T. Geenen - Academia.edu (original) (raw)

Papers by T. Geenen

To provide insight in the geodynamic evolution of converging lithospheric plates and to allow for... more To provide insight in the geodynamic evolution of converging lithospheric plates and to allow for the interpretation of various types of observational data, geophysical, geodetical and geological, we developed a 4D (space-time) numerical mantle convection code. The model is based on an spherical 4D Eulerian fem model on top of which we constructed a 4D Lagrangian particle in cell (PIC) method. We use the PIC method to transport material properties and to incorporate a viscoelastic rheology. We present preliminaire results of a 4D subduction model, focussing on the role of viscoelasticity and the evolution of the stress and strain fields, in a deforming subducting slab.

Solid Earth, 2014

The level set method allows for tracking material surfaces in 2-D and 3-D flow modeling and is we... more The level set method allows for tracking material surfaces in 2-D and 3-D flow modeling and is well suited for applications of multi-material flow modeling. The level set method utilizes smooth level set functions to define material interfaces, which makes the method stable and free of oscillations that are typically observed in case step-like functions parameterize interfaces. By design the level set function is a signed distance function and gives for each point in the domain the exact distance to the interface as well as on which side it is located. In this paper we present four benchmarks which show the validity, accuracy and simplicity of using the level set method for multi-material flow modeling. The benchmarks are simplified setups of dynamical geophysical processes such as the Rayleigh-Taylor instability, post-glacial rebound, subduction and slab detachment. We also demonstrate the benefit of using the level set method for modeling a free surface with the sticky air approach. Our results show that the level set method allows for accurate material flow modeling and that the combination with the sticky air approach works well in mimicking Earth's free surface. Since the level set method tracks material interfaces instead of materials themselves, it has the advantage that the location of these interfaces is accurately known and that it represents a viable alternative to the more commonly used tracer method.

Journal of Geophysical Research: Solid Earth, 2014

No consensus exists on the tectonic evolution of the western Mediterranean since~35 Ma. Three dis... more No consensus exists on the tectonic evolution of the western Mediterranean since~35 Ma. Three disparate tectonic evolution scenarios are identified, each portraying slab rollback as the driving mechanism but with rollback starting from strongly different subduction geometries. As a critical test for the validity of each tectonic scenario we employ thermomechanical modeling of the 3-D subduction evolution. From each tectonic scenario we configure an initial condition for numerical modeling that mimics the perceived subduction geometry at~35 Ma. We seek to optimize the fit between observed and predicted slab morphology by varying the nonlinear viscoplastic rheology for mantle, slab, and continental margins. From a wide range of experiments we conclude that a tectonic scenario that starts from NW dipping subduction confined to the Balearic margin at 35 Ma is successful in predicting present-day slab morphology. The other two scenarios (initial subduction from Gibraltar to the Baleares and initial subduction under the African margin) lead to mantle structure much different from what is tomographically imaged. The preferred model predicts slab rotation by more than 180°, east-west lithosphere tearing along the north African margin and a resulting steep east dipping slab under the Gibraltar Strait. The preferred subduction model also meets the first-order temporal constraints corresponding to Mid-Miocene (~16 Ma) thrusting of the Kabylides onto the African margin and nearly stalled subduction under the Rif-Gibraltar-Betic arc since the Tortonian (~8 Ma). Our modeling also provides constraints on the rheological properties of the mantle and slab, and of continental margins in the region.

