 Now I will be speaking about this how we can assimilate some data which comes from observations for measurements, particularly the space and airborne infrared sensors, which is operating from the surface. I hope do you hear me correct. Yes. Do you hear me. Yes. Yes. Okay, thank you. Thank you. Because it was something in my computer indicating that it's normal. Space, as I mentioned the space airborne infrared sensors, they allow in general to determine this absolute temperature at the surface of the measure at the measure area on the surface and how they are doing they are at each time step let's say like that. The satellite or the airborne sensors, they are measured the reflectivity and then it says they can tell about the absolute temperature and from the absolute temperature also they can understand this or assess the heat flux on the top of the surface. And it is a very important for us to understand the, what is the dynamics of the lava we see, especially when the lava start to be covered by the crust and from the top, you cannot see the dynamics how it flows. You know, as I showed you movie, when it is covered by the black pieces, you don't feel lava itself but suddenly it ruptures and lava comes. It means that it's a lava is rather hot, and it's a six area from where it can escape. And that is really important, especially when it's created some cracks from this tax can be even moving out. And for this aim question can be imposed. Is it possible to use the service thermal data, which can be temperature and the heat flux. When it is obtained them. Is it possible to constrain the thermal and dynamic condition beneath the surface, meaning they say beneath the surface of the measurements or beneath the crust, for example, of the lava. And that's quite interesting to understand what is the dynamics what is the temperature what is the flow within this particular area. And now I will show you again as usual, it is a set of equation which we saw, and I'll show you how we optimize this problem. This is a problem related to the determination of the conditions at the low boundary, but we don't know that, I think they see here it is a gamma two, and the gamma two actually, we don't know temperature, if we know temperature at gamma two and that's gamma on the surface, just the temperature we can reconstruct that some solution based on the equations for this equation, but we don't know here but with what we know on the top we know the temperature and we know heat flow. It's in the forward modeling, it is a too much to have a two conditions on the top. You can either use a heat flow or the path when you don't know, there is a temperature at the bottom of the layer lava flow, it is impossible to measure. But in this case, it is a really very important to have the additional knowledge about the temperature, which means that temperature and heat flow, heat flow measurements. In this case, we can assimilate this data to understand the temperature within the layer and particularly on the bottom of the layer. Let's consider that's what I mentioned is the boundary conditions here we have at this boundary, we have a temperature and the flow because we need to have a in the model the some flow which comes with the velocity let's say you want. And then at this boundary we know only that it is there is this no sleep conditions. That's why we put you equals zero. At this boundary will have a summer quail for example we know temperature we know that it's a pressure is zero, and we also impose a such kind of the conditions. And this boundary which are related to the stress. It's actually the normal stress. And at this boundary which is the most important gamma for we know as I mentioned temperature. As I mentioned we know heat flow, which we can this way. I mean it's a mathematical and fee is a measurement. You know the measure you know T for as a measurements part of measurements and you know fee as a part of measurement. And also there's some condition we impose on the. The velocity and the relevant relevant the cancer of this sigma. The next step is to develop a selection problem, what it means this problem is a, let's say over over estimated in one place, because we have at this boundary, as I already mentioned two conditions for temperature, but here no condition for temperature because it's actually we don't know this temperature condition would like to determine this condition, but in the artillery. The problem we what we do, we tell that let's let's temperature at this boundary be T2 we don't know it just to prescribe some temperature T2. Here is a temperature remains the same. But we tell that it's a no heat fluxes here. We take out a hex flux in this case the boundary condition together with the stocks incompressibility and stationary heat equation becomes the same. And the. Sorry, the same I mean it's stocks and consider and stationary question are the same as in the direct problem, but the condition are different only for this boundaries bottom and upper boundaries of their lava flow layer, which are of our interest. Exactly I mentioned here that's two boundary condition differ based on the latter a problem from their direct problem. But as I mentioned you we develop a joint to this problem and then we use a variational approach which I was talking about during the previous lecture. And in this case that is our joint here I just to show the equations, but it's indeed it's based on the some theory the inversion of the matrix and so on, but the point is that it's what what is the nice part of this work was that to the derive the joint. It is a really was not a simple