A probabilistic model of seismicity: Kamchatka earthquakes |
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| Authors: | V V Bogdanov A V Pavlov A L Polyukhova |
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| Institution: | 1.Institute of Space Physics Research and Radio Wave Propagation, Far East Division,Russian Academy of Sciences,Kamchatskii Krai, Paratunka,Russia |
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| Abstract: | The catalog of Kamchatka earthquakes is represented as a probability space of three objects {Ω, $
\tilde F
$
\tilde F
P}. Each earthquake is treated as an outcome ω
i
in the space of elementary events Ω whose cardinality for the period under consideration is given by the number of events.
In turn, ω
i
is characterized by a system of random variables, viz., energy class ki, latitude φ
i
, longitude λ
i
, and depth h
i
. The time of an outcome has been eliminated from this system in this study. The random variables make up subsets in the set
$
\tilde F
$
\tilde F
and are defined by multivariate distributions, either by the distribution function $
\tilde F
$
\tilde F
(φ, λ, h, k) or by the probability density f(φ, λ, h, k) based on the earthquake catalog in hand. The probabilities P are treated in the frequency interpretation. Taking the example of a recurrence relation (RR) written down in the form of
a power law for probability density f(k), where the initial value of the distribution function f(k
0) is the basic data Bogdanov, 2006] rather than the seismic activity A
0, we proceed to show that for different intervals of coordinates and time the distribution f
elim(k) of an earthquake catalog with the aftershocks eliminated is identical to the distribution f
full(k), which corresponds to the full catalog. It follows from our calculations that f
0(k) takes on nearly identical numeral values for different initial values of energy class k
0 (8 ≤ k
0 ≤ 12) f(k
0). The difference decreases with an increasing number of events. We put forward the hypothesis that the values of f(k
0) tend to cluster around the value 2/3 as the number of events increases. The Kolmogorov test is used to test the hypothesis
that statistical recurrence laws are consistent with the analytical form of the probabilistic RR based on a distribution function
with the initial value f(k
0) = 2/3. We discuss statistical distributions of earthquake hypocenters over depth and the epicenters over various areas for
several periods |
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| Keywords: | |
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