| 00:01 | this conference. This conference will now recorded. Okay, so let's go |
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| 00:09 | this hypothesis is an explanation for an . Uh So it's not an observation |
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| 00:19 | it's not an exploration an explanation minus observation. It's not a statement of |
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| 00:27 | , it is an explanation no matter ridiculous of the observation. So the |
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| 00:32 | is C a strict theoretical upper bound average. So most of you got |
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| 00:39 | two right. The third question I was bad. Probably drove some of |
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| 00:45 | crazy. Uh huh. The Royce journal the voice average computed using the |
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| 00:59 | wave module is not a proper lower . If you did the homework, |
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| 01:05 | would have seen that if you use bulk module lists and share module is |
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| 01:11 | averages and then we constitute the plane modules. You'll find that if you |
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| 01:19 | the plane wave module listen to the weighted reciprocal average, you get an |
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| 01:25 | that's a little bit higher uh than true lower bound. And so the |
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| 01:33 | A is a wrong answer. B the right answer. But see is |
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| 01:38 | a right answer. I I worded badly. So there were two right |
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| 01:46 | . So most of you uh picked which is not correct. And that |
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| 01:54 | have been clear from the homework. one thing I could say is those |
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| 01:59 | you who didn't do too well if done more of the homework, she |
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| 02:03 | have done better. Okay. I was surprised at the number that |
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| 02:09 | this wrong. Uh We're talking about lit defied rocks. That's the gardener |
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| 02:17 | , The wildly time average equation is well lit the five rocks. And |
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| 02:23 | we said the critical porosity model acts a uh an empirical upper bound. |
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| 02:33 | and so that is for, you , completely liquefied rocks and the most |
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| 02:38 | rocks. So the correct answer was uh affiliation usually increases anti Satrapi's |
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| 02:48 | Uh Number six, What needs to constant for a unique relationship between ferocity |
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| 02:55 | velocity? Well, everything else pressure to be the same for shape has |
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| 03:01 | be the same degree of lift, and other things not mentioned. So |
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| 03:09 | in order to have a precise relationship ferocity and velocity and this is one |
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| 03:16 | why there is so much scatter around velocity trends because there are other variables |
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| 03:23 | affect how well the trend is Uh which type of ferocity will have |
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| 03:29 | greatest effect on seismic velocity that see ferocity. I was surprised at the |
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| 03:37 | of you that got this one wrong . My shell must be composed primarily |
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| 03:43 | clay sized particles. It doesn't matter they're clay minerals or not. In |
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| 03:48 | , shells could be primarily course. So, um, you know, |
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| 03:56 | long as you are mud rock and fissile, you would be called a |
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| 04:03 | , um True false and anti psychotropic cannot by definition be homogeneous. That's |
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| 04:10 | . You could be anti psychotropic. microscopically homogeneous where the degree of anti |
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| 04:17 | is the same every place. And I Satrapi refers to directional |
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| 04:23 | not spatial independence. Yeah. 10. We got over that one |
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| 04:30 | class. Um and if you look zero porosity there you see the trends |
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| 04:36 | still offset so it can't have anything do with the ferocity. So the |
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| 04:42 | answer is mineral module I 11. the answer is infinity. All got |
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| 04:50 | . 12. None of the It was, it would be about |
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| 04:55 | halfway between courts and calcite. So answer is none of the above. |
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| 05:04 | percentage of an iceberg is exposed? . Some of you said 90%. |
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| 05:10 | assume that was just carelessness, 90% submerged. Which fear pack has a |
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| 05:18 | specific surface area. That's a simple . It has the highest ferocity. |
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| 05:23 | if you remember the equation you multiplied one minus uh one minus ferocity. |
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| 05:30 | the bigger the ferocity, the smaller specific surface area. Uh As historical |
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| 05:38 | size increases the ratio of surface area volume decreases. Uh So, you |
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| 05:45 | , it's a one over our 16, 16 through a false uh |
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| 05:53 | uh this was a homework problem. I also showed the answer in |
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| 05:58 | Uh the grain size has a much effect on the sphere pac arrangement. |
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| 06:04 | the answer is false, 17. homework question. And I talked about |
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| 06:10 | in class, poorly sorted me a range of grain sizes. And if |
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| 06:18 | a cumulative hissed a gram five is a wide range, one is showing |
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| 06:24 | arrow range, So five is the answer. The 13. Sorry, |
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| 06:30 | know actually question about 13. I got confused because the assumption is |
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| 06:37 | density of the ice is 1.1. ice is terrible. nine and it's |
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| 06:43 | than some water and that's why it's but in your own country. Gosh |
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| 06:48 | Oh my gosh, that's very I goofed. Okay, anybody. |
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| 06:55 | , I get it. Anyone Very . Thank you for speaking up. |
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| 07:00 | anyone please email me and I'll give credit on that. Okay, very |
