ORCID Profile
0000-0001-8746-5430
Current Organisation
University of Oxford
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Publisher: Copernicus GmbH
Date: 04-03-2021
DOI: 10.5194/EGUSPHERE-EGU21-7631
Abstract: & & It is broadly accepted that magmatism plays a key dynamic role in continental and oceanic rifting. However, these dynamics remain poorly studied, largely due to the difficulty of consistently modelling liquid/solid interaction across the lithosphere. The RIFT-O-MAT project seeks to quantify the role of magma in rifting by using models that build upon the two-phase flow theory of magma/rock interaction. A key challenge is to extend the theory to account for the non-linear rheological behaviour of the host rocks, and investigate processes such as diking, faulting and their interaction. Here we present our progress in consistent numerical modelling of poro-viscoelastic& #8211 lastic modelling of deformation with a free surface.& & & & Failure of rocks (plasticity) is an essential ingredient in geodynamics models because Earth materials cannot sustain unbounded stresses. However, plasticity represents a non-trivial problem even for single-phase flow formulations (Spiegelman et al. 2016). The elastic deformation of rocks can also affect the propagation of internal failure. Furthermore, deformation and plastic failure drives topographic change, which imposes a significant static stress field. Robustly solving a discretised model that includes this physics presents severe challenges, and many questions remain as to effective solvers for these strongly nonlinear systems.& & & & & We present a new finite difference staggered grid framework for solving partial differential equations (FD-PDE) for single-/two-phase flow magma dynamics (Pusok et al., 2020). Staggered grid finite-difference methods are mimetic, conservative, inf-sup stable and with small stencil & #8212 thus they are well suited to address these problems. The FD-PDE framework uses PETSc (Balay et al., 2020) and aims to separate the user input from the discretization of governing equations. The core goals for the FD-PDE framework is to allow for extensible development and implement a framework for rigorous code validation. Here, we present simplified model problems using the FD-PDE framework for two-phase flow visco-elasto-plastic models designed to characterise the solution quality and assess both the discretisation and solver robustness. We also present results obtained using the phase-field method (Sun and Beckermann, 2007) for representing the free surface. Verification of the phase-field approach will be shown via simplified problems previously examined in the geodynamics community (Crameri et al, 2012).& & & & Balay et al. (2020), PETSc Users Manual, ANL-95/11 - Revision 3.13.& & & & Pusok et al. (2020) 0.5194/egusphere-egu2020-18690& & & & & Spiegelman et al. (2016) 0.1002/2015GC006228& & & & Sun and Beckermann (2007) 0.1016/j.jcp.2006.05.025& & & & Crameri et al. (2012) 0.1111/j.1365-246X.2012.05388.x& & & & & & & span& & /span& & & & / & & / & & & & / & & / & & & & & & span& & /span& & & & / & & / & & & & / & & / &
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2014
DOI: 10.1137/130946678
Publisher: Copernicus GmbH
Date: 15-05-2023
DOI: 10.5194/EGUSPHERE-EGU23-16161
Abstract: Observations suggest that the oceanic lithosphere is shaped by dike intrusions and faulting in proportions that depend on the spreading rate (Carbotte et al., 2016). Yet it remains unclear how the interplay between magmatism and faulting during seafloor spreading affects mid-ocean ridge (MOR) axial morphology, fault spacing, and the pattern of abyssal hills (Buck et al., 2005, Huybers et al., 2022). Here we present two-phase flow numerical models of oceanic lithosphere extension that reconcile the nonlinear brittle behaviour of the lithosphere with mantle melting and magma transport through the lithosphere.& Fast-spreading ridges show symmetric normal faulting and axial highs, while slow-spreading ridges show an asymmetric fault pattern and axial valleys. Previous work has focused on explaining the MOR fault pattern by tectonic or magmatic-induced deformation. In the first scenario, faults result from tectonic stretching of the thin axial lithosphere during amagmatic periods (Forsyth 1992), while in the second scenario, dike-injection may create stresses that activate extensional faults (Carbotte et al., 2016). Current state-of-the-art models (i.e., Buck et al., 2005) use a single-phase formulation for the deformation of oceanic lithosphere in which a prescribed axial dike may accommodate both magmatic and tectonic extension. In these models, the fault pattern depends on M & #8211 the fraction of plate separation rate that is accommodated by magmatic dike opening. While M-models are able to explain a number of observations, M represents a simple parameterization of complex fracture dynamics of sills, dikes, and faults. In particular, M-value models neglect fault& #8211 dike interaction and other modes of melt transport and emplacement in the lithosphere (Keller et al., 2013).