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00:01 this conference. This conference will now recorded. Okay, so let's go

00:09 this hypothesis is an explanation for an . Uh So it's not an observation

00:19 it's not an exploration an explanation minus observation. It's not a statement of

00:27 , it is an explanation no matter ridiculous of the observation. So the

00:32 is C a strict theoretical upper bound average. So most of you got

00:39 two right. The third question I was bad. Probably drove some of

00:45 crazy. Uh huh. The Royce journal the voice average computed using the

00:59 wave module is not a proper lower . If you did the homework,

01:05 would have seen that if you use bulk module lists and share module is

01:11 averages and then we constitute the plane modules. You'll find that if you

01:19 the plane wave module listen to the weighted reciprocal average, you get an

01:25 that's a little bit higher uh than true lower bound. And so the

01:33 A is a wrong answer. B the right answer. But see is

01:38 a right answer. I I worded badly. So there were two right

01:46 . So most of you uh picked which is not correct. And that

01:54 have been clear from the homework. one thing I could say is those

01:59 you who didn't do too well if done more of the homework, she

02:03 have done better. Okay. I was surprised at the number that

02:09 this wrong. Uh We're talking about lit defied rocks. That's the gardener

02:17 , The wildly time average equation is well lit the five rocks. And

02:23 we said the critical porosity model acts a uh an empirical upper bound.

02:33 and so that is for, you , completely liquefied rocks and the most

02:38 rocks. So the correct answer was uh affiliation usually increases anti Satrapi's

02:48 Uh Number six, What needs to constant for a unique relationship between ferocity

02:55 velocity? Well, everything else pressure to be the same for shape has

03:01 be the same degree of lift, and other things not mentioned. So

03:09 in order to have a precise relationship ferocity and velocity and this is one

03:16 why there is so much scatter around velocity trends because there are other variables

03:23 affect how well the trend is Uh which type of ferocity will have

03:29 greatest effect on seismic velocity that see ferocity. I was surprised at the

03:37 of you that got this one wrong . My shell must be composed primarily

03:43 clay sized particles. It doesn't matter they're clay minerals or not. In

03:48 , shells could be primarily course. So, um, you know,

03:56 long as you are mud rock and fissile, you would be called a

04:03 , um True false and anti psychotropic cannot by definition be homogeneous. That's

04:10 . You could be anti psychotropic. microscopically homogeneous where the degree of anti

04:17 is the same every place. And I Satrapi refers to directional

04:23 not spatial independence. Yeah. 10. We got over that one

04:30 class. Um and if you look zero porosity there you see the trends

04:36 still offset so it can't have anything do with the ferocity. So the

04:42 answer is mineral module I 11. the answer is infinity. All got

04:50 . 12. None of the It was, it would be about

04:55 halfway between courts and calcite. So answer is none of the above.

05:04 percentage of an iceberg is exposed? . Some of you said 90%.

05:10 assume that was just carelessness, 90% submerged. Which fear pack has a

05:18 specific surface area. That's a simple . It has the highest ferocity.

05:23 if you remember the equation you multiplied one minus uh one minus ferocity.

05:30 the bigger the ferocity, the smaller specific surface area. Uh As historical

05:38 size increases the ratio of surface area volume decreases. Uh So, you

05:45 , it's a one over our 16, 16 through a false uh

05:53 uh this was a homework problem. I also showed the answer in

05:58 Uh the grain size has a much effect on the sphere pac arrangement.

06:04 the answer is false, 17. homework question. And I talked about

06:10 in class, poorly sorted me a range of grain sizes. And if

06:18 a cumulative hissed a gram five is a wide range, one is showing

06:24 arrow range, So five is the answer. The 13. Sorry,

06:30 know actually question about 13. I got confused because the assumption is

06:37 density of the ice is 1.1. ice is terrible. nine and it's

06:43 than some water and that's why it's but in your own country. Gosh

06:48 Oh my gosh, that's very I goofed. Okay, anybody.

06:55 , I get it. Anyone Very . Thank you for speaking up.

07:00 anyone please email me and I'll give credit on that. Okay, very

07:10 . Sorry. Well what a brain thing for me to do. Very

07:16 . Thank you. Thank you Okay, um Most porosity reduction with

07:27 depth is accomplished by rearrangement of I should mark the rest of you

07:32 , I got that right now. only kidding about that. Okay,

07:37 rearrangement of grains and compaction accounts for porosity reduction. 20 all of these

07:47 as you bury a granule Iraq, have less point contacts. They get

07:53 out. You have an increase of as you rearrange the graves more touch

08:01 and you have more flat or intellect contacts. The answer is all of

08:05 above 23 was bad. Bad question , badly worded. Um actually,

08:15 , in a mud as you as increase the pressure. I didn't specify

08:19 kind of pressure. So right It was a bad question, but

08:23 I decrease the pressure ferocity would But as I decrease, the grade

08:30 ferocity will increase and as I decrease ability to go into suspension, the

08:40 would increase. So, um, , that was a mistake I

08:45 I was looking for all of the the correct, you know, there

08:48 no correct answer. So I crossed out. I'm sure some of you

08:53 going crazy with that one. 22 to a false Mont Marila Night

08:59 a swelling clay. True Sandstone has maximum prosperity at 15%. Well,

09:05 know that's wrong. We talked about critical porosity at 40%. Right.

