VideoPoints

• ••• • •• • ••••• • •
GEOL7324 Rock Physics - Day1 10-21-2022
Help Tour
© Distribution of this video is restricted by its owner
Transcript ×
Auto highlight
Font-size
00:00 good. Alrighty. Welcome to Rock . Oh by the way, let
00:11 ask. Do you do you have spreadsheet with you? The spreadsheet on
00:16 computer. Yeah, so um we stop recording for a minute. Um
00:27 right, welcome to Rock Physics There we go. Okay, so
00:36 the way, this is all in ford. So this contact info is
00:40 there and any questions along the The best way to get immediate response
00:48 me is email. So there's my but and I normally I usually don't
00:56 this, but I have in my class. So here's my cell phone
00:59 . Right? So you can call but please don't don't pass that
01:05 Okay, so how are you going be graded in the class? Uh
01:11 in class. So we're gonna be exercises and um you know, just
01:16 through all those in participating in class questions and answering questions and then there's
01:24 final exam and by the way we'll giving certificates along the way and that
01:30 have to be based on your class and exercises. So here's the course
01:41 . I always start with a highly introduction. Get you excited about taking
01:47 course and then the topics will be space properties, porosity, and permeability
01:55 , which is a fundamental component of impedance. Also important for gravity type
02:04 . Um We'll move on to basic mechanics. Uh that's really the mathematical
02:11 for rock physics. So we'll go that. But there are also important
02:17 like in hydraulic fracturing shales. Wellbore so we'll uh we'll do better rock
02:25 . Um I then want to talk pressure because there are different types of
02:31 pressure is really important for drilling. important for production and so forth.
02:37 it has a first order influence on velocities. So we'll cover some pressure
02:45 then move on to seismic velocities and factors controlling compression and shear wave
02:53 That's really kind of the meat of course. That's what everything else is
02:57 towards. And we'll talk about VP B. S. Ratios and these
03:02 important uh in a video analysis. for direct hydrocarbon indication and also for
03:10 elastic module I like in unconventional reservoirs so forth. And finally uh we'll
03:18 with fluid properties and fluid substitution. do modular velocities change as we change
03:26 fluids in the rock or we changed fluid properties in the rock. Uh
03:33 we have time and we didn't get last year, we'll also get into
03:38 more advanced topics like composite media and and dispersion. If you want additional
03:50 to supplement my lectures in the that I'm not perfectly clear and haven't
03:57 covered everything to your satisfaction. Uh here are a variety of books.
04:02 Given the short timeframe of the you may not really have time to
04:07 them although um S E. For example uh that offers vernon X
04:14 . Uh they offer that online so can um his book is is really
04:21 good in the sense that he's got lot of brilliant insights. Uh It
04:27 sometimes a little bit hard going and terms of understanding exactly the points he's
04:36 to make, but really excellent insight into shells. There are some important
04:46 now on blackboard. I posted a of papers, so if I put
04:52 there on blackboard, uh they're important to be there, right, because
04:57 are thousands of papers to choose right? So if I posted on
05:01 , I think it's a particularly good . Uh But so but the very
05:07 of the best, in my opinion relevant to this course are these
05:13 Gardner and Gregory uh in geophysics, where the famous gardener relationship comes
05:20 if you've heard of that one. Gregory also has an excellent review paper
05:27 a pg memoir, 26 it's out print. Uh But like I
05:32 uh look to see what's in you never know what you'll find
05:37 That's all I can say on the . And um my paper and my
05:44 93 S E G A B O offset dependent reflectivity uh is very relevant
05:52 to what I'm teaching. So you'll a lot of the same materials and
05:56 there when we get into fluid substitution smith has a very excellent tutorial 1993
06:05 think in geophysics. Um And um I said there's there's a lot loaded
06:12 blackboard so you have a lot to from. So you should have no
06:17 of supplementary reading, although we don't an official textbook. Okay, so
06:25 always like to start with discussion of method a little bit because I think
06:31 is often lacking in our in our work. Right? We um we
06:39 right into the subject matter and somewhere the line, I think a discussion
06:43 of scientific method is important. I it lacking in a lot of our
06:49 and the fundamental building block of the method is the concept of a
06:58 So I'm gonna ask the question. both welcome to answer what is a
07:08 . What ah you finally hit it explanation. So a lot of students
07:18 it's what you predict will happen or you hypothesize is. But really what
07:24 is is an explanation for observation. so in the earth sciences we have
07:31 specific meaning of the term hypothesis, explanation for an observation. There is
07:38 hill over there. Why is that there? Right. So that explanation
07:45 the hypothesis um in other disciplines that have other meanings, but for us
07:51 not a prediction. A prediction may from a hypothesis, but it's not
07:55 prediction. It's an explanation, stoke is an explanation for observations. And
08:06 a very important point is hypothesis How do we test the hypothesis?
08:14 is an attempt to disprove the And again, this is where students
08:22 go very wrong. They feel that test a hypothesis by trying to prove
08:29 . But the fact of the matter you can't ever prove a hypothesis.
08:34 strictly speaking, there is no such as proving a hypothesis true. Not
08:41 the earth sciences. You can show consistent with data that's called confirming,
08:48 really confirming it's called supporting the hypothesis you can fail to falsify the hypothesis
08:57 your hypothesis testing should be designed to to falsify the hypothesis and you
09:05 we're we've been were very negligent in petroleum industry for example, in because
09:11 acquire a lot of data. So fact we're doing a lot of experiments
09:16 often our experiments are badly designed because design our experiments to support the hypothesis
09:25 as a result is not necessarily the data to test the hypothesis. Or
09:31 much emphasis is made in acquiring data do not have the opportunity to falsify
09:39 hypothesis. So that's something for you carry in your future career, keeping
09:45 in mind. How am I going spend my money? Okay, so
09:51 hypothesis is a proposed explanation for an phenomenon. Uh so in order to
10:02 part of the scientific method, the must be a valid hypothesis must be
10:10 if you cannot test the hypothesis if if there's no experiment that could be
10:15 to falsify the hypothesis. It's not speaking, a hypothesis for our
10:22 Um, so typically a hypothesis arises an attempt to explain observations that cannot
10:35 explained or that don't have a ready with existing scientific theories. Okay,
10:43 the question arises. What's the difference a hypothesis and a theory?
10:49 So we talk about the theory of , Right. That's a theory.
10:56 does that differ from my hypothesis? , the theory of gravitation came around
11:02 describe how an apple was falling right a tree. So the theory of
11:09 was an attempt to explain an So in fact there's no difference between
11:18 hypothesis and theory in terms of being to explain an observation. Right?
11:24 what is the difference between a hypothesis theory? It's just a matter of
11:29 . You may think of a hypothesis a small theory. A theory
11:35 Uh further ranging it may be a concept. It uh, can explain
11:44 more and it has more scientific Right? But essentially a theory is
11:53 grandiose hypothesis. Let's put it that . Okay, so, um,
12:00 the earth sciences, we often uh have the near term ability to test
12:11 hypothesis. Like um, the volcanic in the middle of the ocean is
12:20 due to plate tectonics. Right? do you actually test that?
12:27 So even though theoretically it may be , it may practically, in the
12:32 term not be testable, but science has to advance. Right? So
12:37 we do is we have the concept the working hypothesis. Right? So
12:45 going to go with this hypothesis for time being. That's a working
12:51 Even though it had, we haven't the opportunity to fully test it as
12:56 as it holds together and it explains data we have um we're gonna go
13:03 it and we're gonna build upon That's a working hypothesis. Now in
13:09 geosciences we have a tendency to have hypotheses that can explain a phenomenon
13:19 You can explain uh continental drift with tectonics or with media radic impact,
13:27 example, I've heard, or with gravity gravitational assist ISI. So there
13:33 been other ways of explaining the same . Um So in the geosciences,
13:42 frequently are faced with the situation of working hypothesis. We have many explanations
13:50 at the same time and we're carrying all and the stronger ones survive and
13:57 weaker ones fall by the wayside as as science advances. Right,
14:07 So which of the following are The Earth's diameter is 8000 miles.
14:16 temperature will increase by 1°C in the 20 years or three fluctuations in global
14:23 over time are primarily caused by natural , which whether you agree with these
14:31 not, which is a hypothesis. is the only hypothesis here. The
14:40 one is an observation that is the . The 2nd 1 is a prediction
14:48 results from a hypothesis, anthropomorphic greenhouse or something. That's the working
14:58 Um Number three, if I added time, um that would be pretty
15:04 accepted as being true. But that a hypothesis because it explains natural
15:11 What are they a variety of natural ? Uh sunspots in the sun for
15:19 . So variations and solar radiation or radio volcanic activity or whatever. There
15:28 a variety of ways to explain over over geological time, mean surface temperatures
15:38 . Okay, so you could think the scientific method as kind of a
15:45 circular type operation where you start with observation here at the top and um
15:54 we want to explain these observations. the first step is to know the
16:01 matter. Right? So research the , find out what other people are
16:08 . Um then formulate your hypothesis, the hypothesis with an experiment or data
16:16 of some kind analyze the data and wish we would do this in a
16:23 statistically rigorous way. Often. We don't, we should, I'll touch
16:29 that briefly and report your conclusions and release that to the scientific computed
16:38 Get feedback and then come back and . The process is more data is
16:45 . The one of the problems with approach is in researching the topic
16:53 You are are distorting your mental You begin to establish a paradigm in
17:02 mind that where you're following the paths what other people have said and done
17:10 that removes a little bit of So I think it's often useful to
17:17 the hypothesis forward before understanding the topic . Well, I mean there's no
17:24 in forming a hypothesis. You can abandon it when when, when you
17:30 better. Right, okay. And want to contrast geoscience hypothesis testing from
17:41 hypothesis testing. Um they're really fundamentally different things. A statistical hypothesis is
17:52 testing an explanation, but it's testing observation and relations that are apparent from
18:01 observations. Right? So there's no or geo science behind it? We're
18:08 explaining the observation. We're just seeing it's related to other data. And
18:17 particular in statistical hypothesis testing, we if the observation could result by random
18:28 . So suppose my observation is a between two variables. Is there a
18:35 that that correlation is just by So we call that trusting testing the
18:43 hypothesis. So for example, um do a regression between velocity and ferocity
18:51 I find a linear correlation between the with a given correlation coefficients a
19:00 What is the probability that that correlation ? Just by random chance. So
19:04 is the probability that just is taking mean value? The mean velocity,
19:11 could have predicted that just as Using the mean value as with this
19:16 line? Um if I only had points, two points would firm would
19:23 a perfect line. Right. So linear relationship from two points has no
19:28 significance. Think about three points. is a probability that if I take
19:35 random points, there's a probability that exist on a straight line.