& Here we build a 2-D oceanic lithosphere extension model that incorporates a new poro- viscoelastic& #8211 viscoplastic theory with a free surface (Li et al., in review) to robustly simulate plastic representations of dikes and faults in a two-phase magma/rock system. We hypothesise that magma supply controls the pattern of dike& #8211 fault interaction in oceanic extension settings. We present simplified model problems to compare results with those from M-value models. These enable us to address the significance of M in terms of fundamental magma and lithospheric processes. We then focus on development of fault patterns, magma pathways and crustal production at fast-/slow-spreading ridges.& ReferencesBuck et al., 2005, Nature, doi:10.1038/nature03358.Carbotte et al., 2016, Geol. Soc. London, doi:10.1144/SP420.Forsyth, 1992, Geology, doi:10.1130/0091-7613(1992)020 :FEALAN .3.CO .Huybers et al., 2022, PNAS, doi:10.1073 nas.2204761119.Keller et al., 2013, GJI, doi:10.1093/gji/ggt306.Li, Y., Pusok, A., Davis, T., May, D., and Katz, R., (in review). Continuum approximation of dyking with a theory for poro-viscoelastic& #8211 viscoplastic deformation, GJI.
Publisher: Frontiers Media SA
Date: 22-08-2019
Publisher: Copernicus GmbH
Date: 04-03-2021
DOI: 10.5194/EGUSPHERE-EGU21-10306
Abstract: & & In the classical model, mid-ocean ridges (MOR) sit above an asthenospheric corner flow that is symmetrical about a vertical plane aligned with the ridge axis. However, geophysical observations of MORs indicate strong asymmetry in melt production and upwelling across the axis (e.g., Melt Seismic Team, 1998, Rychert et al., 2020). In order to reproduce the observed asymmetry, models of plate-driven (passive) flow require unrealistically large forcing, such as rapid asthenospheric cross-axis flow (~30 cm/yr) at high asthenospheric viscosities (~10^21 Pa.s), or temperature anomalies of & K beneath the MELT region in the East Pacific Rise (Toomey et al, 2002).& & & & & Buoyancy-driven flows are known to produce symmetry-breaking behaviour in fluid systems. A small contribution from buoyancy-driven (active) flow promotes asymmetry of upwelling and melting beneath MORs (Katz, 2010). Previously, buoyancy has been modelled as a consequence of the retained melt fraction, but depletion of the residue (and heterogeneity) should be involved at a similar level.& & & & & Here, we present new 2-D mid-ocean ridge models that incorporate density variations within the partial-melt zone due to the low density of the liquid relative to the solid (porous buoyancy), and the Fe/Mg partitioning between melt and residue (compositional buoyancy). The model is built after Katz (2010) using a new finite difference staggered grid framework for solving partial differential equations (FD-PDE) for single-/two-phase flow magma dynamics (Pusok et al., 2020). The framework uses PETSc (Balay et al., 2020) and aims to separate the user input from the discretisation of governing equations, thus allowing for extensible development and a robust framework for testing.& & & & & Results show that compositional buoyancy beneath the ridge is negative and can partially balance porous buoyancy. Despite this, models with both chemical and porous buoyancy are susceptible to asymmetric forcing. Asymmetrical upwelling in this context is obtained for forcing that is entirely plausible. A scaling analysis is performed to determine the relative importance of the contribution of compositional and porous buoyancy to upwelling, which is followed by predictions on the crustal thickness production and asymmetry beneath the ridge axis.& & & & & Balay et al. (2020), PETSc Users Manual, ANL-95/11-Revision 3.13.& & & & Katz (2010), G-cubed, 11(Q0AC07), 1-29, 0.1029/2010GC003282& & & & Melt Seismic Team (1998), Science, 280(5367), 1215& #8211 , 0.1126/science.280.5367.1215& & & & & Pusok et al. (2020), EGU General Assembly 2020, EGU2020-18690 0.5194/egusphere-egu2020-18690& & & & & Rychert et al. (2020), JGR Solid Earth, 125, e2018JB016463. doi. org/10.1029/2018JB016463& & & & & & Toomey et al. (2002), EPSL, 200(3-4), 287-295, 0.1016/S0012-821X(02)00655-6& &
Publisher: Copernicus GmbH
Date: 27-03-2022
