 Dobro, svoj, vse. Zato sem zelo, da možem tudi zelo, ne zelo. Zato, ki so vizila, da možem izvori, zelo sem zelo, da se vse predovnimo. Vzelo, da se vzelo, da se pogodno izkovno. Kaj je zelo, da so vzelo, da se gleda očen, zelo se zelo, da se gleda, da so gleda očen, in pričo se prišli všeč všeč. Zato smo pričovali v magma čamberu, zelo pričovali je večo mekanikov. Zelo pričovali je bilo odličnje studičnih, v literaturnih vrtičnih, kako je vzelo v tem, v magma čamberu, kvakšnji, kristalizacije in migrativno pospraviti in pačatati pospraviti. A zdi se izgleda robotnje perspektiv, in zelo je vladična, vzelo plače. Se, ki je izgleda in kako je vladična, zelo je vladična v vladičnji velik, kot je zelo vzelo, a kot je izgleda katera. Valerio je vladičnja odrga je za vladičnja katera, sem zelo vzela katera in zelo posledajte. Tako, Makma čembeče je tudi veliko kristaline. Znamenjamo, tudi kompleks geometrije z tukaj ellipsoids, tako, da je počkala, da je počkala. They generally form by accumulation of macma pockets. They may form by accumulation of plutons, they may form by accumulation of dikes, or of sills, or of funeral shaped intrusions. What I would like to talk to today is that, of k. And one control as we saw by Claude, Klauda požegala dveče na vsega priročanju tih zemlju v veliko vsega vrkana. Vsem počekaj da bi izgledano to in izgleda, da edifice strani so konstručnje, zelo vsega, sega glasejevstvenje, odmah, nekaj proces, that changes the loading on the surface, but also tektonic processes, for example, crustal thinning. If we see volcanoes as actually a larger scale tektonic features, but also auto-genesis, false-scarp development, how this not only influence magma storage depth, which is what he addressed in his talk, but also magma chamber shape, possibly, in tudi v vsega naprejkačna vsega, če je odvala do vsega. Zatah je tudi z Tarzan, tudi v seminali v 2000 roč, ki sem bilo prezentirati model numerikov, na kvalifikaciji transjakterov, in vkonega strasja. Zelo se vse zelo. Zato zelo, nekaj so jačo zelo, da ne zelo res nekaj, da je pa ne neč del, Sve je za vziv o neurologi. Vedno se sva pasite. Ako tudi bilo nesimovati do bojantov, nekaj pr해요b ima previsar, nekaj nečo do bojantov, bojant vse prino priživamo potreč za prinfes вр surprises. This is an additional model done by McAfherri et al in 2011, where we show a couple more features. One feature is that we see also the deviation of dykes. These dykes are not interacting with each other, they are just displayed one close to each other as a summary diagram. And also this shows that whatever the direction at which they start, they tend to deviate and be attracted by a volcanic load. But we also see another thing, which is what actually Claude pointed out, that they stop. So they are attracted, but then they get arrested just below the surface due to the strong compression that the edifice is exerting on their tips. Here we see that depending on their dimensions, so this was also one of the questions, small dykes, big dykes, one of the possible effects is that a larger dyke is more buoyant, is maybe more buoyant if the magma is buoyant, and may have a higher driving pressure, and therefore is able to erupt even if most dykes would stop. There is another thing that we can see here that was not pointed out in this paper, it came to my mind later, which is that a strong volcanic load is attracting dykes in vertical trajectories. So they may come from very far away, but really if they come from relatively below, then they will form somebody below the volcano, which will have a vertically elongated shape. So before going a little bit more into this, I would like to explain two methods that may be used, one together with the other to study these processes. So one is this boundary element modeling of that propagation, the figure here is from a kafari et al, but it's exactly at least how the model is constructed as a tors and developed it in 2000. So how does it work? So here what we do, we take a lot of dislocations. These locations are formulas that are developed that they work at the scale from the nano scale, from crystal scale to tectonic scale, and they describe the stress and the displacement due to in crystals it would be an imperfection. In geology it would be a discontinuity in the earth. So in this case we open, sometimes we may shear, so we take actually two different formulas for this location, not only tensile, but also deep sleep to account for this shear, especially when the dikes bend, and what do we do? We create discretization over the dike surface, and then we require that the stress at the center of each dislocation is equal to the difference between magma pressure and lithostatic pressure, so what was called over pressure during these days. The crucial is in this model that dislocations are interacting, meaning that the stress caused by each dislocation on all the others is taken into account. So the stress at the center will be, so you will have several parts of it. One is dislocation number one on dislocation number one, then you will have dislocation number two on number one. So you will have a lot of coefficients, which are called influence coefficients, and then in the end you will have this delta p as your known vector. So basically you build up a very big, not excessively big, a big linear system, depending on how many dislocations you want to put, and then you may add to the system also some other constraints, for example magma compressibility, and then you say that while my dike is ascending, for example, so you may ask that the volume is conserved, if you think that you are losing very little volume in detail, or you may say not volume is conserved, but