 As I promised, I will start with the, I hope do you see my screen, correct? Yes, very good. Okay, as I promised, I will tell a few words by end of the last lecture, I told you that I wanted also to show you some examples which are related to the mentor based on evolution. And that's why I would like to start this lecture with this part of there. I just will show some slides to you related to the simplest way which we call the backward advection technique which apply to sedimentary based on evolution. Again, let me remind you that the backward advection means that it's, you have a particle which move with some specific velocity, prescribed velocity or the velocity which is calculated through some equations related to the dynamics of the, and then you calculate it at a forward in time or not calculated just to consider particle moving forward in time with some velocity. And then if you would like to reconstruct the history of these movements, you just move this point to the back position with the same velocity, but the change of the sign of the velocity. This is possible only in the case when there is a no diffusion of the temperature or the processes with a very, very little diffusion. That's why in this case, it is possible to go there. What I will be speaking today, actually there are several problems and several inversions, but I have no time to show it as another lecture. But I wanted really to show you this sample also because it's a part of geodynamics, this sedimentary basin evolution. And it is also important because the sedimentary basins are related to the oil industry. And even today we are moving from the non-hydrocarbon energy to the renewed energy to preserve our earth, to preserve our climate definitely. Nevertheless, it's more than 50% of the hydrocarbons today are used, well, sorry, energy are used in terms of the hydrocarbon. That's why the science of the sedimentary basins developed dramatically during the time period or let's say last century. And actually probably starting by end of the 19th century, early 20th century, when the oil and oil production becomes a part of industry. And since that time, it was a great interest to understand how sedimentary basin evolves. Well, if we consider the solid battery reason, my question is, do you see my full screen? Because I see my screen with the top part, which is a huge top value. And so I don't know how to leave it from my screen. But I don't know, do you see my screen just normal without any panels on the top? Yes. Not any panel, great. Thank you very much. Because I don't see the top line of my slides, I don't know how to read off this of my screen. But anyway, we are speaking about the solid battery reason why? Because it's many layers, not only salt, but also sometimes it's layers with low density, behave as a body which start to move as a response to the accumulation of the sediment from the top. Why? It is less dense. That's the basic physical phenomena here and particularly in salt they appear, which is a density, salt density is around two, 2.1, 2.2. And the sedimentary sediment density which accumulates on the top of the salt normally it's something like 2.4, 2.6. That's why if you have a two-layered system, the related lore or gravitational instability take over in this so-called the stratified geological structure and the structure start to deform greatly. Why it is important actually because of the following. How to reconstruct the history of sedimentary basins? What means sedimentary basis for those who don't know? First of all, it is depression on the surface of the Earth which is a start to be filled by sediments. If sedimentary it's a field from the sides, let's say normal way, which means that it's one layer, the second layer, third layer, fourth layer, et cetera. And they are also stratified normally, meaning that it's a when the first layer comes with the density 2.2, when the next layer comes, it comes with a less density normally, but because of the weight of this layer, the lower layer becomes more dense in terms of the, it is actually not dense, density doesn't chase. I'm talking about effective density because it is also filled by the some pores and so on. And the porosity is changed of these layers. And then next layer, et cetera. When the normally in geology, in geological petroleum industry, they look at the profiles which they see. How they understand history? They take the first layer out and then they restore the whole structure upward because at that time, let's say the layer was accumulated within the last 2 million years and within the 2 million years, this is as they restore these sedimentary layers up for. It is a rather simple technique and it's called the backstripping analysis. But if we have some layer which is a ductile and swell as a lower density, this layer immediately starts to move upward as soon as some heterogenesis in terms of the movements occur. Why? Again, because of the relative lowering stability, which tells if, let's say consider it's a very simple case, two layers, one on the top of other and the top layer are denser than the low layer. And if there is a very small perturbation at the interface of these two layers, the low layer starts to go upward because it wants to go up, it is a lighter and heavier layer will go down because it's heavier. And structure which appears is called diapid. And salt exhibit exactly this behavior, that is why complications comes how to reconstruct the history of the sedimentary basin which complicated by deformation due to salt. And why restoration? Why reconstruction of sedimentary basin? Because in this case, we know exactly the time, the position of layers and let's say calculate the temperatures and layers and the stand when the oil or gas started to be produced. As probably you heard, this oil and gas can be produced only at a specific pressure and temperature conditions. That's why it is very important to have a structural history in one hand and the thermal history in another hand. Thermal history is quite interesting, more complicated. That's why I will drop this part because I have no time