VideoPoints

• ••• • •• • ••••• • •
GEOL7324-Rock Physics - TuedOct19
Help Tour
© Distribution of this video is restricted by its owner
Transcript ×
Auto highlight
Font-size
00:00 drug conference will now be recorded. , so by the way, a
00:08 . B. S. ratio of is about a person's ratio of
00:13 And it also means the ratio of to shear modules is equal to
00:20 In fact, you may remember from critical ferocity model, according to that
00:27 , the ratio of frame module i a dry rock is the same as
00:34 ratio in the mineral that's taken uh be an inadequacy of the critical ferocity
00:42 because that's not always the case. , in the case, of course
00:48 is the V. P. S ratio for pure courses about
00:54 And for Porous courts, dry porous is 1.5. So in that
01:03 uh stands have a frame both modules shear modules ratio of about one.
01:10 they're about equal. And we're going use that fact in a bit.
01:14 here we did numerical modeling using the toxicity equations to show the same
01:20 added more and more a ferocity to . Uh including flat pours this was
01:28 poor aspect ratio spectrum. So, full spectrum of different aspect ratios.
01:35 adding more and more of it to dry rock didn't change the V.
01:40 . B. S ratio very much was until you got to abnormally high
01:45 probably nonphysical concentrations that you started to below the dry line, but still
01:53 low B. P. B. ratio. Uh huh. You you
01:58 from our trends for Brian saturated rocks RVPBS ratios until you get towards zero
02:06 are always higher than 1.5. so now we can take samples measured
02:15 dry rocks and we could uh make measurements on the same sample fully bright
02:26 . And we could also do that using gas fruits equations which we'll cover
02:32 on in the course. But this done in the laboratory. The open
02:38 or the open symbols here are dry . You have a couple of points
02:43 deviate dramatically from the dry rock This was a a very limey
02:50 So it had a higher V. ratio. And this rock may have
02:54 very Shelly. But most of these , the open circles are along the
03:00 line and then a tie line is to the brian saturated Iraq. And
03:09 see that these sent to follow along mud rock line. In fact,
03:12 of these data points was a laboratory on a shell. So it's got
03:18 low B. P. B. ratio. Like a dry sandstone and
03:22 add water and uh it falls on dry line. I mean on the
03:26 rock line. So the general tendency their constant, the pds ratio for
03:34 stand stones A V. P. . S ratio that follows mud rock
03:39 more or less, which means that . PBS is increasing dramatically as you
03:44 to low velocities. Because here, we approach zero Shear wave velocity,
03:50 just have we still have a finite all philosophy. So, the limit
03:55 this intercept has a V. V. S ratio of infinity up
04:00 where courses we have a V. . V. S ratio of
04:04 So V. PBS is bearing along mud rock line. So for low
04:11 rocks, a tremendous difference in PBS between shells and brian, saturated
04:18 and dry sand stones. And for matter, gas saturated sand stones.
04:23 we'll see. Now some of these are acting very normally. For
04:31 these are very poorest beach sands and you add brian, you actually decrease
04:43 shear wave velocity a little bit. ? Because you're increasing the density.
04:51 you increase the p wave velocity far . So you move slightly to the
04:57 . Now some of these other laboratory have very different behavior, their lower
05:04 , and yet the shear wave velocity decreasing dramatically dramatically in this case.
05:11 that's a shell. But here is sand increasing dramatically. But we have
05:17 other samples where the shear wave velocity increasing. So I need hypothesis.
05:25 , you have to put your thinking on now and tell me, why
05:29 these laboratory measurements, why might we when we add water? Why might
05:35 get a huge decrease in shear wave bigger? That can be then?
05:40 be explained by the increase of density some samples. And in other samples
05:46 get an enormous increase in shear wave along with an increase in p wave
05:53 . So, I need a I need hypotheses to explain these two
05:57 situations. Uh The case where she velocity drops dramatically and p wave velocity
06:05 in the case where p wave velocity shear wave velocity both increase as I
06:11 brian. So I'm going to wait your thoughts and there's no wrong
06:18 Remember that? I'm happy if you come up with a hypothesis, it
06:29 be because of maybe some some sort fractures opening up and the rock due
06:36 fluid intrusion. Well, there you . That's a very good hypothesis.
