Modelización físico-numérica 2D y 3D de procesos de subducción. Influencia de las características de las placas superior e inferior y de la interacción con el flujo mantélico
Resumen Abstract Índice Conclusiones
Juan Rodríguez González
2014-A
RESUMEN TESIS DOCTORAL
Modelización físico-numérica 2D y 3D de procesos de subducción. Influencia de las características de las placas superior e inferior y de la interacción con el flujo mantélico.
En la primera parte de este documento se realiza un resumen de los contenidos la tesis y en la segunda parte se enumeran brevemente las aportaciones principales de la misma.
1.Resumen contenidos
Introducción
La dinámica del hundimiento de litosfera en las zonas de subducción ejerce un control importante en la evolución del sistema manto-placas tectónicas. En consecuencia, se han desarrollado durante las últimas décadas una gran cantidad de estudios centrados en diferentes tipos de observaciones, así como en modelización analítica, en laboratorio y numérica. Sin embargo, algunos aspectos importantes del proceso de subducción aún no se comprenden bien, como es el caso de la contribución relativa de los diferentes factores que causan la variabilidad observada en los ángulos de subducción. Por ejemplo, cabría esperar que la litosfera joven, y por tanto relativamente caliente y poco densa, causara una flotabilidad negativa pequeña y en consecuencia su buzamiento fuese menor. Sin embargo, esto contrasta con el elevado buzamiento de la litosfera joven de la placa de Cocos bajo Centroamérica.
Además del torque gravitacional asociado a la flotabilidad de la laja (slab), interviene un torque de succión hidrodinámica generado por el flujo inducido en la cuña mantélica (entre el techo de la laja y la base de la placa superior). Este torque tiende a succionar la laja hacia arriba y disminuir su buzamiento. El balance entre estos torques controla el buzamiento resultante de la laja. Como punto de partida de este trabajo, se hipotetizó que el estado térmico de la placa superior debía ejercer un importante control sobre la estructura de viscosidad en esta cuña, y por tanto sobre el torque de succión hidrodinámica. Previamente a este trabajo de tesis doctoral, se había estudiado con modelos numéricos 2D el efecto del espesor de la placa superior, pero no se había realizado un estudio de los efectos del estado térmico de dicha placa en la dinámica de la subducción. Además, se observa comúnmente importantes heterogeneidades térmicas de la placa superior, tanto en dirección paralela como perpendicular a la fosa de subducción. El estudio de la influencia de estas heterogeneidades no se ha realizado en ningún estudio previo a esta tesis y requiere considerar una geometría 3D.
Objetivos
En esta tesis doctoral se desarrolla un estudio exhaustivo de la influencia del estado térmico de la placa superior. Se ha desarrollado modelos numéricos termo-mecánicos en 2D y 3D, con el objetivo de mejorar la comprensión de la dinámica de la subducción y de explorar diferentes factores que pueden jugar un papel importante en la geometría de la laja y el flujo mantélico asociado. Nos planteamos, además, los siguientes objetivos específicos.
•Analizar la influencia del estado térmico tanto de las placas superior y subducente en la geometría de la laja.
•Analizar la influencia de un hipotético flujo mantélico horizontal en la geometría de la laja y en la evolución a largo plazo de los procesos de subducción.
•Aumentar el realismo de los modelos incorporando las características 3D. En particular, nos planteamos analizar los efectos de las heterogeneidades térmicas de la placa superior y de la existencia de flujo alrededor de los bordes de la laja en la geometría de la misma y en la distribución de flujo mantélico resultante.
Resultados
Se ha aplicado el método de los elementos finitos para resolver el sistema de ecuaciones acopladas de conservación de la masa, momento y energía para un fluido incompresible. En los Capítulo 3 y 4 se ha desarrollado modelos en los que se fuerza cinemáticamente la subducción, utilizando el código comercial Comsol Multiphysics. Estos modelos predicen que la subducción bajo placas superiores viejas ocurre con ángulos menores. Este efecto es más importante para lajas jóvenes, además, resulta ser más importante y persistente en el tiempo que el de la edad de la placa que subduce.
