Model dissection from earthquake time series: A comparative analysis using modern non-linear forecasting and artificial neural network approaches

Abstract

This study utilizes two non-linear approaches to characterize model behavior of earthquake dynamics in the crucial tectonic regions of Northeast India (NEI). In particular, we have applied a (i) non-linear forecasting technique to assess the dimensionality of the earthquake-generating mechanism using the monthly frequency earthquake time series (magnitude ⩾4) obtained from NOAA and USGS catalogues for the period 1960–2003 and (ii) artificial neural network (ANN) methods—based on the back-propagation algorithm (BPA) to construct the neural network model of the same data set for comparing the two. We have constructed a multilayered feed forward ANN model with an optimum input set configuration specially designed to take advantage of more completely on the intrinsic relationships among the input and retrieved variables and arrive at the feasible model for earthquake prediction. The comparative analyses show that the results obtained by the two methods are stable and in good agreement and signify that the optimal embedding dimension obtained from the non-linear forecasting analysis compares well with the optimal number of inputs used for the neural networks.

The constructed model suggests that the earthquake dynamics in the NEI region can be characterized by a high-dimensional chaotic plane. Evidence of high-dimensional chaos appears to be associated with “stochastic seasonal” bias in these regions and would provide some useful constraints for testing the model and criteria to assess earthquake hazards on a more rigorous and quantitative basis.

Introduction

During the past several years a number of linear and non-linear statistical techniques have been successfully applied to study earthquake occurrences (Gardner and Knopoff, 1974; Jones, 1985; Kantz and Schreiber, 1997; Rundle et al., 1997). Some of these studies relied on the Poisson cluster model where the earthquake occurrences are considered to be a field of random processes. Alternatively, several others have attempted to characterize the nature of earthquake dynamics using the methods of fractals, chaos and b-value. Earthquake data obtained from the Northeast India (NEI) and the Himalayas have also been subjected to similar analyses (Khattri (1995), Sunmonu and Dimri (1999), Bhattacharya and Kayal (2003)). Teotia et al. (1997) have calculated the generalized fractals dimension D_q for the Himalayan earthquake records using the Grassberger–Procaccia (G–P) method (Grassberger and Procaccia, 1983) and concluded that the seismicity pattern of the Himalayan region is multifractal in nature and the characteristics vary with time. They related multifractality to the heterogeneous distribution of seismic activities and fractured nature of the crust in these regions.

Some earlier studies of the NEI earthquake data indicated contrasting evidence for the presence of randomness and a low-dimensional “strange attractor”. Dasgupta et al. (1998) studied the temporal occurrence of earthquakes (M⩾5.5&6.0) using the Poisson probability density function. They suggested that the temporal pattern of earthquake occurrences in this region follows the Poisson distribution. Srivastava et al. (1996) applied G–P algorithm to study the NEI earthquake time series and suggested that the earthquake dynamics in this region is governed by low-dimensional chaos. Evidence of low dimensionality or “strange attractor”, of the order of 6–7 in the NEI earthquake data, suggests that smaller number of variables are required to model the dynamics of the underlying system. From a practical point of view, a system dominated by a low-dimensional deterministic chaos bears an interesting feature, which implies that the immediate future evolution of the chaotic phenomenon could be predictable with a considerably high degree of precision (Eckmann and Ruelle, 1985). However, detecting low-dimensional chaos from the earthquake time series using the G–P algorithm requires large number of data points, which are generally not available. Even if enough data are available, a finite attractor dimension might not be an actual indication of low-dimensional deterministic chaos due to the low signal-to-noise ratio (Osborne and Provenzale, 1989). In addition to this, although evidence for the ‘low-dimensional chaos’ in earthquake data series has been invariably reported in many cases, there is no general consensus on their modes of origin (i.e. high dimension/low dimension) due to the reasons cited above. The future evolution of the stochastic systems can be predicted to varying degrees, but their predictability is usually lower than those of the chaotic systems. Distinguishing these classes of evolutionary seismicity is, therefore, of paramount importance for understanding the physics of the underlying process. It is also essential for constraining models of the crustal dynamics.

To overcome some of the above problems, we examine the important problem of characterizing the model for the NEI earthquake data from the following two perspectives: (i) a non-linear forecasting approach to distinguish between high- and low-dimensional chaos and (ii) an ANN-based method to compare and confirm the above result. Application of the multiple non-linear techniques would reduce bias and provide more confidence for understanding the physical processes in the NEI region.

A significant feature of the non-linear forecasting technique is that it is robust, even for the analysis of a small number of data points (Sugihara and May, 1990). Recently, several workers have successfully applied the method on short-term meteorological and seismological time series to assess their irregular and unpredictable behavior (Tsonis and Elsner, 1992; McCloskey, 1993; Tiwari et al., 2003, Tiwari et al., 2004; Tiwari and Srilakshmi, 2005). Artificial neural network (ANN) is another powerful tool, which is being extensively used for modeling, forecasting and prediction of different types of data. The major advantage of the ANN technique is its ability to model the underlying non-linear dynamical system without any prior assumptions and information regarding the dynamical processes involved. This superiority of the ANN approach over the traditional methods to solve complex geophysical and geological problems needs further support.