Prediction of Large Earthquakes using Pattern Recognition Method and Chaos Theory

Abstract

The prediction of Large Earthquakes (LE) constitutes a global challenge. Several methods of earthquake prediction including Pattern Recognition (PR) have been proposed but sometimes produce patterns that are not suitable. Occurrence of earthquakes is always assumed to be random when these methods produce unreliable pattern. The fact that these patterns considered to be random could be chaotic (predictable but difficult) has not been investigated. This study was designed to use chaos theory to investigate patterns of occurrence of earthquakes where PR method gives unreliable pattern. Earthquake data (1899-2009) of the Circum-Pacific seismic zone were extracted from the catalogue of Advanced National Seismic System (USA). The zone is the source of 90% of the world's earthquakes and the one with most recorded data. The zone was divided into five regions [Rl(Lat 55° to 67° ; Long -170° to -145°), R2(Lat 32° to 44° ; Long 134° to 148°), R3(Lat 39° to 50° ; Long 140° to 157°), R4(Lat -42° to -29° ; Long -80° to -66°), R5(Lat 48° to 54° ; Long -179° to -160°)] based on the pattern of occurrence of small earthquakes. Events in each region were divided into constant time intervals and annular width of 100 km for the investigation of temporal and spatial distribution of the earthquakes respectively. The PR method was applied to the data in each time interval and annular width, and the pattern monitored using seismic b-values and the locations of the maximum seismic energy. The b-values were determined from Gutenberg-Richter law using the linear curve fitting method, while the locations of the maximum seismic energy were determined using Compicat program. Using chaos theory, the phase space plots of the seismic activities were constructed to determine the space clustering of the seismic events associated with LE. The Lyapunov Exponent (LEX) and its spectrum were obtained using Wolf and Sprott procedures to provide a picture of the system's dynamics and determine whether it is random or chaotic. The temporal and spatial variations of the b-values for all the regions were oscillatory but with variable periods, indicating unreliable patterns. The pattern of propagation of the maximum seismic energy was non-linear and appeared to be geometrically fractal. The phase space was densely filled with scattered points (chaotic trajectory) which showed that the occurrence of earthquakes had chaotic characteristics. The LEX was positive for all the regions, indicating the chaotic nature of the earthquakes occurrence. This was highest for R3 (LEX = 2.688) and lowest for R4 (LEX = 0.688). The LEX spectrum behaved asymptotically prior to the occurrence of the LE. Chaos theory showed that unreliable pattern from Pattern Recognition method was chaotic. The asymptotic behaviour of the Lyapunov Exponent spectrum could be used as a precursor in seismic hazard management. Chaos theory should be incorporated into Pattern Recognition method for effective prediction of large earthquakes.