I take into account compressibility. So if pressure is decreasing, I will have actually a little volume increase. So you may put your physics, add your physics into this model, and then in order to get propagation what do you do? You check virtual elongation of one little dislocation, so you add one dislocation at the tip, you do it in a fan of possible angles, and then you calculate how much energy would be released in this step, and the trajectory that is preferred is the one that releases the maximum stress, the maximum strain energy. Therefore, in this way you select the trajectory. So it's crucial to know your stresses, as we discussed already in the past, because the stresses and the dislocation, so the dikes that enters into the stresses, I mean the energy depends on the normal stress, on the shear stresses, and on the opening and shearing that the dike will have in the stress field. So if your stress field is wrong, your result will be wrong. Therefore, a lot of effort needs to be put really in understanding the stresses. One more thing is, there may be also a gravitational component, so if you have a buoyant magma, you need to maximize the release, not only of elastic energy, but you may also take into account gravitational energy to get a total energy. Another type of method that you can use, that is very good to complement this type of models, is experiments in gelatin. I will show you a couple of movies just to show you how these movies are instructive. To me, they were very, very instructive. I really understood a lot through these models. So I will show you just one or two movies. So why are they so complementary? Because most dike models are in 2D. And therefore you lose the third dimension component. And we saw also Claude talked a lot about that, that if you lose the third dimension, for example, you are not able to model when a dike is ascending and then propagating laterally, because you only take one cross-section. So then you have to turn your cross-section, and this is very difficult. So one very wish for development is to go to 3D. So this is one important aspect that needs to be addressing the future. So here it's not working very well. I just get out of the presentation because I would like to show the movies. So I'll just look for them. Okay, so just a couple of them just to show you how they can be used. So in this movie here we have a homogeneous medium and we have an injection of a dike at the bottom of a gelatin that has been put into the refrigerator and is therefore stiff. And we are injecting with a syringe at the bottom of the container. So you see that something develops that really looks like a dike. It has this shape that was also pointed out by Thorsten. It's similar to a shape that is seen in the field except maybe for the tail that is getting really here thin. So really very close. This would not be true. You would have a little tail that is left behind. And you see that you develop completely spontaneously this geometry of a tabular intrusion, vertical. And in this case we have linear overpressual profile because we have air in gelatin. So we just injected air and then we have eruption. And just to show you another a couple just two cases this one here. Okay, this is so there is a lot of consideration to scaling that we may discuss later because it's a bit longer. So it's a density is one but viscosity is another one there are many, many considerations. So this one here shows you what happens if you have a layer and I'll just put it a bit ahead because it's slow otherwise. Okay, so here we have more compliant gelatin on top of a stiffer one. And so we see that there are a lot of features that just occur spontaneously because you have these cracks propagating. And then the last one I have more and they are nice to watch. The last one is this one. So here you will see that the crack will stop at the interface because actually you have a stiffer material at the top. And then once you inject it cannot really penetrate until at some point instead of penetrating in the upper medium it develops something like this. So similar to a seal. This is not the only way that you can form a seal. There are many ways but the point is you will see all these 3D effects and if you complement numerical methods with analog experiments you may have information on the 3D aspects while the numerical methods allows you to change all the parameters quite easily and quickly and therefore you can explore a lot of models without the effort that you have to do in the laboratory. Unfortunately I don't have any good movies for topography effects but this is also to illustrate what was done. It's in gelatin and it has some brick on the surface of the gelatin and so you see the same effect that numerical models reproduce and it is that a crack even if it is relatively offset from the volcano it's going to be attracted by the volcano and then stop just below because of the compression that is generated. If magma is not coming from the volcano but from below they will actually be relatively vertical features but then what happens so Valerio already talked about unloading so here we have a paper about unloading due to glacier melting in Iceland in the glaciation so if you take a load away then you have the opposite instead of putting forces that push on your medium and compress it like this making sigma 1 very strongly towards the load you do actually the opposite you lift some weight away and then what you do you pull and basically you create a sigma tree which is completely flipped and then you promote something that is actually deflected away from the volcano if you have a source below magma will tend to get away this