problem but it's still analytical adjoin that is a possible to try. You don't need to use a discrete adjoint like in many cases in, let's say atmospheric sciences and so on it's a very complicated when you need to do the some additional problems, but here it is a possible was possible to develop an analytical adjoint. And in this case you see that it's at this boundary we prescribe the difference between the observed heat flux and the heat flux which will be at this surface. In the case here heat flux observed and this one is a heat flux if we assume that at this boundary temperature is equal to the temperature. And in this case we take such kind of the differences we insert and we solve this problem adjoint problem is well post problem. That's why again we receive a two well post problems. One, it is an auxiliary problem, and the second problem is adjoint. And solving these two problems, forward and backward in time, this one backward in time and auxiliary problem is forward of time. It is possible to find such a tx which will give a very small differences to this cost function. Now, a few words about this I specifically mentioned here by red it's term related to the viscosity, viscosity is not so simple as let's say in the mental dynamics when we use a viscosity dependent gestal temperature and sometimes of the pressure and rather simple the viscosity relationship. But here it is a lava actually depends not on the temperature but also as I mentioned on the volume fraction of crystal. And that is a really very important because it's a crystallization brings us to the case when you see the so called the black crust on the top, because it's a crystals and crystals are developed based on the various issues of the gaseous, it gives a race to the crystallization, as well as the temperature with the cooling, the number of the crystals increase and so on and the volume fraction of crystals in place. And here it is the equations which correlate this crystal content. This is the volume fraction of crystals fee. Actually this fee but it's a ratio is such fee open fee and this is a growth fee. And this is a function which tell us about the F function which are inserted into this equation. What is important how this relates to temperature and you can see here, teacher, and this teacher is a related such a way where the T s is a temperature of crystallization. I think for some lovers it can be a little bit over the thousand Kelvin. The parameters are mentioned here, but right now it is not necessary to go in details of these things, the publications and you can look at the most important issue is that it's a function of viscosity or rheology of lava is a rather complicated in this case because it takes into account not only the temperature but also how temperature influence the crystallization of the lava to generate this. And again it's just returning back and reminding you what needs a variation or a joint method. We as I showed this create this norm or here it's integral. This is a cost function, and we would like to minimize minimize here heat flux, here is heat flux, it is observed, coming from the observations, and the here we see, we will have a temperature as a solution for auxiliary problem. The auxiliary problem is possible to be solved, because we, you know, the transfer there is one of the condition from the top or the upper surface to the lower surface in this case it's possible to solve this problem as a direct problem. And there is, there is the auxiliary problem and the solution and we insert and we get a some heat flux in this case, and we would like to optimize this difference to get then finally such a temperature, which will get us closer to the measured heat flux distribution. As I mentioned that in this case also it is possible to prove that it's this equation, this this objective functional as a unique minimum. And we would search for this unique minimum using the gradient of the object objective functional, but again I don't show here the how we derive here and the old methods and so on, how we use it. Again, it is a something long story, but it is a everything is written and possible to read and I will refer you to. If you are interested in our publications where it is every single set in details and describe. The last slide of this present as this part of my presentation related to the case case study and we had a flow on the. You can have from here it is a vent here, and this is a ghost flow down the toward the area I mean this is this you see you see here the dimensions of the model domain here you see the cross section along this line. And this is the whole and what we did we took at this part, and we wanted to understand the temperature and dynamics of the lava flow within this part. This is the results of our simulation actually, and you see that it's a crust which has developed this is a color is a brown and the blue is a lava which flows and this is actually. They say one blue is something like one viscosity, again, it is a dimension less and three order of magnitude higher is the viscosity of the top here you see the temperature and temperature difference is a from 3.6 to 4.4 again non dimensional temperature here and you see that. Here is the temperature are high, it is indeed there is a lava or within the. Bottom of the channel is a. Much hotter than on the top, and here it is a cross becomes a more see if we consider this cross, but here is a viscosity in this scale, but when you look in the temperature you can see the stratification within the cross, this is a most. Let's say colder part of the cross and here it is a less colder. And