but it is very close to what I already mentioned about let's say thermal convection is very similar but it's more complicated because it is addition to the structural evolution. Now I will be speaking about the structural evolution and there is a basic components that's written here. It is a gravity, it is isostasis and the differential loading. Do you know what means isostasis? I think so, it is just a compensation due to the masses which is there operating within the earth's structure. It is a some position of the normal to the surface. Let's say and differential loading is the following. If it's from one side, you have a big pile of sediments from another side, smaller pile of sediments, that is a differential loading to the sedimentary base. Finally, it is a mathematical problem of the Saldiapirism described by a set of equations and it's a very simple equation. It's again stocks equation principally and the incompressibility equation or it's called motion and continuity equation as is written here. And in this case, we have a no thermal equation because it is the other part of the research related to the thermal history. Now we are talking about structural history and within the structural history, we will consider only now we are stocks equation to be coupled with the advection of density and viscosity. Advection is different and definitely is present because of the dynamics of the system because it should advected the density and viscosity advected with the equation. Or we can consider that heat also can be advected but we have to remember that in this case, heat is only the part which is advected here, not a heat which is a diffuser. In this case, we can solve that problem. This is some, let's say known techniques which comes from the American geologist, Richard Ella, who working for the oil industry and so on. And how normally the geologist reconstructs the history. Look here at the starting configuration where it is written, it's below is a soul and on the top are layers and the layers are fractured. There are faults, some it's a list of faults, some it's just trusting faults, et cetera. But anyway, it is a fault which the geologists want to reconstruct. What they are doing, they take this green one, look down now, strip, as I mentioned, it is basically stripping analysis. This is, they took this one and then they start to unfold the layers but it is something like a handmade. They are unfold each the layers, then they rotate these layers, it is on the right top, they rotate this layer, they rotate it, then they move this layer toward the left to align with the previous, with the layer here and then finally they decompact them. They decompact because of the porosity, the reason, the sediments and then they compact the porosity increase and then it's a, sorry, porosity decrease and when they decompact the porosity increase and then the volume looks like a bigger and they are doing the same way, the same way. Doing this way actually, they ignore dynamics of the salt. Look what they are doing. They cut salt from here again by hand, put here and salt. But look here, so big amount of salt was here. At this area, salt disappears somewhere. It's also, you know, the strange things but anyway, it was a simple for the geologists to do such kind of reconstruction. When first time I saw it, I thought, oh my God, why people do not using this some even simplest mathematical techniques which allows them easily to do such kind of reconstruction with the deformed salt shapes. But it is, look, it is cartoon but if you are going to the real area and I will show there by and they say example real, it is not so simple. Yeah, to do this way because there are many interpretation. This is a one of the interpretation, how it was developed but there is a something which you don't need a specific interpretation just to give a nature to move backward in time. No. Well, and this here I just put that as objectives of this study was to allow that they say not only they say to use this geometrical reconstruction but also to do some dynamic reconstruction where we consider the salt mobility. And that's the important. And we use this bad technique which is a backward advection technique and well, this is a method which you already know. Let's show you a very simple sensitivity analysis just moving to the real example which I will show you because it is a sensitivity analysis important to understand how well we are reconstructing this not to just believe me it is true. And what I am doing, I will show you how sensitive our results to restoration of small change in density because it's a game it depends on what is the density of the layer structure. And the second one I will show when it is a diep, it is very mature. What means mature? It is like as I showed in terms of the mantle plume when they develop a structure as a mushroom structure the very long be overhangs or the mushroom head and very thin and smaller the part of the tail of the diep or plume. Well, this is the first one when we consider the differences in the area. This is the overburden. Everything what is there on the top of the salt it is called in structural geology overburden, overburden of salt. Yeah, and this is a salt and initial position was this way, this line T equals zero. And then we made a forward analysis and this moved to this line and this after the some here is non-dimensional time don't link to the specific time but it's non-dimensional. And this is after the about 1500,000 time steps. And you can see that now is a position that we see as a very prominent salt dome here or salt, salt, the diep here and here is a smaller salt diep here but it is because of the relationship of the wave number to the wave length, et cetera. But it is a different story. I just would like to show the sensitivity Now what we are doing, we did, we took this diep here and run the backward in time to see the how, how it developed. And it's moving as backward in time we came to this position and you don't see actually the very big differences but I took this area, you see a very narrow area and I zoomed this area here and