19:41 Usually it'll form a curve, but some chance it would fall on the
19:46 . So, um the fewer data I have and the more independent variables
19:52 use to make a prediction, the chance that that correlation is just accidental
19:59 has no meaning. So, so uh a typical uh statistical
20:09 if I measure two populations and population has a mean value that's larger than
20:19 B. So one set of rocks a mean ferocity. Another set of
20:24 has a mean ferocity. You could yourself the question. What is the
20:30 that remember these populations are just sampled a larger population. Right. We
20:35 sampled all rocks. Right. So have one sample of a population a
20:42 in north America. I have another of the population maybe in europe?
20:48 there's a difference in the mean value those ferocity is, can I say
20:54 has higher porosity is than europe. I make that generalization? Well,
21:00 is the statistical significance of that difference the mean, remembering that I haven't
21:05 the entire population. If I have the entire population then the difference in
21:10 mean is statistically significant. So how points do I need? You know
21:17 there is 10,000 data points enough to able to say there's a statistically significant
21:22 in the mean, It depends on variance of the data. If all
21:27 porosity measurements were exactly the same, would take very few points to conclude
21:33 a statistical significance. But if I a broad distribution in America and a
21:38 distribution of values, remembering that I've done a poll, I just used
21:45 few data points of the entire And with all that spread, am
21:50 truly representing the mean value of the ? So, so I have to
21:55 a statistical significance test. And so actually will measure we can well,
22:01 have to make some assumptions, assumptions Gaussian distributed otherwise. It gets very
22:07 . But I could actually come up a number that gives me the probability
22:13 the mean is is significantly different and smaller that probability uh the more explanation
22:22 needed to believe the difference. So if I have a hypothesis explaining
22:28 difference and I strongly believe in that , I may accept that difference as
22:35 true. Even if I don't have high score of statistical significance.
22:44 so let's get into the course So rock physics. So what is
22:51 rock? We should know what we're what's the definition of Iraq.
23:06 so I think sociology went over. , so it's an aggregate thing.
23:14 like that. I like that. actually a good definition. Um If
23:19 go into the geological dictionary it will it's an aggregate of minerals. But
23:26 fact there are other things in rocks minerals like fluids and organic, some
23:33 matter is quite amorphous. It does not a crystalline solid. So it
23:37 really classify as a mineral. So it's it's a an aggregate of
23:44 let's say a naturally occurring aggregate of . Okay, so then what is
23:50 physics got to be a little more than that? Yes, I don't
24:07 . Yeah. So um suppose I a stone and suppose I throw it
24:13 trajectory of that stone follows the science ballistics. Is that rock physics?
24:22 . So in physics we're specifically thinking how the rocks respond to mechanical stress
24:32 applied to the rocks. So that's be the entire thing we study,
24:37 know, passing a seismic way through is providing a mechanical stress to the
24:44 . So how the rock deforms over very short time period to this mechanical
24:51 is what we study in rock Um Okay, well that Alright,
24:58 restricted the signs of rock physics. shouldn't say mechanical stress. Let me
25:03 to stimulate geophysical stimuli. Okay, it could be elected. We could
25:09 thinking about electrical? We could be about thermal conductivity. Even though I'm
25:13 gonna hit those in this course, are all aspects of rock physics.
25:19 , why is it important? Why is this the required course?
25:34 it underlies, let's put it that . It underlies all geophysical measurements.
25:40 . It's the medium that we're Okay. So what are the primary
25:47 that control the geophysical properties of Yeah, you could include those.
26:00 what what controls the strength of Iraq example. Huh? Okay. The
26:11 . Uh, Okay. Let's differentiate solid and fluid constituents. Right.
26:16 , uh, as this as the and the fluids change as the solid
26:22 and the fluids change the rock properties change. What else? So,
26:26 it's made of? That's one What else is critical beyond what it's
26:34 of? All right. But we're we're trying to say what controls how
26:45 responds to the outside stimulate. So what it's made of right
26:55 how those things are put together. ? So, we talk about the
27:00 arrangement and how those things are Like cement, how they're cemented
27:10 how their lip defied. So degree lytham fication is a big thing.
27:15 , composition arrangement, degree of with . There's one more very important controlling
27:30 development where the temperature. So the conditions. And let me also say
27:39 composition if I specify the composition and have solid materials and fluid materials.
27:48 I add up all the solid fraction all the fluid fraction that gives me
27:53 ferocity? So that is also a factor in affecting both. Uh Well
28:01 I mean, mechanical properties, seismic , electrical properties, thermal properties,
28:10 is a big factor. So, definition of rock physics and this picture
28:20 meant to be facetious. Uh Rock is the systematic study of the relationship
28:27 rock properties and geophysical characteristics, at . That's the way we're defining it
28:33 this course. Now, the picture just showing that a lot of observations
28:38 been made and the observer is wearing lab coat. So this is very
28:43 . Right? So they're looking at systematic variation of the observation uh versus
28:51 maybe the efficacy of a deodorant. , so let's look at the relationship
29:00 the rock properties and the seismic So, the three main rock properties
29:07 we're going to talk about, our ology ferocity and pour fluid content.
29:15 are the most important rock properties for Now, but these rocks are under
29:26 environmental conditions. So we have the and pressures, temperature. We also
29:34 the orientation of the experiment because the you measure can be dependent on the
29:41 . So, these are the environmental and we have the rock parameters and
29:47 these to the velocities or the electrical or thermal conductivity or magnetic properties whatever
29:56 are, The geophysical properties uh in seismic world we deal with velocities.
30:03 deal with density and the attenuation. ? So, somehow these geophysical properties
30:11 the rock are dependent on the environmental and the rock parameters. So the
30:21 in the forward direction. This is we do in rock physics. We
30:26 have velocities, density and maybe But that's a little great out because
30:32 not going to pay a lot of to that in this class. We
30:35 how the velocities and density are related these other factors. So, the
30:42 controlling the geophysical properties are very important us in this class. And by
30:49 way, there are thousands of pages the literature studying these relationships.
30:56 the three dimensional distribution of the geophysical is what gives you the seismic response
31:04 in the forward direction. Various types seismic modeling are used to predict the
31:11 response from the three dimensional distribution of things. Now, the reverse process
31:20 far more difficult and in many ways more intellectually challenging. And that is
31:31 what rock physics tells us is going the rock properties and the environmental parameters
31:39 the geophysical properties is an entirely non transformation. Going backwards from velocities and
31:49 to the rock. The rock and properties is non unique. Furthermore,
31:58 modeling tells us that going backwards from seismic response to the geophysical properties is
32:05 unique. So we're doubly non So to go in the inverse direction
32:12 much harder than going in the forward , but we have no choice but
32:17 do that, we're gonna, we're make decisions. We're going to drill
32:20 well or we're gonna build a building whatever it is we're going to do
32:24 So we have to constrain the problem best we can and use uh you
32:31 , seismic inversion or optimization, other along with our interpretive ability to go
32:40 . So that that's very much a game. Okay, now, in
32:48 , I didn't explicitly mention mention texture structural arrangement because I include that in
32:55 term mythology. So lift ology includes composition and texture. So what is
33:03 texture, the way the constituents are and under ferocity, I did not
33:13 out permeability or pore structure. They both included as part of the pore
33:20 . Now, permeability doesn't seem to a first order relationship to geophysical
33:28 but there are second order relation or relations. So, um permeability tends
33:35 be in a particular rock tends to highly correlated to porosity. But if
33:40 look at the theoretical equations for the response, you don't see much contribution
33:47 permeability. In fact, in what call a poor elastic medium at high
33:55 , the fluid mobility does affect the velocities. So you've been lied to
34:01 everybody else before this class, Because they haven't talked about the effect
34:07 how permeability directly affects velocity, it exist, but we ignore it because
34:16 a very small effect at the frequencies dealing with. Um now, poor
34:31 , it turns out the shape of porous has a first order influence on
34:36 velocities, and not all ferocity is same. So we're going to talk
34:41 different types of ferocity and how they affect velocities differently. This means that
34:48 can never have a universal relationship between and velocity, because porosity just tells
34:56 the amount of pore space, it tell you anything about its shape.
