Łańcuch Markowa jako stochastyczny model sedymentacji fliszowej
Abstract
Markow’s chain as stochastic model of flysch sedimentation
Modelling of the sedimentary processes is the most advanced stage of utilizing mathematical methods in sedimentology. Results of such modelling can serve, above all, to verify conceptual models formulated by a scientist. The paper presents a suggestion of a model based on the following assumptions. The sedimentation of flysch formations can be regarded as a sequence of following in succesion depositions of beds having different lithological character and erosions. Then among the depositon factors, it is possible to differentiate turbidity currents, bottom currents (in the wide sense of the term as factor redopositinig a deposit already deposited) and purely gravitational settling of particles from freely floating in water suspension (pelagic sedimentation). The sequence of sedimentary acts (i.e. depesitions and erosions) can be described with the help of transition probability matrix, whereas the differentiation of lithologies — with the help of conditional probabilities of deposition of a defined (lithologically) bed by a defined factor. On the basis of the above mentioned assumptions it is possible to calculate the transition probability matrix between the states of the system, interpretated as beds of a given origin and lithology, with additional allowance for the state of erosion. Further transformation of the model has the aim of eliminating all the probabilities impossible (or very difficult) to estimate on the basis of field observations, i.e. probabilities connected with the state of erosion and with homogeneous multistory lithologies. Harving executed the transformations, we arrive at a model which can be verified directly in reality. Interpretation utility of the suggested model is being examined with the help of computer calculations.
Modelling of the sedimentary processes is the most advanced stage of utilizing mathematical methods in sedimentology. Results of such modelling can serve, above all, to verify conceptual models formulated by a scientist. The paper presents a suggestion of a model based on the following assumptions. The sedimentation of flysch formations can be regarded as a sequence of following in succesion depositions of beds having different lithological character and erosions. Then among the depositon factors, it is possible to differentiate turbidity currents, bottom currents (in the wide sense of the term as factor redopositinig a deposit already deposited) and purely gravitational settling of particles from freely floating in water suspension (pelagic sedimentation). The sequence of sedimentary acts (i.e. depesitions and erosions) can be described with the help of transition probability matrix, whereas the differentiation of lithologies — with the help of conditional probabilities of deposition of a defined (lithologically) bed by a defined factor. On the basis of the above mentioned assumptions it is possible to calculate the transition probability matrix between the states of the system, interpretated as beds of a given origin and lithology, with additional allowance for the state of erosion. Further transformation of the model has the aim of eliminating all the probabilities impossible (or very difficult) to estimate on the basis of field observations, i.e. probabilities connected with the state of erosion and with homogeneous multistory lithologies. Harving executed the transformations, we arrive at a model which can be verified directly in reality. Interpretation utility of the suggested model is being examined with the help of computer calculations.