Combinando diferentes edades de ambas placas, hemos sido capaces de reproducir un amplio rango de estilos de subducción: plana, de bajo y de alto ángulo. Deducimos que la subducción de la placa de Cocos bajo Norteamérica tiene un ángulo menor que bajo la placa Caribe debido al estado térmico mas caliente de la segunda.
El objetivo del Capítulo 4 es realizar un análisis sistemático de un flujo mantélico hipotético (ya sea global o regional) en el ángulo y en la evolución a largo plazo de la subducción. Se muestra que este flujo produce desviaciones notables de ángulo de subducción, incluso considerando lajas resistentes.
Finalmente, en el Capítulo 5 se desarrolla una serie de modelos 3D más realistas, donde la subducción es forzada dinámicamente por el propio peso de la laja, utilizando el código abierto CitcomS. El objetivo era generalizar los resultados de la geometría 2D y evaluar el efecto en la geometría de la laja y en el flujo mantélico de las variaciones a lo largo de la fosa del estado térmico de la placa superior. Estos modelos indican que la mayor succión hidrodinámica bajo la porción fría de la placa superior es suficiente para mantener a lo largo del tiempo las variaciones preexistentes del ángulo de subducción. Además, se muestra que esta succión variable es capaz de deformar lajas inicialmente uniformes, creando variaciones importantes de ángulo de subducción a lo largo de la fosa. Este resultado supone una aportación importante respecto a los modelos 3D recientes, en los que las variaciones de ángulo no se obtenían de manera autoconsistente, sino que eran impuestas y fijadas desde el principio. Debido a la variación de succión hidrodinámica y geometría de la laja, se crean intensas celdas de flujo horizontal en la zona donde cambia el estado térmico de la placa superior. Estas celdas producen una componente de flujo en la dirección paralela a la fosa, lejos de los bordes de la laja, que además no está relacionado con el flujo alrededor de estos bordes.
Cuando se añaden placas laterales en estos modelos 3D, se permite que el material del manto fluya alrededor de los bordes de la laja, lo que genera amplias regiones de flujo paralelo a la fosa, por debajo y por encima de la laja.
A los largo de todos los capítulos, se ha comparado en términos cualitativos los resultados obtenidos con ejemplos reales de zonas de subducción. En particular, se ha discutido las variaciones del ángulo de subducción observadas en las zonas de Centroamérica y Sudamérica en relación con los factores estudiados.
Discusión y Conclusiones
En los modelos desarrollados en esta tesis, se ha realizado simplificaciones para poder aislar los efectos que se deseaba estudiar. Una simplificación importante ha sido imponer una posición fija del límite de placas. En este sentido, una mejora futura que se espera introducir es permitir el movimiento de este límite, lo cual aumentará el realismo de los modelos. Otra mejora que permitirá la comparación directa de las predicciones con los datos de anisotropía sísmica es calcular las direcciones de propagación rápida de ondas de cizalla a partir de las predicciones de distribución 3D de flujo mantélico. La aplicación futura de los modelos al estudio de zonas concretas de subducción permitirá validar y perfeccionar estos modelos.
En esta tesis hemos extraído las siguientes conclusiones:
•Las placas de mayor edad son más densas y por tanto están sometidas a un torque gravitacional mayor. Como consecuencia, subducen con un mayor ángulo que placas jóvenes.
•El material del manto bajo una placa superior vieja es más frío y por tanto la succión hidrodinámica es mayor. Como consecuencia, el ángulo de subducción es menor.
•La influencia del estado térmico de la placa superior en el ángulo de subducción es más importante y persistente que la del estado térmico de la placa que subduce.
