're using data and we're doing a couple of
126:18 . One we're using on 100 millisecond , we're using 25 samples instead of
126:25 samples. So we've got a random . If we were gonna like average
126:33 , we would have 25 to 12 square root of 12, about
126:39 times better signal to noise just by more samples. OK? And,
126:47 all the attributes work that way the attributes coherence, et cetera. Then
126:53 other thing is uh oh, we're , we're not averaging, we're looking
126:58 10, 2030 40 50 60 7080 . We're looking at a whole bunch
127:06 things that we're cross correlating with. doing weighted averages, right?
127:12 and then we're gonna pick out the we like best. We're going to
127:16 out the ones that stands out. it'll turn out that a lot of
127:22 images don't look like anything and the that are close to each other look
127:29 similar. So the 25 Hertz looks the 26 Hertz looks like the 24
127:34 . So human interpreter is saying, , I'm seeing a channel at the
127:38 Hertz and at the 70 Hertz, don't see much of anything.
127:43 So you've got, you're looking at whole bunch of cross correlations and then
127:48 human interpreter is picking the one they because they got a geologic model in
127:54 head. OK. So here's a one Michael Poor did when he was
128:01 Apache. He's got uh 40 He plotted against blue, 50 against
128:09 , 60 against red. And then they're, they're white, like down
128:14 , well, they're all strong and and if they're cyan colored,
128:19 it means they're probably tuned at 45 . So this is uh I believe
128:24 West Africa, I'd have to look mine annotation on the bottom there.
128:30 then over here they, they're thinner they're in reds and yellows.
128:39 Thanks and Balance specter are blue and and, well, that's gray and
128:46 . OK. Here's one of those examples we did at Amao Alio,
128:52 River. Uh red is a low green, middle, blue is
128:57 That's a more common pattern to use because blue can we think of blue
129:03 a high frequency light and red is frequency light, but you'll, you'll
129:06 it the other way as well. . Then um we gotta worry about
129:13 balancing. So you can do spectral with that equation I showed, but
129:19 can't do that in patrol. So you're gonna do in patrol, you're
129:23 take your data and you're gonna well, this, this uh spectral
129:32 component, let's say uh 18 hers between uh zero and 25,000.
129:41 OK, I'm gonna, I'm gonna at 0 to 25,000, going from
129:45 to bright red and then a higher 36 Hertz. Well, it doesn't
129:50 to 25,000, it goes to So I'm gonna change my color bar
129:56 go zero to bright blue, 0 5000. So what I'm doing is
130:02 balancing graphically. OK? And, that's what I did with this
130:09 OK. So you can rescale the graphically. That's fine. And the
130:14 uh interpretation software like a Geo Teric is Foster Findlay and Paleo Scan,
130:22 are real nice tools to be able , to balance that. In this
130:28 , yellow and red are uh thicker and Cyan's greens are thinner.
130:36 Same picture. Um A lot of , what do you call it?
130:45 lot of bad pics in the Why? Because uh 1999 Amaco got
130:52 by BP and Mart had two weeks to do everything he wanted to do
130:57 the data before getting laid off. . So this is my picking in
131:02 weeks time, a very large It's got some artifacts in it.
131:07 blue is gonna be thicker, the is thinner. It, it looks
131:14 ? We had done the coherence Oh, hair looks great. Corren
131:22 in powerpoint 5050. Hey, that pretty darn good. I'm staying thick
131:33 , thickness, peak frequency uh where channels are thickest up here. Let's
131:41 this one here then. Ah That's point part over here. Yellow,
131:49 point bar, a beer, yellow bar here, I'm thick. Uh
131:56 channel is wide so it's probably thicker over here, the channel is
132:04 probably thinner yellow. So we get just for a and this is uh
132:14 OK. Continuous way, boy dress , this is probably the most common
132:21 you'll see today. Uh This is of the Foster fan with terror.