finally, you see here the velocity how the mother lava moves with which velocity, what is the how well where the velocity is higher, where it's velocity is a smaller and indeed the velocity at the bottom is zero and close to zero because. As a boundary condition, the velocity imposed to be zero at the straight at the boundary of between the. And the lava on which the land lava flows. And now now I will speak about the cell problem of that jointly just a few things about the residuals, because it's very important to see that at the beginning when we don't know exactly what was the temperature below, because our our aim is reconstruct this temperature below. And once we reconstruct the temperature below with just the one salt the problem forward the time and we found that all these things, you know, all this constant temperature is constant velocity can be found the strive forward when we know the temperature at the bottom but we don't know that's why we prescribe some temperature here, and when we prescribe some temperature that first iteration is looks very bad. You see the is just a war. I mean if you compare to the scale, it's a very bad at first iteration. And there are, sorry, not here it's here it's residuals here here temperature is each one of these. And you see that it's a very big velocity residual here especially in this part, which is a. But with the after the search iterations at the 31st iteration you could see that it's almost very well we reconstruct that means that what means that actually residual residual means exactly there is a difference between the temperature, which is, let's say known at the temperature which can be construct, and this here it's also the temperature residual here viscosity residual temperature residual and the velocity residual after the search iteration, meaning that it's 30 iteration is not a load, and it is possible to resolve these things. And actually it works quite well, but but it's very important. First of all, as you remember this is a steady state problem, meaning that the we assume that the flow one established becomes the same during the time means no change because it's steady state flow, no change in the flow patterns. It is not true actually, yeah, because because it is a flow changer this time. And to do it, you need to introduce additional term in the heat equation. And in this case, I joined is a very difficult, if possible, to derive analytically. In this case, you have to go to the discrete case, or you, we did it, we did it, we did it. That's a fantastic but it's in our group that some mathematicians did it they derive the analytical side, but it is intractable to resolve, you know, and they spent about several months to derive this analytically, but it becomes a really intractable problem. And that's why we thought about the some other methods in determining let's say viscosity, within the lava flow or lava don'ts because we started to be doing lava don'ts as well. Well, now I will finish this part. This is a related to the lava flow. That's the meaning that it's what I showed you it's we propose our group proposal is some approach to solving the optimal boundary control problem arising in the studies of lava dynamics and there was a really, let's say, increasing the quality of sorry not quality of let's put the solution, the solution of satellite observations on the lava thickness volume flow and, indeed, the methodology will give more exciting results in terms of resolution, and maybe maybe even we can reduce the number of iterations and so on, and you see what we wish to get. And this is some technology which we started to develop recently, and this this can give us some further further, further further consideration for inversions using observations in lava flow. And for this part, but I will move to another part I am very sorry that it is not within the one I couldn't just make these things happen. I will stop screen now, and I will open another file. Sorry, it's a post. Okay, that's another file related to the type of it is not a machine actually learning but type of the vision. Okay. I hope you see my screen and here. Well, that is a something which is related to predicting of the viscosity of lava done by analyzing it's observed morphology. Sorry, I wanted to show you it's really the how exciting are the lava domes. You know the lava don'ts are like a mountain operating within the, you know, small window of time, you know you can see within small window of time, let's say several years. So mountain looks like definitely it is not mountain is something which can be like a 60 to 100 meters in the length, you know, and up to about also 100 meters to the in the high. Suddenly you see the something start to go up or, you know, it moves, it sometimes collapse, and there comes to some lava flow and then again, it is a girl and so on I am very sorry but I had no time to show you a movie movies fascinating. But anyway, anyway, here at the background probably you see this part of the lava dome on the top. So what is the exciting point of lava don'ts is the following. Initially they look like oh very interesting things. Look, it is like a, you know, grow growth of the mountain. You never see actually how the mountain grows, but when you look at the you are curious or what is a fantastic things. Definitely you don't see it's like a within several seconds of the growing. This is the time scale if it's a, you know, your time scale something several months to years, you could see the how the dog grows up. If it is a record that you know for example by permanent permanent, the video recording can, then it