 So now we'll change the settings. We're still going to be handling volcanic eruptions, of course. But one thing I would like to, we're going to do the same kind of arguments that I've been using before, simple arguments. And then we'll back them up with equations if need be. But we'll start with this. This is mostly going to be driven by observations. And one thing that I think has been neglected in the behavior of volcano is the buildup of a volcanic edifice. It's not a buildup of a lava flow. It's a buildup of an edifice, a volcanic edifice like this one. This is Mount Adams. Mount Adams rises something like two kilometers above the original first surface before the volcanic erupt in that area. It's a beautiful volcano. It's extinct now, but it's linked to Mount Adams in another volcano. It's been heavily studied. And it shows very interesting features. So it's extinct for about 100,000 years if I remember correctly. One thing we have to remember, this is a typical magma differentiation series. For those of you who are not petrologists, these are a series of lavas that are simply produced from one another by fractional crystallization. You start with basalt. You crystallize it. When you crystallize it, you have dense mafic cumulates. These usually will settle to the base of a reservoir. We'll generate what we will call an evolved lava. This endosite might also crystallize, settle some heavy minerals. Then this will derive base sites. And then, right, the names are not that important. You can figure out what the differentiation trend is by looking simply at the construction of SiO2s, silicate oxide. The remarkable thing is that you will find all these lavas in the same volcanic system, showing you, of course, that if you have rhyolites, that implies that there was some basalt at some point. And the other thing that's important is that you will find usually basalt at the surface. And the question is, what makes basalt stop somewhere to produce the rhyolite? That's an important feature. Why do eruptions occur at the surface with basalt? And then after some time, you start building up an edifice and then you are rhyolite. And that's the questions I'm going to ask today in this talk. The other thing that you have to know is that I'll show that later on. There's a change of viscosity across that compositional range. Basalts are the most fluid lavas, rhyolite are the most viscous lavas. But there's also a change in density. And this is a typical density. You can see, of course, that basalt is not a single liquid. It's a family of liquids over a range of composition. And that's the density range. The important thing is that it goes down as you go up the differential series. The more evolved the magma is, the less densities usually. You will notice that I have not accounted for volatiles. And we'll introduce them later on. But I will talk only about dry magmas. Volatiles are an important feature, but not that important for what I'm going to talk about today. And density has got to be compared with other types of densities. Average cross density, we know that from gravity studies, et cetera, it's about 2.7. So this is telling you something that you would have already known if you had looked at the field, is that basalts are able to rise through the crust because they are just about the same density, usually slightly less dense. So basalt can make it to the surface. And in many volcanic systems, they do make it to the surface. On the other hand, if you have an old or on the continent, et cetera, with sedimentary rocks or fractured crystalline rock, fractured crystalline rocks is rocks filled with fractures filled with water, so it's less dense. If you have built up a superficial cover, supercostals, they're usually less dense, and they can be as low as 2.35 in density. You can see a basalt will be able to rise through average crust, will not be able to go through these shallow coastal systems. So you can see that the dense difference between magma and surrounding rock may be positive or negative, and may change sign during transport simply because you will encounter rocks of different densities. So that's an important feature to you. Now if you look at the, sorry, the only thing that you have to know about the volcanic system is that usually they end up building big volcanic edifices, much thicker than individual lava flows. Shield volcanoes, stratovolcanoes, the shield and stratovolcanoes are different because of their slopes. Shield volcano is a small slope. They derive their name for ancient shields, or if you like Game of Thrones and stuff like that, so that's the shield. And stratovolcanoes, they don't show up in Game of Thrones, but anyway, there are much steeper slopes. That's an old shield volcano on continents. They occur on continents and oceans. But you can see how large the radius extends to 24 kilometers, big, big lateral extent. Height now is less than it used to be because it's an old volcano. It's been really the workout a lot, 800 meters. Mount Adams, radius 10 kilometers, height about 2.5 kilometers. What I'm gonna show is what matters more and more than anything else is the radius. I will see why. So these things represent large loads on the surface. The loading has got an effect on the stress distribution, and this is mostly what I'm gonna talk about in this lecture. If we look at what happens, look at Mount Adams. He's still working for a graph. That's an ancient volcano. It's dead now, but we can see as time evolved, this volcano changed, and it changed how? It changed because it started erupting more and more evolved lovers. And the erupting lava through some advance became increasingly involved with time. So initially you had basals coming out of the system, then you build up an edifice, and eventually you started to erupt. I'm sorry, you can't see the difference between andesite and daisite. There's a daisite flow here. There's very few daisite flows in that system. But then it started to erupt andesite. I'm sorry, this is in French, so