you see that is a change and initial, initial the line was the line which is a here indicated by solid sin line. All of three lines are because of the differences in their density. And please note that density actually is something like 2,000 kilogram per square meter. And that's why here it is a very small perturbation to the density. Nevertheless, you see that it is a, that we have a really very good performance of the algorithm. Another actual case, sorry, yeah. Another case it is about the maturity. It's not only to run to this position but it's further. Now you see here orange color is a forward modeling and the blue color is a backward modeling. And the way we start with this line and then we are going to this position which is a more close to the what I showed you and this is the next time is here running for the, for the direct problem. And because it's a time F, it is a time the forward modeling. Here even more mature, even more mature and that's the final position from where we start the backward modeling. And the backward modeling starts from here and goes this way up to this position. And you see the differences here, small orange area show the differences between the backward and forward model. Again, I can tell that it's for even a very mature structure that our method is really perfect for working. I can tell that this is a very specific method published in the some literature and so on. By end of this lecture I will show you some of the textbooks where you can take these methods which we developed for many years and so on. But anyway, the point is that it's the reconstruction is really very good when you have a more diffusion. And now I will show you like a final point of this part. It is something which is from the nature. This is a seismic profile and the experts can recognize here. There is a very remnant small biathetic here, there is a very remnant small biathetic and rather big biathetic here. Also it could be recognized the many layers of the sediment and it looks like a turtle back and so there are other sediments here and here. Finally, it is possible. This is a time series. Sorry, it is a time here, time seismic profile. And then it is possible to convert it in the depths and the lengths. And in this case you could see here, this is a salt layer here, also this is also salt layer and this is layers, all other layers are sediment layers. There is some description of this sediment. Actually it is taken from this profile, taken from the very well known basin. It's called pre-Caspian basin. It's called here. There are many publications about this pre-Caspian basin. First of all, scientifically it is an amazing basin because it contains something like 1,800 different diapers and the walls and domes of the salt structures. Moreover, there are many giant oil and gas fields in this area. Again, it's a quite interesting topic to be discussed and we did a lot of modeling, thermal and others, but now I would like to tell you about the inversions which we used. And finally what we did, we constructed, we took this model, we prepared this kind of the layer system. These are all colors show the different layers. These are layers which were accommodated something in the palliative time were rather flat and it is rather simple to use the technique which we call the backslip analysis process. But as soon as we are going down to this area, the layers are deformed indeed by diapers and you will see now how salt dynamically changed the configuration of the basin and it will be a small movie related to this and you see how we reconstructed it. We first of all made them to the stride horizon and then we stripped them out we performed the analysis of normally applied by the backslip analysis but here you see the salt itself moves. It is not adjusted something like by hand we make it unfold them and then we adjust them they are all continuously changing they are looking how time ago it looked like, you know and this is something indeed in some places you can see when we strip the sediments immediately there is some time of the fall indeed it is not fall because the stripping is a permanent it is an instantaneous function but it is not instantaneous it is very small layers if we could apply these small layers to, I mean this time then it would be something maybe 2-3 hours moving that's why you see something which is sometimes it's like a deep I mean it's a hole but it is not actually but anyway you can see now how salt moves and if you will run now the history back you will see, oh sorry you will see that it is how mobile is salt and how the salt goes it was initially it is like a layer, horizontal layer you saw at the end of this movie and then sediments start accumulate here, then here, then here and the accumulation this is differential as I mentioned differential loading really moves these diapers up for because the salt is light and that's in this case you could reconstruct this area and this is indeed important technique for oil company and for example such companies like AGP and ExxonMobile they were quite interesting in this technology and so on and we work with them sorry, ExxonMobile is a different area but with Chevron company we worked on this topic for a while and this is a last sample which I wanted to show you it is something which our reconstruction in three-dimensional case because it's on the top you see the very large three-dimensional structure within the same basin and the question was how this very big dome developed and we showed it was not developed from the big perturbation it was developed from very small perturbations but then these small diapers merged during the evolution and they become a very big dome that was a quite interesting finding because the geology sometimes believed that the big domes is because of the very big perturbation on the basis of the salt and the presale and so you see that here is a small perturbation which gave a rise to the big one and here is the differences again it's always we are interested how well we can reconstruct and then we are doing the forward analysis backward analysis and then we