is a merge the each each slides and you can see it's really fantastic that's a USGS D actually and this is a part of the movie of USGS. Anyway, anyway, this is an exciting point but what is the most after the excitement of the evolution and another part of excitement of the nature, but there is another very dangerous part. So this is a seems to be very peaceful development of domes, sometimes can rupture occasionally, meaning the collapsing the part of the dome, and the pyroclastic flow can come. This is the most powerful man so awful it is that many things is mixing together, and it's a moving down slow with a very high speed, and it's everything that's the what is the coming base on the way is just, you know, eliminates on the way of motion. This is a very dangerous part of the dome lava domes that's why it is a very important to understand the internal structure of the especially for example what is the viscosity, even the viscosity is small in the, let's say in the core of the dome, it can generate the such kind of if during the long period of time they are developing the generation is probably not immediate but indeed it can be because of the, you know, the guessing, and the coming new portion of the lava from the same vent and then it can collapse because of the very high, very high pressure and also very high, let's say column conditions, column stress conditions within the carapace or the uppermost are also gone. And if you can calculate the things and so on, or estimate them that will be great to understanding of hazards of collapsing of the dome and generating that very hazardous flow. Well, now we would like to solve for some inverse problem. Using the shape shape of the lava dome. For example, there are different types of the lava dome. Here it is from the work of the one of the group of the volcanologists from UK, and they started the specific domes in the field, and you see such kind of lava domes which they sometimes call the walls, not walls, it's obelisks, you know. And because because they look like obelisks, you know, that's that's what we did recently the last year, published this modeling, and you see that it's in the form of the obelisks, you know, the going up one. And here it is a rather less viscous part of the internal of this but on the surface it becomes a very viscous part or the carapace here. You know there is this is another structure and also here model structure, this is the third type of the structure also remodeled this way, but the point is the following, if you have a s zero as a shape of the observed dome. You know, here is on one side of the left hand side is observe and you have a shape of model flow for lava dome here, but this model lava dome shape depends strongly on viscosity. Then you can construct the your norm or your residual. Simply speaking, with respect and can minimize these difference with respect to viscosity. And this way we try to solve the inverse problem and to find the lava viscosity this way, just looking on my forge, look here on the left, look here on the top, on the right and help. This is correct or not, but well, it looks like exactly this. For example, the uppercase and looks like this, but this is this is where we need to understand what is the viscosity inside. Right. And for this aim, what we did. That is our approach very recently developed with just this year publish this is very recently development. And sorry, I didn't mention actually, this is a developed by the first author, which I thought here, it is a Ulias to Radoopsevashi with the basic calculations and so on. The point is that here, first of all, we developed a series of their based on the model of the lava dome evolution, which we use, and particularly again I don't show the all equations this time. But I would like just to mention it is a game that you can, I can give your exact reference you can go there to the paper and see these old details of the study, but the most important issue here is that we use the dependence viscosity, which depends essentially on the principle of crystal content, meaning that it's crystals plays a principal role and crystallization is because of the gas, the gas thing when they say magma moves to the top of the surface it start to the pressure drops down this becomes the gases that start to go away and with this the crystallization start to play a very essential role and when it comes to the surface is already rather crystallized. That is why it is not a flow immediately down or slope like in the case of the lava flow, because already on the top there, the lava is quite high. It's around 10 to the 10 Pascal second something like 10 to the nine at the beginning and then it grows up to the 10 to the 12, even 10 to the 15. Then consider lava viscosity as a control variable. Then the third part of the our approach is that we run a set of experiments depending on the control variable, meaning that the lava viscosity, which depends on the time. And we created very big database of morphological forms of the model lava dogs. And since it means we have a model, we develop many lava domes shapes, how they look like, it is, you know, going up, it is a more shaped like, for example, lobes like you showed, or it's a very seen it's called sometimes it's a pancake structure and so on. Anyways, we develop a many based on this principle control variable, meaning the lava viscosity. It means that the shapes, morphological shapes of the lava don't depends on the viscosity, and we are just going calculating calculating, and they're feeding the database. And we compare the observed lava dough morphology, we have some