is actually very common much more common than people think and there are so many cases people also intrusion at El Hierro flank collapse episodes that drive dikes away and they are not any longer so you start to have flank eruptions you start to have lateral propagation when you have these cases there are many many cases and if you keep this unloading unloading in mind it becomes much more clear so Valerio already of time on this because Valerio already explained it so if you put forces that pull into the air the caldera floor due to the removal of weight that was caused then you end up with the sigma tree vertical and then you promote the seals and if this stress pattern is actually only below the caldera then it fades away while if you have a volcano with flanks in effect of topography and effect of topography is actually to to drive dikes laterally as we saw by Torsten when he was talking about stress gradients so therefore you go from a seal you need to go from a seal to a radially propagating dike and the only way they can do is to twist and then go and this actually was seen by Marco Bagnardi into his into analyzing the formation now what about the development of magma chamber so suppose that you have a stable structure really like a stable caldera then what you would do is to promote seal ascent you would have several seals if it's only one probably it will freeze away relatively quickly but if you have a relatively high supply and if you have a stable stress field then we add several of those seals and then through thermal effects develop a big body below the caldera this depends also on magma composition because anyway basals are more mobile so you may wrap them relatively easily still you can develop a magmatic systems if magma is felsic then you may find actually that they are less mobile because they are much more viscous and then you have even more stable system and so now of course we have a question which is the chicken and the egg because the usual view is that if you have a big magmatic system then you can have a caldera while here what I'm telling you is actually the opposite if you have a caldera you develop a big magmatic system because the rims are those that are going to stop the seals and if you have a seal it will stop the rim and therefore you develop in this way something quite large and we can debate about this so of course of course I'm not telling you that it's just like this I'm telling you that mechanical models point at this effect that so far has not really been recognized so basically what is the message of this first party if you have a big load, if you have a big volcano you develop a vertically elongated magmatic system it cannot be very large because it will stay narrow, relatively narrow the more so the more the volcanic load is developed and the more so the last the volcano has not a caldera if the volcano has a caldera on top then it's a bit more complex this is seen because at Monsantelen Monsantelen is a big stratovolcano and it's seen that it's Paul mentioned that a good model for a magma chamber there is a proletalipsoid etna has the same has a vertically elongated system while Toba for example here through seismic analysis was found to have a system composed by a lot of scenes one stuck over the other anyway the structure is more horizontal while in the other case the structure is more vertical this is simplified as actually what happens this was also shown by Thorsten dykes interact when they ascend because you will have the stress caused by the previous dyke there are several studies looking at this and you can see that the first one will be possibly vertical but then the second one will intersect the first one the third one will intersect these two and then in this way you build a structure depending on what thermal effects you have depending on the supply rate you may have a different way to develop this but in general you will depending on the stress you may find something in the end that is more vertically elongated or more spherical or more laterally elongated only if you allow if you have either a lot of compression this could also be a mechanism for example in the Andes or if you have a topography change mass waste event there are several papers that point out that if you have intersecting dislocations so it's a theoretical paper also by Bona Fede that was my PhD advisor he has a paper where he shows that it's completely analog to have pressurized cavity a point source and the three intersecting dislocations in all directions from a theoretical point of view if you are far enough from these sources because you need to be in the point source approximation so you need to be far enough as soon as you are outside already they have very similar fields three dislocations intersecting doesn't seem to be a particular realistic arrangement but if you think at something like this it's not the three dislocations intersecting but it's several likes intersecting with each other meaning that you cannot distinguish from the surface and from deformation because they will be totally equivalent and this may be one answer to the question why does the moggy source work so well because actually from a theoretical point of view or from a stress field point of view from a deformation point of view they are equal unless you go very very close unless they are very shallow and you can may see some deviations from this so this is a desert rose crystal think of this arrangement and here is a figure from Daniela Kuhn master thesis PhD thesis in Hamburg who showed that stress field once you add one dike one dike one dike you really develop this stress field similar to an ellipsoid which was also shown by