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| 07:10 | . Sorry. Well what a brain thing for me to do. Very |
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| 07:16 | . Thank you. Thank you Okay, um Most porosity reduction with |
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| 07:27 | depth is accomplished by rearrangement of I should mark the rest of you |
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| 07:32 | , I got that right now. only kidding about that. Okay, |
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| 07:37 | rearrangement of grains and compaction accounts for porosity reduction. 20 all of these |
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| 07:47 | as you bury a granule Iraq, have less point contacts. They get |
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| 07:53 | out. You have an increase of as you rearrange the graves more touch |
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| 08:01 | and you have more flat or intellect contacts. The answer is all of |
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| 08:05 | above 23 was bad. Bad question , badly worded. Um actually, |
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| 08:15 | , in a mud as you as increase the pressure. I didn't specify |
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| 08:19 | kind of pressure. So right It was a bad question, but |
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| 08:23 | I decrease the pressure ferocity would But as I decrease, the grade |
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| 08:30 | ferocity will increase and as I decrease ability to go into suspension, the |
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| 08:40 | would increase. So, um, , that was a mistake I |
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| 08:45 | I was looking for all of the the correct, you know, there |
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| 08:48 | no correct answer. So I crossed out. I'm sure some of you |
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| 08:53 | going crazy with that one. 22 to a false Mont Marila Night |
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| 08:59 | a swelling clay. True Sandstone has maximum prosperity at 15%. Well, |
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| 09:05 | know that's wrong. We talked about critical porosity at 40%. Right. |
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| 09:11 | , I had already given you these . Um, So if I dry |
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| 09:17 | and immerse it in fluid in water look at the volume of water that |
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| 09:23 | entered the poor space. That's effective . Uh, Not all, not |
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| 09:31 | water won't get, be able to into all the pores. So it |
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| 09:34 | be total process. Um Using known city measure density, you get total |
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| 09:42 | . So the density log response to porosity. If I subtract effective ferocity |
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| 09:49 | total ferocity, what's left is, , fractional bound water and or trap |
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| 09:58 | , seismic velocities respond to all porosity to different amounts to each type of |
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| 10:07 | , but it responds to all. the answer is all of the above |
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| 10:11 | , I would have accepted B or . Because I didn't give you the |
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| 10:16 | of water. So you could have that you didn't have enough information, |
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| 10:23 | 2.3-4 is pretty close to the right . Depending on the density of |
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| 10:29 | Uh, to Z over A equals is a bad approximation for hydrogen because |
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| 10:34 | has no neutrons true of false. one maybe there should be some discussion |
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| 10:44 | most of you said false and I the answer would be true. So |
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| 10:50 | someone want to argue why the answer false? I'll argue it. But |
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| 10:56 | realized where our mistake was. Have us? He wanted, who |
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| 11:03 | the answer is false? Very much . 30. Oh yeah, So |
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| 11:17 | were talking about that and you said It could typically be much higher than |
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| 11:26 | g per cc. Uh, this a, this is semantics then, |
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| 11:32 | ? Because I said high as but said no, I didn't say no |
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| 11:36 | than okay. It could be, said that point verify was typically the |
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| 11:44 | that you would uh consider um, correction. Uh, yeah, but |
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| 11:55 | was, that was helped to So anyway, you know when you |
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| 12:00 | a rule of sales, when you the sale stop selling, right? |
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| 12:06 | you needed to stop the argument as as I was gonna uh, as |
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| 12:11 | as I was willing to admit Okay. Otherwise you go to talk |
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| 12:16 | out of it. So if I you wrong on 30, go ahead |
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| 12:21 | email me and I'll give you I could see uh, that's a |
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| 12:28 | issue. It's not Iraq physics I said as high as uh, |
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| 12:32 | some of you took that to me higher than so. Um, let's |
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| 12:39 | kill that question. Okay, If a gas reservoir has invaded the |
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| 12:47 | density may give the density of the zone uh and thus may be too |
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| 12:51 | . That's true. If delta is than .805g for CC, the density |
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| 12:58 | may seriously be an error and I argue is probably seriously in error. |
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| 13:03 | , the answers to 33 as I reading it, I was, I |
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| 13:10 | not, there should not have been word density, porosity log, |
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| 13:15 | Um, density long. But the are in grams C C. I |
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| 13:20 | have said a density log. And all got it right anyway, But |
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| 13:24 | decided to kill the question because of term ferocity with the answers being in |
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| 13:31 | for CC. So nobody got I got that wrong, but I'm |
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| 13:35 | that question. All right. 34 false. The General Gardner Equation is |
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| 13:41 | rough average. True. According to relation, density is related to the |
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| 13:47 | race to the 1 4th power Doesn't matter if there is a constant |