Solid Earth Discussions, 2012

Subduction modelling in regional model domains, in 2-D or 3-D, is commonly done using closed, ver... more Subduction modelling in regional model domains, in 2-D or 3-D, is commonly done using closed, vertical boundaries. In this paper we investigate the merits of using open boundaries for 2-D modelling of lithosphere subduction but with implication for 3-D modelling. Open sidewalls allow for lateral in-and outflow consistent with the internal 5 dynamics of the model and may simulate the real-mantle environment of subduction much better than closed boundaries, which induce return flows. Our experiments are focused on using open and closed (free-slip) sidewalls while comparing results for two model aspect ratios of 3:1 and 6:1. Slab buoyancy driven subduction with open boundaries immediately develops into strong rollback with high trench retreat velocities. Man-10 tle asthenosphere flow forced by rollback is predominantly laminar and facilitated by the open boundaries. In contrast, free-slip sidewalls proof restrictive on subduction rollback evolution unless the lithosphere plates are allowed to move away from the sidewalls. This, however, initiates return flows pushing both plates toward the subduction zone speeding up subduction. Increasing the aspect ratio to 6:1 does not change the overall 15 flow pattern when using open sidewalls. Again, in contrast, for free-slip boundaries, the slab evolution does change with respect to the 3:1 aspect ratio and does not resemble the 6:1 evolution obtained with open boundaries. We notice a general drop in the amplitude of mantle flow when changing to the 6:1 aspect ratio, which is caused by the increasing shear friction between mantle and lithosphere while the driving slab buoyancy 20 is the same. Based on energy-dissipation arguments we applied a flow speed scaling to convert between flow fields of different model aspect ratios. This proved succesful for the open boundary model. We have also investigated the effect of far-field stress conditions in our open boundary models. Applying realistic normal stress conditions to the strong part of the overriding plate we show that "intra-plate" stresses control sub-25 duction dynamics resulting in slab roll-back, stationary or advancing subduction. We conclude that open boundaries are to be preferred for modelling subduction evolution (rollback, stationary or advancing). The relative independence of model aspect ratio 708 SED 4, 2012 avoids the need to place sidewalls at large distance and allows to focus all computational resources on a smaller modelling domain. Open boundaries simulate the natural subduction environment better and avoid the adverse effects (e.g. forced return flows) of free-slip boundaries.

Lecture Notes in Earth System Sciences, 2013

ABSTRACT Being able to accurately model the free surface of the Earth is important for nearly all... more ABSTRACT Being able to accurately model the free surface of the Earth is important for nearly all geodynamical problems. Importantly, free surface deformation is coupled to vertical motions and therefore allows for selfconsistent modelling of topography build up. Such modelling allows for additional prediction from numerical models which can be compared to real Earth observations. When using an Eulerian framework, modelling the free surface is not straightforward and the so called "sticky air" approach is often used in which the "air" is modelled as a zero density fluid which has sufficient thickness (~100km) and a low viscosity compared to the underlying crust-mantle system (~5 orders of magnitude less, e.g. Crameri et al 2012). Tracers are commonly used to account for the tracking of all materials and interfaces. We here propose to use the level set method to track the interface between the crust and the air as a simulation of the free surface. The level set method represents a n-dimensional interface by a (n+1)-dimensional function chosen to be zero at the interface and it is mathematically described as a smooth (signed-distance) function. The target interface coincides with the zero-level set and its location can be traced through time by solving the advection equation for the level set function and subsequently locating the zero-level set every time-step. The level set method has several advantages over tracers, namely 1) with the level set method the exact location of the interface is known, 2) the exact distance of every point in the domain to the interface is known and 3) it is computationally less expensive compared to using tracers (particularly in 3-D applications). We will show results of benchmarks and 3-D numerical subduction models which contain multiple level sets representing the free surface and selected internal surfaces. This research is funded by The Netherlands Research Centre for Integrated Solid Earth Science (ISES).

