Temporal distribution of recorded magnitudes in Serbia earthquake catalog

• Hypothesis of random temporal distribution of earthquake magnitudes is tested.
• Piece-wise low cross-prediction error confirms stationarity of magnitude sequence.
• High zeroth order error independent of advancing time imply random distribution.
• Low determinism factor indicates random sequence of recorded magnitudes.
• Randomness is implied by majority of autocorrelations within 95% confidence limits.

We focus on earthquakes that were recorded in Serbia between 1970 and 2011 within shallow parts of the Earth’s crust, having local magnitudes from the 1.2–5.8 interval. The main goal of the performed analysis is to examine whether the temporal sequence of these recorded magnitudes exhibits some deterministic pattern or whether it simply represents a series of random events. For this purpose, the temporal distribution of earthquake magnitudes above the magnitude of completeness is analyzed by means of nonlinear time series analysis and surrogate data testing, as well as by means of the autocorrelation function. Piece-wise low cross-prediction errors, with 75% of segment pairs having the error smaller than its average value, indicate stationary properties of the examined sequence. Results of surrogate data testing indicate high zeroth-order prediction error that is independent of prediction time for the original dataset and 20 different surrogates, implying that the observed magnitude sequence is a series of independent random events drawn from some fixed but unknown distribution. These findings are supported further by a low value of the determinism factor for an earthquake treated as a system with four degrees of freedom (epicentral latitude and longitude, hypocentral depth and magnitude). The randomness in observed data is indicated further by the properties of the autocorrelation function, whose values for different time lags fall within the 95% confidence limit without an apparent pattern.