09:11 , I had already given you these . Um, So if I dry

09:17 and immerse it in fluid in water look at the volume of water that

09:23 entered the poor space. That's effective . Uh, Not all, not

09:31 water won't get, be able to into all the pores. So it

09:34 be total process. Um Using known city measure density, you get total

09:42 . So the density log response to porosity. If I subtract effective ferocity

09:49 total ferocity, what's left is, , fractional bound water and or trap

09:58 , seismic velocities respond to all porosity to different amounts to each type of

10:07 , but it responds to all. the answer is all of the above

10:11 , I would have accepted B or . Because I didn't give you the

10:16 of water. So you could have that you didn't have enough information,

10:23 2.3-4 is pretty close to the right . Depending on the density of

10:29 Uh, to Z over A equals is a bad approximation for hydrogen because

10:34 has no neutrons true of false. one maybe there should be some discussion

10:44 most of you said false and I the answer would be true. So

10:50 someone want to argue why the answer false? I'll argue it. But

10:56 realized where our mistake was. Have us? He wanted, who

11:03 the answer is false? Very much . 30. Oh yeah, So

11:17 were talking about that and you said It could typically be much higher than

11:26 g per cc. Uh, this a, this is semantics then,

11:32 ? Because I said high as but said no, I didn't say no

11:36 than okay. It could be, said that point verify was typically the

11:44 that you would uh consider um, correction. Uh, yeah, but

11:55 was, that was helped to So anyway, you know when you

12:00 a rule of sales, when you the sale stop selling, right?

12:06 you needed to stop the argument as as I was gonna uh, as

12:11 as I was willing to admit Okay. Otherwise you go to talk

12:16 out of it. So if I you wrong on 30, go ahead

12:21 email me and I'll give you I could see uh, that's a

12:28 issue. It's not Iraq physics I said as high as uh,

12:32 some of you took that to me higher than so. Um, let's

12:39 kill that question. Okay, If a gas reservoir has invaded the

12:47 density may give the density of the zone uh and thus may be too

12:51 . That's true. If delta is than .805g for CC, the density

12:58 may seriously be an error and I argue is probably seriously in error.

13:03 , the answers to 33 as I reading it, I was, I

13:10 not, there should not have been word density, porosity log,

13:15 Um, density long. But the are in grams C C. I

13:20 have said a density log. And all got it right anyway, But

13:24 decided to kill the question because of term ferocity with the answers being in

13:31 for CC. So nobody got I got that wrong, but I'm

13:35 that question. All right. 34 false. The General Gardner Equation is

13:41 rough average. True. According to relation, density is related to the

13:47 race to the 1 4th power Doesn't matter if there is a constant

13:53 front is still related. two density the 1 4th power 36 was a

14:02 question for those of you who have done the homework. That was a

14:06 question. And you would have had have done the problem to realize that

14:11 is true. So the answer is . So the moral of that story

14:18 the lesson to be learned is do homework's before the next test.

14:25 37 true false shell. And given shales tend to be more dense than

14:32 stones. That's true elastic module. are the same as stress constrained as

14:38 list. That's true. 5.93 was answer. If you work out the

14:44 39, the answer. C 40 isotopic rocks can be composed of anti

14:52 minerals that they're randomly oriented. So answer is for 41. Believe it

14:59 not. The theoretical lower limit of ratio is -1. That's true.

15:06 that was in your notes, a lower limit is zero, but the

15:11 lower limit is -1. What would mean? That would mean as I

15:19 uni actually compressing a rod, it actually get thinner and it's theoretically possible

15:27 that to happen. Okay, fluids in compressible and thus have infinite bulk

15:34 . That's false. Uh If you find them, they're not uh they

15:41 have an infinite both modules. In they're very easy to compress the plane

15:47 module. This is for a constrained with zero lateral strange. So no

15:54 is allowed in the experiment. And uni actually compress And that's what P

16:01 do. That's what compression waves The answer is true, fluids have

16:07 V. P. B. S of infinity. That's true. This

16:12 was a little bit of a trick because I addressed this Iraq exhibiting history

16:20 uh huh cannot return to the same of zero effective stress. Well,

16:27 can see why one might say But the fact is as you're decreasing

16:32 pressure, you may have velocity not to the original. But if you

16:39 it all the way, you may all the damage. And we saw

16:43 couple of examples where the velocity came to the starting point. So at

16:50 pressure, uh the rock couldn't heal but at low enough pressure it went

16:57 to its original shape. So it exhibit histories. Is but not at

17:03 extremes. Okay. 46. uh have a high velocity rock that has

17:14 large increase in velocity with increasing effective . Um Well, if it's high

17:24 rock, uh it can't be very unless those pores are high aspect

17:35 And if you have a big change velocity, it must be due to

17:40 flat boys. And uh so the over which uh you closed or the

17:51 increase isn't isn't an estimate of how flat boys you have. Does anyone

18:00 to argue? 46. I'll take try. Okay. Right.