132:30 as well. Now instead of a square wale paper square window, we're
132:43 use the Gian itself and traditionally, , standard deviation without Fernando pointing into
132:54 theory. All right. So I a B let me see what is
132:58 do now because of the dominant the period brings up to 40
133:05 So the period is gonna be like milliseconds here. It would be 100
133:11 . So that's my, you curious. So if I have higher
133:19 , I'm gonna have higher temporal, , lower temporal rate, the frequency
133:30 . If I make this, why spectrum have to be narrow if I
133:35 a narrow, oh, my mic on the floor. I was waving
133:44 arms again. Sorry folks. My mic was on the floor,
133:52 put this in my pocket. So was what we do with the continuous
133:58 would transform. We make the size the analysis window. A function of
134:06 dominant period. OK. So if have a, a short period,
134:12 frequency, I'm gonna have a narrow window. And if I have large
134:21 lo a lower frequency, I'm gonna a wider analysis window when we do
134:29 . And signal analysis, if I wide in the time domain, I
134:34 narrow in the frequency domain. If go narrow in the time domain,
134:39 go have less resolution in the frequency and the product uh are constant for
134:47 cases. OK. Now the thickness these windows is the same in
134:53 It turns out if you, if like music and if I want to
134:58 higher resolution in the frequency domain, I have to sacrifice temporal resolution in
135:05 time domain. Why do we want do that? Or we may wanna
135:10 attenuation or cue and things like OK. So forward in inverse continuous
135:19 transform, here's my seismic uh I have a synthetic and then I've
135:27 some mathematics. OK. So I take these little wavelets, they're called
135:32 wavelets with Gaussian spectrum. And I'm gonna run them up and down the
135:38 cross correlate or convolve. If you , alternatively, I could go into
135:44 frequency domain and apply these different colored banks and the fitment you'll make,
135:52 can do either one. OK. doesn't matter which way we do
135:57 I'm gonna end up with a complex spectral components here, I'm showing the
136:06 . We will also have a phase and then we can take the
136:14 take the cosine of the phase component it by the magnitude. And that
136:20 us a respectful voice. OK. I add the voices, I get
136:26 to the original trace. So why I using the word voice of the
136:32 is just a band past filtered version the data. So I'm trying to
136:37 you feel comfortable with what specialty composition doing. Voxel Geo, the way
136:44 compute the continuous wavel transform, they apply a bunch of Gaussian filters or
136:51 banks in signal analysis to the spectrum the original data and then transform back
136:58 give you the voices. Calculate the of the voices. That's the spectral
137:03 , calculate the phase of the voices phase of the voices. That's the
137:08 phase. OK. So there's a ways of doing that. Let's look
137:13 this group here of voices. A VC each have different voices, they
137:28 carry different information, sum them What do you get? Le not
137:36 the fi OK. So if you've to an opera recently, I know
137:43 haven't been to East Texas. So probably haven't been to an opera
137:46 OK. Very not. Yeah, guys just haven't lived. Ok.
137:51 you've been to an opera, you , they'll have the subtitles on the
137:56 and all four of the opera Oh, sometimes they're singing the same
138:01 but just as often they're singing different . And the idea here is different
138:07 can carry different information at the same . And Mozart was clever enough to
138:14 it harmonized just beautifully. Ok. look at some of them. Here's
138:19 uh original broadband data and oh, is that uh sinesis stuff I was
138:27 about in one of those data sets , I have pro gradation, a
138:33 of channels coming down the slope, cetera broadband. I've got an eight
138:39 component 12 Hertz, 1827 42 65 Hertz. So there's, I've got
138:51 and all of these different frequencies. there low frequencies here? But
138:57 that's good data. Now, this , OK. Let's, let's figure
139:02 what, what that is. That's of peculiar. So these are the
139:07 voices and in the seismic processing this is how the processor determines which
139:14 to keep. And the prosecutor oh, yeah, I see geology
139:18 each of those, I'm gonna keep and on four Hertz they probably didn't
139:23 anything and on 100 and 20 Hertz probably didn't see anything. OK.