35:07 , so in rock physics, if look at the literature, most of
35:13 literature is involved with deriving theoretical Uh So actually from the physics starting
35:23 an arrangement of in grains or um predicting how the velocity is going
35:33 change with composition or with arrangement We have a lot of theoretical equations
35:41 I would say most of the published is based on the theoretical equations and
35:48 of these are useful in a practical . For example, Woods equation tells
35:53 the compressibility of a composite and this for gas bubbles and water, for
36:04 , it also works for solid grains in a fluid. So the compressibility
36:11 the effective medium, that's the mixture materials is just a volume weighted
36:19 X, the X is of volume . So this, in this
36:25 I'm writing it for, I'm writing equation for two constituents with different ma
36:32 K one and K two and the of uh the bulk module Asus K
36:40 called the compressibility that you can see the volume weighted compress abilities of the
36:49 . That equation works. Another equation use, that works is the mass
36:55 equation. Uh and that relates the of a material to the density of
37:01 constituents. So those are exact theoretical that work and we use them By
37:09 way, a very popular theoretical equation we've used a lot and I have
37:15 a lot uh since its inception over years ago is gas men's equation.
37:22 we'll look at Gaston's equations, that's theoretical equation that turns out it works
37:30 too badly, but it turns out wrong. Leon Thompson just had a
37:37 rejected from geophysics, which really irritates that they would dare reject his paper
37:45 it's wrong. And uh he won paper, the 21 scG conference where
37:53 presented it. I mean how it be rejected from geophysics is beyond
37:58 But anyway, that's that's the side . Um So he may have mentioned
38:04 in his course when you took it . So that's a very popular equation
38:08 we're going to use. And in I think it may there may be
38:15 errors with it because it's not too And we've used it for 70
38:21 but it's wrong, but really those equations are probably the only three theoretical
38:28 that turn out to be useful for a practical way to predict velocities from
38:37 rock parameters, which means that most the useful equations are empirical. And
38:46 we'll talk about a number of empirical in this class, one of which
38:51 the famous Wiley time average equation. And it says that the sonic transit
38:59 , delta T is again a volume average of the transit times of the
39:05 material and the fluid material. It looks like a theoretical equation.
39:11 ? It looks a lot like Woods . Uh But in fact it's purely
39:21 . Another advantage of the empirical equations their simple, so people are more
39:27 to use them. Um Another group equations has arisen and uh these are
39:37 of these have come out of stanford these are what Moscow calls heuristic
39:45 And what does a heuristic? What heuristic mean? It means rule
39:51 Right. So what is a rule equation? Well, uh one heuristic
39:57 they put forth is called the critical model and that says the modular
40:03 This is K plus four thirds mu K plus uh I mean lambda
40:09 I mean K plus two lambda lambda two mu the plane wave module Asem
40:17 related to the module Isse of the material in a porous medium. The
40:25 of the solid material times. This in front, which is one minus
40:30 Prasit. E divided by something they the critical porosity. That equation doesn't
40:40 data and it's not derived from It's something that just somebody thought it
40:49 a good idea to express that Right. Um So the question isn't
40:58 it's right or wrong. The question is it useful? Right? All
41:06 equations we're going to use our wrong some extent the theoretical equations?
41:10 except for the mass balance equation. the theoretical equations all make assumptions which
41:14 not be perfectly right. And of the empirical equations all have scattered around
41:20 . They're a statistical fit. So not a matter of the equations being
41:27 or wrong. It really comes down a matter of are they useful?
41:31 the way to judge the critical porosity , even though it's not derived from
41:35 and it's not derived by matching The question is is it a useful
41:41 ? And will it help you advance thinking and will it help you make
41:47 ? And uh the answer is in cases it can be useful in other
41:52 . It may not be. one of the keys in all of
41:55 equations is when do I use When is it applicable? That's something
42:01 keep in mind. Especially for empirical . Emma, you know, what
42:10 of conditions were they? Those empirical derived under. And if my conditions
42:16 different from those uh all those equations going to be applicable. Alright,
42:26 here's an example of the critical porosity . And so he's cross plotting the
42:33 wave module ascent here, K plus thirds mu divided by the mineral modular
42:39 just pull the mineral modulates over to other side. And I uh have
42:44 my horizontal axis, the porosity divided the critical ferocity and the slope of
42:50 one right, there is a negative in front would give you a trend
42:54 this. Now, if the critical model were exactly right, you would
43:01 right on the diagonal and you see lot of these data points do follow
43:06 diagonal, but a number of them below the dialect. All right.
43:12 the answer is sometimes the critical porosity works. Sometimes it doesn't. If
43:20 happen to be operating in a situation it works, it may be uh
43:26 may be other equations, which could more useful. Okay, now,
43:32 question I have. Okay, so we have where the critical porosity model
43:37 working. So you can see there points lined up along that line and
43:42 lot a lot of these fused glass tend to follow the critical porosity
43:47 but other rocks do also. Um , one thing I might ask
43:55 what are the saturation conditions of these ? Right. So what is the
44:03 fluid in these rocks? So for to be true, you see there's
44:11 dependence on the saturating fluid here. , so um this particular model is
44:20 for what saturation conditions and the answer the saturating fluid here is air.
44:28 , so really the critical ferocity model written in this case is for the
44:37 , absent liquids being in the rock the way they usually call this,
44:42 dry rock, I don't like that because when you dry rock you change
44:48 properties. So this is, this applicable, I would say to the
44:53 frame that fluids are gonna be Okay, so you don't want to
45:01 the critical porosity model in this in a brine saturated rock, you
45:06 to use this to predict the frame , but then you need to put
45:11 fluids in some other way. so needless to say, I'm a
45:19 fan of the empirical equations and uh really struck me, I call it
45:25 empirical gardeners. In uh 1956. Gregory and Gardner published the wildly time
45:36 epic equation. Um just a remarkable in terms of the amount of number
45:45 experiments they did really well worth Um In 1962, Gardner, Gardner
45:53 Gregory came out with Gardner's equation by way, these are two different
45:59 Larry Gardner and Jerry Gardner, um always thought Larry was the father,
46:05 was the son. It turns out not relationship, which was a surprise
46:12 me, I don't know why I this. But so jerry Gardner,
46:17 professor here at the University of one of the most brilliant guys I've
46:22 dealt with. He became he was only leading leading the field in rock
46:27 , he then spent three years doing car design and then came back to
46:33 and worked on imaging. And there Gardner D. M. O.
46:37 example in imaging uh really an amazing . He um was also consistently under
46:47 from by the FBI because he was war and things like that. Very
46:53 interesting guy. Um By the way here when I was a graduate student
47:04 U. T. My office was the basement and there was a guy
47:08 had an office down, we're not in office who had a room down
47:11 . I thought he was one of janitors turned out to be this guy
47:17 and he was given a seminar and and uh G. T. And
47:24 of my office mates when he presented wily equation. The office mate said
47:30 my office mate Rose's hand and said know there are problems with that equation
47:35 he didn't know who Gregory was we thought he was the janitor.
47:39 are problems with that equation. And said yes I know. But anyway
47:45 the uh wildly time average equation and gardener equation uh Some years later slumber
47:53 out with a paper roemer. Hunt john Gardner also unrelated. Okay,
48:02 the rain or hung gardener equation, don't know if you ever saw the
48:05 being there, peter sellers, one my favorite movies of all time main
48:11 , there was chauncey Gardner. But , different points. Okay, so
48:19 this were during the semester, I'd giving you a homework assignment now,
48:23 I won't do today um which is Wiley Gardner in nerve papers, the
48:31 paper here again, it's on, on blackboard introducing the critical ferocity
48:38 And I asked the question if you estimating ferocity from velocity, which approach
48:43 you prefer to use when and Right. So rather than ask you
48:49 do it, let's let's discuss it , this critical porosity, If you
48:57 at this equation, this critical porosity is really suggesting that when the porosity
49:04 equal to the critical porosity, this goes to zero. You see that
49:10 goes to zero when ferocity equals critical , that goes to zero. So
49:16 goes to zero. So what ferocity that it's the ferocity that is so
49:24 that the rock is no longer a become disaggregated. Right? So the
49:32 from stanford and actually this was our dr han here when he was a
49:37 student at stanford suggested the idea that some critical ferocity, the rock loses
49:45 and is no longer a rock, a sediment at that point. Um
49:51 for sand stones, that's usually somewhere 40%. Um, a simple cubic
49:58 of spheres as a prostitute of Right? So a very loose pack
50:05 40%. And the rock starts to cohesion. Um Now, suppose I'm
50:11 to predict ferocity here. Um, , I'm using a point really out
50:23 . I'm using this point out here predict the porosity in between.
50:30 So, I'm using a value outside range of my data. If I'm
50:36 with liquefied rocks, I may have is up to 30% 35% usually more
50:42 the uh, around 20%. I'm using a value, which is
50:49 hypothetical value that I don't measure. don't see it in the logs.
50:53 guessing that the rock becomes, incoherent at 40% porosity. So,
50:59 using an unmeasurable value outside the range my data to calibrate this curve.
51:09 ? And so what you would do you would vary for these points,
51:12 ? You would put the critical ferocity and put a line there.
51:17 So, you you but you vary point, that is outside the range
51:21 your data. So, there's always potential for non linearity. Who says
51:27 gonna be linear all the way out that point. Right? Maybe it's
51:31 curve linear relation like, maybe that instead of a critical porosity over
51:37 Maybe it's actually a curve like Right? So you're assuming linearity.
51:44 you're using a point outside of the of data to calibrate your curve.