06:43 I accept that hypothesis. I I don't think that's going to wind
06:51 being the preferred explanation, but that a perfectly valid hypothesis. So,
06:56 to you for that. Mhm. when I add water to Michelle,
07:13 I see shear wave velocity decreasing And think about walking around in Houston
07:20 the rain, the clay grains swell ? Yeah, well, they they
07:28 lubricated. Right, clay. Did ever try walking on hard play in
07:34 rain? It's very slippery. So, um this is a phenomenon
07:41 we call frame softening. It's possible by adding water we're actually decreasing the
07:48 of Iraq and you see it on rich soil when it's dry, it's
07:54 , You walk on it. No when it rains. It's squishy,
07:58 get all muddy. Right, So an example of frames softening and that
08:04 happen in shells but it can also in Shelley sandstone. What about the
08:11 way? What about the shear wave increasing when I add water? Why
08:17 that happen? Think about how measurements made in the laboratory. Let's say
08:40 made I made my first measurement on dry rock. So how do how
08:47 I make that measurement? Think about procedure. Remember our velocity versus pressure
09:00 . It's very common to put the in the laboratory apparatus in the pressure
09:09 and make velocity measurements as you're increasing confining pressure. Right? And this
09:16 the actual rock. So you have jacket it so that the pressure fluids
09:24 bath of sometimes an oil bath. you are applying the confining stress does
09:31 go into the pore space and you're the pressure. You're squeezing this
09:37 So you're statically volumetric lee compressing the and you increase the pressure. Okay
09:47 , suppose that we want to repeat experiment on the same sample and we
09:54 the pressure back to zero. We saturate the sample and then we measure
10:00 velocity as we increase the pressure. see a problem with comparing those
10:11 suppose these these are the results that that were measured shear wave velocity for
10:16 V. P. M. S. For the dry rock at
10:19 pressure and V. P. V. S. For the
10:21 saturated rock at high pressure could could says be checking the velocity. Yeah
10:39 could be one thing at work by it up to high pressure. You
10:45 be changing the rock and that could happen again if you've got clay's in
10:51 you could be compressing those clays. you could be fundamentally changing the rock
10:58 you pressure cycle it. Uh Another thing that could happen is
11:04 this can happen with swelling clays. clays can expand and act like this
11:12 by expanding. They're actually binding the frame together uh more so so the
11:21 can act in funny ways depending on they are distributed in the rock if
11:27 structural clays. So uh the rock , some of the sand grains are
11:34 by clay grains. Right? So sand grains might be separated by a
11:38 grain wedding that rock makes the clay . Could actually make the rock less
11:45 less rigid. On the other if the clays are not structural meaning
11:50 not acting as framework grains in the the sand path but they are sitting
11:57 the pores, expanding them may actually the rock more rigid. So so
12:05 idea of uh adding water and the decreasing is called frame softening and the
12:14 increasing is called frame hardening. Okay we're going to accept the fact now
12:24 for a dry rock, especially if a clean sandstone, we're going to
12:29 the fact That the frame Balkan share are about equal, which is what
12:35 implied by the PBS 1.5. we're going to see can we use
12:43 fact to predict the sandstone, V trend. And so the way we're
12:49 to do this is uh we're going estimate the porosity from the p wave
12:57 . We're going to assume a frame module lists. And then we're going
13:03 say the frame. Both modules is to the frame share modules. Then
13:09 going to do fluid substitution, which do later in the course. And
13:15 the frame both module lists, we're to calculate the fully water saturated both
13:20 using gas months equation. So that us a predicted P wave velocity,
13:27 ? We have ferocity. So we the density of the rock filled with
13:32 and we have the frame. Both is the sheer modules is independent of
13:37 fluids. So, we have k Amro, we could predict BP and
13:44 see if that matched the original If it uh if it does uh
13:52 we guess right when we get the models, if it doesn't match the
13:58 VP, we got to keep trying we could just iterate, we could
14:03 if we want to get fancy or could just iterate through all possible frame
14:07 module. I and we can find sheer module lists that gives us the
14:12 prediction of VP. Um So we the sheer modules is the one that
14:20 us the minimum error. And given modulates in density, we could predict
14:26 yes. All right. And then could see then uh if that gives
14:32 the V. P. B. . So we have to start by
14:36 ferocity from V. P. So will assume a velocity ferocity relationship and
14:44 what Bs versus VP trend that porosity relationship implies. So by the way
14:55 it's it was done on a number rocks where we uh have the observed
15:01 wave velocity and then compared to the shear wave velocity. And uh we
15:07 right on the money in this case . These were laboratory measurements. So
15:12 had the ferocity right, we didn't to assume a velocity porosity relationship,
15:19 in the in the trends I'm going derive, we do assume a velocity
15:24 relationship and we'll see what that So for one thing I could do
15:34 for uh the spear packs, remember the spear paths, we know the
15:40 and we could calculate how the frame , I will change with pressure and
15:49 we can and then we could fluid . And so we could starting with
15:55 dry spear pack, we could predict the VP vs. V.