observations in the field, we take this a morphological shape, and we find such a model shape, which gives a really very close fit to the observed one. Meaning the game searching for the model lava shape lava don't shape, which fits or match the best way the shape of them observations. And similarly we consider this computer vision technique and I will show you what it means in a few slides later. It is can be considered as a part of the pattern recognition as a part of the, let's say artificial intelligence and so on. And related to machine learning can be taught this way, you know that's how how to distinguish fast way between these many many lava shapes which model develops. Actually model can be noted you need model can be different models, you know we use this viscosity we can use another this constant zone, but anyway, once we had that many of such kind of the models shape. We can use a computer vision technique to understand this which model model don't shape morphological shapes it's match the morphological shape of the. We consider the response of the model domain which shapes fit the shape of observed on in the best way that is our aim and it's we can tell about the our lava responsibilities and okay well this is a very fast again there is a set of equation which we use and I specifically highlighted this is the velocity which as already I show depends on the flow and indeed depends on the fee is content of the crystals. And this is a model like that it is the lava is going through the. When it's on the top of the surface become lava and to the air and start to develop the lava don't hear again in the some cases it's a common the top on the surface, very low viscosity and it flows down and it's creates a lot of flow, but when it's a viscosity is high, then it creates a door. It's like a big don't solve what I showed you here I already show they said you initial they say how we calculate but in this specific case, we consider more complicated they say equation by replacing the fee, which are found in the previous case through temperature. We consider in kinetics equation, meaning that they say we consider how we really understand the change or with time of the crystal content content using this equation. And how is called sometimes it is a so called is characteristic. Actually the cold sometimes is the relaxation time, but it is a characteristic time of the crystal content growth, meaning that it's the we know this characteristic time, for example, that we know that within the five days crystals reach this level. Okay, always like that. And that's that's a fee equal equilibrium here meaning that it's a fee cannot be actually in the nature equals one one actually means that it's everything is already crystal there is no any fluid there is no analog everything is crystallized. But normally, even when we see a hard lava, they are inside they have something like 10% is not a fully crystallized material. And that's why equilibrium is something like 0.8 or 0.9 in between. This is a equilibrium so called the equivalence that's why in the volcano just tells that if you reach the equilibrium of the crystals that mean that it's you are almost done in terms of the crystallization of lava. So from one hour work it's just to show the different shapes of the lava, which depends on the viscosity indeed but as well as from this towel with the so called relaxation time, and also depends on the extrusion of the lava, meaning the rate of extrusion or in the volcanological community it's called discharge rate. It's what is the discharge of the lava on the top. This is just to show how this model works and how we use this model to generate a different shapes of the last different shape of morphological shape of last. Finally, we developed here I showed there's something like a 300 different cases with a different towel with a different radius of that with a different timescale steps, etc. We had all this information in there our data set. Now comes the most important issue that it's our examples, which we developed and this is a, we don't preserve all details for us, most important is only the top morphological shape why because in the field you don't know what is inside you would like to understand what is inside, but you know quite well the shape of your dome, how the dome looks like. Here is, as you know, a systematic problem because of the mathematical formulation. That's why it is just the half of the dome, but dome is like that you know it's another part is here, another part is here. This is a part of things because of that. Yeah, and here I indicated this word but actually it was accepted in 20 but published in 21. Now, that is a very important issue what we need when we are talking about the computer vision models. Here is some fun for you. When you were a little girl and little boy, you were interesting to look in the book, and then your parents gave you and told, look, where is there is a difference between these two, you know, the very identical pictures. You can find these differences. No. Okay, well, we are human. Yeah, we are very good and defined in finding the difference in pictures, especially if we are given that some type of things like that. And you can see that that is the first difference. I mark by red. Yeah, oops, sorry. And there is another difference also, etc. I don't show these all of them but it's a, you can find is a difference by difference and so on the top. Another one is a cloud. It's missing here, and here is a some some vegetation and so on. Anyway, anyway, that is something important what it means actually. It means that how to teach