How much randomness do we have in data series of geophysical catalogues?

This paper presents a research of random event theory in EQ datasets with respect to sequences of timeframe records. We had processed records of events in Iranian EQ catalogue since 1900/01/01 till 2015/03/03 and the global NEIC catalogue since 2000 dealing with so-called binormalized randomness parameter S, the invariant of Russian academician V. I. Arnold, to estimate a real randomness of the both EQ catalogues. As known, S tends to the two asymptotically for the really random configurations and to the one or infinity, otherwise. The EQ randomness rating is done with putting S into an order, and we may conclude that random theory of EQ is not correct and should be revised. The similar results we obtained for the popular indices K, Kp and Ap of geomagnetic activity since 1932 taken from the different data series.