check how the density residuals okay well I think that is all what I wanted to tell you with this chapter and I will stop now sharing and before I will go to the main topic of this lecture I would like to ask you if you have questions related to this particular presentation related to okay I now would like to share my screen how the inversion of time to depths what about what means how the inversion of time to depths how do you say you can ask the question if you would like or explain it how did you do you mean how I converted seismic profile to depths this is a special technique yes I didn't make something special I mean because it's with profile and there is a special program for conversion this is I mean I mean it was another my idea I mean it's my work to convert it there is a special program which converts the lines of the seismic profiles into the density definitely we need some information from boreholes to correct for densities to correct for the thickness of layers and so on indeed indeed the borehole data are quite important and it was used actually in precast basin there are a lot of data on the peripheral part of the basin because the depths of the basin in the center more than 20 kilometers there is a no borehole which today I mean it's still today it's a drill in the center of the precast basin it's really very big basin something like a 600 kilometers to 400 kilometers in the center the depths are down to the 20 kilometers but it's information from borehole is definitely in doing such kind of things okay now I share the screen I hope you see the screen as well okay the title of the lecture will be the data simulation and the machine learning in the models of lava dynamics I am very sorry that I had no time because you know there is my lecture schedule tomorrow to bring this all in one file because you will see there is several files but now I will be speaking about the lava flow and then I will be speaking about the lava domes in another file I couldn't merge them because of no time but anyway let's start with this very interesting and exciting topic in dynamics of the earth and the volcano dynamics we probably you heard that it's during already about one month there is a very big eruption in the islands canary islands and it's damaging infrastructure and so on it's mostly mostly the interesting part of the dynamics of the lava domes are there they are both temperature and there is internal let's say crystallization what means internal crystallization meaning that the crystallization depends on many factors as well as the temperature I will show you these things later just now it's to tell indeed it is one of the exciting natural phenomena which we can see and there are even more the lava flow sometimes they say the volcanologists go so closely to them just a few meters because it's the flow of the lava is not a very fast it is fast in many cases but it is when it's already on the very long process it becomes colder and you see already here it starts to be covered by the crusts let's first of all to tell this in general the structure of volcanoes who are not much familiar but you know there is some area just the beneath sometimes volcano sometimes a little bit shifted it is so called the magma chamber and it's how to develop magma chamber it is a special topic and this is an exciting topic also I will not be speaking today about this development or dynamics of magma reasons a magma chamber but I will be mostly speaking about the surface processes which we observe that's why we can use the observation to assimilate this data into understanding of the flow of the lava and here you see many things related to the I mean many terms related to the volcano dynamics particularly here you see ash clouds and I am very happy that tomorrow we will hear the lecture of professor Volk and he is a well known expert in the area of the modeling of the ash clouds and he is right now very busy he is from Spain he is from Barcelona and he is very busy this is a volcano ongoing volcano nevertheless he promised to join us and to deliver tomorrow the lecture and probably he will be speaking also about ongoing actions today I will be speaking about the lava flow you see here lava flows here seen here seen and later also I will be speaking about the so called the domes which are effusive effusive meaning that's not a eruptive volcanic activity but it's rather slow which develops lava flows normally or they can develop a dome and I will show you that later now I will try to run this movie and I hope you will see the movie and I will explain what is exciting you see that it's a very hot material from the earth interior comes to the top of the surface and start to move it's created on the top it creates crust which can rupture suddenly at some places and the hot lava can come over you see that it's a lava already and the top becomes a colder because of the conductive and mostly it's because of the heat flow which is an occur and then now it will be rupture you will see and there is a new lava will come and go that's why one of the exciting point here at this particular for me particularly was to understand how really the lava flows how the pieces of the crust ruptures and they flow how they are accumulated on so well for this aim we developed some interaction of lava and crust models this will be direct problems we are actually working partly on the understanding how we can resolve the problems of the also inverse problems but the practical meaning of inverse problems let's say how from the crust to bring the crust backward it is a maybe not a very important in the world technology but still it's also information if you have information about your crust sickness and the crust pieces is it possible to reconstruct let's say temperature in the past at the beginning of the eruption and so on but what is a quite important things in terms of the inverse problem is dynamics of lava flow inside a channel what it means channel channel mean that it's a lava flow generated channel because at the borders of the lava flow lava becomes a colder and generator let's say some barrier