18:07 This is more of just, I the clarification questions aren't really flat voids

18:13 to have really high aspect ratios. , they have low aspect ratio.

18:21 isn't the, the, the heights the poor versus the length.

18:29 Sure. It's the shortest rate is by or the shortest diameter divided by

18:36 biggest diameter. That's the aspect Okay. A oversea Okay. But

18:43 somebody else wanna try. I'm looking somebody to give me a reason

18:50 I was I was confused to pick uh, you know, in previous

18:55 courses, uh, you know, talked about stress orientations and orientations,

19:00 know, in relation to the Okay. But you but you made

19:05 comment, didn't you? Yeah. . I meant to comment. I

19:08 know if you were looking for me put it out there. Okay.

19:12 see. I see. Um, hmm. Yeah. Just in

19:20 you know, very specific scenario in these orientations are, you know,

19:26 way it could be the case Yeah, I thought you should get

19:32 just for having made the argument, I didn't think it was necessarily a

19:36 argument has been. You see what mean? I mean, your point

19:42 well taken, but I don't think um, it changes this, but

19:49 . Do you want me to be advocate for the class? Let me

19:53 being the advocate. If the flag are important, it won't be high

20:00 . Right? I mean, if a big change in velocity and,

20:06 that's due to flat boys, then shouldn't be high velocity in the first

20:12 , should it? I shouldn't you know, leveling often velocity and

20:19 pressure or something like that. So , you guys didn't help. But

20:25 , as I've chewed on it, decided not to count this question.

20:30 whoever got marked wrong on this email and you'll get credit for it.

20:38 , yeah. I mean, according Marco's slide, the change in velocity

20:45 pressure overall is related to the The how quickly that change is accomplished

20:55 related to the number of flat So, in fact, this question

21:00 not worded as well as it should been. Uh, one A could

21:06 as easily have been correct. um, we'll just throw it out

21:12 I marked you wrong, uh, me. Okay, 47.

21:17 A false dynamic module are usually greater static module. I true.

21:24 48 velocities of Iraq sample measured at same effective pressure will be the

21:34 But remember the differential pressure is not equal to the effective pressure. So

21:41 answer is false. Even though a of rock physics experimentalists don't seem to

21:47 that they call differential pressure effective pressure their plots. Okay, 49 through

21:54 false density increases with death the overburden versus depth trend will not be

22:05 Does anyone want to argue that Okay, well I'm going to have

22:22 argue for you because as I was it, I said the overburden versus

22:27 I didn't say overburden pressure, the pressure got left out. So I'm

22:32 that one. If I mark you . Um Let me know.

22:39 And 50 gear pressure occurs when the pressure is greater than that caused by

22:44 weight of all the line fluids. true. This conference will now be

22:54 . And the important point here is the direction of displacement is orthogonal to

23:01 direction of propagation of the wave. so shear waves or transfer slaves.

23:09 waves on the other hand are longitudinal . The defamation, which is a

23:16 or a rare faction is in the of propagation. So in this unit

23:27 speak mostly about compression ways. Now like to uh when we're propagating through

23:38 solid, we like to talk about elements. And you may remember these

23:44 and as we pass a p wave a an elastic medium, these volume

23:55 get stretched in the direction of So I'm moving from left to right

24:00 they get compressed in the direction of . So do two things happen to

24:06 volume elements. They get longer or and their volume increases or decreases.

24:16 there is a volumetric change and a a shape change. And that's why

24:22 wave velocities depend on the biometric module for the rigidity which is sheer

24:30 Hold on a second. I'm Uh huh. Mhm. It's I'm

24:47 sometimes family is annoying. Okay. can you all hear me now?

24:56 . Okay. So um the p are lengthening or shortening the volume elements

25:08 they do not get wider. And is why it's the plane way of

25:13 escape plus 4/3 view. Which is because it's a uni axial compression or

25:20 or stretch in the direction of But they don't get wider because the

25:27 volume elements are also trying to get . And so they're working against each

25:34 and the results of force or stress is zero uh in the transverse

25:42 So p waves depend on bulk modules they changed volume and they depend on

25:49 modules because the volume elements change On the other hand, if you

25:55 at shear waves, what you have the change of shape only, but

26:01 maintaining a constant volume. Uh And can think of this as if I

26:07 at the center of one of these elements. Uh The volume element is

26:13 to some extent around the center. right, So these are also called

26:18 waves. Now you can imagine then if we have a fluid saturated porous

26:29 , the p waves of the shear are going to act very differently because

26:34 volume of uh ever of a volume for a shear wave has not

26:41 You don't get element to element pressure . And so the fluids are not

26:51 told they're not being influenced to move one volume element to another.

