 Thank you very much to the conveners for the invitation to give this presentation on 3D computational modeling of lithospheric deformation, a stenospheric flow and deep melt generation with aspects. So this work has been collaborative with Dr. Sahiri Rajan arson. He's now a postdoc in New Mexico Tech. I'm Annual and Jen Ju, who's a postdoc in my group, John Nalaboff and Asanath Kwagalakwe. What I'm going to present today has been funded by NSF, particularly through a geoprisms grant and a grant through the EarthCube program. And I'm also using a code that's been developed by the computational modeling, the computational infrastructure for geodynamics. So my talk has five parts. I'm going to go through an introduction to aspects for those of you who are not familiar with it. And then I'll go through these three developments that have evolved in my group for lithospheric deformation, a stenospheric flow, and deep melt generation, and then I'll provide some conclusions. So what is aspects? It stands for advanced solver for problems in Earth's convection. NSF CIG code. It's a finite element code. And it's very much a community code that evolves over time. There's even a hackathon going on right now, I believe, according to all of the GitHub alerts I'm getting in my email. And then it builds upon deal two, trillinos and P4s libraries, and it has many applications. So it started from mantle convection on Earth, but it's been applied to Mars and Venus. And then in my group, we've done lithospheric deformation and melt generation. So aspect solves the stokes equations for velocity and pressure, particularly the conservation of momentum and conservation of mass. These are for the compressible flow equations. But I'm going to show a couple of examples that actually use the extended Boozan-esque approximation. In aspect, coupled to the stokes equations is the energy equation to solve for temperature, and you have some options as to which parts of the energy equation you want to solve for. So if you wanted to do internal heat production, you could turn that on or off, viscissure heating, adiabatic compression of material, and then latent heat, which is really important if you want to do melt generation. So if you want to use aspect, there's several ways you can get a hold of it. The screenshot to the right is for the actual CIG page. So you can get the release version through the CIG page itself. There's also the development version. So if you wanted to extend aspect yourself for maybe surface processes, you can get that through GitHub. There's also all of the other versions as well through GitHub. And then for people who extend aspect, sometimes they will do Zenodo or GitHub extensions and make their code available through those resources as well. Okay, so lithospheric deformation. I think this will be the most, the component that's most probably applicable to this group, because we are involving the surface. The work that was published last year in GRL. And we have made the code open access through Zenodo by linking it with our GitHub repository. So all you have to do if you wanted to use this model is download the zip file, compile aspect, and all the files are available for reproducing this work. And it was led by Dr. Sahiri Rajanarsan. So if you wanted to use this model, you need to set up your lithospheric structure. In this particular region, we applied it to East Africa. We decided to use synthetic lithospheric structure, which was based on three seismically constrained models. And the specific regions are shown down here at the bottom. We also have the ability to read in crustal structure. So you can use, we used crust 1.0. So you can have a base of the upper crust, a base of the middle crust and a base of the lower crust. So these are all constraints that you can, you can use yourself. Then for the temperature condition. We used a steady state conductive geotherm for the surface down to the base of the lithosphere. We constrained lithospheric thickness and surface heat flow for the key tectonic regions, and shown here on the left is the crotonic domain. In the middle is mobile belts and then the right is the rift domain. So these are showing temperature profiles, so temperature along the x axis and depth along the y axis. So these are for the conductive geotherm for three different domains. Below the, below the lithosphere we have the temperature increase adiabatically. So that's an option you can choose yourself. For the density structure for this model, we assume isostatic compensation at 100 kilometers depth. And so we do that by constraining the mantle lithospheric density to be laterally varying so that we so that the system is isostatically compensated. So in this figure to the left, it's the mantle lithospheric vertically average density. If it's a red color it's a lower density if it's a blue color it's a it's a higher density. For the crust we used input from crust 1.0 again. So we had three different layers in the crust density in the upper crust middle crust and lower crust, and in these figures to the right. If it's a red color it's a lower density if it's a blue color it's a higher density. For the viscosity setup, it's realistic to the best of our ability. For the crust it combines nonlinear quartzite dislocation creep with plastic failure. Again, this is probably the most relevant for this community because you would be able to couple this with surface processes if you wanted to extend this model. In the mantle lithosphere we have dislocation creep with plastic failure, and then the sub lithosphere mantle. It's on its composite rheology so a harmonic average of diffusion and dislocation creep. This is a 3D model of the East African rift area and surroundings. If it's red it's a lower viscosity and you can see that we did capture the asthenosphere in this red region through here. We also imposed some deforming zones based on some work I did in 2018. Okay, so I wanted to show you just a quick example of applying this model to an area and what you could determine. We found that lithospheric buoyancy forces so this is a model that constrains the density