15:59 Relationship would be for different package. , so if I have a simple
16:08 packing, I would as we increase pressure, I would move along that
16:15 . And um you know eventually we don't go that high because we can't
16:21 the ferocity very much so uh you we'll be left with our high aspect
16:29 pores. Uh So uh there we've well agree with the V.
16:36 V. S. Relationship for these stands. Um So that's pretty good
16:43 . But you see we're pointed in direction here right now for a denser
16:50 . Uh huh. It suggests I have that line and you can see
16:55 the terminal point is kind of aiming this direction here. Right? So
17:03 could argue that just taking a beach and put it in the laboratory,
17:06 not gonna it's not gonna be packed densely. So the argument here was
17:13 is that these are probably loose And so the simple cubic gets you
17:18 close the face into cubic would have you actually closer to the mud rock
17:25 . But if we look at the here as we move towards the highest
17:32 . You see we're kinda headed over . All right, so that this
17:36 the spear pack end of things and can see that for these sand
17:41 we could be on the mud rock or we could be slightly below the
17:46 rock line depending on how we deformed grains with pressure. Now let's come
17:54 the other direction. Let's start with and uh do something like the
18:00 I'm sorry, we haven't gotten we will come back to this and
18:04 will handle uh the higher velocity But we could use this same technique
18:13 calculate what sandstone V. PBS will versus death. Using data given by
18:22 , this is in Gregory's review he gave sandstone velocity and porosity versus
18:29 which allowed us to predict uh sandstone . PBS ratio versus death. He
18:36 gave shale velocity versus death. And the mud rock friend, we could
18:40 that relationship. And so what we is that at a given death shells
18:46 to have a higher P wave velocity . PBS ratio than sand stones
18:53 Now this is also how could that if everything is more or less following
18:59 same trend. And the answer is sand stones are faster than the trail
19:04 . So they are further down on trend, right and also slightly below
19:10 mud rock trends. So the general in the gulf coast is at a
19:16 depth. The sand stones to be lower V. P. V.
19:19 ratio than the shells. Remember. are Brian saturated sand stones. The
19:25 saturated sand stones of clean will be PBS ratio of about 1.5. And
19:33 this knee, this is where we uh fully compacted and now we're just
19:40 as we get deeper. By the , this was a multi component data
19:49 was collected in the open morrow, and uh this was an area where
19:55 sand presence or absence was quite Sometimes it was shell sometimes in the
20:03 in the same interval probably due to uh huh and channels and so
20:11 And uh we had GPS measurements or could plot VP VS. V.
20:18 . From the multi component seismic And what we found is that when
20:24 the result was shell, we were along the V. P.
20:29 S. Relationship for mud rocks. huh. There was one point that
20:35 brian saturated and it followed around the and there was a discovery with hydrocarbons
20:44 it plotted right on the dry So this provides kind of Iraq physics
20:51 template that you can use to predict interpret these V. PBS ratios.