the big translation, if you look at your dictionary, basalt with an E is French, and basalt without an E is English, and andesite with this accent here is French, and andesite without this is English, and daisite, you're fortunate, no difference. So anyway, so initially you had lots of basaltic lavas coming out, and then you started to erupt andesite and daisite. Of course, if you erupt these old lavas, this implies that the reservoir has formed, but why is it that we had basalts coming out, and why is it that the basalts eventually were prevented from coming out and generated devolved lavas? So primitive lavas are always present in the system, but when there is a volcanic edifice, they do not erupt centrally, they erupt in peripheral vents, distal vents and fissures. So there's always basalts coming in, but the basalts do not erupt centrally, they erupt away from the axis. That's an observation. Just an example, post-lacial period, which is nicely studied because the glaciers have just eroded the edifice, so you can build up some stratigraphy of that. There's one cement andesite, so that's an evolved lava, and the sites with high elevation flanks, and also some peripheral basalts. So you can see that if you go from this side, the denser lavas, remember basalts are dense, low altitudes away from the central system, and then andesites higher up, and then eventually there was some desite right at the top, just when the volcanic activity stopped. So it's not something that's only observed at Maud Adams, it's observed in most retovolcanoes and large continental shell edifices, and Medicine Lake, for example, has got exactly the same kind of features, and I will show you other features in other volcanoes, that's exactly similar to that. So this is a very specific and reproducible pattern. You can also see that there's rapid changes of migra composition, this is mountain islands, basically average composition of mountain islands is basically desites, close to andesite desite, and red is the evolved lavas, and that's time, year before present, 4,000 years before present, now, and there was a big change, and this occurred several times in the history of this volcano, where you suddenly shifted to another composition and a more primitive composition. So there's activity that sustained for quite a while the same compositions, and then the abrupt changes. And the disubrupt changes, in this particular case, were heralded by a return to more primitive compositions in the summit area. And so there's a problem of time scales here, last span of volcanic system is something like between 10 to the 4 and 10 to the 6 years, mountain islands has been active for about 50,000 years. Mount Adams altogether was active for about 400,000 years. And there's two types of evolution of my compositions, slow, differential trend toward more and more evolved magmas, and fast, return to primitive compositions. How can we account for, after all, this is the same plumbing system, how can we account for such a marked change in the time scales for lava composition? Well, one things which I will try to convince you of is that the fast thing is simply due to the fact that an edifice is unstable and might get destroyed by slope failure. These are thick edifices, they are not always at the static angle of repose, so they're not exactly granular piles, but they still have to obey some strengths relationship, so they can't go to any thickness. And they also are unstable because they are gonna be affected by alteration, the rainfall is coming through and changing and alters the rocks. And they can also be destroyed by magma intrusion itself, and this is what happens at Mount Adams, there's a big magma intrusion there, and it's just the destroyed, you lost about a kilometer of edifice, and that's a big change in edifice size, and that's rapid. So I think you'll see what I'm gonna drive at, slow means you build up an edifice, fast you destroy it, as you build up the edifice, you build up pressure. Pressure prevents lavas from reaching the surface, and prevents primitive lavas from reaching the surface, you destroy the edifice, you can erupt primitive lavas again, because you just dispense with the load that was applied to the crust. So when there's an edifice, no cement eruptions of vessels, primitive lavas, and at Mount Adams you can check the observation, what happens there? Well, there was a change, a rapid change, but we know the edifice got destroyed, and it was a big length slide, slow failure, that's not clear, because that's an old deposit, but we see the edifice was completely destroyed, and we see, of course, the deposits that came out of this diffusorction, and the consequence was that a very fast return to the basaltic primitive lava compositions. That's an observation. And this is again not something that's only observed at Mount Adams or Mount Adams, it's observed in many other volcanoes, Mount Adams, Hawaii, Santorini, and others. So again, this is not something that's specific to one volcano, it's something that is quite general. So what I'm going to go through in this series of lectures is what is the stress field due to loading by an edifice? I'm not gonna talk a lot about implications for daggers and towards the summit, because that is something that Thorsten Dam has worked a lot on, so I'm not going to step on his toes, and Elia Nora has done some work on that too, and I'll deal with a little bit with implications for natural magma transport. So again, this again plot where we're gonna have to worry about is not going to worry too much about viscosity, I will go back to that a little bit, but not much, look at this remarkable increase of viscosity. This is for dry magmas, if you add water, as maybe Michael others have mentioned, water acts to decrease magma velocity tremendously, but there is still going to be a general trend of increasing viscosity with increasing differentiation or increasing concentration of silica. Density again, so these are things that we have to worry about. The