139:32 here we are back to aliasing Ah That's probably the question I'll ask
139:37 week. Then thanks. And from I Joe, I'm gonna take my
139:46 on a particular source receiver pair broadcast event on an ellipse. The size
139:52 shape of the ellipse depends on the . Then I move to the next
139:56 location. I broadcast the next I go to the next surface
140:00 I do it again and I add up. OK? I'm just collecting
140:04 assembling and it'll turn out that when are all in phase and line up
140:13 that will be tangent to the reflector that point. OK. So I'm
140:19 out that reflector and up here they're . Oh Over here they're destructively
140:28 My peaks and troughs are overlapping. add them, I get nothing
140:33 I get a good reflector there. here. There's nothing to destructively interfere
140:42 these little wavelengths. If I look it on the vertical axis, I
140:49 this long frequency thing. So this called migration operator aliasing. And I
140:58 to go back to the first This one. Hang on. Gotta
141:05 this. I will you there, will send her a text and I
141:37 and are one. OK? I get interrupted again but, but I
141:47 for that but carpooling taking Uber to airport together with my spouse, she's
141:57 the train down. OK? So see this low frequency, this is
142:03 apparent frequency. So I think we about it last week that if I
142:09 a um a a tilted reservoir, I go vertically through that reservoir with
142:19 , well, I'm measuring a parent , I really are interested in true
142:25 here. I've got these ellipses that destructively interfering. This is high frequency
142:34 across there but it eight Hertz going in apparent frequency. OK. So
142:42 what we're seeing on this. So , this is operator alias and migration
142:46 alias and stuff. OK. So the spectrum, we can measure the
142:57 , we can measure the peak we can measure the mean frequency and
143:02 can measure uh the uh magnitude, peak magnitude. There's other things we
143:08 measure as well. Here's the peak frequency like I showed you for that
143:15 19 2001 Gulf of Mexico survey. here is the peak spectral magnitude.
143:25 is co rendered frequency and magnitude. where is gray is very low amplitude
143:34 then co render it with coherence. now we start to see, oh
143:39 got an orange channel and a green and the orange channel is tuned at
143:45 Hertz and the green channel is tuned 50 Hertz. So that one's
143:50 OK. So we get relative thickness . OK. Um Matching Pursuit.
144:08 do this one. Let me How much more do I have to
144:12 here? I got. Oh I can finish this. OK.
144:19 we're gonna read in a seismic We're going to generate, we have
144:26 trace and the Tober transform we can that a complex trace. And then
144:33 , last week I talked about, , you know, you got a
144:37 and when you're up here, you minimum kinetic energy, maximum potential energy
144:43 then you slide down at the you got maximum kinetic energy, minimum
144:49 energy. You come back up. did talk about this right? Or
144:53 I do that in an O I can't remember now. My mind
144:55 fuzzy. OK. No. Cho we can think of one part
145:02 kinetic energy, the other as All right. So here I am
145:08 real part. Uh oh I'm measuring with uh seismic uh geophones. I'm
145:16 particle velocity because I have a a magnet on a spring going up
145:22 down. OK. Through an electro a coil of wires that's gonna generate
145:28 in magnetic field, generates an electromotive . And that's my voltage I get
145:34 of like on your bicycle generators think . Got a little magnet in there
145:40 around. OK. So it's going and down generating that electromotive force.
145:46 the kinetic energy is the part we're . OK. The the proportional to
145:55 velocity and the potential energy is the we're not measuring but it's still
146:00 OK. So they're out of phase degrees from each other. The total
146:04 is always the same. So it'll to amount of clock always the
146:08 OK. If you add them So um we got a complex
146:14 OK. It's got a bunch we can call it a complex
146:16 We can call it an analytic trace and imaginary parts uh Hilbert transform and
146:21 original data. OK. I'm gonna the instantaneous envelope and the frequency of
146:28 current version of the data. You know how to calculate envelope.
146:32 done that, you know the frequency pretty stable at the peak of the
146:39 . So let's look at the peaks the envelope and I'm gonna go down
146:43 trace and pick every peak of the . I got 2000 samples. Uh
146:50 got maybe 100 and 50 envelopes. biggest one is 25,000. Then I'm
146:58 ask Stephanie for a number between zero one 0.6 good. If you pick
147:06 would crash, we'd finish the lecture now. OK? So 0.6.