21:00 right, So, the implications for module, I remember for the dry
21:08 , the bulk modules and the sheer lists are about the same Now for
21:13 saturated rock. Remember the sheer this isn't going to change. Uh
21:18 know, ignoring uh frame hardening or softening but mechanically they're not going to
21:25 . Um and if we use the rock trend than to predict, we
21:29 have a much higher bulk modules. here the ratio both modules to share
21:35 is more than 2-1 in the saturated . But in the dry rock they're
21:41 equal. And similarly you could plot in terms of persons ratio. So
21:48 have courts over here. And as add ferocity, the compression of velocity
21:55 And pretty constant. Hassan's ratio. 2.1. And if you if we're
22:02 the mud rock trend, then you'll a increase in prisons ratio corresponding to
22:08 V. PBS ratio as we reduce velocity. Of course, for the
22:14 rock, we're not going to go water velocity. Course for the dry
22:21 you can get significantly slower than water . Okay, now we're going to
22:30 from the other end. Remember I the simple sphere packs, bring us
22:36 here and aim in this direction. And what we did here is we
22:43 the aspect ratio spectrum for Boise sandstone we added more and more of
22:49 And that's the green line. And can see it's plotting pretty close to
22:54 mud rock line. So the craft with low aspect ratio pours plots essentially
23:02 the mud rock line. But if model, if we close all the
23:07 , the very flat pores and leave the pores with aspect ratios of .1
23:12 bigger. You see, we're headed towards here. So we have lower
23:19 . PBS ratios. Uh We can't further with these models because we violate
23:25 non interacting assumption of the model. that's as slow as we were able
23:30 get right. But you can so we're coming at this uh you
23:35 , this group of points were coming two directions from the sphere packs which
23:40 aiming up here and from the the solid, but with the low aspect
23:48 pores closed. So we can conclude liquid, such saturated rocks that we'll
23:57 an elevated B. P. S ratio uh As as compared to
24:03 Shannon fractured rock of course. Remember also shown in the in the dry
24:09 that the factors make no difference. ? So what happens is you fill
24:14 fractures with fluid and now they're gonna very differently than fluid filled uh round
24:21 pores. Okay, now we can any V. P. N.
24:29 . V. P versus ferocity relationship want and we could see all right
24:35 the PBS relationship does that imply? so here's the time average line.
24:42 this is V. P versus ferocity the time average equation going through the
24:48 I said before, where we estimate from the time average equation. Uh
24:54 we assume that the frame balkan share july are equal. And then we
25:00 gas mains equations and that gives us line which is below the mud rock
25:06 . And you see many of the points fall along that line. So
25:11 is why we have a slightly different trend from the, from the
25:17 Now we can compare how this you know, we could see how
25:21 will compare to the two The Brian sand line that we have remember.
25:27 a clean and presumably unfair action because are from velocity measurements made it uh
25:35 higher pressures. Yeah, to obey lines. So by the way,
25:45 there is a P wave time average . Uh huh. Then it implies
25:51 sheer weight of time average equation. ? Because the V. P.
25:55 that the S. And so we fit that data. And what we
26:00 is porosity. Is the shear wave time minus the share wave transit time
26:05 the solid divided by the share wave time of the fluid. Isn't that
26:11 minus the share wave transit time of solid? Right. So obviously this
26:16 not the actual share wave transit time the fluid. Um frumpy wait time
26:23 equation. We could use uh the wave transit time and the fluid.
26:29 that won't work for shear wave. , and I think in both cases
26:33 is just an effective uh fluid transit . It's not the real transit
26:42 It also raises the question of why we care? I mean, why
26:50 we want to use the sheer weight time average equation? Uh So do
26:55 see an advantage in using shear waves estimate ferocity over using p waves to
27:02 ferocity? Think about the equation for wave velocity and the equation for shear
27:20 velocity. What doesn't affect your wave very much phillips exactly. So,
27:38 know, if I'm trying to use p wave time average equation, I've
27:43 to know the fluid transit time in rock. So I've got to know
27:49 hydrocarbon saturation and I've got to know the hydrocarbons are, right, and
27:55 got to work for that velocity. ? So that really complicates matters.
28:00 I if I don't take specific account the hydrocarbons, you know, at
28:07 , they could greatly perturb the velocity relationship on the other hand, for
28:12 , waves, they're only going to very weakly affected by the fluids.
28:17 so a potential advantage of using share to predict ferocity. Okay, so
28:28 the question is, does it Right, ken if there's a p
28:33 time average equation, does that mean a shear wave time, a corresponding
28:39 wave time average equation? And the is yes, it does.
28:44 what we did is we went into and we found a bunch of points
28:49 happened to obey the p way time equation. I'm not saying all
28:54 I'm not implying that all points obey time average equation. Remember different conditions
29:01 result in different velocity ferocity relationships, for those points that do obey the
29:08 wave time average equation, What we is that they also obey the sheer
29:14 , time average equation. In some have argued that the shear waves
29:21 greater sensitivity to porosity because uh because this change is bigger as and
29:28 is potentially uh huh we got better . Um I'm not so sure about
29:35 because the precision of the shear wave measurement is usually not as good as
29:40 precision of the p wave velocity but certainly the shear waves are going
29:45 be far more insensitive to the Okay, now let's move to the
29:54 Gardner equation, which I kind of this equation. Uh This is a
30:02 empirical equation, we have no idea it came from. Um It was
30:09 by slumber J So they apparently had lot of data to fit it to
30:14 far as I know, it's purely empirical equation and they had velocity equals
30:20 minus ferocity squared times the velocity the plus ferocity times the fluid velocity.
