Research Article An Application of the Coherent Noise Model for the Prediction of Aftershock Magnitude Time Series Stavros-Richard G. Christopoulos 1,2 and Nicholas V. Sarlis 2,3 1 Faculty of Engineering, Environment and Computing, Coventry University, Priory Street, Coventry CV1 5FB, UK 2 Solid Earth Physics Institute, Department of Physics, School of Science, National and Kapodistrian University of Athens, Panepistimiopolis, Zografos, 157 84 Athens, Greece 3 Section of Solid State Physics, Department of Physics, School of Science, National and Kapodistrian University of Athens, Panepistimiopolis, Zografos, 157 84 Athens, Greece Correspondence should be addressed to Stavros-Richard G. Christopoulos; strichr@phys.uoa.gr Received 18 July 2016; Accepted 9 October 2016; Published 20 February 2017 Academic Editor: Alicia Cordero Copyright © 2017 Stavros-Richard G. Christopoulos and Nicholas V. Sarlis. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Recently, the study of the coherent noise model has led to a simple (binary) prediction algorithm for the forthcoming earthquake magnitude in afershock sequences. Tis algorithm is based on the concept of natural time and exploits the complexity exhibited by the coherent noise model. Here, using the relocated catalogue from Southern California Seismic Network for 1981 to June 2011, we evaluate the application of this algorithm for the afershocks of strong earthquakes of magnitude ≥6. Te study is also extended by using the Global Centroid Moment Tensor Project catalogue to the case of the six strongest earthquakes in the Earth during the last almost forty years. Te predictor time series exhibits the ubiquitous 1/ noise behavior. 1. Introduction Te prediction of the magnitudes and occurrence times of afershocks is of crucial importance for restricting the losses caused by strong earthquakes (EQs, hereafer) because build- ings already damaged by the mainshock may collapse upon the occurrence of a strong afershock. Recently, an algorithm has been suggested [1] on the basis of the coherent noise model [2–4] and natural time [5–7] that might be useful for the determination of both magnitudes and occurrence times of afershocks. It is the main scope of the present paper to investigate the applicability of such an algorithm to afershock time series in Southern California. Tis area has been selected in view of the publication [8] of an accurate waveform relo- cated EQ catalogue for Southern California from 1981 to June 2011 [9] that exhibits tighter spatial clustering of seismicity than the routinely generated catalogue does. Te coherent noise model [2–4] is a model that shows reorganization events (avalanches) whose size distribution follows a power law over many decades and displays afer- shock events. Tese events have been shown [3, 10, 11] to exhibit a behavior similar to that of the Omori-Utsu law [12]; see also [13, 14], for real EQ afershocks. Moreover, it has been recently shown [15] that it is compatible with the unifed scaling law [16] of waiting times between EQs. In a time series comprising  avalanches (or EQs), natu- ral time   = / serves as an index for the occurrence of the th event [5–7]. Natural time focuses on the sequential order of the events and the analysis is usually made by using the pair (  ,  ), where   is a quantity proportional to the size (and hence to the energy) of the th event. Natural time analysis has found useful applications in a variety of felds: Statistical Physics (e.g., [17–23]), Cardiology (e.g., [24–27]), Geophysics (e.g., [6, 28–32]), Atmospheric Sciences (e.g., [33, 34]), Seismology (e.g., [35–40]), Physics of EQs (e.g., [41–45]), EQ prediction (e.g., [5, 46–52]), and so on (for a recent review see [7]). For the case of EQs [36],   ∝ 10   , where   is the magnitude of the th EQ and  ≈ 1.5. Te two quantities Hindawi Publishing Corporation Complexity Volume 2017, Article ID 6853892, 27 pages https://doi.org/10.1155/2017/6853892