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| 13:53 | front is still related. two density the 1 4th power 36 was a |
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| 14:02 | question for those of you who have done the homework. That was a |
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| 14:06 | question. And you would have had have done the problem to realize that |
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| 14:11 | is true. So the answer is . So the moral of that story |
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| 14:18 | the lesson to be learned is do homework's before the next test. |
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| 14:25 | 37 true false shell. And given shales tend to be more dense than |
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| 14:32 | stones. That's true elastic module. are the same as stress constrained as |
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| 14:38 | list. That's true. 5.93 was answer. If you work out the |
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| 14:44 | 39, the answer. C 40 isotopic rocks can be composed of anti |
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| 14:52 | minerals that they're randomly oriented. So answer is for 41. Believe it |
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| 14:59 | not. The theoretical lower limit of ratio is -1. That's true. |
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| 15:06 | that was in your notes, a lower limit is zero, but the |
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| 15:11 | lower limit is -1. What would mean? That would mean as I |
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| 15:19 | uni actually compressing a rod, it actually get thinner and it's theoretically possible |
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| 15:27 | that to happen. Okay, fluids in compressible and thus have infinite bulk |
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| 15:34 | . That's false. Uh If you find them, they're not uh they |
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| 15:41 | have an infinite both modules. In they're very easy to compress the plane |
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| 15:47 | module. This is for a constrained with zero lateral strange. So no |
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| 15:54 | is allowed in the experiment. And uni actually compress And that's what P |
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| 16:01 | do. That's what compression waves The answer is true, fluids have |
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| 16:07 | V. P. B. S of infinity. That's true. This |
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| 16:12 | was a little bit of a trick because I addressed this Iraq exhibiting history |
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| 16:20 | uh huh cannot return to the same of zero effective stress. Well, |
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| 16:27 | can see why one might say But the fact is as you're decreasing |
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| 16:32 | pressure, you may have velocity not to the original. But if you |
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| 16:39 | it all the way, you may all the damage. And we saw |
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| 16:43 | couple of examples where the velocity came to the starting point. So at |
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| 16:50 | pressure, uh the rock couldn't heal but at low enough pressure it went |
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| 16:57 | to its original shape. So it exhibit histories. Is but not at |
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| 17:03 | extremes. Okay. 46. uh have a high velocity rock that has |
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| 17:14 | large increase in velocity with increasing effective . Um Well, if it's high |
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| 17:24 | rock, uh it can't be very unless those pores are high aspect |
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| 17:35 | And if you have a big change velocity, it must be due to |
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| 17:40 | flat boys. And uh so the over which uh you closed or the |
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| 17:51 | increase isn't isn't an estimate of how flat boys you have. Does anyone |
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| 18:00 | to argue? 46. I'll take try. Okay. Right. |
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| 18:07 | This is more of just, I the clarification questions aren't really flat voids |
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| 18:13 | to have really high aspect ratios. , they have low aspect ratio. |
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| 18:21 | isn't the, the, the heights the poor versus the length. |
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| 18:29 | Sure. It's the shortest rate is by or the shortest diameter divided by |
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| 18:36 | biggest diameter. That's the aspect Okay. A oversea Okay. But |
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| 18:43 | somebody else wanna try. I'm looking somebody to give me a reason |
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| 18:50 | I was I was confused to pick uh, you know, in previous |
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| 18:55 | courses, uh, you know, talked about stress orientations and orientations, |
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| 19:00 | know, in relation to the Okay. But you but you made |
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| 19:05 | comment, didn't you? Yeah. . I meant to comment. I |
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| 19:08 | know if you were looking for me put it out there. Okay. |
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| 19:12 | see. I see. Um, hmm. Yeah. Just in |
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| 19:20 | you know, very specific scenario in these orientations are, you know, |
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| 19:26 | way it could be the case Yeah, I thought you should get |
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| 19:32 | just for having made the argument, I didn't think it was necessarily a |
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| 19:36 | argument has been. You see what mean? I mean, your point |
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| 19:42 | well taken, but I don't think um, it changes this, but |
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| 19:49 | . Do you want me to be advocate for the class? Let me |
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| 19:53 | being the advocate. If the flag are important, it won't be high |
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| 20:00 | . Right? I mean, if a big change in velocity and, |
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| 20:06 | that's due to flat boys, then shouldn't be high velocity in the first |
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| 20:12 | , should it? I shouldn't you know, leveling often velocity and |
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| 20:19 | pressure or something like that. So , you guys didn't help. But |
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| 20:25 | , as I've chewed on it, decided not to count this question. |
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| 20:30 | whoever got marked wrong on this email and you'll get credit for it. |
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| 20:38 | , yeah. I mean, according Marco's slide, the change in velocity |
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| 20:45 | pressure overall is related to the The how quickly that change is accomplished |
