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

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.