26:56 very locally microscopically, that's not necessarily as that by. Um element is

27:04 shape. Uh You may be compressing pours, expanding other pours depending on

27:10 shape and orientation. So you can what is called local flow. But

27:16 don't have long range pressure gradients, don't have long range flow for share

27:23 . On the other hand, p , you could see that these guys

27:26 being compressed. These guys are being . So you're going to increase the

27:32 pressure here and the fluids are going try to move from high pressure to

27:37 pressure. So they're they're going to a long range movement as well as

27:42 local flow. So, for p , you have both types of fluid

27:47 . For shear waves, you only the local flow. Um Now we're

27:54 going well, probably we're not gonna much about attenuation in this class.

28:01 hope to get there. Uh But past classes, I haven't gotten that

28:06 . Uh But I think we've talked attenuation being due to internal friction.

28:14 actually attenuation is a loss of mechanical . Now energy is never created or

28:22 . That mechanical energy is being converted heat energy. What's happening is you

28:26 away through the rock and you and parts of the rock rub against each

28:34 . Uh There's friction. This is internal friction that generates heat. So

28:41 wave is losing energy as it by the way. That's not an

28:47 uh mechanism. That's a visco elastic . So elastic waves don't have

28:56 Pure elastic waves don't have attenuation, Poirot elastic media do have attenuation uh

29:05 to the fluid squirting around and sloshing and rubbing against the solid. So

29:12 called fluid solid friction. So, can imagine that p waves and shear

29:17 have different amounts of fluid, solid because they have different kinds of

29:24 Uh So not only are the velocity different, but the attenuation can be

29:30 different in particular. Uh If you gas in Iraq, that makes the

29:37 , you know, no rock is gas unless you're at the surface right

29:42 the water table. Right? And there, you could be moist,

29:46 in the laboratory, we have uh can actually have dry rocks, fry

29:53 have very low attenuation. The grains against each other don't cause much friction

30:02 all. The majority of the friction fluid solid friction. Now, if

30:06 have a partially saturated rocks, say in a reservoir or I have shallow

30:13 in the subsurface. Um The uh , The water is very free to

30:22 just by compressing the adjacent gas. could shrink the gas bubbles.

30:27 So so the water at the presence the gas gives the water more ability

30:34 move, creates more fluid solid So p waves attenuate greatly as you

30:43 through gas bearing zones, which zones free gas, free gas, meaning

30:48 exist as bubbles. The gas is in solution, it exists as a

30:53 phase and is easily compressible, allowing water to move more freely. So

31:02 P waves will attenuate more than shear , which share waves. You only

31:07 local flow with p waves, you local and what a longer term

31:13 sometimes called sloshing losses. Okay, this is illustrating the same concept,

31:24 they're showing different snapshots in time. it's showing uh uh this compression moving

31:34 the rock as a function of This time is increasing, which is

31:39 because if I take a particular volume uh at one time a volume.

31:46 volume element may be stretched at another . That volume element may be

31:53 And what this results in is a dependence of the attenuation, because if

32:00 very low frequency and I induce a gradient, say from here to

32:08 the fluid has plenty of time to there. So it will travel a

32:12 distance and there will be a lot fluid. Solid friction on the other

32:20 , uh if I go to infinite uh before the fluid has a chance

32:29 migrate through all those volume elements, is now at a different point in

32:37 , it may now the volume element in may have switched to being stretched

32:42 it's being told move, don't move, don't move. That fluid

32:46 essentially be frozen in place. So there is some frequency at which

32:53 get the massive movement. And and a frequency called the characteristic frequency.

33:01 a frequency where it's continually bouncing back forth. Go here, no,

33:05 , go, go back, go , go back. So there's some

33:10 that gives you the maximum attenuation. low frequency is a relatively small amount

33:17 attenuation. Infinite frequency is relatively small because the fluid has moved very far

33:25 somewhere in between the fluid has moved most and you have the most

33:31 By the way. If you have dependent attenuation, then it's required that

33:37 have frequency dependent velocity. So, you have an attenuating rock, you

33:42 have a disperse of rock dispersion being frequency dependence of velocity. Okay,

33:52 , just reviewing some of the issues discussed early on, I have the

33:59 properties of the rock mythology ferocity for . Permeability, um pore fluid saturation

34:09 , fluid type ferocity amounts, connectivity, et cetera. Uh and

34:16 , also connectivity and size of four , etc. Uh These are the

34:22 I'd like to determine uh the elastic that I measure. Uh If I

34:28 at the velocity equations, for are the bulk module is the sheer

34:35 lists. And the density. by the way, those equations that

34:40 have for velocity square root of O. Borough or square root of

34:45 overwrote. They don't have anything to with the with frequency, there's no

34:51 term in there. Those are equations elastic rocks, not poor elastic rocks

34:59 would pour elastic rocks, fluid mobility important as we go back to Darcy's

35:05 , the ability of the fluid to through the rock determines the amount of

35:11 . Solid friction uh determines the attenuation therefore determines the frequency dependency of the

35:20 . Uh Unfortunately at seismic frequencies there not a strong direct permeability dependence.