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| 20:55 | related to the number of flat So, in fact, this question |
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| 21:00 | not worded as well as it should been. Uh, one A could |
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| 21:06 | as easily have been correct. um, we'll just throw it out |
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| 21:12 | I marked you wrong, uh, me. Okay, 47. |
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| 21:17 | A false dynamic module are usually greater static module. I true. |
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| 21:24 | 48 velocities of Iraq sample measured at same effective pressure will be the |
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| 21:34 | But remember the differential pressure is not equal to the effective pressure. So |
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| 21:41 | answer is false. Even though a of rock physics experimentalists don't seem to |
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| 21:47 | that they call differential pressure effective pressure their plots. Okay, 49 through |
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| 21:54 | false density increases with death the overburden versus depth trend will not be |
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| 22:05 | Does anyone want to argue that Okay, well I'm going to have |
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| 22:22 | argue for you because as I was it, I said the overburden versus |
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| 22:27 | I didn't say overburden pressure, the pressure got left out. So I'm |
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| 22:32 | that one. If I mark you . Um Let me know. |
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| 22:39 | And 50 gear pressure occurs when the pressure is greater than that caused by |
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| 22:44 | weight of all the line fluids. true. This conference will now be |
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| 22:54 | . And the important point here is the direction of displacement is orthogonal to |
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| 23:01 | direction of propagation of the wave. so shear waves or transfer slaves. |
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| 23:09 | waves on the other hand are longitudinal . The defamation, which is a |
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| 23:16 | or a rare faction is in the of propagation. So in this unit |
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| 23:27 | speak mostly about compression ways. Now like to uh when we're propagating through |
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| 23:38 | solid, we like to talk about elements. And you may remember these |
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| 23:44 | and as we pass a p wave a an elastic medium, these volume |
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| 23:55 | get stretched in the direction of So I'm moving from left to right |
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| 24:00 | they get compressed in the direction of . So do two things happen to |
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| 24:06 | volume elements. They get longer or and their volume increases or decreases. |
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| 24:16 | there is a volumetric change and a a shape change. And that's why |
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| 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 |
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| 24:47 | sometimes family is annoying. Okay. can you all hear me now? |
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| 24:56 | . Okay. So um the p are lengthening or shortening the volume elements |
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| 25:08 | they do not get wider. And is why it's the plane way of |
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| 25:13 | escape plus 4/3 view. Which is because it's a uni axial compression or |
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| 25:20 | or stretch in the direction of But they don't get wider because the |
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| 25:27 | volume elements are also trying to get . And so they're working against each |
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| 25:34 | and the results of force or stress is zero uh in the transverse |
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| 25:42 | So p waves depend on bulk modules they changed volume and they depend on |
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| 25:49 | modules because the volume elements change On the other hand, if you |
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| 25:55 | at shear waves, what you have the change of shape only, but |
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| 26:01 | maintaining a constant volume. Uh And can think of this as if I |
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| 26:07 | at the center of one of these elements. Uh The volume element is |
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| 26:13 | to some extent around the center. right, So these are also called |
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| 26:18 | waves. Now you can imagine then if we have a fluid saturated porous |
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| 26:29 | , the p waves of the shear are going to act very differently because |
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| 26:34 | volume of uh ever of a volume for a shear wave has not |
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| 26:41 | You don't get element to element pressure . And so the fluids are not |
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| 26:51 | told they're not being influenced to move one volume element to another. |
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| 26:56 | very locally microscopically, that's not necessarily as that by. Um element is |
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| 27:04 | shape. Uh You may be compressing pours, expanding other pours depending on |
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| 27:10 | shape and orientation. So you can what is called local flow. But |
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| 27:16 | don't have long range pressure gradients, don't have long range flow for share |
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| 27:23 | . On the other hand, p , you could see that these guys |
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| 27:26 | being compressed. These guys are being . So you're going to increase the |
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| 27:32 | pressure here and the fluids are going try to move from high pressure to |
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| 27:37 | pressure. So they're they're going to a long range movement as well as |
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| 27:42 | local flow. So, for p , you have both types of fluid |
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| 27:47 | . For shear waves, you only the local flow. Um Now we're |
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| 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 |
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| 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 |
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| 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 |
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| 28:41 | wave is losing energy as it by the way. That's not an |
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| 28:47 | uh mechanism. That's a visco elastic . So elastic waves don't have |
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| 28:56 | Pure elastic waves don't have attenuation, Poirot elastic media do have attenuation uh |