important physical parameters, we're gonna deal a little bit with fracture, not much, because again Thorsten, I think Elia Nora will talk a bit about it. I will spend some time on the stress field due to edifice. This is gonna play a big role, and this is of course something which I can relate to observations. Again, I'm out of bounds, this is not imagined, this is the, we know the composition of these avas, we can figure out what their densities were. You can see the difference in density between all these. And then we're gonna worry about supply rate a little bit and magma viscosity, and magma viscosity depends on the temperature and just a reminder of that. But we're not gonna talk about temperature here today. So the edifice, big load, how deep this effect goes into the crust. Well, what I'm gonna show you is that the depth extent of the load is determined not by the heights, so as much as the radius. So you can solve for this problem, you will consider an elastic half space, we can discuss this later on. We have a, here it's a cylinder, but I can do the calculation for a cone, it's not a big issue. So you load the surface and below we have an elastic medium, that can be relaxed in many other cases, sufficiently deep, you will go into viscoelastic behavior, but I'm gonna assume elastic behavior here. And in this particular system, you have to solve for the equation in a cynical coordinate system. You can show that at the axis, these are the stress components in horizontal plane, sigma r, sigma theta, here it's a symmetric potensor. You can show that there's no divatric stresses along the diagonal terms, and the two diagonal terms are equal to one another. And so that looks like a pressure field, there is no divatric stress. So essentially what you have along the axis is a variation of the local pressure. So you can solve for these and you can again make things dimensionless. You scale your pressure perturbation, that sigma v was these diagonal terms that I've shown previously, and you scale this by the edifice load. So the edifice load plays a role, row m is the average lava density, the lava that makes up the edifice, h e is the height of your edifice, you scale that, and then the depth has got to be scaled by the radius of the edifice. And that's the theoretical solution that you get. This involves calculations that are straightforward, that I've done using standard techniques. If you like vessel functions, that's good for you. And so you split, there's an area under compression down to a depth of about 1.5, the radius of the edifice, and then you have a slight region of tension, and then you go back to zero. So you can see that the edifice impacts the upper crust over a thickness, which is about two times the radius of the edifice. If you look at the off-axis distribution, you can solve for this. That's the, this component of velocity of stress, which might not be equal to that if you go away from the axis. So at the axis, you're here at zero, that's the solution corresponding to that plot. Then if you go to a radial distance, which is half of the radius, it is not that different. So the stress field is close to the axis, it's quite homogeneous, and you have to go to quite large distances away from the axis for the stress field to change in an important way. So stress decreases with increasing depth, of course, increasing the sense from the axis, of course, and stress become negligible at the distance of about three times the edifice radius. So you can see that the footprint of the edifice influence is large, because that extends to quite a large. Now is this important? Well, it's difficult to get constraints on the reservoir depth, and so this is what I was able to get. This is usually done by, by petrology. So you get lavars that erupt, you look at the minerals that have been crystallizing at depths, and depending on the pressure, you can get different minerals, and then if you study the minerals, you can get pressure. The important thing, I think, is something that's been overlooked, is that what you get is the pressure of the reservoir, and to turn the pressure of the reservoir into a depth, you have to assume the pressure in the reservoir is addostatic, and this is not always the case, and I could show, if you're interested, I could show you that in many cases you can show that it's not true, and I've shown you in my previous lecture that you would expect the pressure in the reservoir to change with time and to be not addostatic. But anyway, this is the best you can get. Reservoir depths using petrological values for several canals, sometimes they have a large range. You're not maybe not surprised. Visuvious is an important thing. Visuvious probably most eruptions are coming from a shallow system, but there's a deeper connecting system. We know the edifice radius now, so edifice radius, kilometers, that's Z equals RE, Z equals three RE. Between that up to three RE, we know that we have some influence, but the largest influence will be between these two curves, RE and about two RE here, and you can see that most of those systems will be affected by the stress induced by the edifice. Mountsperr has a very deep reservoir, obviously, but there's a shallow system, that's of course the shallow system that during the Pinatubo there was a famous eruption, that was the second largest eruption in the 20th century, and it's clearly a shallow. The other thing that's important, I think, is that it's well known that most active magma reservoirs are shallow coastal depths, and there's been a lot of discussions about why is that so, and I think I hope to be able to convince you that it's mostly something which is due to the edifice. So magma is sent between beneath the edifice. So we're now going to relax some of our assumptions and look a little bit. We know that still we have magma buoyancy and overpressure. This is something which we saw in the previous lecture. The overpressure might come from the reservoir, a deep reservoir. The one thing that I