of the lithosphere. We did find that it primarily can explain east west extension across East Africa, and the figure to the left is showing in red modeled velocities and in yellow, a kinematic velocities constrained by GPS. We found that lithospheric buoyancy forces are aligned with the kinematic predictions, and then additional forces for regions and deforming zones which is the figure shown to the right. These are actual GPS velocities in the deforming zones. Those are not well explained by lithospheric buoyancy forces alone. So, we would need to invoke some other process like mantle tractions to explain those. So that was my example for lithospheric deformation. Let me show you an extension for asthenospheric flow. This was also published a couple years ago in 2020 by Dr. Tahiri Rajanarsan. And this one is not on Zenodo it's actually built into the release code of aspect so if you downloaded the development version or the release version you could get you could reproduce this work. So for this initial temperature, the initial temperature conditions, we also impose a lithospheric structure. The figure to the right is a lithospheric model for Madagascar and surroundings from the Fishwick 2010 model. If it's blue it's thick lithosphere if it's red it's a thinner lithosphere. We impose an approximately approximate conductive geotherm for the lithosphere. So we start at a constant temperature of 273 or 293 whatever you choose at the surface and produce a linear gradient down to the base of the lithosphere. Below that it's approximately adiabatic and so this one was 0.5 Kelvin per kilometer. And then this is a 3D representation of that initial temperature condition for Madagascar and surroundings. The red colors are hotter temperatures and blue are the cooler temperatures. For the viscosity and density setup for this particular model you we chose a rigid lid model so the lithosphere is high viscosity. We had composite rheology for sublithospheric mantle. The figure to the left is a 3D representation of our viscosity model for Madagascar and surroundings. And then on the left it's showing profiles through the viscosity structure for a thin lithosphere and red and a thick lithosphere and blue. The density is temperature dependent below the lithosphere. So our case study for this particular model extension was from Madagascar. These are figures showing slices through deeper deep parts of the model. So at 175 kilometers depth and 200 kilometers depth the one on the right is 200 kilometers. If it's a blue it's showing downwelling if it's red it's showing upwelling and the yellow vectors are showing horizontal velocities. So we calculated esthenospheric flow. I'm going to show you a profile through this region. So you can see what the model looks like in depth. And these are for two different time steps aspect is time dependent so you can run it forward in model time. The profile at the top is showing as an instantaneous model and the profile at the bottom is showing a model after 35 million years showing that this type of convection is stable. And what we call this type of convection is lithospheric modulated convection, because it's purely constrained by the structure of the lithosphere, the initial temperature condition is. And in the background here we have temperature. So blue is the cooler temperatures and the redder colors are hotter temperatures. So for this particular project I can't go into all the details but I'm more than happy to discuss it after the talk. So we find that lithospheric modulated convection produces produces a flow field, and we also did mantle wind modeling. So we imposed boundary conditions to test different flow fields. And then we predicted shear wave splitting parameters and found that they had an esthenospheric source and Madagascar and they could be produced by lithospheric modulated convection. Finally, by using the composite rheology we found that dislocation creep extends into the upper esthenosphere beneath continental regions, particularly in Madagascar. So this map here is showing the ratio of dislocation creep to diffusion creep. And so if it's red it's dislocation creep if it's blue it's diffusion creep. My last example is deep melt generation, which may or may not be as relevant for this community but I hope that maybe you know you could extend this it may be useful for you at some point. So this one's also published last year in JGR, and it's available through Zenodo open access. So the initial temperature setup is very similar to the one I just showed you, we use a lithospheric structure, and this one in particular we applied it to the Malawi rift in East Africa. We have an approximate conductive geotherm from the surface to the base of the lithosphere, and then adiabatic geotherm an adiabatic increase in temperature below the lithosphere. This is a 3D representation of of the Malawi rift region of our initial temperature condition. Blue is a cooler temperature and red is hotter temperature. In viscosity we also impose the rigid lid assumption, but someone could easily couple this to our lithospheric deformation model and have it deforming as well. And then below the lithosphere we did the harmonic average of dislocation creep and diffusion creep for a composite rheology system. And then this is a 3D representation of our viscosity structure. The blue is showing the rigid lid model and then below that we have laterally varying viscosity. Now this model than the previous one I just showed you for a stenospheric flow is how we calculate density and how we allow for melt generation. So the lithospheric density is fixed, but below the lithosphere it is pressure and temperature dependent, and we can calculate density for melt and solid regions. And then on the right we have the melt fraction equation so we're able to determine and differentiate if the if the temperature crosses the solid is or not and if it crosses the liquid is or not. So whether the part of the model actually meets the conditions for melting. So again we applied this to the Malawi rift. The figure to the left is showing in the white dashed lines that's that's