•Las predicciones son consistentes con las variaciones del ángulo de subducción de la placa de Cocos. La subducción plana o de bajo ángulo se relaciona con la litosfera fría de Norte América, mientras la subducción de alto ángulo se relaciona con la litosfera más caliente de la placa del Caribe.
•Existe una fuerte influencia del flujo mantélico horizontal en la dinámica a largo plazo de la subducción. Para un flujo en el mismo sentido que la subducción el ángulo disminuye con el tiempo, pudiendo dar lugar al acoplamiento de las placas y al cese de la subducción.
•Hemos desarrollado modelos 3D que incluyen geometrías, condiciones de contorno y reologías más realistas.
•La mayor succión bajo las porciones frías de la placa superior es capaz de mantener variaciones preexistentes del ángulo de subducción, e incluso de generar estas variaciones a partir de una laja inicialmente uniforme.
•Las variaciones de succión hidrodinámica producen fuertes variaciones del flujo en la cuña mantélica.
•Los modelos con placas laterales y variaciones de la placa superior predicen la aparición de amplias zonas de flujo paralelo a la fosa, tanto bajo la laja como en la cuña. Esto es consistente con las direcciones de anisotropía sísmica.
2.Resumen de las principales aportaciones
Publicaciones más relevantes (catalogadas en SCI):
Rodríguez-González, J., Billen, M.I., Negredo, A.M., 2014. Non-steady-state subduction and trench-parallel flow Induced by overriding plate structure. Earth and Planetary Science Letters. En prensa. Cuartil de la revista: primero (Q1)
Fullea, J., Rodríguez-González, J., Charco, M., Negredo, A.M., 2014. Upper mantle structure under the Atlantic-Mediterranean transition zone: new constraints from GOCE mission and other potential field data. International Journal of Applied Earth Observation and Geoinformation. DOI: 10.1016/j.jag.2014.02.003. Cuartil de la revista: primero (Q1)
Rodríguez-González, J., Negredo, A.M., Carminati, E., 2014. Slab-mantle flow interaction: influence on subduction dynamics and duration. Terra Nova. DOI: 10.1111/ter.12095. Cuartil de la revista: primero (Q1)
Rodríguez-González, J., Negredo, A.M., Billen, M.I., 2012. The role of the overriding plate thermal state on slab dip variability and on the occurrence of flat subduction. Geochemistry Geophysics and Geosystems. 13, Q02009, DOI: 10.1029/2011GC003859. Cuartil de la revista: primero (Q1)
Otras publicaciones SCI del periodo predoctoral:
Pavón-Carrasco, F.J., Rodríguez-González, J., Osete, M.L., Torta, J.M, 2011. A Matlab tool for archaeomegnetic dating. Journal of Archaeological Science, 38, 408-419, DOI: 10.1016/j.jas.2010.09.021. Cuartil de la revista: primero (Q1)
Otras aportaciones:
Esta tesis ha dado lugar a cuatro presentaciones orales (una de ellas invitada) y diez posters en congresos internacionales.
La presentación invitada es:
Autores: J. Rodríguez-González, M. I. Billen and A.M. Negredo
Título: Time-dependent evolution of slab geometry and trench-parallel flow due to non-uniform overriding plates. Results from numerical modeling.
Tipo de participación: oral (invited)
Congreso: 2013 American Geophysical Union Fall Meeting
Lugar celebración: San Francisco (EEUU)Fecha: 2013
The dynamics of sinking lithosphere at subduction zones has a strong control on the evolution of plate-mantle system. Accordingly, a large number of studies focusing on observational data, as well as analytical, laboratory and numerical models have been developed during the last decades. However, some important aspects of subduction process remain poorly understood, such as the relative contribution of different factors causing the observed variability of slab dip. While the effects of overriding plate thickness on slab dip and on trench motion have been recently studied by means of 2D modeling, a systematic analysis of the effect of overriding plate thermal state has not been performed before this thesis. In the present study, 2D and 3D numerical thermo mechanical modeling were developed to obtain a better understanding of the dynamics of subduction, and to explore different factors that might play an important role in controlling the geometry of the slab and associated mantle flow.
