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Description of geological processes starting from Markov chains


In our approach, the tectonic plates are considered bounded surfaces in such a way, that sliding along Earth periphery, they have three degrees of freedom and the distribution of their mass is superficial. Then, the movement of a plate is giving by the latitudinal and longitudinal angles and by the spin angle around the plate's center of mass. According to the seismological data, such movement occurs stepwise. Each step is performed in two phases: during the first phase, the interactions with adjacent plates are weak enough for them to be considered only reversible effects while the second phase includes (one at a time) all the irreversible deformations of the step. For this reason, the movement in the first phase is considered as a deterministic motion of rigid bodies. However, during the second phase, any deterministic description is unfeasible and useless and it is where we have applied the theory of catastrophes. Since, the number of oscillators in a plate is finite (even huge), “the hot spots” (the sites of distributions of the springs – see the related abstract “A simplified model of interaction between tectonic plates” sent as well for the AAPG Europe Region Conference – 2015 Lisbon – is finite too) are considered as elements of a countable (finite or infinite) set. An event of our Markov chain is any irreversible change in the respective hot spot while its probabilities (with respect to the step transitions from a hot spot to another) are introduced (for now) as unknown parameters which form a stochastic matrix. Assuming that the Markov chain is homogeneous, we can decompose its events into equivalence classes of communicated stats and if a class is periodic into subclasses as shown (transitions via) in the following figure which presents the stochastic matrix by blocks: (Go to Search and Discovery to view image)