the outline of the Malawi rift. And then in the northern part is a place where we had melt generation, which is very close to the Rungway volcanic province. So it figures to the right or a profile through this region at different time steps, and then there's some insets that highlight where we found melt generation, very near the Rungway volcanic province. So some key conclusions from this particular paper are the lithospheric modulated convection does produce melt beneath the Rungway volcanic province. So it should entrain plume material and this work suggests that a plume is necessary beneath the Rungway volcanic province to produce these conditions for melt. So again I can't go into the details but I'm more than happy to discuss this work afterwards. To summarize, I've shown you three developments in aspect, some some extensions to do lithospheric deformation, a cynospheric flow and deep melt generation. I showed you a couple of examples about the East African rift, where lithospheric buoyancy forces can be used to explain rigid plate motions. I showed, I showed you a Madagascar example, where dislocation creep extends into the upper asthenosphere, and then the Malawi rift where we found lithospheric control and melt generation beneath the Rungway volcanic province. So all of these are available open access through a note or within the development code of aspects, and I'm happy to take any questions at this point. Thank you. Two questions, if you don't mind. One, one technical and one sort of bigger picture, the technical one is just how long do these integrations usually take when you run, I guess you run them on an HPC. The more conceptual one is, can you tell us a little bit more about the asthenospheric flow examples and how they impact the surface. Because it looks like you were seeing millimeter to two millimeter a year vertical rates plus and minus, and over what kind of spatial length scale does that usually happen. So for the technical question, it varies depending on how long we're running the model and model time. Some of them can take up to a week, some of them just a day. So that's the kind of the range and yes they are on high performance computing machines. And if we're running a low resolution models, we can do them in an hour or so, you know, for just testing out. We're doing quick experiments for the general question. So the asthenospheric flow example that I showed it's lithospheric modulated convection and it is pretty slow. It's kind of like secondary convection of the mantle right below the lithosphere. And we've seen rates up to like three centimeters per year. Yeah. I have a question to you. I have to as well. And one is very outside the field question I think I remember what dislocation creep is but do you tell us what diffusion creep is diffusion creep is usually a rheology that's input that happens in the deep mantle from here, what we what we know about. It's linear, and it, it's not non linear rheology like dislocation creep, but diffusion creep is like. Anyway, it's, it's mostly imposed in deep mantle structure. And it's, yeah, that's, that's going to be my general explanation for that one. What is the mechanism behind that. I think it's, it's not grain boundary sliding. I think it's where at the atomic level. You actually have a replacement of the atoms. And it's actually replacement not sliding. Thank you. You're welcome. And another perhaps dummy question, but I think I learned something big and new today. You showed that the structure of the lithosphere can induce a scenospheric motion so that stretching and thinning of the lithosphere could cause the upwelling and divergence of flow that could feed back on stretching and thinning of the lithosphere is that a feedback like it seems like it would be well that what you're describing is like passive upwelling. Yeah, if stretching and thinning of the sphere is happening you can get, you can get upwelling just as a result of the thinning of the lithosphere and the asthenosphere filling that space that occurs. But what we're doing is not actually thinning the lithosphere we keep the lithosphere rigid. So it's, it's truly just the temperature variations that it's so it's thermal convection just just do the structure of the lithosphere. But would that then tend to cause thinning of the lithosphere and reinforcing the process. Yeah, if you allow the lithosphere to deform. Yes. Thank you so much. That was amazing. I already saw one talk before, like one of your talk before and this was different but also so good. Thank you. So my question is, can we apply this type of models to subduction zones and change like the angle of the selection zone and see how that change topographic, like a long lithosphere, like the crystal lithosphere and like change it with the ocean. Like, can we model that to in this. Absolutely. Yeah, there's a lot of people that use aspect to model subduction. Yeah, absolutely. Hello, great talk. So I want to expand on that question so dislocation creep or diffusion creep. These are kind of very micro scale processes be observed on in minerals or on grains. So what all assumptions go when you're extending these concepts to understand more macro scale conviction processes. I think your question was like what kind of assumptions go into the rheology, essentially. Yeah, so like since. Yeah, so like we have to make a lot of assumptions about the material parameters. You know is it dry olivine or is it wet olivine. Is it in the crust is it dry distilled is it dry quartzite or wet quartzite so we have to make some some important assumptions about that. So we've, we've in the past chosen dry olivine for the deep mantle or for the sublative spirit mantle, and that makes convection slower. If we use wet olivine it would make it faster. So those are some important assumptions we have to make and choices we have to make, and we'll do that based on the tectonic setting. So if we were in a subduction zone setting it would be more appropriate to use wet olivine, but in the continental area far from subduction we we feel that dry olivine is the more appropriate material parameter.