ABSTRACT Since ~30Ma ago the westernmost Mediterranean region (Betic-Rif-Alboran region) has unde... more ABSTRACT Since ~30Ma ago the westernmost Mediterranean region (Betic-Rif-Alboran region) has undergone a long and complicated subduction evolution comprising rollback and lithosphere tearing processes. A number of geodynamic reconstructions have been proposed for this region which differ in length, position, and width of the initial subduction zone, as well as in the initial amount of the subducted slab, position of transform faults, the major direction of slab rollback, or even in initial direction of the subduction. Proposed tectonic reconstructions are purely kinematic based on plate reconstruction and describing the motions of subduction trenches and geological fragments. Here we model the subduction processes that possibly underlie the tectonic reconstructions such as slab rollback, lithosphere tearing, back-arc opening and slab stagnation. Detailed seismic tomography images of this region allow us to compare our results of the 3D subduction modelling with the present day slab position and shape in the mantle which may help to discriminate between proposed tectonic reconstructions. We create a 3D numerical subduction model of the region incorporating rheological and paleogeographic data and corresponding to the past ~30Ma of tectonic evolution. We implement visco-plastic rheology consisting of diffusion and dislocation creep using a stress limiter approach to control lithosphere strength in our model. Selective weakening of lithospheric material at continent-ocean boundaries is (optionally) used to allow for lithosphere tearing. To minimize the influence of the side-boundaries of the 3D model on the subduction process, we implement "open" side boundaries (Chertova et al. 2012). We use constraints from plate motion models to incorporate Europe(Iberia)-Africa convergence. The different tectonic reconstructions of the Western Mediterranean region are based on different interpretations of the initial lateral extent of the subduction trench and the initial amount of subduction at ~30Ma. We use this as initial condition on our modeling and predict present-day slab position and -geometry, which can be compared to the tomographic image of the slab. As the main result, we present a 3D numerical fully dynamic model of the evolution of this region, which correlates with geological, tectonic, paleogeography and seismic tomography data. We demonstrate that tectonic reconstructions based on initially short (~50-100 km) NW dipping subduction restricted to the Balearic margin shows a better correlation with present-day mantle structure than slab predictions from other reconstructions.

Physics of the Earth and Planetary Interiors, 2011

International Journal for Numerical Methods in Fluids, 2011

In this paper, we discuss various techniques for solving the system of linear equations that aris... more In this paper, we discuss various techniques for solving the system of linear equations that arise from the discretization of the incompressible Stokes equations by the finite-element method. The proposed solution methods, based on a suitable approximation of the Schur-complement matrix, are shown to be very effective for a variety of problems. In this paper, we discuss three types of iterative methods. Two of these approaches use the pressure mass matrix as preconditioner (or an approximation) to the Schur complement, whereas the third uses an approximation based on the ideas of least-squares commutators (LSC). We observe that the approximation based on the pressure mass matrix gives h-independent convergence, for both constant and variable viscosity. ON proper scaling factors. The Schur method is a good choice to use in high-viscosity contrast problems because it gives a more accurate solution at lesser cost than PMM and LSC D .

To provide insight in the geodynamic evolution of converging lithospheric plates and to allow for... more To provide insight in the geodynamic evolution of converging lithospheric plates and to allow for the interpretation of various types of observational data, geophysical, geodetical and geological, we developed a 4D (space-time) numerical mantle convection code. The model is based on an spherical 4D Eulerian fem model on top of which we constructed a 4D Lagrangian particle in cell (PIC) method. We use the PIC method to transport material properties and to incorporate a viscoelastic rheology. We present preliminaire results of a 4D subduction model, focussing on the role of viscoelasticity and the evolution of the stress and strain fields, in a deforming subducting slab.

ABSTRACT Our research is concerned with the establishment of links between deep mantle processes ... more ABSTRACT Our research is concerned with the establishment of links between deep mantle processes and surface deformation. Our main focus is on the instantaneous mantle dynamics of the European-Mediterranean region and its surface responses. Here we have constructed instantaneous 3-D dynamic models of the Western Mediterranean region with focus on subduction below Betic-Rif-Alboran region. The driving forces in the models are due to temperature variation, which is derived from seismic tomography. The tomography model, which is used in our research, is the global P-wave speed model UU-P07 (M. Amaru, PhD Thesis, Utrecht University, 2007; Van der Meer et al., Nature Geoscience, 2010). For the subducted slab in this region we have assumed a temperature profile according to the Jurassic-Early Cretaceous age of the oceanic lithosphere. The boundary conditions used in the dynamic models allow us to include constraints from motions of the larger tectonic plates regarding the convergence of African and Eurasian plates. We present the topography response and the predicted patterns of surface deformations for this region based on a number of assumptions regarding the scaling of tomography to temperature and density, and rheology. A depth and temperature dependent rheology is assumed for most of the domain. Lithosphere faults are modeled with low viscosity zones. The mesh-generating tool used enables us to have finer resolution at the scale of a few kilometers in fault zones and along plate boundaries in the area of interest. 1) This research is part of the EUROCORES TOPO-EUROPE, particularly of project TOPO-4D