51:51 that's a practical difficulty in using the porosity. Okay, what about these
51:57 relations? The gardener, famous gardeners , density relationship tends to work really
52:07 for poorly lit defied rocks in the of Mexico. The widely time average
52:18 works for a certain range of clean sand stones over limited porosity range.
52:28 ? So wildly time average equation is for more liquefied rocks than the gardener
52:34 . Raymond Gardner equation, as we'll , is for the most liquefied rocks
52:40 get. So, as I there's no unique velocity porosity transform,
52:46 depends on the poor shape, it on the degree of with indication,
52:49 depends on the effective pressure. We'll about that concept later. So it
52:55 depends on what fits your data in area. You're working. Alright,
53:04 , because at a given for a ferocity, there could be a wide
53:12 of velocities. It's useful for us talk about bounds, we want to
53:17 bounds on what could that range of I. D, what could that
53:22 of ferocity is B. And the possible bounds you could have are called
53:28 Royce voice bounds. These bounds um derived oddly enough, assuming a random
53:42 of crystals and doesn't consider the anisotropy the constituents. But with that
53:52 if you think about as I distribute uh constituents, What would the stiffest
54:00 be? And what would the most arrangement be? And the stiffest arrangement
54:07 if if I'm stressing in the vertical and consider this as a piston.
54:13 ? I've got a plate and I'm every component at the interface, the
54:18 amount. Right? So it's a compression, right? Like a plane
54:24 coming at the volume element. Um the most resistant arrangement I could come
54:33 with is columns. This is why use columns. In architecture. You
54:37 imagine. Uh The stiff material in here being one of the columns and
54:44 white, the more compressible material being right between the columns. So for
54:50 given amount of concrete or given amount stone having columns is the stiffest arrangement
54:58 can come up with. Which is architects, the ancients started using
55:04 They arrived at that conclusion empirically. that's been proven mathematically and that is
55:12 the void bound. It's the stiffest . Uh So how do you calculate
55:20 module asse of that stiff arrangement? , the voight Oculus is a weighted
55:28 . So here we have a summation summing over the number of constituents.
55:33 we can have many many constituents and here is the volume fraction. I
55:38 to use little X. For volume fraction. Mafco uses f. So
55:44 of constituent I and that's a So not 20% but 200.2.
55:51 It's a volume weighted linear average of module I of the constituents. And
56:01 this kind of arrangement the stiffest constituent gonna dominate. Also because it's a
56:15 compression, every constituent is straining the amount. Right again? Imagine a
56:24 here at the top and a plate the bottom. And you're squeezing in
56:29 piston, the column, the volume the column and the volume of the
56:36 softer material in between is going to to the same degree. So the
56:44 , the amount of defamation in each is the same. That's called an
56:50 a strain situation and that gives you void bound and that's a linear volume
56:57 stump. On the other hand, I arrange things in layers here and
57:07 a foam rubber between would uh plywood for example. Right. If I
57:15 on this, what's gonna happen? boards themselves are not going to compress
57:20 much, but the foam rubber in is going to compress a lot.
57:25 ? So in this situation the strain different. The softer material strains more
57:32 the harder material. So this is most compressible arrangement you could have because
57:40 have no hard material supporting that soft . So the soft material absorbs most
57:46 the compression. So this is called eye. So stress situation, the
57:52 in each layer is the same but strain is different and this is a
57:58 volume, a volume weighted sum. is called the Royce average. and
58:05 , whereas in the void, the heart and heart of material or
58:10 compressible material is absorbing most of the . In in the Royce case,
58:17 the weak material which is going to the most. Right? So that
58:25 is dominated by the smallest module Now, uh if you go to
58:35 extreme case of the soft material being fluid, therefore you can see that
58:41 resulting share modulates is going to go zero, which brings us to our
58:53 laptop exercise. And so we're going use these simple equations and we're going
59:00 make some rocks and we're gonna think a binary mixture of quartz and
59:10 And we're gonna compare the void and bound only, we're gonna compute things
59:18 few different ways. We're gonna compute void and Royce bound for the balk
59:27 , and we're going to compute it the sheer modules and we're going to
59:30 some conclusions there. And then we're to compare computing em from the Royce
59:38 void K. And the Royce and . New. We're going to compute
59:42 those ways, or we're going to them directly from these equations. Do
59:48 see the difference? Um We could these equations for K instead of M
59:57 we could get the void, bulk K. Or the void, sheer
60:03 mu And then construct the effect of from those bounds, see what I'm
60:10 what I'm saying here. Um or could do it directly, we could
60:15 the plane wave ma July one and the bounds on the plane with plane
60:20 module. So you understand the So we're going to assume we're going
60:29 vary the fractions from 0-1. So if I have zero courts,
60:37 I have 100% water. If I uh 0% water, I have 100%
60:44 . And I'm going to use these july that I give you at the
60:50 for the balkan share modulates of quartz and water. So you understand the
61:02 . Okay, so I'm here to steer as you're going along. So
61:06 ask for help as she needed. could stop recording while you're while we're
61:14 on this. So good. Let's . Okay, so again, we're
61:23 to the motivating introduction. So why we doing this? Well, this
61:29 is to show that the seismic data sensitive to, for example, the
61:36 . P. V. S ratio the rocks. I think in
61:40 you probably talked about um the dependence seismic reflection data on impedance contrast,
61:48 when we consider offset, we're also on Watson's ratio contrast. Maybe leon
61:54 covered that or. Okay, so is just to show that kind of
62:00 . So this is a a synthetic move out, corrected pre stack,
62:06 . Right? So this is near here and we're increasing the offset.
62:12 this is the case where we have sand in a shell and in our
62:18 we have a V. P S ratio 1.83 In the shell of
62:24 PBS ratio of 2.13. And this the event down here. And you
62:30 a big amplitude increase with off step . It turns out that this is
62:36 brine saturated sand. Okay, now going to add gas when we add
62:44 , we're gonna lower the V. V. S ratio in the
62:47 but also gas is going to get the shell and we're going to lower
62:51 V P V. S ratio to the result is no amplitude increase with
62:58 . So this is opposite to what expect with a B. O.
63:02 expect a gas and to have an increase with offset. In this
63:08 we're seeing that on a brian sand they expect uh flat response in the
63:14 stand. Now, we're seeing it a gas sales. Right? So
63:19 seismic response is very, very sensitive little changes in these be PBS
63:25 And so that's a motivation where we to be able to predict what these
63:30 BE PBS ratios are gonna be with fluids and in sands and shells.
63:37 , so a variety of applications, going to use rock physics in reservoir
63:44 and in time lapse seismic. for what I call reservoir geophysics,
63:50 we're trying to characterize reservoirs in the flowing through the reservoirs. Also very
63:59 for direct hydrocarbon detection and both conventional type department indicators like bright spots,
64:06 spots and also A B. O and geotechnical drilling engineering support near surface
64:16 and hazards and things like that. , so what I call reservoir geophysics
64:24 I think dr Stewart has a little different definition. He tends to uh
64:31 the reservoir around the borehole. And my definition, we don't even
64:36 a borehole. It's just we're trying characterize the reservoir or the target.
64:41 so this is the use of surface if you have it borehole geophysical data
64:47 quantitatively determine with ology porosity pore, content, lateral extent of the reservoir
64:55 of the reservoir, compartmentalization, pressures, stresses, and internal architecture
65:02 the reservoir. Right. These are things we're trying to do. Rock
65:06 is intimately involved in all of And this could be exploration before you've
65:11 drilled a while or it could be after you have wells. So,
65:18 one of the questions before we apply geophysical technique is we want to do
65:23 feasibility study, we wanted to be . Is it worth the time the
65:28 and the cost of doing the So, according to Wayne Pennington,
65:34 is is now a Dean at michigan and by the way, was on
65:37 dissertation committee at UT and worked many in the petroleum industry after that,
65:43 was an earthquake seismologist when I knew , will the geophysical technique being
65:49 Be able to differentiate between the competing models and will they be able to
65:55 it sufficiently well to be worth the and the cost? And to answer
66:00 question, we have to do rock and we have to understand the rock
66:05 of the reservoir and the neighboring Mhm. An example of that is
66:14 seismic data. So we have a cube seismic volume and we convert the
66:21 wiggles to ferocity for example. So are ferocity logs here in black with
66:27 porosity to the right and the reds the seismic predictions of high porosity and
66:36 the blues are shells. Right. we've done seismic quantitative seismic analysis and
66:43 the seismic wiggles, we've predicted the properties and here you see a nice
66:50 sand, here's a nice porous And if you just looked at the
66:54 logs, you would think there was flow continuity between the two.
66:59 look at say you have these two here all the way on the
67:04 Um And they look like beautiful sands correlate very well and you would guess
67:09 flow continuity and maybe the performance in wells showed good flow continuity and then
67:14 drill this well, you expect it be the same compartment. But look
67:18 the seismic data in between the seismic in between is showing complexity. So
67:24 strata graphic variability suggesting though even though logs look identical, we don't expect
67:31 flow continuity between them. So part the value than in doing rock fist
67:40 . And of course as direct hydrocarbon , here's an example from Nigeria is
67:46 seismic wiggles plotted in a couple of ways. And if you plot it
67:50 right, you could see very well gas oil contact and an oil water
67:57 . So what's happening? How are rock properties changing? Obviously the impedance
68:03 be changing with the hydrocarbons. So we predict the difference in reflectivity that
68:10 would expect for gas for oil or brian? So that's an important component
68:16 what we're trying to do. Also seismic attributes in this case A.
68:25 . L. Attributes. This is fred Hiltermann did. Oh gosh,
68:29 years ago. Um, he's got well log here showing clean sands and
68:36 shells and green thin Shelley sands in and hydrocarbon filled sands in red.