DOI: 10.5194/EGUSPHERE-EGU22-5594
Abstract: & & It is broadly accepted that magmatism plays a key dynamic role in continental and oceanic rifting. However, these dynamics remain poorly studied, largely due to the difficulty of consistently modelling liquid/solid interaction across the lithosphere. The RIFT-O-MAT project seeks to quantify the role of magma in rifting by using models that build upon the two-phase flow theory of magma/rock interaction. A key challenge is to extend the theory to account for the non-linear rheological behaviour of the host rocks, and investigate processes such as diking, faulting and their interaction (Keller et al., 2013). Here we present our progress in consistent numerical modelling of poro-viscoelastic-viscoplastic (VEVP) flow. We show that a VEVP model with a new, hyperbolic yield surface can help to robustly simulate both shear and tensile modes of plastic failure in a two-phase system.& & & & & Failure of rocks (plasticity) is an essential ingredient in geodynamics models because Earth materials cannot sustain unbounded stresses. However, plasticity represents a non-trivial problem even for single-phase flow formulations with shear failure only. In two-phase systems, tensile failure of rocks can also occur due to an overpressured liquid phase. Robustly solving a discretised model that includes this physics presents severe challenges, and many questions remain as to effective solvers for these strongly nonlinear systems.& & & & An appropriate rheological model is required to meet this challenge. The most straightforward choice is a Maxwell visco-elasto-plastic model, but this leads to grid-scale localisation and hence mesh-dependence. To obtain mesh-independent shear localisation, we employ the visco-elasto-viscoplastic model by introducing a viscous dashpot in parallel to the plasticity element. Whilst this formulation has shown promise in regularising shear failures in a single-phase flow model (de Borst and Duretz, 2020), its incorporation within two-phase systems has not been examined. We will show that the linear Griffith criteria for the tensile failure can lead to convergence issues whereas a new, hyperbolic yield surface is proposed to resolve these numerical issues. This yield surface provides a smooth transition between the two modes of failure.& & & & The underlying PDEs are discretised using a conservative, finite-difference, staggered-grid framework implemented with PETSc (FD-PDE) that supports single-/two-phase flow magma dynamics. Here, we present simplified model problems using the FD-PDE framework for poro-viscoelastic-viscoplastic models designed to characterise the solution quality and assess both the discretisation and solver robustness. It has been observed that employing the hyperbolic yield surface improved the robustness in simulating plastic failures in both modes.& & & & & & & & & & strong& References& /strong& & & & & Keller, T., May, D. A., & Kaus, B. J. P., (2013). Numerical modelling of magma dynamics coupled to tectonic deformation of lithosphere and crust,& Geophysical Journal International, v195, 1406-1442, 0.1093/gji/ggt306.& & & & de Borst, R., Duretz, T., (2020). On viscoplastic regularisation of strain-softening rocks and soils. International Journal for Numerical and Analytical Methods in Geomechanics, v44, 890-903. 0.1002/nag.3046.& &
Publisher: American Geophysical Union (AGU)
Date: 07-2014
DOI: 10.1002/2013JB010906
Publisher: Copernicus GmbH
Date: 23-03-2020
DOI: 10.5194/EGUSPHERE-EGU2020-18690
Abstract: & & All ergent plate boundaries are associated with magmatism, yet its role in their dynamics and deformation is not known. The RIFT-O-MAT project seeks to understand how magmatism promotes and shapes rifts in continental and oceanic lithosphere by using models that build upon the two-phase flow theory of magma/rock interaction. Numerical models of magma segregation from partially molten rocks are usually based on a system of equations for conservation of mass, momentum and energy. One key challenge of these problems is to compute a mass-conservative flow field that is suitable for advecting thermochemically active material that feeds back on the flow. This feedback tends to destabilise the coupled mechanics+thermochemical solver.