To provide insight in the geodynamic evolution of converging lithospheric plates and to allow for... more To provide insight in the geodynamic evolution of converging lithospheric plates and to allow for the interpretation of various types of observational data, geophysical, geodetical and geological, we developed a 4D (space-time) numerical mantle convection code. The model is based on an spherical 4D Eulerian fem model on top of which we constructed a 4D Lagrangian particle in cell (PIC) method. We use the PIC method to transport material properties and to incorporate a viscoelastic rheology. We present preliminaire results of a 4D subduction model, focussing on the role of viscoelasticity and the evolution of the stress and strain fields, in a deforming subducting slab.

Solid Earth, 2014

The level set method allows for tracking material surfaces in 2-D and 3-D flow modeling and is we... more The level set method allows for tracking material surfaces in 2-D and 3-D flow modeling and is well suited for applications of multi-material flow modeling. The level set method utilizes smooth level set functions to define material interfaces, which makes the method stable and free of oscillations that are typically observed in case step-like functions parameterize interfaces. By design the level set function is a signed distance function and gives for each point in the domain the exact distance to the interface as well as on which side it is located. In this paper we present four benchmarks which show the validity, accuracy and simplicity of using the level set method for multi-material flow modeling. The benchmarks are simplified setups of dynamical geophysical processes such as the Rayleigh-Taylor instability, post-glacial rebound, subduction and slab detachment. We also demonstrate the benefit of using the level set method for modeling a free surface with the sticky air approach. Our results show that the level set method allows for accurate material flow modeling and that the combination with the sticky air approach works well in mimicking Earth's free surface. Since the level set method tracks material interfaces instead of materials themselves, it has the advantage that the location of these interfaces is accurately known and that it represents a viable alternative to the more commonly used tracer method.

Journal of Geophysical Research: Solid Earth, 2014

No consensus exists on the tectonic evolution of the western Mediterranean since~35 Ma. Three dis... more No consensus exists on the tectonic evolution of the western Mediterranean since~35 Ma. Three disparate tectonic evolution scenarios are identified, each portraying slab rollback as the driving mechanism but with rollback starting from strongly different subduction geometries. As a critical test for the validity of each tectonic scenario we employ thermomechanical modeling of the 3-D subduction evolution. From each tectonic scenario we configure an initial condition for numerical modeling that mimics the perceived subduction geometry at~35 Ma. We seek to optimize the fit between observed and predicted slab morphology by varying the nonlinear viscoplastic rheology for mantle, slab, and continental margins. From a wide range of experiments we conclude that a tectonic scenario that starts from NW dipping subduction confined to the Balearic margin at 35 Ma is successful in predicting present-day slab morphology. The other two scenarios (initial subduction from Gibraltar to the Baleares and initial subduction under the African margin) lead to mantle structure much different from what is tomographically imaged. The preferred model predicts slab rotation by more than 180°, east-west lithosphere tearing along the north African margin and a resulting steep east dipping slab under the Gibraltar Strait. The preferred subduction model also meets the first-order temporal constraints corresponding to Mid-Miocene (~16 Ma) thrusting of the Kabylides onto the African margin and nearly stalled subduction under the Rif-Gibraltar-Betic arc since the Tortonian (~8 Ma). Our modeling also provides constraints on the rheological properties of the mantle and slab, and of continental margins in the region.