68:45 he's calibrating his seismic data to the uh to the well log. And
68:51 finding that as you go up dip the well log here, we have
68:55 beautiful amplitude anomaly up here. So we drill that well, rock physics
69:01 gonna help tell us the probability that due to hydrocarbons. Same thing
69:06 You have a sand, you're going dip and there's red. There's also
69:11 attribute also is showing red here, looks like it's maybe assault uh,
69:20 interface. You know, this looks a salt dome here. So it
69:24 like we're on the flank of a dome. So red could mean hydrocarbons
69:29 sand. It could also mean So differentiating all of that. Rock
69:35 can help us do that. This the use of rock physics in geotechnical
69:42 at one time, uh, in deepwater gulf of Mexico. When we
69:48 first drilling there, there was the for example, shell set surface
69:54 They had a discovery well, so going to develop and they knew they
69:58 going to have to drill about eight wells. So the thing they did
70:04 right away. They said the surface . So they drilled the shallow
70:09 it was actually seven shallow boreholes. set the casing with the idea that
70:15 they're ready, they'll come back and extend those down to the target.
70:20 they drilled on that surface casing and they came back, the,
70:27 the wells, they couldn't get down the bottom of those shallow wells,
70:33 casing had sheared and deformed to the that those boreholes didn't exist anymore.
70:41 ? Uh it's a good thing, didn't happen after they had drilled eight
70:45 , it would have killed, you , hundreds of millions of dollars
70:49 And this was called shallow water And what would happen is there would
70:54 shallow sands that were encased in And so these sands had high pore
71:01 because there wasn't any way for the to leak off. So you bury
71:05 sands and they developed high fluid pressure you compress them. The water wants
71:11 squeeze out. And if these were a slope they were in a very
71:18 equilibrium, you put a well in , you disturb them and you get
71:24 mudslide, submarine mudslide. So you huge volumes of sediment sliding. And
71:31 was enough pressure on these wells to the surface case. So these were
71:37 shallow water flows. And so then was the desire to detect these things
71:42 you drill through them. These were hazard. Right? And so what
71:46 noticed about these, these were had high pore pressures in sands. That
71:52 you an extremely high B. V. S ratio. So,
71:55 looked at the deviation in the inverted seismic data, the inverted V.
72:00 . V. S ratio relative to the PBS ratio for normal rocks.
72:08 what we found here was this anomaly on a slope and this was the
72:12 location. And that was precisely where surface casing had been sheared off.
72:21 , um, the answer is you situations like that abnormally high V.
72:26 ratios on a slope. Okay, moving on question, what is the
72:36 common mineral in the crust? You ? No, it was important to
72:52 . Yes, feldspar which you remember our rocks and minerals class.
73:01 Yeah. Most people will answer courts it was a trick question because I
73:05 the crust. So you know in rocks the answer would be courts or
73:12 you're in carbonates calcite. Right? in sedimentary rocks, quartz calcite and
73:18 the other most dominant mineral in sedimentary ? Most common, most abundant sports
73:28 and clay. We're gonna talk about by the way, where does clay
73:35 from weathering of feldspar? So that's clay is so abundant. And really
73:44 you look at the sedimentary rock what are most of your rocks
73:49 Okay. So now in sedimentary why is courts dominant? And the
73:59 is exactly it is most resistant to . So here we're looking at the
74:06 the mineral grains and there are a of fell spars here at the bottom
74:10 you see there are three orders of difference between courts and the most resistant
74:16 sparks. Right, so feldspar, as weather? Much more rapidly than
74:25 . Okay. Some terms that are to be important to us. Um
74:33 is facility by the definite by the , what's the definition of a
74:46 What is a shell french? okay. Think about shells. You
75:04 and love a shell is the definition strict definition of a shell is a
75:14 mud rock. What is a mud ? It's a rock composed primarily of
75:20 and stilt sized particles. So fine now. So you could have a
75:28 stone, you could have a silt , you could have a mud mud
75:33 , a mud stone. What in to be called a shell?
75:38 it has to be fissile. What means is a tendency to part along
75:46 planes. So think about it. have a shell with, you
75:51 betting horizontally and there's a tendency to along those bedding planes. What if
76:00 talking about seismic waves propagating through that ? What does it mean about the
76:08 properties as I propagate through that If I'm going perpendicular to this
76:16 I'm gonna be closing that those Right? So if I'm perpendicular to
76:23 facility, I'm more compressible. My are gonna be lower. If I'm
76:30 to the facility, you're not as . Alright, so shells are,
76:35 definition is going to be an icy . And I said, and I
76:41 tropic, meaning the geophysical property depends direction. All right now, cleavage
76:51 similar to facility, but there are different types of cleavage. There's mineral
76:56 like in a book of Mika's and slate like cleavage like a blackboard in
77:04 old days. Blackboards were made made slate because they would break along
77:10 This cleavage, those are our different mineral cleavage depends on the orientation of
77:18 mineral itself. Where a slate like . That direction has nothing to do
77:24 betting it has to do with the or the direction of minimum stress at
77:31 time of metamorphosis? Right. So a direct correlation to betting cleavage not
77:39 to betting. There's another term called ation. It is banding that looks
77:50 layering. But again, that is metamorphic reaction. And that depends again
77:58 the principle and on the principal stresses the time of metamorphosis. Okay then
78:05 layering and lamination. What is Well, different changing rocks but in
78:12 restricted area you tend to get layers rocks. Right. What's the difference
78:19 lamination is and layering? Lamination are fine layers on the order of a
78:27 . Something like that. So as far as seismic data is
78:33 will produce anisotropy. The low frequency wave will see that as anisotropy.
78:43 a rock sample in the laboratory won't layering as anisotropy and may see it
78:50 heterogeneity in the sample, but it see it as anisotropy whereas lamination will
78:59 seen by everything as anisotropy by the data and in the laboratory.
79:10 more definitions. What is porosity? , fraction fractional void space. So
79:19 have the void volume divided by the fine. And is there a unique
79:25 between porosity and geophysical properties unique. there one relationship? Now, we've
79:34 looked at three or four different Right. So it's a non unique
79:39 between porosity and geophysical properties. Because the porosity changes its shape depending
79:47 the type of ferocity. Now, I held everything else constant, the
79:54 , the pressure, temperature conditions, else constant. Could there be a
79:59 relationship between ferocity and geophysical properties? if I help you know composition,
80:08 mean the same exact rock. The difference and the porosity is all the
80:14 shape. The only difference is the of it then theoretically can be a
80:21 relationship, but generally everything else is at the same time with the
80:27 So we don't have a unique So there's no one equation that's going
80:31 work every place. Does all porosity seismic velocities in the same way.
80:41 the answer is no. And we're to look at the effect of very
80:46 equant pours versus the effect of very pores. Think about it around poor
80:55 a shape like this. Sam compressing round Poor. If you don't structurally
81:02 consider this one poor being compressed. , What does that look like structurally
81:08 about architecture? What is that? an arch, arches are strong.
81:14 why they're used in architecture. On the other hand, take a
81:19 poor and say I'm normal to the long axis. Right? So I
81:25 a flat poor like this, that very compressible. Alright, so different
81:32 affects the velocities in different ways. , so let's talk about different types
81:40 ferocity. Some of these are important their effect on velocity, some of
81:46 are important in their effect on fluid . I mean their effect on velocity
81:52 effective fluid flow. So what is ferocity? How would you define connected
82:06 anyway? Yeah, it's that I mean yeah, it's like topological
82:16 connected. If I had a scan the pore space, I could actually
82:22 a connection between the two and I always be in poor space. That's
82:27 we call connected porosity. Total porosity the total void space divided by the
82:34 life. So what do I get I subtract connected porosity from total
82:42 How much, how much isolated poor I have. And we call that
82:51 disconnected porosity. Now, that's that's topological definition, right? There's a
82:59 definition which is called effective porosity. is effective ferocity? Mhm.
83:20 true. In what sense? You got it. True. In
83:27 sense? I don't know. It's proximity that fluids will flow through.
83:46 . So what is trapped ferocity? . Okay. You got the
83:53 Now, by the way, effective is not exactly the same as connected
83:59 ? Why can fluids flow through all porosity? No, why not?
84:11 fluids have capillary forces. If a a connection between pores is too
84:21 the fluids won't be able to flow . So in general, the effective
84:28 is going to be slightly less than topological e connected porosity. And the
84:34 ferocity will be slightly more than the disconnected porosity by the way. I'm
84:40 to have these definitions. It'll be your notes. Okay what is buggy
84:53 ? There was money. What's a ? What do you think? A
85:00 is a bug is a roundish poor , it could be angular but in
85:08 of the length of the axis of poor is relatively equal and you stay
85:18 type of ferocity in often in One way to create a bug report
85:24 to dissolve a crystal. You get buggy before. Similar is vesicular
85:32 What is vesicular porosity? It's like bubbles that or liquids that uh
85:48 They get boiled off and they leave a void so that's cool. And
85:54 frequently get this in the salts or bas dissolution Prasit E. Is dissolution
86:05 mineral grains, molded porosity. So porosity will inherit the shape of the
86:13 that got dissolved. To set the order. Anyway molded porosity is dissolution
86:21 shell material. So again molded ferocity have a shape that is controlled by
86:32 shape of the original. Usually broken . Okay, inter granular ferocity ferocity
86:40 grains into crystalline porosity porosity between How do you get ferocity between
86:49 Well for example suppose I have calcite and then I have idle um a
86:56 them. I bring some magnesium in hydrothermal fluids or something and or at
87:03 very near surface the same thing can and I turn calcite which is
87:08 A. C. 03 to C A M G M G.