Thorsten this is a tomography for Montana which shows this famous high rigidity body that is below Montana it's this lila body here that has a very high very strong vp velocity meaning that is probably an accumulation of basalt one can figure out why exactly this shape I think there is a strong control on this from the topographic load and ok, etna is not a perfect cone and there are other stresses extension stresses and sliding of a flang maybe if one goes well into the stresses then one figures out exactly why the shape of this body most accidents now ascend to the left of it to the west while in big calderas we have the opposite arrangement now I want to go into rifts Cindy has told a lot about rifting we have and I want to make the argument that is similar just at a larger scale so in rifts what do you have you have that crustal extension, thin the crust it's a different process you are not removing anything you are just thinning however if you have lower crustal layers and magma in lower crustal layers what they will experience is a decrease of weight at least this model assumes this that you have a decrease of weight due to crustal thinning and lacking so here you see first thinning is maybe ductile but then at some point you develop folds and then these folds which are the border folds for the rift absorb all the deformation and therefore you start to develop a deep grab this is the grab at Lake Baikal it's filled with sediments and with a lake and it's very deep, it's 10 km deep and during seismic studies these authors, Steuben Nielsen observed that there was in the lower crust so they found a completely flat moh the assumption in general is that the moh will uplift because while you are necking the crust you will thin from above and thin from below and this actually would be the cause of the melting because you are decompressing the magma we didn't talk at all about melting but decompression melting is maybe the main mechanism for melting on the earth so you need to take some volume of magma and decompress it you can do it by lifting it up or you can also decrease some weight from the top and then they found lower crust so the moh is flat, there is no uplift of the moh but they found a very high VP velocity between that of basalt and that expected for the lower crust so and also what they saw is a strong, strong, strong reflection at many layers so in the end they interpreted it as intrusives, seals this is actually very common in many rifts I have not seen at all so while I was revising literature I have not seen a single rift for which if you look at it you don't find seals in the lower crust and this was long thought to be a problem because actually most rifts occur during extensions so actually you should expect to have vertical dykes and so why why that so a previous hypothesis was that reological problem and discontinuity reological discontinuity and not a stress a stress factor but what I am arguing here that actually it is a result of the decrease of weight at the top occurring over long time scales I am objecting to myself for this hypothesis because I think how long will this the compression last this is millions of years sometimes however when I object to myself I answer to myself ok this is true and it should be actually looked into more detail however how are you going to compensate for the compressions and compressions it is very easy to dissipate shear stresses you may find an earthquake you may have ductile motions you may have many processes that dissipate shear stresses especially if you have high heat but how are you going to dissipate a strong compression or the compression so maybe this will last longer I don't know I'll throw it to the audience anyway what is observed in the biker rift and in many rifts is that most volcanic fields so there is no evidence at all of any magma above the seals most volcanic fields and some of them are really very large extremely large they are at quite a distance from the rift itself and so the same model that torsendil developed may be applied to study how if you believe at this unloading process how this will change stresses in the crust and therefore turn into seals any dykes that will ascend from below and force them actually most of them get even stuck because they lose all their buoyancy meaning that they are buoyant the magma may be buoyant however they are horizontal and therefore all their driving pressure due to buoyancy is lost because they are horizontal and they don't have so much stresses at the tip due to their buoyancy therefore most of them get stuck and only a few escape and they go far away from the rift so they are buoyant I think in this model not once so first they would take these trajectories but then of course over the millions of years every seal would be the next magma chamber and nucleate may be a little dyke this dyke will also be forced to become a seal you will nucleate another little dyke this dyke will be forced to be a seal in this way you develop stocked seals which is what is seen in many rifts so you really have a continuing extension and continuous melt supply then you may reach I forgot to say something the color here is the inclination of sigma 3 it's completely vertical where it's rad so 90 degrees or 100 here especially at the center and it's horizontal here here you see this pattern here so for some reason of stress for some reason you have below just below the unloading actually sigma 3 is not vertical sigma 3 is vertical in a vertical depth that is below so what do you do so if you develop a lot of seals all here, all here, all here at some point you will reach this level this will be the last seal the shallowest seal and