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[MGI29-P01] Plate motion in a three-dimensional spherical shell mantle convection model with stress history-dependent viscosity
Keywords:mantle convection, plate
Plate motion is a dominant cause of tectonic activities on the Earth's surface, as well as material circulation between the Earth's surface and the interior. These activities influence the surface environment and its changes on the Earth. To investigate these processes, it is necessary to precisely solve the coevolutionary process of plate motion and mantle convection.
Even though nearly the same stress is applied, plate boundaries are formed in some places and not in others. A plate that cracks under strong stress does not immediately stick and return to its original state even if the stress is reduced. In other words, the mechanical state of the plate is not determined only by the magnitude of stress at that moment, but also depends on the stress history, such as whether or not it has experienced fracture in the past.
We are investigating plate motion and associated phenomena using a three-dimensional spherical mantle convection model (ACuTEMan, Kameyama et al. 2005; 2008) that incorporates a model that can handle plate motion more accurately than past models by using stress history-dependent viscosity (Ogawa 2003). Calculation of a similar model in a three-dimensional rectangular box (Miyagoshi et al. 2020) reproduced some characteristics of plate motion on Earth, such as plate deformation concentrated only at plate boundaries and rigid body motion that is stable over a long period of time. However, in the box model, the position of the trench is almost entirely determined by the side-walls of the box. So it is not suitable for observing the behavior of plate motion over a period longer than hundreds of millions to billion years (e.g., changes in plate motion and internal structure formed by subducting slabs). In addition, the difference in area between the surface and the core-mantle boundaries is not accounted for. Since a spherical shell geometry of the mantle essential for detailed comparisons of models with various observational results, we are aiming to extend the box model to a spherical shell model.
The key parameters are: (1) the ratio of the viscosity at plate-margins formed by rupture of the lithosphere in the past relative to the intact plate interiors; and (2) the strength of the temperature dependence of viscosity: a solid lithosphere will not develop unless it exceeds a threshold. The calculation becomes more difficult as these factors become larger. Furthermore, since plate motion does not occur unless convection is active to a certain extent, the Rayleigh number (3), which is a parameter as a guideline of activity of convection, is also important.
In particular, the viscosity contrast (1) is difficult to handle, because it is necessary to find a convergent solution under a situation where the viscosity decreases significantly at a very localized plate boundary. The required value for the contrast (1) is a factor of about 103.5 or more. However, we could not reach a convergent solution when we assigned this extreme value from the beginning of the calculation. So we started from 0 and gradually approached the target value.
After a continuing effort for more than a year, we reached the target value of 103.5 for (1). As for the factor of (2), the required value, 103~4, has also been reached in the course of this effort. We raised the Rayleigh number to a target value, too (3).
Here, we present an example of plate motion that we are calculating: the calculated plates are bounded by narrow ridges and trenches and rigidly and steadily move. The plate motion is still not in its statistically steady state, and further calculations are required.
Even though nearly the same stress is applied, plate boundaries are formed in some places and not in others. A plate that cracks under strong stress does not immediately stick and return to its original state even if the stress is reduced. In other words, the mechanical state of the plate is not determined only by the magnitude of stress at that moment, but also depends on the stress history, such as whether or not it has experienced fracture in the past.
We are investigating plate motion and associated phenomena using a three-dimensional spherical mantle convection model (ACuTEMan, Kameyama et al. 2005; 2008) that incorporates a model that can handle plate motion more accurately than past models by using stress history-dependent viscosity (Ogawa 2003). Calculation of a similar model in a three-dimensional rectangular box (Miyagoshi et al. 2020) reproduced some characteristics of plate motion on Earth, such as plate deformation concentrated only at plate boundaries and rigid body motion that is stable over a long period of time. However, in the box model, the position of the trench is almost entirely determined by the side-walls of the box. So it is not suitable for observing the behavior of plate motion over a period longer than hundreds of millions to billion years (e.g., changes in plate motion and internal structure formed by subducting slabs). In addition, the difference in area between the surface and the core-mantle boundaries is not accounted for. Since a spherical shell geometry of the mantle essential for detailed comparisons of models with various observational results, we are aiming to extend the box model to a spherical shell model.
The key parameters are: (1) the ratio of the viscosity at plate-margins formed by rupture of the lithosphere in the past relative to the intact plate interiors; and (2) the strength of the temperature dependence of viscosity: a solid lithosphere will not develop unless it exceeds a threshold. The calculation becomes more difficult as these factors become larger. Furthermore, since plate motion does not occur unless convection is active to a certain extent, the Rayleigh number (3), which is a parameter as a guideline of activity of convection, is also important.
In particular, the viscosity contrast (1) is difficult to handle, because it is necessary to find a convergent solution under a situation where the viscosity decreases significantly at a very localized plate boundary. The required value for the contrast (1) is a factor of about 103.5 or more. However, we could not reach a convergent solution when we assigned this extreme value from the beginning of the calculation. So we started from 0 and gradually approached the target value.
After a continuing effort for more than a year, we reached the target value of 103.5 for (1). As for the factor of (2), the required value, 103~4, has also been reached in the course of this effort. We raised the Rayleigh number to a target value, too (3).
Here, we present an example of plate motion that we are calculating: the calculated plates are bounded by narrow ridges and trenches and rigidly and steadily move. The plate motion is still not in its statistically steady state, and further calculations are required.