87:13 . I 206. Right? Dolomite much denser than calcite. So if
87:22 making a more dense mineral I have I have conservation of mass.
87:28 I make the crystals more dense. have to compensate that somehow by creating
87:33 space elsewhere. So that produces into porosity, fracture porosity that's obvious it's
87:41 by fractures, fracture porosity can tend be aligned which creates an iced atrophy
87:48 it could be aligned usually in a sense. So it produces as a
87:54 anisotropy also. Um And fractures tend be very compressible because they're playing and
88:02 easy to repress micro porosity, very porosity. So micro porosity tends to
88:12 be trapped fluids can't get out of . Not on a human timescale down
88:20 is water associated with Claes now, on how it's measured, it could
88:27 chemically bonded to the clay or it be physically trapped within the clay lattice
88:34 it can be trapped in clay. porosity. So bound water could exist
88:40 a number of different ways usually associated clays. Okay, and then there's
88:46 porosity which is the initial ferocity at time of deposition and there's secondary porosity
88:53 is process produced later. Bye. genesis or uh fractures or dissolution.
89:08 all these different velocities will affect the in different ways. And one mistake
89:15 often make is they take the ferocity the geologist or the uh the petro
89:24 gives them and they don't ask what of ferocity is this? If you
89:31 at a density log ferocity, what's density law gonna see? It shoots
89:36 rays into the formation and it counts number of gamma where gamma rays that
89:41 back and the more mass in the , the less come back. So
89:47 type of porosity does the density locks of all of these? Well,
89:58 , is that additional ferocity? You say a primary plus secondary. But
90:04 what it sees is the total It's measuring, it's seeing the amount
90:09 void space filled with liquid as opposed the amount seed filled with solid.
90:16 the density logs responding to total But you see the sonic log may
90:21 have a very clean relationship to total . If the porosity is changing its
90:27 , a lot of buggy porosity may the same velocity as a little bit
90:32 fracture porosity. For example. if the petro physicist is giving you
90:41 ferocity or in the oil industry, petro physicist is going to be giving
90:46 the effective ferocity. Okay, so is showing carbonates and it's showing pores
90:55 different shapes and carbonates here. The are the are the are the open
91:02 And so you see different sizes, should see different amounts of ferocity and
91:07 see different, uh, poor So carbonates are particularly troublesome. Sand
91:16 tend to more or less to have types of ferocity. It's a granular
91:22 of ferocity, but carbonates very all the place. Okay, so I've
91:31 the point that flat pores are much compressible than spherical pores. Okay,
91:39 point of confusion that we often have the term clay. What does,
91:47 does clay mean? Often that's what means. It could also mean a
91:55 mineral because clay minerals aren't they break easily and they're often very fine.
92:02 those are two different things. Clay and clay sized particles. Because clay
92:09 particles are not all clay minerals. can get a lot of courts in
92:15 clay sized particles. In fact, shells are primarily courts and some shells
92:20 primarily calcite. The Eagle. For , a famous shale reservoir.
92:27 it's mostly counseling. Okay, so term clay can refer to grain size
92:34 mineralogy, The grain size. It's particle less than .002 mm or it's
92:42 type of, or a Kamina clay , which is a type of silicate
92:47 a sheet like structure. Okay, terms, what is the gas?
93:00 has no shape. So what else has no gas. What's the difference
93:11 the liquid and gas? I mean has no shape. They're both
93:19 That's the definition roof look, the you're having trouble is because it's a
93:23 of degree. So gas molecules are rapid motion. They move independently and
93:31 have no orderly arrangement in the The molecules move more slowly or closer
93:38 and have little ordinary orderly arrangement. actually have some, for example,
93:44 surface tension. There's laminar flow, ? So there is some degree of
93:53 . Both of these have zero So so they take the shape of
93:58 container. And so they're both Was the definition of a solid?
94:11 45. Okay. It doesn't have have order because you could have an
94:17 solid. So my definition of the is a material that resists a change
94:24 shape. You try to change the of a fluid and it'll just square
94:28 away, whereas a solid will fight . It'll try to resist the
94:34 So solid has rigidity. Uh by way, there's another misconception, people
94:41 call a liquid like water. They say it's in compressible, right?
94:51 doesn't mean that it has a high modules. Right? What it means
94:57 that if you try to compress it going to square it away. But
94:59 you can find it, you can it quite easily relative to a
95:05 Okay, now, orderly arrangement, have a crystalline solid. So in
95:13 crystal and solid you have a crystal . On the other hand, you
95:19 have an amorphous solid like glass or or in this case you have you
95:27 have an orderly arrangement of molecules. . And we already defined rock and
95:33 say it's a naturally occurring aggregate that a mixture of the above.
95:41 another challenge we have in rock physics the different scales of measurement we're dealing
95:51 in the laboratory. We measure velocities a little sample like that. In
95:58 well logged, we measure over a of feet, Bsp maybe over tens
96:05 feet or seismic data, more tens feet to hundreds of feet. So
96:11 seeing, we're going to measure velocities different scales of measurement and we know
96:20 to upscale velocities, we know how go if we had thousands, if
96:25 had little high resolution velocities at every over thousands of feet, we would
96:31 how to upscale that to a longer seen hundreds of feet. Right by
96:38 way, in reservoir engineering, we necessarily know how to upscale. For
96:42 , permeability doesn't upscale readily like that it depends on the arrangement of the
96:49 . Whereas with, with seismic we know how to upscale. On
96:54 other hand, we don't know how down scale. That's completely non
96:59 So we don't know how to go a core scale of measurement to a
97:03 . Now, often in our business gonna be comparing measurements at different
97:11 So that's not always a straightforward thing do. Also, there's the fact
97:19 the scale of measurement, the the dimensions of the piece of rock that
97:27 investigating depend on the frequency we're right. Low frequencies average a lot
97:34 rock, high frequencies average a smaller of rock, but we also have
97:41 a porous material. The velocities also on frequency. So, we have
97:46 factors working there. There's dispersion that in real rocks. Real real rocks
97:54 not perfectly elastic. So we have , but we also have we're seeing
98:01 pieces of rock. So that's gonna that's gonna plague us constantly. All
98:09 , now, the other thing that on is we're measuring the velocity on
98:14 little piece of rock, but there's in the earth. So that little
98:21 of rock we're investigating may not be of what's around it. In
98:27 there's definitely sample bias. I rocks that fall apart are less likely
98:32 be measured in the laboratory than rocks will stay together. Okay,
98:39 the seismic waves will see the heterogeneity , depending on their frequency.
98:45 what do I mean by homogeneous homogeneous the property is the same, every
98:54 at a given scale. So, example, if I'm measuring the velocity
98:58 a sandstone here, it may be same. If I go to that
99:05 over there, the velocity may be same. I would call that
99:09 But if I went to a very scale and I'm measuring the velocity of
99:14 sandstone, if I'm inside a quartz , that's going to be giving me
99:18 different velocity than if I'm inside a . So when we see home,
99:23 we say Iraq is homogeneous, we its macroscopic li homogeneous Heterogeneity means that
99:32 property values at the scale that I'm things, the property varies as a
99:37 of position. So, I'm in channel here, you're in a floodplain
99:42 there and there's a bank between Right? So that's heterogeneity layering is
99:51 type of heterogeneity. So it's a heterogeneity. Okay, so what I
99:57 , microscopically homogeneous or heterogeneous. I at the scale of the measurement and
100:04 it's homogeneous at one scale and maybe at a different scale. Now,
100:11 icy tropic is different and I say means the property varies with direction.
100:17 if I'm in a in a microscopically material, the property may also vary
100:25 direction in a in a particular but on the average it may not
100:30 with direction. So, we have distinguish heterogeneity from anisotropy. Anisotropy is
100:38 to the an orderly structural arrangement that me preferred orientations that have particular
100:47 Okay, and can an anti psychotropic be homogeneous, Yes, you could
100:57 could have the same directional dependence every in which case it's homogeneous.
101:05 so different scales of measurement as I saying, I can make measurements on
101:10 plugs on longer pieces of core called or I have a well log
101:17 I have a borehole geophysics scale, have a surface geophysics scale.
101:25 so one thing I'm gonna want, gonna do frequently in this course is
101:30 gonna show you observations and I'm going ask you to explain those observations.
101:36 don't care if your explanation is right wrong. I just want you to
101:40 through the process of coming up with hypothesis to explain the observations. If
101:48 get in the habit of doing then you suddenly you'll find out that
101:51 look at observations. Then you understand , why you're seeing what you're
101:56 So no hypothesis is too crazy. talk about the hypothesis, but you
102:02 as many points with me coming up a nuts hypothesis as you do and
102:07 up the right hypothesis. So don't shy about offering hypothesis. Okay,
102:15 here we have a case we're applauding or I should say velocity versus porosity
102:23 as the porosity increases, the velocities and we're going to see that again
102:28 again. But for lime stones we a similar relationship with ferocity, but
102:37 the same ferocity, the lime stones to be faster than the sand
102:42 Okay, so give me a hypothesis explain the difference in velocities between these
102:49 stones and these sand stones just get home. Ah good. Right.
103:03 that's the other thing you have to ask me questions because I haven't given
103:06 all the information. So in this all these rocks are saturated with
103:15 So saturation is not doing it, could have been another hypothesis.
