Abstract:
The present work aims at the introduction and application of Markov and semi-Markov
models in estimating the waiting times and magnitudes of the great earthquakes in future.
These model assumes that the successive earthquakes in same structural discontinuity are
not independent events, which means that time and place of future earthquake events are
related to previously occurred earthquake in the region considered, as demonstrated by
elastic rebound theory. While other most commonly used models such as Poisson model
assumes spatial and temporal independence of all earthquakes including great earthquakes
i.e., occurrence of one earthquake does not affect the likelihood of a similar earthquake at
the same location in the next unit of time. Such models may apply to regions characterized
by moderate frequent earthquakes in larger areas. While Markov and semi-Markov models
describes the sequences of events more adequately at small regions with great infrequent
earthquakes. In this report, these probabilistic models are applied in the central Himalayan
region, by considering the sequence of earthquakes to form a stationary Markov chain. The
occurrences of earthquakes in these models is described by discrete time and discrete states
for the earthquake magnitudes and locations. In Markov and semi-Markov models, the
successive states are governed by the transition probabilities depending on the just previous
state and not on the history of reaching to that state. The use of probability distributions for
earthquake magnitude and inter arrival time as continuous random variables is unable to
account for such a dependence. It has been discussed that how this dependence can be
utilized to carry out a time dependent seismic hazard analyses. On the basis of
seismotectonic characteristics, the study area is divided into four sub regions and the
application of these models has been illustrated to predict the probability of the next
earthquake in different sub regions as a function of time from the previous earthquake,
conditioned on the magnitude and the sub region of the previous earthquake. The results
obtained indicate that the next major earthquake can occur in any of the sub regions with
almost equally high probability. Thus, the so called central Himalayan seismic gap is
expected to be closed in near future.