the only way is to develop a vertical dyke because here sigma 3 is horizontal and then you see actually it may be just stress what you see also in the aphard dyke so that you see magma chambers they are seals some of them are below the volcanoes this changes a little bit the stress field the overall stress field and then from there you start to nucleate dykes that propagate laterally in this way thanks for this question so you may actually calculate it quite quickly if you have a graben of 1 km depth your density I don't know you take easy numbers you do raw gh yes so actually the stresses are very strong because extension stresses are limited by the faulting processes so once you start to develop faulting much more than 5 mega Pascal extension you cannot accumulate while this if you have a deep graben you may reach very easily 10 20 mega Pascal very easily because you are so this is thank you for this question because this is actually crucial it may be a dominating effect and the extension will modulate this by turning the trajectories vertical once you are far away but below you will have this strong effect so the same phenomenon can be applied to much smaller scale features like for example here is a fault scarps of the dimension of a few tons of meters but even this if you have a fault scarp the difference in load between here and here will attract the dykes to the highest part Valerio provided some beautiful pictures of volcanoes that are just above the fault scarp on the foot wall of the normal fault and here these are two normal faults you have two steps like this and most volcanoes are actually right on the normal fault some of them are even further away and there is a majority of monogenetic cones on the foot wall and only a few of them on the fault which is the usual explained mechanism that you need to have a fault to take the magma to the surface no you don't is independent can go on its way to the surface and only a few of them are on the hanging wall of these normal faults so this would be the view you may have an uplifted or flat mo and then you may have seals due to this topography or unloading feature and then you may at least in some phases of reef development depending on the competition between extension and these unloading forces you may develop off rift volcanoes which are seen in many many rift worldwide and I was wondering at some point some people asked my volcanoes are all aligned in some lines so look at this feature so look at loadings loads on the surface because maybe your volcanoes are actually helped by maybe they are along so also seen this showed that this very big volcano was exactly on the foothold of the of the grub and fault so this is so the more I look into this in the examples and the more one can see it there are cases where so like this is the red sea it's a rift that has developed into crustal splitting and all the lava fields also huge all on one side most rifts are not symmetric the loading and loading is asymmetric so you need to take this into account and any asymmetry of course in the source below but also in the grub in geometry will drive asymmetry at the surface this is another example the Rio Grande rift most of volcanic fields are not in the rift they are outside it's this yellow fields here and this red fields here ok, this is what happens if the loading is little and then it's basically the caldera case that Valerio may be applied to the caldera case it may be applied also to shallow rifts for example in Iceland the north volcanic zone and the rifts they are very shallow and they are very broad therefore your vertical sigma tree area goes deep mathematically it goes deep and in shallow rifts you will have distinct trajectories so you will have separated trajectories you will not have a focusing of all the macmatism in one point this may be also the early stage of rifting when you start to decrease thinning to start to thin thinning is very little and I read that in many cases you have monogenetic volcanism at the beginning of the rift rifting and this would be an explanation for that because the unloading is still too little it's not dominating towards extension but it's making the trajectories to be slightly separated from each other ok, so this was this part how we may accumulate magma of course it will be more complex than this and of course there will be thermal effects but we may accumulate magma below stratovolcanos and more horizontally below calderas what is the implication for eruptions so in order to model this there is a very simple way to model this which is to consider mass input into a magma chamber or mass output so these equations are not difficult I will explain you so if you have a mass change you will have rho dv change but when you make differentiation you get rho dv plus v the rho ok and so if you differentiate with respect to pressure you will have rho dv over the p plus v the rho over the p times the p and you can define two constants which are magma compressibility of the outer medium which is not directly the bulk modulus but depends on shape and you can write the formulas actually like this so a variation of mass due to a variation of pressure or variation of pressure due to a variation of mass as you want to see it depends on total volume not only on total volume it depends on two quantities one is how much I can squeeze magma because it's compressible so I can make space into the medium with pressure they are both important because they happen to be similar these compressibilities for most cases now we will go a little bit more into detail so magma to give numbers magma compressibility if it is bubble free is around 10 to the minus 10 10 to the minus 