147:15 , so this is so I said multiply 25,000 times 0.6 everything. That's
147:23 the envelopes above them. I'm gonna them. So instead of 100 and
147:27 I'm gonna have for yourself. Then gonna take the frequency of that say
147:32 that's the wavelength but I don't know phase. So I'm gonna use a
147:37 wavelength. So what I've done up the upper left hand corner, I
147:43 computed a whole bunch of complex woods their spectrum. So I got a
147:49 Hertz W wit 5.25 Hertz way wit 0.756 up to 100 and 20
147:58 So I have this table of wavel . We calculated the first guy and
148:04 first, the first envelope peak instantaneous was a 28.3 Hertz. I get
148:11 wavelet. It's a complex wavelet got complex trace. I'm gonna least square
148:20 it. That gives me a complex . Complex number of the magnitude is
148:25 strong the event is the phase is a zero degree phase. Wait,
148:30 ? 90 degrees 1 80 46. that's how we get around the phase
148:37 . And then we continue to do . We iterate, get them all
148:42 . OK. So we reach squares . So we reach square fifth complex
148:46 , its subtract it, it gives residual, we have stuff left
148:50 Yeah, let me go iterate a of times. But at the end
148:53 the day, we're gonna sum the spectrum. All right, West Texas
148:59 set. I got a bunch of here. Original data. First iteration
149:07 pick 0.8 instead of 0.6. So can say OK, it's got the
149:11 things. Second iteration. OK. using those wavelets four iterations eight
149:23 everything's plotted the same scale. I can model the data with a
149:28 of these wavelengths. Different voices. . Let me then see what the
149:34 is. I take things off. I, I subtract the biggest
149:38 Oh, look underneath that baritone. an alto singing with a own
149:45 OK. So I'm gonna continue the . Oops, continue the process after
149:52 iterations, four iterations, six or 16. Nothing left. OK.
150:05 , I've got all those complex Now I'm gonna add them up.
150:08 gotta add them up, amplitude and magnitude and phase. So here's one
150:14 and then two or eight 16. these are the kind of images you
150:22 with spec decomposition. OK. Let's at the this time choice. And
150:32 I've got a little channel here, little channel here and here is the
150:38 Hertz component. So OK, we and then the 20 Hertz component and
150:47 30 Hertz. So you're gonna see channels kind of come in and out
150:50 focus 60 Hertz 70 Haiti. OK. Let's go color code
151:04 Uh And this time they were uh frequency. This work was done here
151:10 this lab in 2005. So high in red, low frequency in
151:16 And here are these little channels coming here. OK. We ran it
151:25 recently and deploited in patrol here. gonna look at the peak frequency with
151:32 coherence on it. You start to these channels coming through nicely tuned and
151:39 going down deep into the uh middle basin. OK. So I'll run
151:46 one more time. Oops. But are the kind of pictures you get
151:54 spectral decomposition. OK. Now I've a channel here, inter flu
152:12 inter flu and I look at the well, OK. Got a wide
152:18 in the channel. Strong amplitude peaked 40 Hertz, low frequency peaked at
152:25 30 Hertz low amplitude and peaked at Hertz. And this one's kind of
152:31 like why do I have a spectrum looks like that? But look at
152:35 vertical slice through the data. And here is a the horizon here.
152:43 here's that one low frequency uh spectrum here with high amplitude. So this
152:52 what a channel looks like. Here's channel, here's another channel, here's
152:57 channel. OK. Then in between have lower amplitude and uh and a
153:07 frequency. So this is a low , this is moderate frequency. And
153:11 here I've got kind of an interference because I have an angular un
153:17 So I have low frequencies up I got very, very high frequencies
153:21 . So I actually have two peaks my spectrum where that angular un conformity
153:29 . So let's, I'll tell you , let's um let's quit there.
153:37 got a couple more pictures, but quit there. And I'm gonna let
153:42 guys on your own here in a , gonna catch a plane because I
153:46 an earlier point. This time I Southwest and I gotta check my
153:50 Um, and then, uh, week we'll get together again and do
153:57 test Friday at one o'clock like we . Oh, this year?
154:05 Do you want to do that? that what you like? I'm all
154:09 . I'm ok with that. As as you got a sound in the
154:15 and, um, talk to you
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