35:30 to first order, it's okay for to talk about the elastic properties.

35:36 If we want to talk about the properties that we might measure V.

35:43 and the PNS wave attenuation. The factor, Q. P. Or

35:48 . S. Quality factor is one attenuation. Again, at seismic

35:57 uh you know, with the wave data, we have little uh

36:05 we have little basis for estimating shear attenuation, but if we have share

36:12 data and we could see different insinuation p waves and shear wave. So

36:18 we could get a pretty good indication the ratio of these QP two

36:25 And and then it's the three dimensional of these things and the density,

36:32 gives you the seismic response. And you know all of this. The

36:39 problem is non unique going backwards. that makes interpretation a ball game.

36:46 what makes it an art. And makes it requires talent to do.

36:51 there isn't just an equation that you plug the numbers into and get the

36:58 . Okay. Like I said, equations that you learned in um Geophysics

37:05 are for elastic ways and until we a little bit more advanced later on

37:12 the course, we'll show how these change with frequency if you have a

37:19 elastic medium. But we are we going to until then we are going

37:24 assume that these equations work. And we've already learned a few lessons about

37:31 equations. For example, we learned uh on the average VP and density

37:38 positively correlated and Bs and density are correlated. If I increase one,

37:43 increase the other. And that's because elastic modular. If I increased

37:49 the elastic module, I increase Uh An exception is related to fluid

37:57 . If I had fluids, uh I had gas to Iraq, I'll

38:02 the bulk module, it's more than drop the density and p wave velocity

38:08 decrease. So, in the basically we generate a pulse, we

38:19 the time at which that post was , assuming it's instantaneous to a

38:25 We then measure the amount of time takes for that pulse to transmit through

38:31 transducer, we know how long this is. We have uh distance divided

38:37 time, that gives us the So we have a transducer that creates

38:43 signal and the sample. And this be a P wave or shear wave

38:48 . And then we have a transducer receives the signal so it receives away

38:54 . That waveform is amplified and is in the early days when I first

38:59 doing this, we used in a scope, we would actually look at

39:03 waveform on the oscilloscope and pick it there on on the cathode ray

39:09 Nowadays of course we digitally record the form in the uh digitally recorded with

39:16 pC. Uh Here we have a digitalis telescope. So, but it's

39:23 an image. You take a picture the image and from the image,

39:27 pick where the wave form is and can see that can be challenging.

39:32 this is the trigger pulse. This the direct recording of the trigger.

39:37 that's the time at which the pulse generated. And now you have to

39:41 a time on the way for maybe a P wave, maybe that's a

39:47 wave. But you can see that is not as precise measurement as one

39:53 like. It'd be nice if we able to record to wave forms and

39:57 at the time difference between two wave . Uh But there's a there's when

40:02 dealing with one way for him, always an ambiguity, There's the interference

40:07 waves, there's the interference with noise what is the onset? Where do

40:13 actually pick the first break? Uh it's it's travel time from here to

40:21 . Travel time divided by distance. if I pick at the first onset

40:29 I'll get a different velocity than if pick on that peak or the if

40:34 pick an envelope and take the peak the envelope, there are all different

40:38 of ways to measure the velocity and ambiguity there. So especially as the

40:45 get weaker and you know these laboratory could be significantly in error. So

40:52 assume that they're all going to be . Always. So um finding discussion

41:01 accurate and precise our laboratory measurements. first of all, what's the difference

41:08 accuracy and precision? Yeah. Um essentially accuracy for describes, you

41:24 , scattered in your data. Am getting mixed up? Well it depends

41:31 you know what your flooded again squad one second what the present. So

41:45 something is precise, inaccurate then it's data is uh not scattered and it's

41:54 to the true value. There you . So which is precise and which

41:59 accurate. Um So precision is based how close it is to the true

42:07 . So you can have something, the other way around. Right?