& & & & & Staggered grid finite-volume/difference methods are: mimetic (i.e., discrete differential operators mimic the properties of the continuous differential operators) conservative by construction inf-sup stable and & quot light weight& quot (small stencil) thus they are well suited to address these problems. We present a new framework for finite difference staggered grids for solving partial differential equations (FD-PDE) that allows testable and extensible code for single-/two-phase flow magma dynamics. We build the framework using PETSc (Balay et al., 2019) and make use of the new features for staggered grids, such as DMStag. The aim is to separate the user input from the discretization of governing equations, allow for extensible development, and implement a robust framework for testing. Any customized applications can be created easily, without interfering with previous work or tests.& & & & Here, we present benchmark and performance results with our new FD-PDE framework. In particular, we focus on preliminary results of a two-phase flow mid-ocean ridge (MOR) model with a free surface and extensional boundary conditions. We compare flow calculations with previous work on MORs that either employed two-phase flow dynamics with kinematic boundary conditions (i.e., corner flow, Spiegelman and McKenzie, 1987), or single-phase flow dynamics with free surface (i.e., Behn and Ito, 2008). In the latter case, the effect of magma is parameterised according to a priori expectations of its role.& & & & & & & & & & Balay et al. (2019), PETSc Users Manual, ANL-95/11 - Revision 3.12, 2019.& & & & Spiegelman and McKenzie (1987), EPSL, 83 (1-4), 137-152.& & & & Behn and Ito (2008), Geochem. Geophys. Geosyst., 9, Q08O10.& &
Publisher: Wiley
Date: 04-07-2020
Publisher: Copernicus GmbH
Date: 15-05-2023
DOI: 10.5194/EGUSPHERE-EGU23-14818
Abstract: Dykes are tensile fractures that rapidly transport magma from the hot, ductile asthenosphere across the cold, brittle upper lithosphere. They play an important role in tectonic extension settings by drastically reducing the force needed for rifting (Buck, 2004). Yet the balance of mechanisms that drive dyke propagation and how they promote rift initiation remain unclear. Here we investigate the physics of dyke propagation in a two-phase continuum model that can approximate both faults and dykes in an extensional tectonic setting.& & Dykes are fluid-filled fractures, typically modelled as discrete inclusions in an extended elastic continuum.& These models suggest that dyking is dominated by magma buoyancy and that its direction can be altered according to the competition between tectonic stress and the topographic load (Maccaferri et al., 2014). However, this method assumes a constant background stress field in the lithosphere during dyking. Therefore this method cannot capture the interaction between dykes and the long-term deformation of the lithosphere. To resolve this issue, dyking has been prescribed as a weak material in a continuum, one-phase rifting model in which dyking is included in the conservation of mass, momentum and/or energy (Liu and Buck, 2018). This method respects the scale separation between dyking and long-term dynamics, but still neglects the feedback of dyking on the stress field.We present a geodynamic model that incorporates a novel poro-viscoelastic& #8211 viscoplastic rheological formulation with a hyperbolic yield surface for plasticity. With this model, both dyking and faulting can be simulated consistently (Li et al., in review). We validate our theory by comparing the stress field at the tip of the dyke with that from the linear elastic fracture mechanics theory. We then investigate dynamics of dyking in a geodynamic rifting model. We show that dyking assists rifting and its localisation. First, it reduces the yield strength in the brittle layer as the pore pressure balances the compressive stress second, it promotes the development of near-surface normal faults localised in a relatively narrow rift region near the rift axis. We investigate the physics of dyke propagation with respect to the balance between buoyancy and tectonic forcing, and the effect of topography.ReferencesBuck, W .R., (2004). Consequences of asthenospheric variability on continental rifting. In Rheology and deformation of the lithosphere at continental margins, chapter 1, pages 1& #8211 . Columbia University Press. doi: 10.7312/karn12738-002.Maccaferri, F., Rivalta, E., Keir, D., and Acocella, V., (2014). Off-rift volcanism in rift zones determined by crustal unloading. Nature Geoscience 7, 297& #8211 . doi: 10.1038/ngeo2110.Liu, Z. and Buck, W. R., (2018). Magmatic controls on axial relief and faulting at mid-ocean ridges. Earth and Planetary Science Letters, 491:226& #8211 . doi: 10.1016/j.epsl.2018.03.045.Li, Y., Pusok, A., Davis, T., May, D., and Katz, R., Continuum approximation of dyking with a theory for poro-viscoelastic& #8211 viscoplastic deformation, in review of Geophysical Journal International.
