Uncertainties, complexities and possible forecasting of the volcán de Colima energy emissions (México, years 2013–2015) based on the fractal reconstruction theorem

Abstract. A time series of effusive-explosive volcanic emissions of energy by the volcanic activity in Volcán de Colima (Western segment of Trans-Mexican volcanic belt, years 2013–2015) is analysed from the point of view of the reconstruction theorem, being considered several fractal computational procedures, such as the Hurst exponent (persistence, anti-persistence or randomness of the series), Lyapunov exponents and Kaplan-Yorke dimension (degree of forecasting difficulty on the series of energy emissions) and the correlation integral of the series, being obtained the Kolmogorov entropy and the embedding dimension (quantification of the degree of complexity and “loss of memory” of the physical mechanism along an episode of volcanic emissions). The analysed series have been chosen by applying the Gutenberg-Richter law to the logarithm of the complete energy emissions, being discarded those not accomplishing the mentioned law. Definitively, a series of 6182 explosive events and its seismic energy along years 2013–2015 has been selected. The reconstruction theorem algorithm is applied to the whole emission series, to 6 consecutive segments of 1000 emissions and to 21 moving window series of 2000 data lengths and shifts of 200 data, being also introduced and validated some examples of a nowcasting strategy. The main objective of this paper is to quantify the complexities concerning the physical and mathematical mechanisms governing these emissions, which are necessary for possible forecasting of explosive volcanic energy emissions with an enough degree of certainty.