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| 29:05 | to the fluid squirting around and sloshing and rubbing against the solid. So |
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| 29:12 | called fluid solid friction. So, can imagine that p waves and shear |
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| 29:17 | have different amounts of fluid, solid because they have different kinds of |
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| 29:24 | Uh So not only are the velocity different, but the attenuation can be |
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| 29:30 | different in particular. Uh If you gas in Iraq, that makes the |
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| 29:37 | , you know, no rock is gas unless you're at the surface right |
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| 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 |
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| 30:06 | have a partially saturated rocks, say in a reservoir or I have shallow |
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| 30:13 | in the subsurface. Um The uh , The water is very free to |
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| 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 |
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| 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 |
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| 33:37 | have frequency dependent velocity. So, you have an attenuating rock, you |
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| 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 |
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| 36:39 | problem is non unique going backwards. that makes interpretation a ball game. |
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| 36:46 | what makes it an art. And makes it requires talent to do. |
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| 36:51 | there isn't just an equation that you plug the numbers into and get the |
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| 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 |
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| 37:12 | the course, we'll show how these change with frequency if you have a |
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| 37:19 | elastic medium. But we are we going to until then we are going |
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| 37:24 | assume that these equations work. And we've already learned a few lessons about |
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| 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, |
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| 37:43 | increase the other. And that's because elastic modular. If I increased |
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| 37:49 | the elastic module, I increase Uh An exception is related to fluid |
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| 37:57 | . If I had fluids, uh I had gas to Iraq, I'll |
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| 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 |
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| 38:19 | the time at which that post was , assuming it's instantaneous to a |
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| 38:25 | We then measure the amount of time takes for that pulse to transmit through |
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| 38:31 | transducer, we know how long this is. We have uh distance divided |
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| 38:37 | time, that gives us the So we have a transducer that creates |
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| 38:43 | signal and the sample. And this be a P wave or shear wave |
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| 38:48 | . And then we have a transducer receives the signal so it receives away |
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| 38:54 | . That waveform is amplified and is in the early days when I first |
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| 38:59 | doing this, we used in a scope, we would actually look at |
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| 39:03 | waveform on the oscilloscope and pick it there on on the cathode ray |
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| 39:09 | Nowadays of course we digitally record the form in the uh digitally recorded with |
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| 39:16 | pC. Uh Here we have a digitalis telescope. So, but it's |
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| 39:23 | an image. You take a picture the image and from the image, |
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| 39:27 | pick where the wave form is and can see that can be challenging. |
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| 39:32 | this is the trigger pulse. This the direct recording of the trigger. |
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| 39:37 | that's the time at which the pulse generated. And now you have to |
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| 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 |
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| 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 |
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| 40:02 | dealing with one way for him, always an ambiguity, There's the interference |
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| 40:07 | waves, there's the interference with noise what is the onset? Where do |
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| 40:13 | actually pick the first break? Uh it's it's travel time from here to |
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| 40:21 | . Travel time divided by distance. if I pick at the first onset |
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| 40:29 | I'll get a different velocity than if pick on that peak or the if |
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| 40:34 | pick an envelope and take the peak the envelope, there are all different |
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| 40:38 | of ways to measure the velocity and ambiguity there. So especially as the |
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| 40:45 | get weaker and you know these laboratory could be significantly in error. So |
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| 40:52 | assume that they're all going to be . Always. So um finding discussion |
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| 41:01 | accurate and precise our laboratory measurements. first of all, what's the difference |
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| 41:08 | accuracy and precision? Yeah. Um essentially accuracy for describes, you |
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| 41:24 | , scattered in your data. Am getting mixed up? Well it depends |
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| 41:31 | you know what your flooded again squad one second what the present. So |
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| 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 |
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| 42:21 | is? How correct it is. it's accurate it's correct. It's it's |
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| 42:26 | right answer. So if I tell my velocity is five km/s. If |
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| 42:34 | accurate, the velocity is five precise means how repeatable my measurement |
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| 42:43 | So you can be precisely wrong. ? I could tell you I can |
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| 42:49 | it 20 times and all 20 I get 5.5 km/s. That would |
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| 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, |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
|
| 5999:59 | |
|