42:13 looking a little figure I have pointed ? So accuracy is how accurate your

42:21 is? How correct it is. it's accurate it's correct. It's it's

42:26 right answer. So if I tell my velocity is five km/s. If

42:34 accurate, the velocity is five precise means how repeatable my measurement

42:43 So you can be precisely wrong. ? I could tell you I can

42:49 it 20 times and all 20 I get 5.5 km/s. That would

42:56 very precise But it would be wrong 10%. Right? So um precision

43:06 just a matter of repeatability. So know, how do I talk about

43:13 in the laboratory? Well if I generating signals on the same sample,

43:17 wave forms are going to be pretty . If I'm picking exactly the same

43:23 I might be very precise. On other hand, if I'm measuring different

43:28 that are supposed to be representative of same rock and I'm I'm on different

43:34 runs. I've cut different samples with amounts of. Uh huh damage to

43:42 samples etcetera. My result may not precise or if my signals are very

43:48 . You know if I'm superimposed on and I'm trying to pick that

43:54 the velocity of that thing. Um may not be very precise. So

44:02 measurements may or may not be How about accuracy? Our laboratory measurements

44:18 ? And maybe that depends on. do you think? The truth

44:24 What, what are you trying to with your measurement? Are you trying

44:29 measure what the velocity of the rock be in the earth under its original

44:37 ? If that's what you're trying to , I would say laboratory measurements are

44:43 inaccurate. They could be seriously wrong that sense. If I accurate,

44:50 mean you're measuring the velocity of the ? Well, then you can kind

44:57 quantify that based on, you different ways of picking the waveform and

45:02 forth. Um but I would argue you could be much more accurate.

45:08 what does that mean? What does velocity of the sample mean?

45:12 in some context, that's important. trying to understand, say how velocity

45:18 with carbonate content and you're looking at number of different samples. Well,

45:24 , you're not Representing your measurement as indicative of the NC two velocities.

45:32 just measuring how a variable is affecting those rocks that you're measuring at the

45:41 . So, seeing how much the changes, for example, the carbonate

45:48 , that number might be very Now, is that representative of what's

45:54 in the subsurface? Maybe? Maybe . But it does give you a

46:01 , if the laboratory measurements, if can attest to their accuracy and if

46:06 if they are potentially imprecise, Especially I send the same sample to?

46:12 different laboratories Will those numbers match very ? Maybe not. So why do

46:19 bother? Why do we go through the expense? Why do we have

46:22 rock physics lab at the University of ? Why did companies pay that Rock

46:27 lab to make measurements? So given inaccuracy and the lack of precision,

46:36 are laboratory measurements useful? I'm gonna you to answer that I guess because

46:50 could have they give a good idea a good approach of uh the

46:56 We're trying to understand. What do mean by the reality? I I

47:01 your focus on understanding. You're trying understand something. But what do you

47:08 by the reality you're trying to Yeah, that's right. Okay.

47:14 huh. What's that? They are to precise with the laboratory measurement.

47:25 . I didn't I didn't understand what were trying to say. There little

47:30 measurements. They are presided the results to take the exact result solution but

47:37 how does that make them useful? I said, they could be precisely

47:46 . Yes. You know to create . Ah So they can help you

47:55 the physics, right? Well they be used to test your hypothesis.

48:00 create a you develop equations to describe happening and you could test those

48:10 you could try to understand the systematics what's going on. Right. So

48:18 would argue that that is they're more in increasing our understanding and creating expectations

48:28 they are in giving us accurate and numbers that could be used directly.

48:38 , so a big component of this is understanding the factors that affect velocities

48:49 so what are the dominant factors? that if the compression wave velocity

48:55 mythology, certainly. And by with we mean the mineralogical composition, but

49:00 also mean the texture, uh the amount and type of ferocity that

49:07 a major factor. Then we have things that are depth related as a

49:15 trends velocities tend to increase with The effective pressure increases with death rocks

49:25 get older as we get deeper. tend to be more compacted and uh

49:33 to be more cemented. So the the older Iraq is, the more

49:39 it tends to be. So the and deeper we have more lymph indication

49:45 then there are poor fluids, gas the big swinger. But even oils

49:51 change the velocities from what the velocity be if you were fully brine

49:58 Uh then there are environmental factors like temperature, frequency, direction of the

50:09 which was related to an eye Satrapi And of course uh pore pressures in

50:18 to confining pressure. Quick question. . So you said that you can

50:26 oils um you know, can you insert an impact. What how do

50:34 classify like high G. O. . Oils like are those better to

50:37 thought of as a gas in terms like properties? It depends on the

50:41 and pressure. So we are we going to go over that at

50:46 Yeah, shallow. Your oils might more like brian, but as you

50:51 deep they'll they'll get more like Okay. And the higher the

50:56 O. Are the the more like you're going to be okay.

51:01 thank you. Okay, now the problem is highly non unique.

51:09 So different rock types can have the exact philosophy. So this was a

51:15 old hist a gram Probably from the showing overlap a lot of overlap between

51:26 and shells. The same hissed a . But even uh unlit ified,

51:32 and clay overlapped with sand stones and . Sand stones overlap with lime stones

51:38 even can overlap with some igneous and rocks. Um salt. Well,

51:47 the way, the range of these , these hissed a grams are not

51:54 . I mean this is old I mean sand stones as you approach

51:58 ferocity could go all the way out at about 19,000 feet per second.