computer to recognize these differences. It is a part of this computer vision or the part of the pattern recognition or the part of the artificial intelligence which we use, but everything is actually based again on the inversions based on the inverse problems based on the let's say assimilation of some knowledge about this thing. And this is also the exciting word done by Wang at all in 2005, when he polluted the shape of the photo by as you see that's a famous Albert Einstein. And this is the original image. And they distort this original images with some technique. And then they try to recognize who is here. And this is again in the methods of the computer vision helps in doing so. And recognize it. It is one of the method which we use also for recognition differences between the model example and the real example in the first. Now you see the shape of our observed lava. Let's see that is the shape of observe lava. And this is what we are doing, first of all, we discretize our area where the shape is located. There are within the each small cell one if the area is covered by the lava dome and zero if the area is not covered. It means we know if we will take now out the shape we know that approximately and definitely it will depend on the discretization of the model domain, we will know where the lava is located. Here I described in some details of the how this way we are managing with these things and so on, but the most important issue now is to define this so called quality functions and the quality functions which would consider are three. For the first model we use a very simple one. It's called symmetric difference based functional. What it means actually, oops sorry, what it means actually it means that it's that we take it to the domains here look here. L star and here L star prime. And then we take difference, it should be prime. Yeah, we took the, I mean we take the both volumes of these domes and we take the intersection of these domes. And we create a function which we try again to minimize where the S is in meter square is the area of the domain for the L star is observed and L is a model. And that is a to guess how how they look they said that they are a shape and how it looks at the intersection of these shapes. It is a one of the simple method it's just that looking at how areas are fit each other, one and another. But it is the simplest way it's not sometimes gives a rather good result, but still alone alone. But we have another method it is a call the peak signal to noise ratio, and this functional is constructed this way it's more more complicated way but still is it possible, because what is PEG it means that it's exactly this is small cells, what is the value in the small cells one or zero, you know, you can insert here you calculate this functional, and then you can look at what which which of the model shapes give a better fit. Which minimize j to better, then you can tell okay well this model better characterize the present observed structure, and then we can look what is the structure internal structure of the. And the final one which I showed in the respect to the Albert Einstein image, which will disturb it is a structural similarity. And this is more based on the, you know, statistical and sorry, it's a probabilistic assessment of the possibility of the changing of the shape and so you know, here is introduced the expected values covariance is the dispersion, and to this is a more. Let's say it's not just based on the structure but based also on the similar, I mean, similarity structure similarity not only based on just observation of the difference between the shape. And the structural similarity, which tells about the what is the change of the curve itself, which is the morphological shape. Finally, we are doing the following for each, for example, we have here you see observed the dome, and here it's a different the shapes of the. What is the algorithm is doing is going through the all the set and select the best, which gives a rather good feet and how we are doing it's just looking at the functional j one j two j three. This is the j j one j two and j three, and the here it is a value of this functions of this functional, and this is a number of the model lava dome, and you see for some of them are for example here is a nine different. And for some of them the differences very big, telling that it is not the case for example this doesn't fit this one at all. And some of them, it's a fit it's a quite well. And that's why we can consider that this is a for gives a rather well as fit to their observations. We chosen the most appropriate which is a let's say 135 F 135. We can take this model. I can tell, look, we now know the level is possible this model, don't add it is a one of the best approximation to the shape of the, this shape of the lava base approximation for the shape of the observed dome. And that's why we can consider this lava viscosity as a target viscosity for the dome which we have as observations from observations, and this in this case, we can characterize the internal structure of the lava dome, because we know it is this case. Well, I think that is all what I wanted to tell you about these methods of the computer vision or tell the artificial intelligence or pattern cognition, I mean it's something which compare the observed shape with their model shape. And if you have a very big database, you can find the best that fit to the observations and you can tell that the viscosity inside is very close to the viscosity of what is fit observations. Well, that's the two books which I would recommend you if you are