would like to now worry is is that, of course, the scent is possible only if the corner remains open. So magma must be overpressured with respect to the surroundings. If it's underpressured, then the corner is not going to be stable. If it's an open fracture, you can open up a fracture by overpressure. That's called hydraulic fracturing, and I think Thorsten and Yander, I will talk a lot about that. If I had hydraulic fractures because the magma is overpressured and breaks up the rock under its own pressure. If it's not overpressured, then, of course, it can't break up the rock and it can't rise. So let's look at addostatics. Remember, addostatics are a very powerful way. Now we just look at magma overpressure with an ecstatic dike. Now, I have two slopes here. We start with the reservoir, and that's the pressure difference with respect to the least ecstatic pressure in the country rock. So we might be slightly off, but then that's a vertical thing because above this, I have only rock with density rho C. Now, if magma is at density of radicals rho C, you can see that I have no problem. I remain overpressured and I have the same overpressure that I have in the magma reservoir. Now, if I've got buoyant magma, if rho M is less than rho C, this is the pressure inside magma column, and the overpressure is the pressure within the dike or the fracture minus the pressure of the host rock, and you can see that it increases and increases as you go near the surface. That's important. You can see that under those conditions, you would expect, indeed, the lava to be able to break up the rocks and reach the surface without any problem. Now, you add the stress due to edifice load. Now, I'm still referring everything to the least ecstatic pressure field. Now, I'm adding my stress distribution to the edifice. You remember that curve? And then you can see that, depending on the magma density, you have different situations. If this is a very low density, again, the magma is always overpressure. Now, the relevant stress field is this one because we have the edifice effect. Low density, no problem. I'm overpressured, I reach the surface. At this particular level, I'm just about right because I'm still overpressured by the time I reach the surface. But now, for this particular case, you can see that the magma density is too big and I end up being under-pressured and therefore, eruption is unlikely under these conditions. So, we can define a critical density threshold which separates two different cases, magma that are less dense than this critical density will be able to erupt. Magma that are denser than this particular threshold will not be able to erupt. That's a simplified version of what happens. You can do more complicated things but it's a basic story. And you can now get a diagram. I've assumed a reservoir with some of the pressure that's starting depths. It is not very essential. You have to assume that for these calculations but you can change that. Slightly, it's not going to change a big story. And you can separate, therefore, on the basis of these simple arguments, simply based on those statics, you can separate two different fields, one in which the magma will be able to erupt and the other field in which magma will not be able to erupt and will get stored. And so, that's magma density and edificeite. What I would like you to notice is that these calculations are done just as a function of density without paying attention to what are the densities of true lavars and without attention to the true edificeites that observe in nature. But in the end, you can see that we are just within the domain that we see in the field. These are edificeites that we see in the field and this is the density difference that we also see in these volcanic systems. You go from basalt to virulite here. So the story is that, of course, if you have a zero edificeite, in this particular case, you can erupt even basalt. And we saw basalts that mount atoms at the surface in initial stages. But if you start building up the edifice, the basalt can't make it. And the larger the edifice, the taller it is, then the more evolved the magma must be to be able to reach the surface. A very simple diagram. And that accounts for what we see at Mount Adams. Primitive dense basalts are always erupted, but when they are in edifice, they can't rise within the influenced domain of the edifice. They have to go laterally and then we'll discuss that in tomorrow. Edifice destruction, I've talked about this. If we, of course, destroy the edifice, then you go back to initial condition and you can erupt more primitive magmas. No problem there. And that diagram that I've shown you before accounts for this very nicely. You can add volatiles. It's gonna change the picture. Mount Adams had about 5% water in solution. So that was the dry diagram and that's the diagram with water. And you can see it displaces the curve here, of course, with water, magmas are less dense. And, of course, they are increasing less dense because as they rise, they nucleate gas bubbles. And I believe that Michael has talked about that. So that would be the hydrostatic pressure. It's calculated on a hydrostatic distribution in a column that has some gas. And you can see that displaces this boundary, but again, we're still in the domain that is relevant to the edifice that we see on Earth. If you have to draw this diagram on other planets, of course, you have to allow for changes in the gravity field. And therefore, the edifice side will be modified. And as you all know, maybe the largest volcanic edifice on the solar system is on Mars. And that's an edifice that rises to about 24 kilometers. 