30:26 , this is the low porosity branch ferocity is less than 37%.
30:34 let's assume that these constants have physical and see what that implies.
30:41 So if there's a p wave Raymond equation, is there a shear wave
30:47 Gardner equation? Well, what I have to do is substitute the shear
30:51 velocity of the matrix here there and shear wave velocity of the fluid
30:59 So this term goes away. So is my because the shear wave velocity
31:04 zero. So if these terms are just arbitrary regression coefficients if in fact
31:14 they have physical significance then I should able to just make this substitution.
31:20 let's see if that works. Oh the way, uh this implies now
31:28 V P D. S relationship. ? Because um I could solve this
31:35 for porosity. So I have a as a function of vp vP
31:42 the fluid and I could stick that there. Right? So now I
31:47 a relationship between shear wave velocity. for any given the BP matrix and
31:54 . S. Matrix. And for given fluid. So this if these
32:00 equations are applicable, then that implies V P V. S relationship and
32:08 can stall the reindeer and Gardner equation ferocity it's ugly. But when I
32:14 a young man, I didn't mind too much uh tedious math. And
32:21 here is the solution for porosity. using the quadratic equations. So there
32:26 two routes there, but you take physical route. That makes sense.
32:33 which means that uh design here is positive. And then you could take
32:40 long expression and stuff it into So you now have a relationship between
32:47 wave velocity and p wave velocity, velocity is known. VP matrix is
32:52 as the S matrix is known. how does this guy behave Well as
33:01 uh huh If I let VP go vP matrix then V. S should
33:07 to the S matrix. And in it does if you if you look
33:12 this carefully, uh and the V B s ratio should go to the
33:19 for the matrix As the fluid velocity to zero or VP goes to VP
33:27 . And if you check that all of those expectations apply. So
33:33 works okay. So uh here we our time average line for p wave
33:42 we have a range rover and Gardner a curve for p way we have
33:48 shear wave time average equation in the wave Ray martin Gardner equation, So
33:55 types of behavior and uh what we is that there is something a lot
34:04 satisfying about the ranger Gardner equation. of all, we were able to
34:09 a physical share wave velocity where we not do that with the sheer weight
34:15 time average equation. Remember that was a coefficient. But with the Raymond
34:20 equation were in fact using Fluid velocity zero for the shear waves and now
34:30 else, We we know that un or poorly consolidated rocks are not going
34:39 obey the time average equation. So log analysts have used, they use
34:46 compaction factor. So it's a correction and it's equal to the true ferocity
34:53 by the predictive ferocity. And you that by the predicted ferocity and you
34:59 a better estimate of the ferocity. uh so if we have uh data
35:07 we know p wave velocity, we porosity, we could compute the compaction
35:13 , what's needed to correct the time equation to give you the correct
35:20 So again, we're going to go the Gregory data, Its porosity is
35:25 death. And uh this is gulf . So we never got to a
35:31 factor of one. Um so uh a correction factor which has to be
35:39 here, which is less than one when we're compacted, but we're not
35:48 . And certainly when we're not fully , that correction becomes really huge.
35:55 we could do the same thing using shear wave time average equation. And
36:00 we find is a tremendously large correction needed. Now, this is strange
36:09 this factor is supposed to be correcting the same geological phenomenon for both p
36:16 and sheer ways. I mean, would think the compaction, you
36:21 it's the same sample or is the rock formations? This is log
36:27 right? It's the same log rock under the at the same depth,
36:33 the same conditions, why should the waves imply you're less compacted than the
36:39 waves? Right. They both should the same degree of with ification.
36:45 uh but for the sheer weight of average equation, you need a different
36:50 factor than for the p wave time equation by the way. A rule
36:54 thumb that log analysts use uh to the compaction factor without core data Is
37:02 take the shale transit time and divide 100. On the other hand,
37:12 could do the same thing using uh roemer and Gardner equation and we can
37:20 at the ratio the compassion factor ratio P waves and S. Waves.
