We present the 2-D self-consistent dynamical model of interactions of a subducting slab with the 410-km and 660-km phase boundaries to further our understanding of the relation between the slab stagnation/penetration and the trench migration. Our model takes into account freely-movable plate boundaries and the difference between tensional and compressional yield strengths in the lithosphere. For the case in which the tensional strength is weaker than the compressional one, the negative buoyancy of the subducting slab produces extension of the overriding lithosphere and, accordingly, the trench retreats. Interactions with the 410-km and 660-km phasetransition boundaries further promote the trench retreat, and the dip angle of the slab is substantially decreased. This enhances the resistance of the 660-km phase boundary against the slab penetration. Slab weakening caused by the grain-size reduction in the transition zone may result in a horizontally-lying slab and trench retreat.

We performed a numerical study to understand the dynamical mechanism controlling the formation and avalanche of a stagnant slab using two-dimensional dynamical models of the integrated plate-mantle system with freely movable subducting and overriding plates. We examined slab rheology as a mechanism for producing various styles of stagnating or penetrating slabs that interact with the 410-km and 660-km phase transitions. The simulated results with the systematically changed rheological parameters are interpreted using a simple stability analysis that includes the forces acting on the stagnant slab. Slab plasticity that memorizes the shape produced by past deformation generates slab stagnation at various depths around the 660-km phase transition. The slab stagnates even beneath the 660-km phase boundary, with a gentle Clapeyron slope. Feedbacks between trench backward migration and slab deformation promote each other during the slab stagnation stage. Slab viscosity also determines the final state of the subducted slab, that is, it continues stagnation or initiates penetration. A low-viscosity slab can finally penetrate into the lower mantle because the growth time of the Rayleigh-Taylor instability is shorter. After the avalanche, the direction of the trench migration changes depending on the lower mantle slab viscosity.

We have developed a two-dimensional dynamical model of asymmetric subduction integrated into the mantle convection without imposed plate velocities. In this model we consider that weak oceanic crust behaves as a lubricator on the thrust fault at the plate boundary. We introduce a rheological layer that depends on the history of the past fracture to simulate the effect of the oceanic crust. The thickness of this layer is set to be as thin as the Earth's oceanic crust. To treat 1-kilometer scale structure at the plate boundary in the 1000-kilometer scale mantle convection calculation, we introduce a new numerical method to solve the hydrodynamic equations using a couple of uniform and nonuniform grids of control volumes. Using our developed models, we have systematically investigated effects of basic rheological parameters that determine the deformation strength of the lithosphere and the oceanic crust on the development of the subducted slab, with a focus on the plate motion controlling mechanism. In our model the plate subduction is produced when the friction coefficient (0.004 -0.008) of the modeled oceanic crust and the maximum strength (400 MPa) of the lithosphere are in plausible range inferred from the observations on the plate driving forces and the plate deformation, and the rheology experiments. In this range of the plate strength, yielding induces the plate bending. In this case the speed of plate motion is controlled more by viscosity layering of the underlying mantle than by the plate strength. To examine the setting of the overriding plate, we also consider the two end-member cases in which the overriding plate is fixed or freely-movable. In the case of the freely-movable overriding plate, the trench motion considerably changes the dip angle of the deep slab. Especially in the case with a shallow-angle plate boundary, retrograde slab motion occurs to generate a shallow-angle deep slab.

The dynamical effects of an asymmetric subduction structure on the generation of plate-like motion were investigated using two-dimensional numerical models of the integrated lithosphere-mantle system. To dynamically generate the plate boundary, we introduce a history-dependent rheology in which the yield strength is determined by past fractures. Only the buoyancy due to the internal density contrast consistently drives convective flow, including the motion of the viscous lithosphere, without imposed boundary conditions. We first investigate the effects of plate yield strength, friction at the plate boundary, and plate age on the emergence of plate-like motion with asymmetric subduction. Plate-like motion is generated when maximum plate strength is as high as that estimated by experimental rheology studies. The reason for this is that asymmetric subduction requires a plate-bending force much less than that for symmetric subduction because the plate gently bends when one-sided subduction occurs. In contrast, the strength of the plate boundary has to be very small for emergence of subduction, as several previous studies on the numerical convection and subduction modeling have pointed out. Development of the subducted slab is also controlled by the age of the plate. In the early stages of subduction, older plates increase their velocities faster because of their larger negative buoyancy. After the slab develops, the plate stiffness, that is, both the yield strength and the plate thickness, control plate velocity so that an older plate subducts more sluggishly. We next explore effects of viscosity layering in the underlying mantle, focusing on the mechanism in which the asthenosphere promotes plate motion. The low viscosity under the lithosphere enhances a mantle drag force that drives the plate, not only concentrating the convective flow beneath the plate but also enlarging its aspect ratio. We also examine longevity of the plate-like motion using the convection models with asymmetric subduction. The asymmetrically structured subduction process continues stably at high yield strength, at which episodic resurfacing or the stagnant-lid mode occurs in the previous convection simulation studies. The asymmetric subduction structure therefore has key roles in generating plate-like motion as well as reducing the strength at the plate boundary.