Solid Earth Discussions, 2012

Subduction modelling in regional model domains, in 2-D or 3-D, is commonly done using closed, ver... more Subduction modelling in regional model domains, in 2-D or 3-D, is commonly done using closed, vertical boundaries. In this paper we investigate the merits of using open boundaries for 2-D modelling of lithosphere subduction but with implication for 3-D modelling. Open sidewalls allow for lateral in-and outflow consistent with the internal 5 dynamics of the model and may simulate the real-mantle environment of subduction much better than closed boundaries, which induce return flows. Our experiments are focused on using open and closed (free-slip) sidewalls while comparing results for two model aspect ratios of 3:1 and 6:1. Slab buoyancy driven subduction with open boundaries immediately develops into strong rollback with high trench retreat velocities. Man-10 tle asthenosphere flow forced by rollback is predominantly laminar and facilitated by the open boundaries. In contrast, free-slip sidewalls proof restrictive on subduction rollback evolution unless the lithosphere plates are allowed to move away from the sidewalls. This, however, initiates return flows pushing both plates toward the subduction zone speeding up subduction. Increasing the aspect ratio to 6:1 does not change the overall 15 flow pattern when using open sidewalls. Again, in contrast, for free-slip boundaries, the slab evolution does change with respect to the 3:1 aspect ratio and does not resemble the 6:1 evolution obtained with open boundaries. We notice a general drop in the amplitude of mantle flow when changing to the 6:1 aspect ratio, which is caused by the increasing shear friction between mantle and lithosphere while the driving slab buoyancy 20 is the same. Based on energy-dissipation arguments we applied a flow speed scaling to convert between flow fields of different model aspect ratios. This proved succesful for the open boundary model. We have also investigated the effect of far-field stress conditions in our open boundary models. Applying realistic normal stress conditions to the strong part of the overriding plate we show that "intra-plate" stresses control sub-25 duction dynamics resulting in slab roll-back, stationary or advancing subduction. We conclude that open boundaries are to be preferred for modelling subduction evolution (rollback, stationary or advancing). The relative independence of model aspect ratio 708 SED 4, 2012 avoids the need to place sidewalls at large distance and allows to focus all computational resources on a smaller modelling domain. Open boundaries simulate the natural subduction environment better and avoid the adverse effects (e.g. forced return flows) of free-slip boundaries.

Lecture Notes in Earth System Sciences, 2013

ABSTRACT Being able to accurately model the free surface of the Earth is important for nearly all... more ABSTRACT Being able to accurately model the free surface of the Earth is important for nearly all geodynamical problems. Importantly, free surface deformation is coupled to vertical motions and therefore allows for selfconsistent modelling of topography build up. Such modelling allows for additional prediction from numerical models which can be compared to real Earth observations. When using an Eulerian framework, modelling the free surface is not straightforward and the so called "sticky air" approach is often used in which the "air" is modelled as a zero density fluid which has sufficient thickness (~100km) and a low viscosity compared to the underlying crust-mantle system (~5 orders of magnitude less, e.g. Crameri et al 2012). Tracers are commonly used to account for the tracking of all materials and interfaces. We here propose to use the level set method to track the interface between the crust and the air as a simulation of the free surface. The level set method represents a n-dimensional interface by a (n+1)-dimensional function chosen to be zero at the interface and it is mathematically described as a smooth (signed-distance) function. The target interface coincides with the zero-level set and its location can be traced through time by solving the advection equation for the level set function and subsequently locating the zero-level set every time-step. The level set method has several advantages over tracers, namely 1) with the level set method the exact location of the interface is known, 2) the exact distance of every point in the domain to the interface is known and 3) it is computationally less expensive compared to using tracers (particularly in 3-D applications). We will show results of benchmarks and 3-D numerical subduction models which contain multiple level sets representing the free surface and selected internal surfaces. This research is funded by The Netherlands Research Centre for Integrated Solid Earth Science (ISES).