11 equals to the minus 1 but it may be much higher 10 to the minus 8 10 to the minus 7 depending on the bubble content if many many bubbles are there of course it's super compressible and then for magma chambers and this is the whole point why I put it here it depends on shape so if you have spherical geometry for a unit variation of mass I will have a very high variation in pressure because of this incompressibility so I cannot really make the medium and large very much due to this shape factor while if I have a crack something tabular is very easy to open and therefore pressure will not raise very much there is another effect that I didn't put here into the slide which is buoyancy suppose that you are stopping an intrusion not because it reached a neutral buoyancy level but because it was stress because you had vertical sigma tree then the magma is buoyant it's there, it's sitting there but it's buoyant it's not neutrally buoyant then what you will have is vertical integration over the vertical distance so the vertical extent of the system generally systems are a few kilometers developed vertically so if you have this limits a bit how much it can be vertically developed of course it strongly depends on the density contrast anyway even if it's only 50 you reach very easily and you can go back up a skull by 10 kilometers so this may be very high stresses in some cases and these stresses are not dissipated by thermal effects these stresses stay there so there were a couple of papers very recently in natural science pointing out that buoyancy may be a mechanism to fuel the largest eruptions because if you have elastic stresses and you have thermal effects of large accumulation there will be a time scale over which they are dissipated these shear stresses and you will not break the magma chamber but then at some point you reach a limit which is due to the buoyancy and then you may have a very larger option so there are two mechanisms one is elastic over pressurization and one is buoyancy here I argue that Tassil is the one most magma without pressurizing very much because it's a crack so it works well for elasticity for elasticity a dike would be equally good however for buoyancy is better to have horizontal because then you are not accumulating so much buoyancy pressure therefore if you develop a seal and you can develop it far away so you have a large caldera as the rim are far away you have a large rift the flank of the rifts are far away so you can actually extend the seal the more magma you have it will just go ahead in this way and only at the very last point it will try to erupt you can actually accumulate huge quantities of magma without pressurizing the system very much what happens once you open this you create a conduit to the surface here there are many effects that I didn't investigate yet and I cannot explore now but it is very simple you open a conduit to the surface you have a pressure gradient there if your system is very large but very limited vertical extent both buoyancy pressure and elastic pressure will decrease very little during the eruption so what you create is a huge eruption because what stops eruptions is that at some point you lose the pressure at the magma chamber there are eruptions in Iceland at Kilauea studied by Paul, studied by Icelandic colleagues where you see very well that the magma chamber depressurizes very fast during the eruption but if you have a system which is a very large seal this will not occur but it will occur over much longer scales so in this paper by Amoruz and Krescentini they calculated the compressibility of different aspect ratios so here in the middle here to the my right hand side you have a proleta ellipsoid and the compressibility is 1 over mu note that it depends on rigidity so if your medium is visco elastic this will also drop in time here in the middle you have spherical spherical aspect ratio consider that everything is normalized to the sphere so therefore sphere is 1 but the compressibility of a sphere is 3 over 4 mu so slightly lower than a proleta ellipsoid anyway consider that here you are going flat so you can build it as proleta as you want it's always 1 over mu it doesn't change however this changes very much when you go to the other side hand side so if you start to have pancake shaped magma chambers because the compressibility starts to be dependent on the aspect ratio a over c a is the radius and c is the half of the vertical extent is actually increasing linearly with that there is a paper by August Gutmusen saying that the aspect ratio of seals is 150 to to to 500 in the field so if you put this number into it you can see that very easily you go much higher, 2 orders magnitude higher at least than proleta ellipsoids this is translated into so we had these equations that relate mass changes and pressure changes in conduci we had a lot of these equations it's a variation of pressures over time depending on the total pressure gradient over a time scale and the time scale for this problem if you look at these equations is of course dependent on mass so the largest is a magma chamber the longest is the time scale but look also compressibility compressibility so compressibility plays a big role in making the eruption big or small compressibility is also made so basically the total volume in the end will be ok you have total pressure gradient along the conduce where you are erupting but the total fraction of volume will be just the compressibility the value of compressibility times the delta p will tell you exactly what fraction of your magma chamber you can evacuate and this fraction is very small exactly due to this for spherical chambers you cannot evacuate