The finite element method was applied to solve the coupled equations of mass, momentum and energy conservation for an incompressible fluid. In Chapters 3 and 4, 2D numerical models of kinematically-driven subduction using the commercial software Comsol Multiphysics were developed. Modeling results indicate that plates subducting underneath cold overriding plates are predicted to subduct with lower slab dip, and this effect is predicted to be more important and persistent than that of the subducting lithosphere age. The purpose of the study in Chapter 4 is to perform a systematic analysis of the effect of a hypothetical mantle flow (either global or regional) on slab dip and long-term evolution of subduction processes. This mantle flow is shown to produce significant slab dip deviations even for strong slabs.
Finally, more realistic 3D dynamically driven models with a more complex rheology are developed in Chapter 5, using the open source code CitcomS. The purpose was to generalize the results from 2D modeling and to test the effect of along-trench variations of the thermal state of the overriding both on slab geometry and the resulting pattern of mantle flow. Models of dynamically-driven subduction indicate that the increased suction beneath the cold portion of the overriding plate is enough to maintain though time preexisting variations of the slab dip. Moreover, this variable suction is shown to be even able to deform an initially uniform slab, creating significant variations on the slab dip along the trench. Due to the variations on the hydrodynamic suction and slab geometry, intense toroidal cells are generated in the region where the thermal state changes. These cells produce a component of trench-parallel flow far away from the edges of the slab, and not related to mantle flow around slab edges. Adding lateral plates to 3D models enables the material from the mantle to flow around the edges of the slab, which leads to wide regions of intense trench-parallel flow both beneath and above the slab.
Through all the chapters, the results obtained in the models were compared on qualitative grounds with natural examples. Slab dip variations found in some subduction zones (e.g., Central and South America) were discussed in terms of the studied factors.
INDEX
Agradecimientos9
Resumen/ Summary13
Resumen15
Summary21
1Introduction23
1.1.Subduction processes25
1.2.Objectives34
2Methodology35
2.1.Basic Equations37
2.1.1Conservation of mass.39
2.1.2Conservation of momentum39
2.1.3Conservation of energy.42
2.1.4Thermo-Mechanical coupling: density and viscosity.44
2.1.5Simplified equations.49
2.2Numerical methods55
2.2.1Comsol Multiphysics and PARDISO solver.56
2.2.2CitcomS and the Geometric Multi grid Solver.59
3Influence of the plates thermal state69
3.1.Introduction71
3.2.Modeling strategy74
3.2.1.Governing equations and numerical method.74
3.2.2.Model setup75
3.2.3.Initial Thermal Structure77
3.2.4.Rheology78
3.3.Results80
3.3.1.Reference model83
3.3.2.Influence of thermal state of the subducting plate84
3.3.3.Influence of thermal state of the overriding plate.86
3.3.4.Subduction styles89
3.4.Comparison to Cocos plate subduction97
3.5.Conclusions100
4Effect of the horizontal mantle flow101
4.1.Introduction103
4.2.Model Setup107
4.3.Results108
4.3.1.Reference model109
4.3.2.Influence of mantle flow on slab dip.109
4.3.3.Influence on long term evolution of subduction112
4.3.4.Effect of the slab strength113
4.4.Discussion114
4.4.1.Slab dip deviation114
4.4.2.Comparison with natural subduction zones and previous works.115
4.5.Conclusions117
53D Modeling119
5.1.Introduction121
5.2.Modeling strategy125
5.2.1.Governing equations and numerical method.125
5.2.2.Model setup126
5.2.3.Initial Thermal Structure127
5.2.4.Rheology130
5.3.Results.131
5.3.1.Kinematically driven models133
5.3.2.Dynamically driven models: Non uniform initial slab dip137
5.3.3.Dynamically driven models: Uniform initial slab dip144
5.3.4.Dynamic models: Uniform initial slab dip and lateral plates150
5.4.Discussion156
5.5.Conclusions159
6Concluding remarks and future work161
6.1.General Conclusions163
6.2.Future work166
References199
6.1.General Conclusions
Mechanisms controlling subduction dynamics and the resulting slab geometry are not yet fully understood. Even though many numerical and laboratory experiments, together with compilations of data, have lead to significant advances in understanding subduction dynamics and related consequences, there are still many questions that need to be answered. The work developed in this thesis addresses some of these questions and allows us to improve our knowledge about subduction processes by means of 2D and 3D numerical modeling.