103:28 philosophy and so on. Lower than ones. So the mineral itself,
103:36 calcite is faster than courts. And can I test test that hypothesis?
103:44 , I'm going to extrapolate these trends to zero porosity. I extrapolate these
103:51 back to zero porosity and at zero , I'm faster in limestone and
103:57 So that supports your hypothesis, had else happened that could have potentially falsified
104:05 hypothesis, but it supported your What students will often say is,
104:11 , the pores and sandstone are flatter the pores and limestone, limestone has
104:17 pours, sand stones have flat So how do I test that
104:23 Well, just looking at this we have the same change in velocity
104:28 ferocity which suggests that poor shape isn't explanation. And if it was strictly
104:35 shaped extrapolating back to zero porosity wouldn't you that difference. So, in
104:41 way those things tend to falsify the that it's a difference in poor shape
104:48 this group of rocks. Okay, measurement, I'm measuring velocity versus
104:58 So versus orientation. And think of as a polar orientation. So I
105:07 a rock sample like this. I'm the velocities and I'm changing the direction
105:15 I'm measuring the velocities in a polar . Okay, so this is p
105:22 velocity. So we're not thinking, different polarization. We're seeing different directions
105:28 the sample. Okay. And I'm this at different pressures, at low
105:35 and at high pressure. So I'm both a change with azimuth change with
105:42 and a change with pressure. I'm seeing anisotropy explain the anisotropy in
105:50 . Nice. Alright, so I've a rock sample and measuring velocities,
105:56 orientations through that rock sample. So why the anisotropy decreases. But why
106:12 directional dependence? The is also called nice tropic Porsche. Spyder,
106:25 tropic. Yeah, that explains the between the curves. Absolutely.
106:31 Great hypothesis. In fact, that's hypothesis, I accept. But why
106:36 dependence on orientation? What could you about these pores? Mhm.
106:49 Right. So here we're going perpendicular the pores and we're closing them here
106:55 going parallel to the pores. So have an aligned set of compressible
107:01 What do you think these pores are a nice What type of ferocity to
107:11 such a well defined orientation? Okay, so let's say the poor
107:22 core is perpendicular to any affiliation. so the foley ation is the
107:29 I I didn't tell you that. you wouldn't have known that.
107:32 But let's say it's that in a and a a sample of a nice
107:41 fracture. So what the answer is have a well aligned set of fractures
107:47 this nice, which would have been along the direction of maximum stress,
107:54 minimum stress would have been perpendicular. the fractures opened up that way and
108:00 we're orientation is in the perpendicular, normal direction to the fractures were preferentially
108:08 those fractures. Good, okay, versus porosity. And we have various
108:19 these uh ferocity transforms that we saw the rain martin Gardner equation, the
108:26 equation and Gardner's density equation. And have three sets of sand stones.
108:34 you see these guys are all following rammer equation and these guys are not
108:41 at the same ferocity we have different . So hypothesis to explain the
109:12 It's the floating in the side of said yeah, that's the same.
109:19 question. These are all brian I forgot to say that in the
109:40 pressure. So I would say the , control the velocity and even.
109:54 , okay, so that's a good and I'm gonna come back and say
110:00 did thin section work and I saw these are all granular sand stones.
110:08 have very similar poor shapes at least the eye. It's possible that there
110:29 the mirror of their forest, they're court sand stones. Good.
110:35 this this is exactly the way you're to be thinking, this is very
110:40 . You're coming up with the correct . So the grains are the
110:47 Their courts, there's no way that uh force. Uh I'm going to
111:06 that the porosity is very similar to eye. I think that the whole
111:12 , uh rain inside. Well, a sphere pack of some kind.
111:17 , These are grains and a similar . one more factor. Good
112:11 The temperature the same today, there's more factor years. Is it possible
112:50 I could have a loose connection of grains? And is it possible that
112:57 could have a very hard collection of grains and have those ferocity is be
113:03 same. Can I take a loose of sand grains and can I make
113:10 hard without changing the porosity very How would I do that could be
113:18 contacts could be precious solution or a bit of the cement goes a long
113:26 . So in this case these are lit ified. Either consolidation, that
113:34 be grain interlocking. But these are . These ferocity czar very similar to
113:40 processes, but these are cemented and are not cemented. So, so
113:48 general rule here, the Raymond Gardner corresponds to your most well with ified
113:57 . Where is the gardener equation applies poorly lit defied rocks? All
114:04 So, if you're plotting up you could say something about the
114:08 this is a well lit defied A strong rock at the same ferocity
114:13 . If I'm following the gardener it could be a very would be
114:17 very poorly liquefied rock. Okay, we have two very different behaviors we
114:33 here kind of a linear drop in with ferocity. And then suddenly very
114:40 dependence on the porosity. Can you this? And let me say there's
114:52 misleading term on this plot. They appointed by. Exactly. So what's
115:16 misleading term here? Mhm Sam stone Okay. That just means mostly coarse
115:27 . That means liquefied. These things sediments. These aren't with ified.
115:32 we'll see later that these are following equation pretty close to the equation for
115:38 . In fact, that's the blue there. So these are not
115:43 And this is the critical porosity where stop being a rock. That's like
115:49 40%. Oh, alrighty. All . Now we're going to get a
116:03 bit complicated. We're gonna look at . Carbonates are always more challenging.
116:11 are not as well behaved. And one thing, there are different ways
116:17 measure porosity in a carbonate. So are different samples and in each
116:23 the porosity is measured three different one is the plug ferocity. What
116:31 does that mean? You actually take rock sample and you immerse it in
116:37 and you see how much fluid goes the sample. Right? That's the
116:43 ferocity. There's a then the scanning microscope ferocity. So that's taking a
116:51 electron microscope image and then digitally doing analysis, figuring out the difference in
116:58 image between poor and solid and measuring amount of porosity from the image scanning
117:07 microscope. And then there's an old way of doing it. Which is
117:13 plug ferocity, I'm sorry. Which the optical mineralogy or optical microscopy.
117:20 you're looking at a microscope image an microscope and visually point counting and finding
117:28 porosity. Or maybe they did it . They would do that recently.
117:33 would be done via image analysis. , so they're getting different ferocity ease
117:44 a general observation most of the Not always. But the plug ferocity
117:50 to be greater than are almost equal the scanning electron microscope ferocity, which
117:56 always greater than the optical ferocity. why why do these different methods give
118:04 different velocities? Well, there could that could be the case if I
118:15 looking at one sample. Right? here we're seeing systematic change in every
118:28 . But you're right. Heterogeneity is an issue because you may not be
118:34 the same exact piece of rock. here we're seeing a systematic difference.
118:39 always happening this way. So we to explain, you know, if
118:43 was just heterogeneity, you would say should be somewhat random unless, you
118:48 , sometimes it should go one Sometimes it should go another way.
118:52 we need a hypothesis to explain why seems to be systematic. You
119:02 I just imagine like a microscope, can only get so much. And
119:07 when you you're able to do larger , don't think about the area.
119:16 about it this way, the Right? The plug in the scanning
119:24 microscope are gonna see smaller ferocity than you can observe optical mineralogy.
119:32 optical microscopy. So what their um here is there's a lot of very
119:40 porosity in these particular rocks and maybe very small pores, Maybe there's something
119:49 about them. Maybe they're not shaped the same as the very large pores
119:54 we can see. And uh they very specific is there is a large
120:09 of large fraction of course, space is smaller than six microns in
120:15 They could see that with the scanning microscope. They couldn't see that with
120:20 optical. Alright, now, let's at the velocities. If you cross
120:37 the velocity versus ferocity, there's a of scatter and They have this less
120:47 50% more than 90%. I'm telling what those are. So offer an
120:57 . You see that there's something different these rocks that say greater than
121:03 And these rocks which say less than . Again, these are all fully
121:10 saturated. Well remember the porosity is same, but you're right, it's
121:30 fraction what it has to do with the fraction of the pore space.
121:34 is very small. So here in rocks, most of the pores are
121:41 small, whereas in in these rocks smaller percentage of the porosity is very
121:50 . So the amount of small porosity you different velocity. Now, one
121:56 about poor shape, the effect on of a particular poor shape is independent
122:04 the size of that poor. It on the total amount of ferocity,
122:10 a small, flat poor or a round, poor proportionate to the amount
122:16 pores. So I could have an ferocity of small round pores, or
122:22 round pores, as long as the pores. If it's an equal amount
122:25 ferocity, the effect on velocity is same. So it shouldn't matter the
122:32 of the pores if the pores were the same shape. But here,
122:37 more small pores we have the lower velocity. That's suggesting that those small
122:43 , there's something different about those small . And what we're gonna see is
122:47 poor shape. Okay, so here's example of big groundfish pores and and
122:59 higher porosity rock, but made of smaller pores. Now, if I
123:15 the round pores, which, relatively , have a smaller dependence on ferocity
123:23 the flat pours. And if I look at the relationship between velocity and
123:29 ferocity, what I find is a there that's better defined than previously.