ABSTRACT Since ~30Ma ago the westernmost Mediterranean region (Betic-Rif-Alboran region) has unde... more ABSTRACT Since ~30Ma ago the westernmost Mediterranean region (Betic-Rif-Alboran region) has undergone a long and complicated subduction evolution comprising rollback and lithosphere tearing processes. A number of geodynamic reconstructions have been proposed for this region which differ in length, position, and width of the initial subduction zone, as well as in the initial amount of the subducted slab, position of transform faults, the major direction of slab rollback, or even in initial direction of the subduction. Proposed tectonic reconstructions are purely kinematic based on plate reconstruction and describing the motions of subduction trenches and geological fragments. Here we model the subduction processes that possibly underlie the tectonic reconstructions such as slab rollback, lithosphere tearing, back-arc opening and slab stagnation. Detailed seismic tomography images of this region allow us to compare our results of the 3D subduction modelling with the present day slab position and shape in the mantle which may help to discriminate between proposed tectonic reconstructions. We create a 3D numerical subduction model of the region incorporating rheological and paleogeographic data and corresponding to the past ~30Ma of tectonic evolution. We implement visco-plastic rheology consisting of diffusion and dislocation creep using a stress limiter approach to control lithosphere strength in our model. Selective weakening of lithospheric material at continent-ocean boundaries is (optionally) used to allow for lithosphere tearing. To minimize the influence of the side-boundaries of the 3D model on the subduction process, we implement "open" side boundaries (Chertova et al. 2012). We use constraints from plate motion models to incorporate Europe(Iberia)-Africa convergence. The different tectonic reconstructions of the Western Mediterranean region are based on different interpretations of the initial lateral extent of the subduction trench and the initial amount of subduction at ~30Ma. We use this as initial condition on our modeling and predict present-day slab position and -geometry, which can be compared to the tomographic image of the slab. As the main result, we present a 3D numerical fully dynamic model of the evolution of this region, which correlates with geological, tectonic, paleogeography and seismic tomography data. We demonstrate that tectonic reconstructions based on initially short (~50-100 km) NW dipping subduction restricted to the Balearic margin shows a better correlation with present-day mantle structure than slab predictions from other reconstructions.

Physics of the Earth and Planetary Interiors, 2011

International Journal for Numerical Methods in Fluids, 2011

In this paper, we discuss various techniques for solving the system of linear equations that aris... more In this paper, we discuss various techniques for solving the system of linear equations that arise from the discretization of the incompressible Stokes equations by the finite-element method. The proposed solution methods, based on a suitable approximation of the Schur-complement matrix, are shown to be very effective for a variety of problems. In this paper, we discuss three types of iterative methods. Two of these approaches use the pressure mass matrix as preconditioner (or an approximation) to the Schur complement, whereas the third uses an approximation based on the ideas of least-squares commutators (LSC). We observe that the approximation based on the pressure mass matrix gives h-independent convergence, for both constant and variable viscosity. ON proper scaling factors. The Schur method is a good choice to use in high-viscosity contrast problems because it gives a more accurate solution at lesser cost than PMM and LSC D .

To provide insight in the geodynamic evolution of converging lithospheric plates and to allow for... more To provide insight in the geodynamic evolution of converging lithospheric plates and to allow for the interpretation of various types of observational data, geophysical, geodetical and geological, we developed a 4D (space-time) numerical mantle convection code. The model is based on an spherical 4D Eulerian fem model on top of which we constructed a 4D Lagrangian particle in cell (PIC) method. We use the PIC method to transport material properties and to incorporate a viscoelastic rheology. We present preliminaire results of a 4D subduction model, focussing on the role of viscoelasticity and the evolution of the stress and strain fields, in a deforming subducting slab.

ABSTRACT Our research is concerned with the establishment of links between deep mantle processes ... more ABSTRACT Our research is concerned with the establishment of links between deep mantle processes and surface deformation. Our main focus is on the instantaneous mantle dynamics of the European-Mediterranean region and its surface responses. Here we have constructed instantaneous 3-D dynamic models of the Western Mediterranean region with focus on subduction below Betic-Rif-Alboran region. The driving forces in the models are due to temperature variation, which is derived from seismic tomography. The tomography model, which is used in our research, is the global P-wave speed model UU-P07 (M. Amaru, PhD Thesis, Utrecht University, 2007; Van der Meer et al., Nature Geoscience, 2010). For the subducted slab in this region we have assumed a temperature profile according to the Jurassic-Early Cretaceous age of the oceanic lithosphere. The boundary conditions used in the dynamic models allow us to include constraints from motions of the larger tectonic plates regarding the convergence of African and Eurasian plates. We present the topography response and the predicted patterns of surface deformations for this region based on a number of assumptions regarding the scaling of tomography to temperature and density, and rheology. A depth and temperature dependent rheology is assumed for most of the domain. Lithosphere faults are modeled with low viscosity zones. The mesh-generating tool used enables us to have finer resolution at the scale of a few kilometers in fault zones and along plate boundaries in the area of interest. 1) This research is part of the EUROCORES TOPO-EUROPE, particularly of project TOPO-4D