24 kilometers, but 24 kilometers on a planet with gravity that is one third out of Earth. If you scale it to Earth, it's something like eight kilometers thickness and it's about as high as the largest volcano that we see on Earth, which is a white. So you can see that there are differences according to gravity, but if we scale for gravity, then we can see the same type of behaviors and the same type of thicknesses. If we want to look at modernity in this diagram, just to make sure that we are not completely off, the peripheral basalts are there. So they were able to erupt when there was no edifice, but the edifice was built up. These basalts were not able to erupt through the center. And then we were able to have flank and the sides. So the flanks, the magma is still able to rise, but they can't make it to the top and the cement and the side is indeed able to make it. So these are the true densities that we can calculate from the lava composition and you can see that they're consistent with this basic diagram. So if we can't erupt, what happens? Okay, we've just shown that the basalts can make it to the surface when there's no edifice. When there's an edifice, they can't make it anymore and we've explained that, so what happens? Well, magma gets stored, but to get stored, magma just can't pile up at one point in space. It has to spread, otherwise it can't occupy the volume. So we'll see what happens. How does storage proceed? Magma can't erupt, so it has to stop. So remember, we are now going to look at situations in which the magma is too dense to be able to erupt and we're gonna see what are the implications for that. If you look at this diagram again, you can see that there's an, for this particular case, magma may be able to reach that height, but the largest overpressure in the magma column is not here, which is zero, it's gonna be over there. If it's over there, the largest overpressure, you can show, depending on what you assume for the strength of rock, that the rock will break. So instead of a column that extends vertically, if it extends up to these areas, then in this particular area, you will have the largest overpressure and then the largest stress that's applied to the walls and the walls will break and you will be able to inject the magma laterally. So we will propagate a laterally dike at levels in which the overpressure is large. Yes? That go far as long? Yes, almost. Yes, but we'll solve for that. They go horizontally, but also vertically. Dykes always extend in both directions because there's magma is overpressured, so it extends in all directions at the same time, but it's gonna be, depending on the pressure distribution, it extends more rapidly in the wrongful direction and in the vertical direction, the wide version, we'll see that. So we're gonna look for the lateral propagation around this level and remember that this level depends on the density contrast and also on the edifice. So in particular, I'd like you to remember that when you're away from the zone of influence of the edifice, then you don't have the additional stress field to worry about and the magma that's born can make it to the surface. And this is why I think we have pastel erupting in distal vents because once the factor that propagates laterally is away from the edifice, there's nothing that can stop this magma from rising again. So we're gonna deal with lateral magma transport. For this calculation, I'm gonna assume there's a density interface that makes the calculation more stable and you can make this density interface go to a very, the density difference between these two things can be as small as you want but it makes the calculation simpler. And so we have magma that has a density intermediate between the two, lower density, higher density here than here because it's a stable stratification and we'll see how the magma propagates away from the central zone. So this had been solved by John Lister some time ago. What we've done with a student called Virginie Pinel, we added the effect of the edifice. So what we have is around this interface. We have a diagram which will propagate horizontally. Now the propagation front is gonna be at some distance from the vent, which is gonna increase with time. We have a magma inside and we're gonna solve for the way the magma propagates. And what I would like you to notice is that it will solve for the vertical extent of the fracture and the way it propagates horizontally as well. And we'll compare what happens with the whiz and without an edifice. So we can start by statics because most of the flow is in the orbital direction so we still are gonna have a basically hydrostatic pressure distribution within your fracture. So the fracture is open because it's over pressured. And so the pressure in your fracture is going to be the difference in pressure due to the different density involved plus the stress field due to the edifice. And then if you want to look at the way the propagation works, you have to look at the horizontal gradient of that pressure, which is the, that's the driving force for your lateral magma flow. So you differentiate it with respect to X and that's what you get. And that's differentially in X and you can see the density differences that comes in and of course the gradient in the stress field due to the edifice. Same thing above and below. Above and below you have different densities because here you have a density of the upper medium and density of the lower medium but that's basically just hydrostatics. So if you calculate over pressure, if it's an elastic medium, we can figure out the crack widths. That's simple elastic theory. Then to close the problem, you have to figure out what happens at the stresses edges. And we use what is called the linear fractional kinetics. And we specify that the, I'll come back to that if you want to. You have to, you must, you need a boundary condition to what happens at this edge. We assume that there's no toughness for the rock. The rocks have been weakened and so we assume that. It's not a major factor here but if you want I will come back to that later on. But you need a closure condition for the two ends here for this factor. So then you go through the same kind of Navier-Stokes equation. You solve for Navier-Stokes equation. You may recognize things that are very similar to the equation that we had for lava flow. The same