Identifying anomalous signals in GPS data using HMMs: An increased likelihood of earthquakes?

Abstract

A way of combining a hidden Markov model (HMM) and mutual information analysis is proposed to detect possible precursory signals for earthquakes from Global Positioning System (GPS) data. A non-linear filter, which measures the short-term deformation rate ranges, is introduced to extract anomalous signals from the GPS measurements of ground deformation. An HMM fitted to the filtered GPS measurements can classify the deformation data into different states which form proxies for elements of the earthquake cycle. Mutual information is then used to examine whether any of these states possesses any precursory characteristics. The class of GPS measurements identified by the HMM as having the largest variation of deformation rate shows some precursory information and is hence considered as a “precursory state”. The performance of possible earthquake forecasts is assessed by comparing a decision rule (based on model characteristics) with the actual outcome.

Introduction

There has been considerable interest in whether GPS measurements have any predictive power for earthquake occurrences. Roeloffs (2006) listed at least ten credible examples of tectonic earthquakes preceded by deformation rate changes, and GPS observations around the future rupture source detected slow slip leading up to the October 2004 earthquake of magnitude 6.6 in the Chuetsu area, central Japan (Ogata, 2007). These anomalies manifested as long-term pre-earthquake slip, but it is possible that precursory GPS signals may operate on a shorter time-scale, and therefore techniques which can detect or extract subtle changes (such as irregular spikes, step jumps and trend changes) in GPS measurements, which may be related to earthquakes, are necessary.

Granat and Donnellan (2002) and Granat (2003) used an HMM based method to analyze GPS data from the southern California region. From the daily displacement time series collected in Claremont, California, they observed a clear separation of the states before and after the Hector Mine quake in October 1999. Granat (2006) applied this method to the daily GPS data from 127 stations from the Southern California Integrated Geodetic Network. Approximately 70 of the stations had state changes on the day of the Hector Mine earthquake, indicating that GPS signals from earthquakes are detectable over hundreds of km. However, the different states were clearly dominated by the long-term trends of each component of the data, and the states are entered and existed only once (see e.g. Figure 5 in Granat (2006)); thus the method is not suitable for predictive purposes.

We therefore introduce a non-linear filter for the GPS process to extract distinguishable signals from the majority of the data. This nonlinear filter calculates the range of the short-term deformation rates and captures anomalies.

Studies concerning earthquake genesis suggest an acceleration in small scale seismicity before a large event (Bowman et al., 1998, Jaumé and Sykes, 1999, Vere-Jones et al., 2001) which may have a cyclic nature (Jaumé and Bebbington, 2004, Bebbington et al., 2010). GPS measurements of deformation may therefore capture this acceleration, indirectly reflecting the underlying dynamics (the unobservable or hidden states) of the earthquake system (cf. Wang et al., in press). Under this assumption, our nonlinear filter and the underlying dynamics form an HMM framework. The HMM categorizes the data into different states, each state suggesting particular dynamics, one or more of which may have a precursory character. We thus use the Viterbi algorithm (Viterbi, 1967, Forney, 1973) to track the most probable sequence of states from the GPS data, and calculate the mutual information (MI) between each state from the most likely state sequence and the earthquake occurrences to examine if there is any association. We also discuss a possible way of producing earthquake forecasts based on the mutual information results. We illustrate the method on data from the central North Island, New Zealand and data from Southern California.