37:25 we're going to look at the ratio over that. And for the time
37:31 equation, that's what the ratio The so uh the compaction factor becomes
37:40 or the ratio of the compaction factors time dependent. But for the roemer
37:46 Gardner equation, uh it's the same both. So the P and
37:52 Wave roemer and Gardner equations both have same compassion factor. So again,
37:59 else that is physically far more satisfying the Ray martin Gardner equation. The
38:06 that the roemer and Gardner equation has nice physical aspects is intriguing because it's
38:15 empirical relationship. We don't know why works. Now, remember we said
38:22 uh rocks that obey the Ray martin equation tend to be the most lit
38:30 the most fully liquefied rocks. And that may be what's happening.
38:39 now I could see what V. relationship is implied. So I have
38:46 empirical trend here which you can barely . Unfortunately these are old figures and
38:52 have to redo all this work. This was all done on paper 30
38:58 ago and I you know, I able to find some of these
39:02 All right, so the empirical P. B. S. This
39:06 our brine saturated B. P. . S. For sand stones,
39:11 sand stones, that's our empirical We could say. What would our
39:15 B If I was using the compression shear wave Bremer and Gardner equations,
39:23 would be that line. Or if am use the compression of grammar and
39:30 equation and then use gas months equations the assumption that Vulcan frame Vulcan uh
39:37 and rigidity were equal. So all of these approaches yields essentially the same
39:43 DP B. S relationship. Uh , there's something satisfying about this Ray
39:50 Gardner equation. All right. Just it to uh some uh uh huh
40:02 . And what we find These are measurements in uh a yeah, a
40:11 of sand formation which has a some in it. And you see
40:19 we've extended this empirical trend for sand down through here. And you can
40:26 that these points are falling below right? So they have high
40:30 It's not all the way to the rock. So these are this is
40:35 uh dry gas but these are gassed reservoirs. But you know at that
40:43 can have uh some significant modular. it doesn't move you all the way
40:49 the dry line in this case, the way, this is just using
40:58 Ray martin Gardner equation predicting the P. V. S.
41:03 And uh well, it brings us these points here and it tends to
41:08 below? Remember, this would be most liquefied and the cleanest rocks?
41:15 ? So most of the stands down are slightly above right. Uh And
41:25 are Gregory's velocities versus death. With gasman predicted shear wave velocities using the
41:33 I just mentioned and it pretty much the screamer and Gardner trend.
41:45 now brings us to the inverse Right. We've talked about different mythologies
41:53 unique V. PBS relationships. Uh can we go in the inverse
42:00 And the answer is no, it's unique. For example, dolomite is
42:05 limestone and sandstone. So if I'm no nothing else and I have
42:10 P. And V. S that on the dolomite line, it could
42:14 a dolomite, or it could you know, half limestone, half
42:20 , where it could be shall or could be a limestone with some gas
42:24 it. Right. So lots of things going on. Let's restrict ourselves
42:29 now to brian saturated rocks. So make our problem a little bit
42:36 And let's assume I have density and a big assumptions. There certainly aren't
42:41 conversions for density are very poor, let's see in a perfect world,
42:48 seismically I were able to get reliable wave velocity shear wave velocity and density
42:56 that information alone without other constraints Could I invert these V. PBS
43:03 VP density relationships. Could I invert for rock properties uniquely And the answer
43:14 um Not necessarily. So here we the actual ethology being, sandstone,
43:22 , dolomite or a mixture. In we had no mixtures. We just
43:30 sam rhinestones and dolomite. Uh But oh I'm sorry. Yeah,
43:36 did have a mixture. I'm Um So if it was Sandstone,
43:43 was predicted to be sanded down 92% the time. It was almost never
43:48 to be limestone but sometimes it was to be dolomite. Uh Might have
43:53 a Shelly sandstone, raised the P. V. S ratio and
43:57 you think it was a dolomite. it was a limestone, 80% of
44:03 time it was called the Limestone, almost 20% of the time it was
44:08 the Dolomite or a mixed pathology. Maybe those were sandy or Shelly
44:16 Here's the real problem. If it a dolomite, about half the time
44:21 was misclassified as the sandstone or So um the conversion will, assuming
44:31 velocity is going in. We're not thinking about experimental error. Um in
44:40 perfect world. Uh Your you can the odds in your favor. Very
44:46 so with sand, a little bit than limestone But it's a 5050 shot
44:52 dolomite. But remember that's a perfect . Okay, so uh let's go
45:03 some of your homework exercises at least what I want and uh I have
45:10 say that some of you have been good about asking me questions and that
45:16 me happy the large majority of you . So I have to admit that
45:21 I'm very concerned that you're not keeping with the homework. If you want
45:27 good grade on that homework, you're going to be able to pull it
45:31 . Doing everything the last week and last week we will have recitation.