interesting to look in, and you will find there, within the right hand side on the right hand side, the book written together with the Russian mathematicians. And right mathematicians and pure mathematicians. It's about the data driven numerical modeling in geodynamics and some methodology and some application here. On the left hand side it is a book with what's published about in 2010, yes, 10 years ago, more than 11 years ago. And it is related to computational method which we use actually to solve the problems in geodynamics in data simulation and in inverse more problems and so on. I mean principle sets of the methods in use in geodynamics. Okay, that's all what I wanted to tell you thank you very much for your patient and for your attention. And now I will look at some questions but you can unmute and you can ask me any question please. Yeah, you are here thank you very much. Yeah, you didn't you didn't know that I will give the talk there is a problem because it's a Vasili is in Seattle and you are in US close to Seattle and you know that Seattle is out there. That's why I was late today we have the same issue here. Oh my God, I see, I see. Yeah, that's why I jumped in and you know it's instead of morning. Thank you. Thank you. Yeah, I'm just, I'm just noticing that there is a question from Igor Collins in the chat you might want to start with this one. Yes, could you because it's I don't see it says why equation doesn't take into account the friction forces, since we know that lava is a viscous fluid. Yes, well, that is a very good question actually there is some other investigations we didn't use a friction forces friction low at the bottom of the lava and the friction on which the lava flow. But there are some, so we just use the no sleep condition. Now which is appropriate in many models of the flow lava flow at the same time that is also is the possibility to introduce a friction low and this gives a something. In between the free sleep condition and the no sleep condition. It's a some burn we did such kind of investigation to understand the how it looks but in some simple cases, when the lava just a flow gravitationally I mean it's a result of the heat equation there. And the how it propagates lava propagate in the terms of the no bound no sleep condition free sleep condition and the friction condition imposed on the topography on which the lava flow. There is some new. Thank you. There are more questions in the chat do you want me to read them or you can. Yes, please. Yeah, if you are. I need to know the best way to estimate the dumping station correction and seismic demographic conversion. You can see that it's the right question address to me. You know, I will I will tell it I don't know they say. What I mean is I cannot tell you as an expert about these things about dumping and so on, especially station correction, because it's I am not dealing with the seismic demographic inversion, but I can tell you that on Wednesday, yes, on Wednesday, please attend the lecture by Professor Fichtner from the it a hot Zurich, he is a one of the well known experts in the seismic photography imaging, and he understands these things quite well, and they say Andreas can tell you about these things about the inversions. It's called the solving large seismic inverse problem with smarter methods. He is a really one of the bright early carrier or meet meet carrier scientists who are dealing with such kind of things sorry I can't answer this is not topic of my research that's why it's a very specific question. Thanks. And another question from Igor Collins, can you share the code of the second part of your lecture. Yes, we can share the code but again they said you mean you mean it's a quote which is introducing the inversions this quote you mean. There are many codes there are many codes behind, you know the code for example for forward modeling is one part, but the code for the inverse modeling it's quite different but because it's a joint is added inside. And then there is all these things is done within their so called flu flu and software, but they are program which was written and incorporated in the fluid. For example, they cannot do a joint, you know, but we did it analytically we derived that joint, and then we inserted inside of the fluent this as an additional part for populations. That's why it is a notice something something like, you know, see C++ code or the it is in written in C++ but it is just a part of support, which is inserted in the main point which is a quote fluent or unsees fluent. You can search in the Internet and you can found it's a very useful code for fluid dynamics modeling. But definitely any code is limited by something what was written and placed inside, and there is no inverse problems inside of this code, but it's a very helpful to solve the forward models. That's why we insert the code inside of this, when we are solving this. Similarly this one it was a not a backward the time but this was this this for lava if you are speaking about this is for determining this boundary conditions, because it was some optimization of the conditions. Thank you, and you good it might be okay you get a sense that your answers his question nice. Thank you. You can just unmute yourself and ask questions if you have you don't have to put them in the chat. Anyone else. Now I understand because I have also a private chat with with one of the participants and I couldn't say now I understand the way how to do it. Some some people hesitate to ask you know, for everybody asked me directly. But anyway, it's a very good questions and so on and I answer also