In order to test the influence of the thermal state of the overriding and subducting plates on the dynamics and geometry of subduction, we have developed 2D numerical models using the commercial software Comsol Multiphysics. We have carried out a systematic study in which we vary separately the age of both plates.
Our results indicate that, as expected, a higher gravitational torque is exerted on older subducting plates due to their increased negative buoyancy. As a consequence, older subducting plates start subducting with a higher angle than young plates. The gravitational torque increases with time until it reaches a period of stabilization in which it barely changes. Therefore, the influence of the thermal state of the subducting lithosphere is only significant during the first stages of subduction, and diminishes with time, as slab geometry tends to reach steady state.
The mantle beneath older overriding plates is colder and more viscous, and therefore, the hydrodynamic suction on the upper surface of the slab in the mantle wedge is higher. Therefore, plates subducting underneath cold overriding plates are predicted to subduct with lower slab dip, due to the increased suction torque. The slab dip is a result of the competing effects of the gravitational and suction torques. The lower viscosity beneath warmer overriding plates produces thermal erosion in the mantle wedge that causes the warm material to migrate upwards. This contributes to further reduce the hydrodynamic torque, leading to steeper slabs. The influence of thermal state of the overriding plate on slab dip can have a noticeable effect even for long evolution times. This study demonstrates that the influence of thermal state of the overriding plate on slab dip is more important than that of the subducting plate, and persists for long term evolution.
We have shown that the thermal state of the overriding and subducting plates has an important effect on the slab geometry independently of other factors. We have run tests for weaker slabs, faster and slower subducting plates and even for different initial dips (by changing the inclination of the weak zone at the plate boundary), and all the results show the same trends: older plates subduct with higher dips during initial stages and subduction beneath older overriding plates takes place at lower dips. We have also shown that the qualitative effects of the thermal state of the overriding plate is independent of the amount of coupling between both plates, and that trench perpendicular variations in the temperature of the overriding plate also have a great influence on slab geometry.
With simple 2D models, varying only the age of the subducting and overriding plates we have been able to reproduce a wide range of slab geometries and different styles of subduction such as high-angle subduction, low-angle subduction and coupled slabs. We have also been able to reproduce long slab segments that subduct flatly for a limited period of time.
Another factor controlling the dynamics of subduction is an external horizontal mantle flow. In order to study its effect on the slab geometry, we have added to our previous 2D models a horizontal flow acting in both senses (opposing and accompanying subduction) and with different velocities.
The mantle flow is shown to have little influence on the geometry of the slab for the early stages of subduction. For longer evolution times, as the slab sinks deeper into the mantle, the flow is channeled between the tip of the slab and the more viscous lower mantle, and flow velocity increases. Therefore, the effect of the horizontal mantle flow becomes stronger and, if the mantle flow has the opposite sense to subduction, the resulting slab dip will be higher. On the contrary, if the mantle flow has the same sense as subduction, the slab flattens with time. In this case, for very long evolution times, once the slab has reached the lower mantle, the slab dip is reduced so much that the overriding and the subducting plates become coupled and subduction stops.
We have also developed 3D models using CitcomS, and we have included more realistic geometry (using spherical coordinates), boundary conditions (allowing for self-driven subduction) and rheology (implementing a pseudo-plastic behavior). With these models we aim to generalize the results from 2D models and to study the different behavior derived from 3D features (e.g., along-trench variations of the thermal state of the overriding plate or trench-parallel and toroidal flow).