52:03 there can be a lot of overlap salt and uh sand stones for

52:14 Okay, so these are just the limits from those hissed a grams meaning

52:21 of the data. But within these , the whole point is just to

52:25 the overlap but not to believe that are representative of what we find in

52:32 earth. Usually these ranges are too . And just one more diagram showing

52:41 on different laboratory measurements range of So there's also pressure dependence. So

52:48 can see just a lot of overlap rock types, especially if there are

52:53 pressures, which brings us to your homework for a unit six. And

53:04 , I have to scold you I mean you guys have not been

53:08 up with the homework. I didn't to give you hard deadlines on the

53:14 , but you need to step up game a little bit here. Um

53:20 we're already the unit six and I've barely gotten much from you guys.

53:27 I got to tell you if you till the last week you're going to

53:32 unhappy, You'll learn more if you're on it as we go, I

53:36 help you. And in the last of the class I'll concentrate on helping

53:42 before you hand, the homework's Well, instead of lectures will have

53:47 and we'll look at the homework I won't give you the answers,

53:50 I'll try to help you get Uh huh. But if you wait

53:55 that week to start doing the you'll learn a lot less than if

53:59 been doing it all along and you'll better on your test, which will

54:04 right before that week, you'll do on that, on your test if

54:09 have started doing the homework. So up to 61 and I'm asking you

54:17 calculate the velocity of the suspension. uh and I want you to plot

54:22 from vine of course from 0-1. these are quartz grains suspended in

54:29 So, uh just for a round , use 40 giga pascal's for

54:35 density of 2.65 and for war to 2.5 giga pascal's for both modules and

54:42 density of one. Um You know is about those are ballpark numbers

54:51 So you'll see how the velocity of suspension varies with the amount of

54:56 And in fact, what that will you is a Royce found.

55:01 now, just to walk to discuss a little bit, what is the

55:07 module? Lists of the suspension? should know the answer to that

55:13 Remember, these grains are not supporting other, they're floating in the

55:19 So, what is the sheer Yeah. Is sierra as the sheer

55:28 ? Zero? The V. V. S ratio is in.

55:35 . How do you get the bulk lists? You use words equation which

55:38 the same as the Royce found the . That comes from the mass balance

55:46 . And of course the velocity comes uh K plus four thirds view,

55:51 root of K plus four thirds. overrode. All right, so wall

55:56 know how to do this. And just an interesting uh, Uh results

56:06 x court or the volume fraction ports .6 I get a bulk module lists

56:13 3.61 giga pascal's. I get a of 1.66. The module and that

56:22 use my different from what you're So you may not be exactly these

56:27 , but you should get close to numbers. Remember, I want to

56:30 the Graph all the way from 0 1. But interestingly, If I

56:38 the p wave velocity, I get , km/s. What's unusual about that

56:49 ? Yeah. Yeah. This is is a number that you should.

56:58 guys should know if you're if you're using seismic data, you should know

57:04 velocity of water. What's the velocity seawater? Approximately anybody that's the number

57:22 got to know 1.5. Yeah, km/s. And you're right to say

57:30 . It depends on the solemnity, , depends on the depth But so

57:38 1.5 km/s. Now I'm 60% courts my velocity is lower than water.

57:48 not a mistake. That's correct. . Why? Because the grains are

57:56 in contact. The bulk modules. when you have a reciprocal, some

58:02 smaller number dominates. So the bulk bulk module is is much closer to

58:08 both modules of water, which is 2.5 say than it is to

58:14 which is about 40. Right, are both modules is very low,

58:21 our density is 50 or 66% higher water. And the result is that

58:29 actually have a reduction velocity. Uh , what ferocity is this this particular

58:39 ? What is the ferocity if the volume fraction is 0.6, what is

58:56 water volume fraction? 24? So Yeah, 40% porosity. Have we

59:04 that number before? Gosh, that's the critical porosity model limit, isn't

59:12 ? All right. So, at this case, at the critical ferocity

59:18 the rock is supposedly losing cohesion, got a velocity that's down there at

59:23 velocity of water. All right, that's what the critical ferocity model says

59:30 happen. And as you reduce the , of course you'll stay pretty close

59:36 the velocity of water. Okay, we're not dealing with suspensions unless we're

59:47 the very water bottom. Right, the grains, if I have enough

59:52 the grains will be in contact with other. Um So we're gonna have

59:58 velocities than that. So, what Did we have? And how do

60:05 depend on the factors we've been talking ? Well, if we go back

60:09 the early 1950s when we were first uh sonic data, both came up

60:17 these empirical equations where he said velocity remember there's no rock type here.