thing, which then are going to be used to derive the thickness of the fracture, the fraction of time and distance. If you, we're gonna use solutions for constant rate of magma input. You can do any input rate that you want to and there are good reasons in nature for why the input rate should vary with time but we're not gonna go through that. And without any risk, the journalista was able to give you a legal solutions that show you that the front propagates as time to the eight over 11th power and the thickness of your dyke is probably to teach the one 11th power. You can see that the thickness of your fracture is not increasing rapidly with time. I'll, in the handout that we're giving you, the handout will give you the references for these equations. So we're gonna compare what happens. So the basic problem is don't worry about fracture, the ends of the fracture. The important thing is the free mechanics here. We're gonna compare what happens without an edifice and with an edifice. The edifice is over here, it's a small part and we inject the radius of the edifice so you can see one. Here there's no edifice but we're still scaled the same distance. It's in French so that's lateral position. Elastic pressure. Co-fondarized depth. And then we're gonna see time is made dimensionless. That's the time scale that's rated to the flow and that depends on viscosity. So we start propagating and now we've reached one. So when there's no edifice, you can see that because of course we're driving the flow laterally. There's always more pressure at the inlet than the way so the fracture extends vertically more at the x equals zero than x equals one. There's just the reflection of the lateral pressure difference. But you can see here that we had a small thickness here because we had the additional, these are exactly the same condition but we had the additional stress field due to edifice. So the fracture here was, could not extend to the same height as before. And at the same time of course because it's the same time, we've injected more magma so the fracture is actually propagating a little bit faster instead of having one here, it's that too because we have the same volume and the same volume could not be fit into a tall fracture so it had to be fit lateral. Now you can see of course that as you move away from the edifice, the pressure due to the edifice decreases and hence the fracture can go taller. So this is a story of everything that's gonna happen. You'll see that without edifice, the fracture propagates. The tallest point is always at the axis when there's no edifice but this is where the pressure is largest. When there's an edifice, you can see that this is not gonna be true. You can see that the fracture will extend vertically and we're gonna go through this. Now I will draw two, these two arrows, the yellow arrow is the dike tip. So that's where the end of the dike is. And you can see that this dimension is time of one. Again, that fracture has probably a larger distance because it's the same volume that's been injected but the fissure could not be tall here so it had to be a farther away and the white arrow is giving you the distance at which the dike is tallest. So what I would like to notice is that for this particular case, this arrow will always be at the inlet because that's always where the pressure is largest but for this lateral propagating dike, this arrow is not gonna be at the dike tip, it's gonna be slightly remote for the dike tip because of course the dike has got to a thinner to zero so the tallest point is not at the front. So we're propagating. Now you can see there's gonna be a difference between the tallest part of the dike and the dike tip and they don't move at the same velocity. So if you monitor seismically what happens, you must be wary about this. Of course, this thing is cracking the rock at all times but what you have to follow is of course the location of the shallowest cracks and this is where the erosion will occur eventually and it's not gonna be at the dike tip. Okay, so you can see same story. You can see why now the dike has developed and basically now you're away from the edifice and away from the edifice, you can paste that. On top of that, it's a very good solution without an edifice here, you're sufficiently far away so that there's no influence of the edifice but you can see how the edifice is determining the propagation. It's determining the propagation over a distance which is much larger than the other radius. Right, so if we look at the location of the eruptive end, we can compare these two cases. So we compare the fracture profiles at different times. T is the time scale, so one, two, three and with the dashed lines, there's no edifice and the full lines are with an edifice. And you can see the same story is that with an edifice, the dike propagates farther away simply because you cannot open up large fractures beneath an edifice because of the confining pressure that the edifice imposes. If there's no edifice, the crack will always extend, will always be tallest at the inlet so you will have some eruptions but you won't have distal eruptions. With an edifice, you will have distal eruptions but the dike will extend to distances that are larger than the site of the eruption. The dike is longer than the eruptive fissure. And if you now change the viscosity, the flux, et cetera, so that's the top of the dike here at the surface. I'm going to show you five curves. Now these curves, because they mentioned as parameters, increasing the flux or increasing viscosity has exactly the same effect. You remember that in the case of the lava flow, it was the same. The thickness of lava was, the thickness of lava in the case of the flow, thickness was, so viscosity and eruption rate had the same effect and it's the same here. So if you have a small flux, small matter of viscosity, you can travel extremely, at large, extremely large distances away from the axis. In fact, you may not even erupt. And if you go to larger fluxes