First, these new models showed that conclusions drawn from 2D models are also valid for the new configuration. If the overriding plate is not uniform but has two regions with different thermal states, the hydrodynamic suction is greater beneath the coldest portion. The subducting plate is affected locally by the different hydrodynamic suction, which leads to along-trench variations of slab dip.
If the subduction is dynamically-driven slabs tend to sink vertically, but the increased suction beneath the cold portion of the overriding plate is enough to maintain preexisting variations of the slab dip. The variable suction in the mantle wedge is even able to deform the initially uniform slabs, creating significant variations on the slab dip along the trench. Also, due to the variations on the hydrodynamic suction and slab geometry, intense toroidal cells are generated in the region where the thermal state changes. This toroidal flow contributes to increase the deformation of the slab, and also causes the appearance of trench-parallel flow far away from the edges of the slab.
Adding lateral plates to 3D models enables the material from the mantle to flow around the edges of the slab. This leads to the formation of toroidal cells in the edges of the slab. Allowing the material to flow around the edges of the slab together with variations of the thermal state of the overriding plate, leads to wide regions of intense trench-parallel flow both beneath and above the slab. Beneath the slab the flow show a simple pattern with a wide region of uniform trench parallel flow with values around 3 cm·yr-1. In the mantle wedge the flow shows a much complex pattern with sudden variations of the flow direction and the velocity magnitude, presenting values between 1 and 3 cm·yr-1.
Finally, we compare our modeling predictions, in qualitative terms, with some subduction zones that show slab dip variability along the trench, as the subduction of Cocos Plate or subduction in South America, where a wide flat slab segment is found beneath Peru and a narrow flat segment subducts in Northern Chile. Regarding Cocos Plate, we provide a plausible explanation for this variability in terms of the change of the thermal state of the overriding plates, with flat and low-angle subduction occurring under the cold lithosphere of the Maya block of North America and steep subduction under the warmer lithosphere of the Chortis block of the Caribbean plate. We suggest that the flat segment in Peru can be explained in terms of the proximity of the area of increased elastic thickness and reduced heat flow in the region.
6.2.Future work
The results drawn from 2D and 3D models show that still some improvements should be made to the model setup and data analysis. First, it would be important to calculate the Lattice Preferred Orientation derived from the flow pattern of 3D models. This would allow us to compare the model results with observations of shear wave splitting data from particular subduction zones such as Central and South America.
It will be suitable to add new features to the models, especially to the three dimensional ones. The first point that should be addressed is the implementation of a mobile trench. A low viscosity layer on top of the subducting plate would substitute the low viscosity channel at the plate boundary. If this layer were advected using tracers, it would act as a decoupling layer but would also move with the plates, allowing the trench to migrate. A free moving trench would allow us to study the relationship between trench migration rates and variations on the thermal state of the overriding plate. Developing 3D models with a mobile trench will allow us to quantify the effects of mantle flow on trench motion and on the resulting stress regime in the overriding plate and slab.
In addition, another feature that should be addressed is the implementation of 3D models that include an imposed horizontal mantle flow. The horizontal mantle flow will most likely increase the toroidal and trench-parallel flow. The mantle flow might also affect the geometry of the slab but not as much as was shown by 2D models, and its influence will be less significant especially for narrow slabs.
Other features that should be added to the current setup are phase transitions and compositional differences. Phase transitions may affect the behavior of the slab when it reaches the transition zone, leading to stagnation. Studying the combined effect of variations on the thermal state of the overriding plate and the subduction of aseismic ridges and oceanic plateaus would provide important information about the causes of flat subduction.
Finally, we will develop models that will mimic other natural subduction zones to validate our results and compare the resulting slab dips and flow patterns with observations. We will set up new models with more realistic trench geometries and adding constraints of the overriding and subducting plates thermal state.