Publisher: Copernicus GmbH
Date: 27-03-2022
DOI: 10.5194/EGUSPHERE-EGU22-4614
Abstract: & & The classic definition of plate tectonics suggests that mid-ocean ridges (MORs) are places of passive mantle upwelling driven by plate ergence, and that the oceanic lithosphere forms by conductive cooling away from the ridge. This model predicts the symmetry of the partially-molten region beneath the ridge axis, and the lithosphere thickening with age (i.e., half-space cooling model). New and classic observations show some inconsistency with these predictions. Here we present dynamic, two-phase flow numerical models of MORs that reconcile theory and observations by incorporating buoyancy-driven flow associated with temperature, composition and porosity.& & & & First, geophysical observations at various MOR segments indicate strong asymmetry in melt production, upwelling and seamount distribution across the axis at fast spreading centers such as the MELT region (Melt Seismic Team, 1998), intermediate-spreading centers such as Juan de Fuca Ridge (Bell et al., 2016) and the Mid-Atlantic Ridge (Wang et al., 2020), and slow-spreading centers such as the Mohns Ridge (Johansen et al., 2019). Passive flow models cannot explain this asymmetry, as they require unrealistically large forcing (Toomey et al., 2002).& & & & Second, both seismic and electromagnetic studies have inferred variations in the lithosphere-asthenosphere boundary (LAB) and plate thickness that do not monotonically increase with age (e.g., Rychert et al., 2020). Sublithospheric small-scale convection (SSC) is generally the preferred explanation of these oscillations (e.g., Parsons and McKenzie, 1978, Likerman et al., 2021). However, seismic anomalies cannot be explained using solely solid-state thermal variations. While other mechanisms have been proposed to match the sharp discontinuities in seismic data, small amounts of melt (1-5.5%) could be the most straightforward explanation (Rychert et al., 2021). Sub-plate partial melt could also explain the cause of intraplate volcanism or petit-spot volcanoes observed on the outer rise in some subduction centers (Hirano et al., 2006).& & & & & We show that melting-induced buoyancy effects may provide an explanation for both the asymmetric distribution of melt beneath the axis and LAB variations. Here, we extend our 2D mid-ocean ridge calculations to incorporate chemical (residue depletion) and thermal buoyancy, in order to investigate how the dynamics of melt generation and migration may influence small-scale convection at the LAB.& & & & We run two types of models: closer to the ridge axis, where melt is generated over an extended region, and further away from the axis, where active flow may induce small amounts of partial-melting. Results show that MOR models with both chemical and porous buoyancy are sensitive to background forcing and can readily induce asymmetry and small-scale, time-dependent convection beneath the axis. Melting and crystallization of enriched material leads to a dynamic LAB closer to the ridge axis. Models of older oceanic LAB are more susceptible to the influence of thermal instabilities, which can erode the lithosphere and limit the base of the ocean lithosphere from cooling.& & & & & & strong& References& /strong& & & & & Bell et al., 2016, DOI:10.1002/2016JB012990& & & & Hirano et al., 2006, DOI:10.1126/science.1128235& & & & Johansen et al., 2019, DOI:10.1038/s41586-019-1010-0& & & & Likerman et al., 2021, DOI:10.1093/gji/ggab286& & & & Melt Seismic Team, 1998, DOI:10.1126/science.280.5367.1215& & & & Parsons and McKenzie, 1978, DOI:10.1029/JB083iB09p04485& & & & Rychert et al., 2020, DOI:10.1029/2018JB016463& & & & Rychert et al., 2021, DOI:10.1016/j.epsl.2021.116949& & & & Toomey et al., 2002, DOI:10.1016/S0012-821X(02)00655-6& & & & Wang et al., 2020, DOI:10.1029/2020GC009177& &
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2018
DOI: 10.1137/14099718X
Publisher: American Geophysical Union (AGU)
Date: 2016
DOI: 10.1002/2015GC006061
Publisher: American Geophysical Union (AGU)
Date: 12-2019
DOI: 10.1029/2019GC008489
Location: United Kingdom of Great Britain and Northern Ireland
Location: United Kingdom of Great Britain and Northern Ireland
No related grants have been discovered for Richard Katz.