45:37 will try to help you in class the homework problems. But you
45:43 it's a lot of work. It's lot of problems and I want to
45:46 sure you're keeping up, otherwise you'll your swamps and you and you hate
45:51 these and but anyway, um, you're doing them as we go
45:57 uh it would be good to ask questions and show me your results and
46:02 my feedback. So I'm going to you to do that. Okay,
46:07 exercise 7.2 cross clock lessons ratio versus , both module is divided by sheer
46:13 and that's the 1 to 1 Uh, you know how to relate
46:19 to both modules and sheer modules and know, how to relate velocities,
46:23 ratio. So that should be easy for you to do. Uh,
46:28 then I asked the question, how this curve vary with mythology and pour
46:32 content. So I'll let you think that and uh, give me your
46:39 . Uh, so for a given modules, what happens when I drop
46:44 the bulk modules, What does that to a person's ratio? And can
46:49 think of uh practical consequences of that ? So think about application. Where
46:56 that really help us? Uh All right. And that's this should
47:06 easy enough plot V. P. G. S. For pure
47:09 So you have a table of pure and different types of clays.
47:15 plot plot all of these up on VP VS. V. S.
47:19 and compare them to the mud rock and draw some conclusions. And by
47:30 way, let me apologize in this . Uh I decided I reordered the
47:36 . So they're not necessarily in order hitting your notes. But uh anyway
47:46 it doesn't matter as long as you the exercise number. It's okay.
47:51 here we have some table of VSP . So uh we have over
47:59 So you have two receivers in the and you're measuring the transit time for
48:03 wave velocity, transit time for p velocity and I mean p waves and
48:10 those two velocities. Uh So uh seeing uh different VPs ratios as we're
48:18 deeper and deeper. So plus these against the mud rock trend and see
48:23 they compare. Okay, you have polynomial. We actually don't need polynomial
48:35 for VP VS. V. S sand and shale, Those are straight
48:39 . These are brian saturated shales and and compare them to the mud rock
48:46 , describe the results and discuss how would affect your use of the mud
48:52 trend. Okay, so here are equations for sandstone and shale. They're
49:00 linear equations. Okay. All Now dr Han uh published a classic
49:10 in 1985 where he gave p wave as a function of pressure and shear
49:18 velocity as a function of pressure for compositions. So his equations uh have
49:27 velocity. We've we've seen this form , velocity is a constant plus a
49:34 times porosity plus a coefficient times volume clay. Um And so these are
49:44 but in the report I copied this , it turns out the coefficients transcribed
49:51 . So you have to go to original paper in 1985 in geophysics or
49:57 trust right that table and figure out wrong with the signs over here on
50:06 , on these coefficients. So now you have you have equations for
50:12 wave velocity and shear wave velocity And could extrapolate them to zero play in
50:19 play. Right? So you can explained well one and that that will
50:24 your share line as you vary porosity you can make X clay equal to
50:30 . That will be your sandlin as very ferocity and I'm asking you to
50:35 that to the mud rock trend and look at the effect of pressure on
50:43 PBS trip. Okay now we're going mixed pathologies where we have mixtures of
50:54 and carbonate and calcite. So again types of equations. And you can
51:02 these equations uh to pure courts and calcite. So here are these
51:11 So V. S. Is equal a constant. And that would be
51:17 Shear wave velocity extrapolated to 100% courts a coefficient written here is a partial
51:26 in velocity with change of catholic by write a coefficient times the calcite.
51:33 calcite not play bye. Infraction plus change in shear wave velocity with ferocity
51:41 the porosity volume fraction. Okay so has the equations of this form for
51:51 . And then he's got the equations for VP. Right? So that
51:57 if you set uh calcite to you have a courts be PBS relationship
52:04 these. So extrapolated from sandy lime all the way to courts. Uh
52:10 you vary porosity for V. And D. P. Or you
52:14 set uh buying a play to one that will give you the pure limestone
52:20 . So anyway, do those uh compare to the V. P.