or larger viscosities, then you may be able to erupt. And what I would like you to notice is that the larger the viscosity, the closer to the actual area you will be. So it's the same basic idea that you have to worry about magma properties and also the rate at which you're filling your system and they are not completely independent, of course, in nature, but if you go to any volcano that you wanna see, you must treat them as independent because they might be determined by other point-dependent factors. So these principles, I think, account for the additionally erupted products at Mount Adams, which I've told you quite a lot about. Permitive magmas are denser than any of the ones. So once they're there in the face, they cannot ride to the summit and this is what we observe. They're less viscous than evolved ones and so they can travel large distances away from the actual zone and that's transported by radially propagating dyes. And that's of course consistent with what we see in these volcanoes. I will show you several observations that allow us to check that this is not completely stable. It's hard to find out fossil magma systems because they're not readily available for inspection. So there's a beautiful system called summer cool. It's in Colorado and that's a Google Earth picture and you can see this concentric feature I will show you the geological map. That's an ancient volcano. There's still remnants of distal lava flows and the distal lava flows allow you to figure out what was there before. There was an edifice. The edifice rose to a height of about two kilometers at a radius of about seven kilometers. You find out simply by looking at the slopes of these distal lavas, a series of them so you can reconstruct what was the edifice. Everything has been eroded away but because you can see you're still close to the surface, you're basically scraped away the edifice and you're down at the original ground surface before the edifice got built which is a beautiful thing. And you can see these, there's some radial structures that you can guess from these photographs and these are radial dykes and that's the geological map. So it's more complicated. So don't be afraid by all these symbols if you're not patrologists. So that's the same thing but now in geology. The color scheme tells you focus on these things, the flows and dykes. The black things are primitive lavas. Pesaltic and the sites in this case. Many, many continental volcanoes in this area are fed by Pesaltic and the sites. And then you go up the differential sequence to day sites and dry lights. So the blue is the most evolved magma and the black is the less least evolved magma. You can see that there's radial dykes everywhere from basels but these radial dykes stop short of the actual area. As you go to more evolved magmas, the more evolved magmas, you can see that they make it somewhat closer to the axis and you can see that the most evolved ones they go right through. So this is consistent with what I've shown you is that what happens is that as the edifice got built there was still basels being fed into the area where the basels could not erupt close to the surface so they fed dykes. And these dykes eventually erupted the surface. There's a complicated story here. There's no, these have not been dated carefully but and then of course as you get more and more evolved you are still able to rise through the cemetery and that's quite the same story as we saw at Mount Adams. Sorry? The dykes aren't being further away from here. These ones because they are thicker and we don't know the age. Okay, so there's a whole story about the age. You can find you see here there's some, I've not shown the picture, there's a basaltic dyke that extends even further away here. And there you can see the thickness is larger here and it's not something that's been invented. These dykes go slightly thinner as you go closer to the axis. It's also consistent with the confining pressure. Okay, so we saw that an edifice act to generate laterally propagating dykes and that's also temporary storage but is it temporary? So now I'm going to go a little bit berserk and I'm going to draw sweeping conclusions about the way magnet system evolved but I think there's some story there and that's a story I think that I need to be worked out in more detail. So one consequence of edifice growth is that you will, the strife with confined dykes at increasingly larger depths and you can see that you're pushing therefore your location of magma storage down. So what could happen? And that is something we can discuss and I'll discuss some observations. We start, primitive magma is going to not to read the surface. We saw that at Modalems. We also saw that at Summercooling. Now this primitive magma, of course, because it's erupting it's able to build an edifice but unfortunately that's a self-defeating mechanism. If it builds up a big edifice then it generates a stress field that's not going to favor continued eruption. So eventually that stops this magma for erupting and it has to get stored somewhere. So the edifice prevents the central eruption. Lateral magma can occur and you might have some eruptions there but you will tend to store some magmas there and maybe form a magma reservoir. That magma reservoir of course is going to differentiate. It depends on the story between what's been erupted and what's been fed from below and that is something that we can maybe work out with models. And now of course if I'm differentiating my primitive magma in that storage zone I'm producing evolved magmas that are buoyant and these buoyant magmas can erupt against centrally but of course these magmas will contribute to growth of the edifice. Then again it's not going to be good but if you still feed the primitive magma from depths then of course because now you've got a larger edifice due to the eruptions of these evolved magmas your new primitive magma storage zone is deeper now. Now of course if you keep feeding primitive magmas they can't rise and