60:24 only got two factors uh it's geological and death. Those are the only

60:34 factors he's got and yet he's got empirical relationship age to the 16 power

60:42 depth to the 16 power. So will be a lot of scatter around

60:47 points, but there is a And what does this say? The

60:54 the rock to hire the velocity, grain of the depth, the higher

60:58 velocity. So not surprising, but wanted to get more precise than

61:04 And so one thing he did is tried to take into account for ferocity

61:10 Iraq and for that, he's this L which was the reason festivity

61:16 So uh in a brine saturated the more resistant the rock is the

61:23 the velocity and the deeper the higher velocity. And presumably ages somehow incorporated

61:30 depth there. But surprisingly, I seen these equations combines. It might

61:37 an interesting thing to do to take a account age, depth and

61:47 Now interestingly about the same time, minds think alike. Gasman came up

61:54 a theoretical equation he took is that are well loved hexagonal packing of

62:02 And he derived theoretically the relationship between , which was a proxy for

62:11 So being that it's a packing of , he knows the ferocity. He

62:16 the grain, the mineral. So so he knows if you have miles

62:24 this, what the affected what the should be. Uh So uh he

62:32 the density of the sphere pack Convert pressure to death. So he's

62:38 depth to the 16 power here. then he's got this other factor which

62:42 related to the composition of the He's got the youngest modules of the

62:49 , the person's ratio of the brain the ferocity of the packing and the

62:55 of the grain. And that was to the 16 power. So,

63:00 enough, a theoretical equation that looks lot like the empirical equation that was

63:08 by the way. Later on, going to talk at length about Gaston's

63:13 , but not this one. Um is different from the actual uh fluid

63:21 equation, which we will look at great great length. This business equation

63:27 not used very much in practice, uh just uh here for intellectual curiosity

63:34 of the relationship too fast equations. , we already said that velocity tends

63:43 increase with depth. Not, not big surprise now, you know,

63:48 going to vary quite a bit from to formation. Rock types are

63:54 but the general tendency is there. can't help but see it. And

64:02 these are the fits that fast made rocks at different ages. Unfortunately,

64:09 doesn't show the data points, I that would have been great, but

64:15 can see a definite tendency for a of a particular age as you get

64:20 , your velocity increases. And at particular death. The older the rock

64:26 the higher the velocity and that is awfully big range. Right? And

64:31 these are just the average values, ? These are the best fit to

64:36 lot of scatter. So the range probably even more than okay, we've

64:46 looked at the dependence of velocity on . So here's the time average equation

64:53 . It's written in terms of slowness one of the velocity is called the

64:59 and it looks a lot like a thumb right? It looks a lot

65:06 the Royce average. But here instead module I in the denominator you have

65:11 velocities, the velocity of the fluid the velocity of the solid. Now

65:17 we said this is not a theoretical . This equation is not theoretically

65:23 It probably started as a heuristic equation I was fit to data. So

65:29 general we call it an empirical Uh so as an exercise,

65:36 This in terms of travel times instead velocities. Right? So travel

65:44 we often call that delta T. sonic blogs. That's what you

65:49 You miss your travel time per unit . So you usually measure microseconds for

65:58 . Um so write this in terms transit time and also extend this to

66:06 constituents. So here this is the of the matrix. But what happens

66:12 the matrix Has, you know five components? Right? This in terms

66:19 the transit times of the components. basically generalize this equation. Mm

66:29 so the time average equation relates velocity ferocity. It's purely an empirical

66:36 It's not been derived theoretically and it for clean pour sand stones at high

66:43 . And we already looked at Gardner's . If density is related to

66:49 then ferocity is related to density through mass balance equation. So gardeners relation

66:55 us the velocity ferocity transform. Here some of uh Wylys original data.

67:07 Gregory and Gardner Ray Gregory has this in his review paper that's on your

67:14 list. And uh here uh at porosity is he's got a linear

67:21 And he shows that if you go very high porosity, rock, she

67:25 from that linear relationship. Okay, , um I'm going to wrap things

67:38 with this slide because I'm worried that recording is getting too long. I

67:43 to get some editing software to be to cut these recordings in half to

67:48 them on blackboard. But until I , I'm worried about not getting them

67:53 blackboard in time. So, uh gonna stop with this slide. We

67:59 the time average equation written in terms velocities with the matrix velocity and the

68:04 velocity. And next time we're going talk more about the rain Gardner

68:10 This is purely empirical, it was any justification for it. And there

68:16 two branches to the reindeer hunt Gardner . Uh for prosperity is less than

68:23 . Uh he uses this equation and see it's one minus ferocity squared and

68:29 not a reciprocal summits linear in the . Well, it's related to the

68:35 directly, but there is the nominee here because of the ferocity. Um

68:41 for very high porosity ease. He another branch and you could see roe

68:46 P square. That's the plane wave . So basically he's saying it's a

68:50 some of the plane wave modules. this was one of your test

68:55 It actually is a little bit higher the Royce bound and it uh produces

69:01 rigidity in in the result. Mm this guy is not zero virginity

69:11 uh and actually there's a third branch these two. He just linearly

69:17 So, you know, being an equation is pretty complicated, but that's

69:22 it takes to get all the And so I'm going to stop recording

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