directly. Okay. Please any other questions to Alik. I see there is some activity in the chat but no direct questions. Tomorrow, by the way, it was really agreed that he will be speaking at the second part of the day but not from 15 to 17 as was planned my lecture but it will be shifted by two hours down to have. I mean his lecture will start at 5pm as a local time like today, like today exactly like today because it's because of him we shifted two hours down. I see. Yeah, you are working with your dynamics I have a question related to my results. Yes, go. You asked me something about seismic tomography and I told you, I did something which took to transfer the seismic tomography image to temperature, and I can tell you many things about it, but not exactly dealing with the station, you know the corrections and so on for the seismic tomography. I don't actually work with seismic tomography imaging. But if it is your questions related to geodynamics, please go ahead. I already explained or somebody asked this question about the responses of the processes processes responsible for all back. And, you know, there are several of them but it's one of the principle issue is the gravitational actually the slide. It means that it's a when it's a slap penetrates the, for example, the continental sorry, it's a oceanic slap goes below this continental sphere. It goes at some specific angle, it's not a penetrate, you know, perpendicularly, it's cool with some slow but we say when it's a progressing it's a flow it is a go down and because of the gravity forces, it starts to, you know, there's a slope of the let's say, top surface of the slap start to increase and this at some and this is increasing and also the movements here of the slap backward because of the, again, there's some generation of the crunch of this area. Again, it is a mostly comes from the some modeling. I personally didn't make such a modeling ID, but there are many issues with these are modeling. You know, this modeling should consider, for example, at this point where the trenches develop a some very specific condition. Otherwise, otherwise, your movements will be like that, and that is all, but not a retreating. That's why you need some specific conditions here and so on in the modeling to understand how it is and so on. It's not a simple things and also I got a senior plate on the top. Yes, you mentioned it. The top at the depths of 2025 after that 300. It goes into yes a correct correct you know why because you use a viscous material most probably not elastic but or visco elastic and so I don't know exactly but it looks like you know that when when you push, when you push some material here, and it is a viscous material. Because of the viscosity below, they start not to go straight down, but also it's a tackle at the, at the some, you know, the area and start to become to generate a like a bubble, you know, big bubble, that's why it becomes really sicker at some specific depths and so on. Probably that is the you meaning that it's it is worth seeing and then it after 10s. It's becomes rather sick. Maybe this this. Again, it's a you are giving us some short information we needed to see how you develop these things. And so, for example, I showed this some relics lab in branch region, and it's how we did modeling that is the same. Initially, it is a rather small. I mean, it's actually actually I did this modeling how many time years ago, but I remember it was just like a parallelepiped you know it's introduced and then it becomes a very seen on the top, and it is a rather seek down because of the gravitational flow. And because this was a very simple model of gravity flow. And that's why it showed that we steps it becomes a seeker. Yeah, exactly to mental flow it's related to me, and is there. Oh, sorry, I don't read it say can you please relate it to the mental flow yeah it is related to mental flow because it's within the mental flow it's a good but again it's I don't know they said rheology of the slap if it is a rheology of the slap also viscous rheology and the mental is also viscous that's exactly what you have to receive. It's nothing strange, but if it is a more nonlinear or different rheology let's say more elastic or plastic elastic and so on the development will be different. You are welcome. Okay. If no one if there's a question probably we can finish today's session, and also we can enjoy the evening or afternoon depending where you are. Let's say we will see each other tomorrow. Tomorrow we have a two lectures. The first lecture will be about the data simulation or volcanic clouds. I told you that it will be given by the but you know that all our speakers are in a critical situation. These are not. He's a really very, very good scientist and so on but he's on the top of the scientific hierarchy related to the disasters in the country in Spain. That's why he's every day was called to some, you know, emergency committee, planning committee meetings and so on. Actually, we last minute change his presentation to this day, because he promised to be free morning on Tuesday tomorrow. That's why I hope we will get our tomorrow and he will be speaking about this volcanic clouds which where he's expert but most probably also he will tell us something about the ongoing eruptions. They are also eruptions and clouds. They are because the clouds also were quite prominent in this during these actions. And the second will be evening. Early evening presentation lecture by my city. Hey, that is all. Okay. Just enjoy your evening. Goodbye. Thank you very much. Thank you again. Thank you. Bye bye. Thank you.