52:24 . S. Trends that I gave previously. These guys and when I
52:32 compare I mean with words. All , look at make the plot look
52:38 the plot and tell me what you . Okay so okay I gave this
52:51 you twice. This was again a where the coefficients got just opposed the
52:57 of the coefficients got just opposed. and anyway, used will the Wilkins
53:03 , which is this plot here? , so uh you have sandstone ferocity
53:25 density and okay, I'm sorry uh you have a table of
53:35 You have brian sand shell and gas V. PBS and density, brian
53:43 shells and gas sands. So you plot uh huh sandstone porosity and density
53:55 fluid densities of 1.1 g per cc Brian and .5 g per cc for
54:03 water mixtures. Okay, so uh calculate the ferocity from the densities.
54:17 , uh you have these measurements, sand and Gaston V. P.
54:22 . D. S. So plot versus porosity and interpret the result.
54:32 brian sand VP versus ferocity, brian S versus ferocity gas, M V
54:38 versus ferocity gas and Bs versus Okay, now draw VP vs.
54:47 . S. Paris for brian sand and gas stamps. And compared to
54:54 trends. These were measurements on synthetic towns and so look VP on the
55:07 . V. S on the And you've got dry measurements and wet
55:14 . So tell me what's unusual about velocities and explain what's going on?
55:21 , why are these not acting like rocks, normal sand stones and what
55:30 different about them. So, I'll you for a hypothesis to explain this
55:37 behavior. So first of all point the unusual behaviors and explain the difference
55:45 at least hypothesis why it's unusual. . Okay. Uh This is an
55:55 for discussion. An opportunity for you show me what you've learned. Why
56:02 laboratory measurements often over estimate the effect effective stress on velocities? So that's
56:10 discussion question you should have by We've discussed this enough that you should
56:17 be able to discuss that pretty Okay. Just in practice calculating elastic
56:26 I from velocities. Uh So from and brian saturated sandstone trends. Cross
56:34 responds ratio versus bulk modules and draw . And so that sheer modules versus
56:42 modules for dry and saturated rocks. showed you these data before Parsons
56:48 So I'm asking you to regenerate these . Okay, now I'm going to
56:58 you to compare some measurements to So these are sandstone velocities. Cross
57:04 Bp versus Bs and B. P poor porosity. And compared to the
57:09 trained currents. I've given you two conclusions. So, these are laboratory
57:17 . So we have uh measured VP measured ves and so you could cross
57:25 against vP vs. V. And V. P versus porosity.
57:36 , uh this is kind of a uh publication. It was a huge
57:43 of data collected in very complex cell . Uh So these were Dominic
57:51 but so you have calcite, you course you have clay, you have
57:56 . Um So um what I want to do is extrapolate rafa vicious
58:04 He gives you these trends versus no play here. But regressions against
58:13 , porosity, buying courts, I want you to extrapolate these
58:19 200% courts. And um I'm 100% goal am I it? Which
58:28 zero court, zero and hydrate, calcite. Right? So extrapolate to
58:38 and compare to the dole. Might that I gave you Do it for
58:45 10,000 psi trend. Do the same for pure courts and pure limestone and
58:57 up with an anhydride BP and implied hydrate the PBS trend and compare it
59:03 the other trends I have not given and I try to be PBS
59:10 So this is an opportunity to uh new territory and there's an ambiguity here
59:20 I'm gonna ask you to make some is because uh you know, you
59:25 have both density as you do these . So you're going to have to
59:30 some assumptions about the bulk density. , here, I'm just asking you
59:39 some long data. So uh there some mineral velocities plotted here and here
59:48 the distribution of VP VS. S. From from some law data
59:53 to trends. So I'd like you interpret these points. So opera
59:59 And by the way it's V. versus VP. So it's a little
60:03 from the way we're used to looking it. But hypothesis why the points
60:08 where they are. See if you identify different trends or different clouds and
60:16 what they make right. And then as a wrap up, I'm going
60:24 ask you to go back to empirical that relates seismic velocity to porosity and
60:31 saturated rock, uh, and uh, when they what the physical
60:39 is and under what conditions you expect to work. So this is going
60:45 to an earlier section, but hopefully now you're a little bit more mature
60:50 your understanding. So go ahead and this discussion at this point.
60:59 that's all I have for
-
+