It is still unclear where a subduction is initiated and what are the responsible mechanisms involved in subduction initiation process. Understanding of subduction initiation will advance our knowledge of how and when plate tectonics started on Earth. Another issue concerning the subduction process is the response to arrival of buoyant continental crust at the trench. Upon entrance of continental crust into subduction zones (known as continental collision), the approximately steady-state subduction turns into a transient state. One of the responses to continental collision is initiation of a new subduction zone on the former overriding plate (subduction polarity reversal). However, there is ample geological and seismological evidence indicating other deformation patterns following continental collision including continuation of subduction, and delamination. The cause of the different responses to collision is still poorly understood. In this thesis, I aim to address both transient stages: subduction initiation and continental collision. To this purpose I use Finite element method. The general conclusion of this thesis is that several parameters such as convergence in the direction perpendicular to the weakness zones at the edges of a slab or continued convergence in collisional settings can result in reorganization of plate boundaries and formation of new subduction zones
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