more than 1 or 3 percent of the chamber you can if you have a delta p which for some reasons siphon effects whatever you are really extracting a lot of magma due to your process while if you have a seal or something shaped like a seal then you can extract even 20 percent no problem because of this equation and possibly you will not even have a strong collapse you may have some sagging as Valerio as Valerio showed that you have different stages and different stages of caldera development if you only evacuate one seal then you can end up with no collapse at all so here I have two batteries when I was talking about this to a colleague of mine and I told him it's like a battery and he said yes it's like a battery but for two different devices one is telephone and one is car when you have a battery for a car you want to have a large current very quickly and you need to start your car you don't care that the supply is continuous you care only about a short time while if you have a phone a telephone you want to you don't need a lot of energy or current in a very short time you need the current to be continuous and reliable for a very long time until you charge it again don't be tricked by the fact that I'm telling you larger options but then the batteries the current is very small and here the current is very high so of course here current will be very high but consider that this one is as big as this one if not more so take a phone battery and make it very big and then you will see that magma chambers are similar to batteries in that they provide the flow it's not current it's not charge it's flow of mass and they provide it depending on their design not only so in this case also shape is a factor is the design of magma chambers so this is a figure showing that so their active volume depending on aspect ratio so aspect ratio here you have spheres here you have seals and the fact that these corvus are bent is a direct consequence of the Amoruzan crescentini corv that shows that compressibility is increasing for seals so depending on what supply of magma you have from below and this supply here fee equal to one cubic kilometer per year is the highest supply rate I would say that is observed for large igneous provinces these are the largest eruptions of earth they are sometimes in excess of 10,000 cubic kilometers in just one eruption several pulses of them generally large igneous provinces very often they result into continental break up sometimes they don't one feature common feature that they have all of they have they have lower crystal seals it's a common often it has been seen as a byproduct some people have tried to say they are actually large igneous province eruptions are fed from the seal here is a reason why they are fed from the seal because a seal is the optimum system especially is very large to keep their option going for very long time without stopping because there is no depressurization and only so I mean this kind of extreme flows you can obtain them for this supply rate only if you have a seal shape chamber the last comment is on thermal aspect because of course a seal is a thin structure it may be a few hundred meter thick so how do you maintain it why it doesn't freeze I would say in these two cases where we have the largest eruption on earth in Calderas and one is rifts is so in the in the case of the rifts they are in the lower cast this helps because they can be maintained in the oven I mean they are hot down there there is not much freezing going on it takes a long time to freeze them away while in Calderas the large accumulation and the fact that stress forbids the magma to erupt very frequently means that they stay there so they are kept hot by a huge body around them which is a crystalline mash probably reacting elastically during short times of eruptions possibly not part of it will not but anyway there are a lot of studies which show that accumulations in this body of melt it's not really a seal it's not necessarily an intrusion that really goes in between a bedding but it's something lentically shaped so from a mechanical point of view it's the same and they are kept hot by this body around them so here I'm concluding three messages so one is that a path to the surface is not simply a fault that the magma can take very over everywhere in the literature you will find this I'm not saying that likes don't follow faults they do sometimes but they can just create their own pathway and when they do they will follow the stresses very often and therefore you need to figure out the stresses of a particular situation to understand why melting is here and the volcano is here it's a frequent situation if you apply these mechanical models to magma chamber formation you would discover that stratovolcano favor vertically elongated systems while caldera favor horizontally developed systems this is seen from crystal deformation 2 I have not seen a caldera where the source inferred from insert is not a seal they are always seals and I have up to yet not seen a stratovolcano where the source is not elongated unless it has a caldera on top and then these are strong implications for the eruptive potential because the larger compressibility I have not talked about the compressibility so compressibility is some of course of the structural term and also magma compressibility this of course will play a strong role during eruptions not so much this huge basal flows because they are not particularly compressible in terms of magma but of course in caldera eruptions it's a different matter so this will help even more to get a larger eruption so structural magma compressibility lead to large typical eruptive size of a given volcano