and the lava flow within this barrier and then it is this barrier becomes colder colder and colder and finally they joined and created big tubes you know that and within these tubes the lava flows and finally when it's a lot of flow stop these tubes are preserved and it is not only preserved for a short period of time they are quite often preserved in geological time scale generating for example the cars you know generating the not so caves and the particular that's a volcanic case there are experts dealing with the caves they are going and finding such kind of caves lava caves anyway now I will start with the interaction of lava and its crust and you see here is a simple example when we had some let's say it is a model it's a model flow inside also called the incline the channel we developed the incline channel and we were quite interesting to see how the lava flows and another issue which we actually used it as it was a first starting the point to understand how in general the lava flows within the channel and well well ok that's here I will I show you I think it's maybe one or two slides here with some formulas but again as usually I mentioned you have to understand not just enjoy the pictures or the movie but understand how it comes to such a stage and this is a Navier-Stock's equation because flow here is the rather fast and this term should not be entirely neglected sometimes people neglect when the viscosity here is very high it is for domes it can be neglected but in the case of the small viscosity this should not be neglected that's why we use also there is a term inertial term so called it's always an inertial term and the point is that in this case it is not a Stokes equation but it's a Navier-Stock equation it's more complicated because of the Stokes and here it is an advection equation for densities and viscosity as I already mentioned we used here as well at the boundary condition I am not going deeply in this case I just show you the essence that's essential governing equations and there are some specific boundary conditions which create the problem which we solve because sometimes people refer only to equations just please remember the problem is equations together with the boundary and the initial conditions and here it is a lava flow with a broken crustal pieces crustal the lava I mean and we wanted to generate such kind of things that's why we have the mesh on the top of the lava flow and we were interesting to understand this how this pieces deform and how they move and look here it is lava which is penetrated look here it's already the lava is cold and it's rather rather hard and there are new lava it's just within this tube you know it breaks this tube and it goes down because it's lava always moves on the you know based on the criteria of the highest steep still how this slope is a steeper the slope and it's based on this principle and what we develop we develop this such a form of the at the same time this we introduce lava crust and then the lava crust is moved upward together with the flow and you can see that there is a red stuff somewhere here it is a pieces which went down why because it's you know by and when the red comes sometimes the part of this pieces goes down and there more light material tops there things on the top and here you see that it's one of the final example which looks very similar to what in the nature you see and again that is the red here under underneath of this top and here it is some pieces which is went down and stuck there stuck on the base of the lava flow where we develop also is a multi-phase fluid flow which are oh it's yeah multi-phase fluid flow from a single went and this is a single went here was it's lava base topography of the volcano it went down and then we used also a new portion of the material and new portion of the material and this is a quite interesting work was unfortunately at that time it was a very simple now we are thinking about the more complicated the similar multi-phase fluid flow but with temperatures which is close to the reality and to see how the barriers are developed or how to develop in the three-dimensional cases that's a rather complicated time-consuming problem but nevertheless it's a quite interesting problem you see here there is a profile through these lines how they see new portion comes on the top of the older portions and how the structure are developed and compare it through the geological let's say drilling and so on how the layers also lava are accumulated within several here's some very briefly a few words about this Yellowstone area you know it's a very famous Yellowstone there so called this all the Yellowstone volcano and the very also interesting part this is a summit lake where the lava flow formed very huge very big the area covered by the lava and it's up to about 200 meters the steep lava in the center anyway anyway we also constructed this special case and we instigated I am going just very fast here this is how it moves this is a part of the lava which presently known and how in our case the lava moves with a different viscosity that's why here it is less viscous here it's more viscous and you can see how it is rather well it's start to cover this area down I showed just a few examples now it's within about the 6 to 12 months it's area is covered within the if eruption so long time but it it occur because it's cover that's very steep well that is the conclusion to this first part which I wanted to tell you and this is it is possible indeed to develop the numerical models which will be later used at the basis for understanding the processes and then to help us in the inversions which will be the next part inversions related to the lava flow and next part I will start with the lava temperature flow from its surface thermal measurements and I will show you its application observational data simulation in lava flow okay now I stop and I give you something like 10 minutes until 6 and then we will continue okay and yes please any question you can pause and I will look this is how I can answer when I can answer okay thank you enjoy your break