they will eventually feed distal fissures and distal vents and then of course you can repeat that sequence and have an edifice growing et cetera you can play the game farther but I think it would be nice to see evidence for pressure variations in your reservoir and I'll come back to that in a minute. So that's a story that's feasible that of course many complicating factors but I think you can see there should be a link between the growth of the edifice and the way you store magma. Now in Nazirans there was a beautiful data set collected by Jim Gardner and others so these are heterological pressure estimates for magma in Nazirans. So last eruption 1980s over here and you can see this is something that extends as far back as 4,000 years. There's an interesting compositional variation but I'm not gonna describe it, it's mostly day sites basically. So there's slight variations which are telling us something but and you can see that the pressure varies this time. So there's an experiment or a similarity these pressure estimates are done very empirically what you start with is a given assemblage and you let it crystallize and you work out what is the mineral assemblage and you compare this with what you see in erupted products. So the mineral assemblage it will several mineral phases and that will also account for variations in the water contents and so you match basically your mineral assemblages in your experimental charge with the observed ones and then you can get pressure. You also get the water content. So this is what they observe. There's an uncertainty of about 0.5 kilowatts which is large but you can see the variation is larger than the uncertainty and what you have is pressure decrease and the large pressure increase, pressure decrease and you have cycles. So pressure is varying in that system. Unfortunately we don't know the story of what happened in these old times so we have a record of what the edifice did. Here we knew there were landslides. There was an edifice, big landslides that decapitated the edifice and you can see that after this landslide the pressure was smaller. So the pressure of storage zone were smaller and quite likely the storage zone was at shallower depths. We know that's the major phase of stradocon growth and multi-halances between the easy eruption and that eruption. There was very little eruption going on away from the summit but there was quite a lot of lava flows, et cetera, flows and domes which built the cone as we had it almost until the last eruption and you can see therefore that between this stage and that stage the major stradocon grows, you increase pressure. So that is very hard to explain. There's very large pressure differences I think can be related to the buildup of this large edifice. The next thing we know here in that particular is we knew again there was a destruction of edifice there between these two eruptions. These two eruptions are separated by a few tens of years. We know that because there's almost no alteration between deposits. So if these had stayed for several decades we would have seen deposits. So this marked pressure release is the destruction and a very fast pressure release which I think is consistent with the fact that you have a very fast event which is the destruction of the edifice and then the story goes again. So you can see that first is that we have changes in the storage system. So that's one thing we have to worry about and some of these changes are clearly related to what happened to the edifice. And the last thing I'd like to see is the system of three sisters in Oregon. It's a beautiful set of volcanoes, three volcanoes in a row. Remarkable system that's been heavily studied. All the lava erupting through that system are co-genetic and are beautiful. If you have never been there, you should. So that's south sister, middle sister, north sister. And there's a nice big lava flow here. And the three cones rise to about the same height. And that suggests again some control on the maximum height that lava can reach. Why would it be here? And there's an interesting story, so I'm not gonna go to everything but just a major fact about this. The basic activities started at north sister. There was a shield stage before 200,000 years ago but when you start having the activity over these edifices, it started about 180,000 years ago. And you build up the cone. As you build up the cone later in the system, you have a basaltic and the sites, flows, et cetera. The big strata cone could build to late in that period. And eventually you stop the north sister activity. The cone is too big. And what happens is that south sister becomes active. It's active until about 27 years ago. Middle sister is at some activity at about the same time but was most active between 25 and 18 years ago. So you can see there's a nice story of activity in a cone that stops and then the activity developed elsewhere. And you can see there's very little overlap between these three different systems. Again, the lavars are all co-genetic. I think the story is, you see there's a lot of radial dykes and there's in fact a big radial dyke that crosses all through all these edifices. It's quite logical to assume that the feeding system was beneath the original volcano north sister. And then eventually eruptions were stopped from central vents in the north sister area and the activity had to develop elsewhere. And you can see that as you go under the fist, you stop the activity and the activity has to develop elsewhere. And north sister eventually became active again at 1910 years ago. Again, no, when it started to become active, middle sister just stopped and he developed a very erupted lavars, almost relight, and the other volcano stopped. So I think there's a very nice story here about the relationship between the edifices growth and the fact that you have to erupt elsewhere. And then through all that time, north sister was cooking and eventually generated very vulva lavars that start to be able to erupt again. And that's it.