123:36 ? When I cross plot against total , I have, I'm almost doubling
123:41 velocity here, I have a wide , whereas here is a smaller
123:47 Alright, so, it's a better curve. If I ignore the round
123:52 pores and only cross plot against the pores. That suggests that the poor
124:00 pores have a similar shape and in we'll talk about aspect ratios. But
124:07 widely time average equation Uh tends to for pores that have an aspect ratio
124:15 that .1, meaning the minor access the long axis. The long axis
124:20 10 times longer than the minor And uh so the wildly time average
124:27 is this red curve here and so within the range of the variation of
124:34 data except maybe at these very high is but at least down here,
124:39 wily equation doesn't do too badly against micro ferocity. So this is suggesting
124:49 t on the order of .1 Aspect . So pretty flat. Okay,
125:00 now breaking out the points according to whether or not the samples are dominated
125:06 macro or micro porosity. Um what suggesting is that um you know uh
125:17 macro porosity gives you higher velocities, means that the velocities are less sensitive
125:23 the macro porosity. And if you plot a velocity versus micro porosity you
125:32 . And so this is the micro in the samples dominated by round force
125:38 get a very including those dominated by porosity. You get a very well
125:44 relationship. On the other hand this permeability. So this was velocity,
125:55 ? This is permeability with permeability of the the samples dominated by macro porosity
126:04 higher permeability than the samples dominated. . Micro porosity. And if you
126:14 plot permeability against macro porosity, you a well defined relationship there.
126:22 What's going on here? Fluids like flow through bigger pores? Mhm.
126:46 be shy. Like I said, can't give a wrong answer. I
126:50 want to see that you're thinking so yeah, you have bigger pipes for
126:56 fluids to flow through. Alright, , I'll let you read these comments
127:05 . Here's another example. These these in plastic rocks. And if you
127:13 plot density, 1st 2 sonic transfer , this is the regression fit.
127:22 not I would not say that's a fit. Right. You tend to
127:27 away from that regression for and it of cuts it in half.
127:35 puts an answer down the middle. very satisfying. Why why would classic
127:43 have such a difference between velocity and or a sonic transit time, which
127:51 one over velocity versus density. Why big spread. Mm. Oh,
128:04 the way, the here is Right. So you find that there
128:09 rocks that at a given depth have similar velocity velocity, they're over a
128:18 range of velocities, but a wide of densities. Do you kind of
128:25 you kind of see a trend like, ignore all these points.
128:31 . Do you see a distinct trend ? Yes. Yeah, deeper is
128:39 here. So shallow to deep. getting denser and denser. Right?
128:48 velocity is increasing. Yeah, that's effect of confining pressure boat. The
128:56 spread of data seems very well I could fit a trend there
129:04 What could you say about the porosity for this trend. Look at the
129:09 in density here, it's not that . And if courts and clay have
129:15 density of about 2.65, you could these are probably shells you buy that
129:24 are low porosity rocks that have a depth dependence. On the other
129:29 um you have these rocks that have wide range of densities and a relatively
129:37 range of velocities. So density is much more than velocity. What's happening
129:44 those rocks? I'm going to argue we were filling pores with clay.
129:52 these are your very clean sand stones these are dirty sand stones as you
129:59 clay to the poor space. The doesn't change very much, but the
130:05 gets more and more. It's it's well known. And and when we
130:11 about Gardner's equated paper, I'll show that shells at the same velocity as
130:17 stones tend to be more dense. , so there's your shell trend.
130:25 going to fit a line to I'm going to call that the shale
130:28 . And I'm gonna say that this here separate your clean shells from your
130:37 and there's a sand line here, would argue. And that everywhere in
130:42 is varying Shelley nous of that So that's a clay volume variation in
130:50 sand. See how what we're doing we're explaining the observation. We're forming
131:07 . And so the act of forming to explain measurements is what rock physics
131:16 all about. So give me a for those points. Oops, What's
132:02 about those points? How are they from the other points? Yeah.
132:13 they're shallow, you can see from color but their sonic transit times are
132:18 low. So they're very fast. these are shallow, very fast
132:25 Um The wide range of density Not so but that's a hypothesis.
132:37 good. What else could it Something with a much higher velocity at
132:41 much shallower depth and a wide range densities throw out something could have been
133:08 . I'm gonna argue. No. of the right wide range of
133:11 But what else could do that? else is high velocity relative to
133:18 High velocity carbonate. Right. So could be happening here? Suppose we
133:26 a buggy limestone? The remember we saw that the velocity is not very
133:32 react very strongly to the bugs, the density would the density would vary
133:38 great deal. So maybe there's a buggy carbonate. Maybe these are just
133:45 values in the log. But we try. We That's the last resort
133:50 you're gonna first you try to explain geologically. If it's absolutely if you
133:55 explain them geologically, then you can to experimental error. But that's too
134:00 a cop out. Right. Anything doesn't fit your preconceived nourish notions,
134:05 are automatically say experimental error. you have to verify that if it's
134:10 error, show me the logs and me why you think that those log
134:14 are wrong. Okay, now we're uh dry and brine, saturated velocities
134:27 these are for mixtures of clays. got two different types of plays kale
134:32 I and smack type. We'll look at how these things are different.
134:40 we're varying the stress. And they're talking effective stress here. What they
134:48 mean is differential stress. The difference the vertical applied uni axial pressure and
134:54 poor pressure. And they're calling that effective stress. And so these are
135:02 observations. So, explain the observations what's happening. That's different.
135:18 okay, a few things velocities are with pressure and p wave velocity increases
135:29 you have brine as as opposed to . Right? So you're seeing an
135:36 in the velocity as well. So this because the travel Well, fluids
135:54 a resistance to compression also, and the fluids can't escape, they could
136:00 you resist the compression. And if in a loose conglomerate of clay's the
136:05 of the fluids could be very significant I'm in a buggy limestone. I
136:09 care too much what's inside the But if I'm in a loose aggregate
136:13 clay's the flu is going to be a lot of work to resist that
136:18 . So that causes the p wave to go up. You notice the
136:22 wave velocity goes down? Why would happen? Why would share wave velocity
136:29 down when I add water? Right. So the equation for share
136:44 velocity, square root of rigidity over . The rigidity is already low.
136:51 a loose aggregate of clays and any . It's not gonna change the
136:57 but it's going to increase the density lot. I'm gonna skip this
137:09 Okay, so we're going to look different approaches to explaining the geophysical
137:18 One approach is to look at the fractions of the components I call this
137:27 modeling. So I'm mixing the components . I care about the mineral
137:33 the porosity and the fluid saturation. , in a way, what we
137:39 doing with the velocity porosity transforms Wiley , uh Ray martin Gardner, we're
137:47 at the variation of ferocity. So were actually looking at the variation with
137:53 essentially the composition. Um We could more so that's kind of a first
138:01 kind of effect. We also can the internal rock geometry, the structural
138:10 of the solids, which results in texture, the grain size and shape
138:21 amount of surface area of those grains and how they're arranged, how they're
138:27 , We could have a loose we could have a very dense
138:31 then we can look at what's happening the interfaces between the grains or the
138:37 . Are the grains cemented? Are interlocking? Have they, have they
138:42 into each other? Uh And if are fluids, there definitely there's definitely
138:49 going on at the interface between the and fluids. And then of course
138:57 are the environmental conditions. This is Shawn's book, he calls them thermodynamic
139:02 , the pressure, the state of and the temperatures. Okay, so
139:11 ways to mathematically deal with these different . We can view, we could
139:22 most rocks a heterogeneous genius in other , they're not made of one solid
139:27 , they have some mixture of solids they have poor space. So we
139:33 call this a compositionally heterogeneous material which complicated, gets really complicated. I
139:41 got a graduate student working on this right now and um in fact we've
139:50 working with leon Thompson on dealing with . But um to first order we
139:58 this compositionally heterogeneous material and we think it as being homo compositionally homogeneous with
140:08 mineral property that is some kind of of those others. So we think
140:15 some kind of average solid material. Okay now we could then, given
140:25 degree of simplification there are other ways can do it, for example,
140:31 can think about handling the different components being different parallel sheets and in fact
140:40 do that with the void and Royce and implicitly the wily equation is doing
140:46 also. Um We can also think different types of geometries, like we
140:55 take regular arrangements of spheres and we calculate the properties. I've got a
141:02 now who's three D printing rocks, we know the arrangement. So we
141:09 the arrangement using physics, we could what the velocities are supposed to be
141:15 we're comparing that to laboratory measurements, ? What engineers do they like to
141:21 of Iraq as being composed of tubes that they can consider fluid flow through
141:27 rock very common. And there are of doing this. Uh we have
141:35 is called inclusion modeling. You take background matrix to some solid material and
141:42 put pores of different shapes in it you put other minerals of different shapes
141:47 the rock. And so the most of these are like Okano Budiansky and
141:53 toxins modeling a lot of different ways do this. So we're gonna,
141:59 gonna look at a little bit of of these different ways of characterizing rocks
142:04 the way, all of these, of these mathematical abstractions are correct.
142:09 all wrong because real rocks are more than any of these. The question
142:17 are they right or wrong, is useful. So these different ways of
142:24 at rocks could give us insights. could help us conceptually understand what's what's
142:30 and maybe help us understand the systematics seen. But they're terrible for predictive
142:38 and a mistake people make is to these highly idealized mathematical models and use
142:44 to make predictions. Those predictions are going to be wrong unless you're really
142:50 . Right? But they're useful. . We already looked at these.
142:59 , well that is our first Bye. I think that this since
143:05 is our first day, I think call it quits here. So,
143:11 questions. Any questions. The more , the longer we stay. So
143:19 , so tomorrow eight o'clock we'll see virtually. We could talk about that
143:37 morning. I mean we can we eat since it's virtual. We could
143:42 eat through lunch and break even earlier doing away with the lunch break.
143:49 that's up to you guys how you to do it. We'll see how
143:53 feel tomorrow. I could always eat you're doing an exercise so I don't
143:59 . It's up to you. And you have the link for the
144:04 zoom. Okay, good.
-
+