A hybrid genetic algorithm for calculating the relaxation time constants of stochastic post-seismic GPS coordinate time series

Abstract

Modeling post-seismic deformation (PSD) of Global Positioning System (GPS) station trajectory models invokes logarithmic or/and exponential decay functions with pre-assigned relaxation time constants (RTCs). We propose a hybrid optimization method combining genetic algorithms and interior-point techniques to determine station-specific RTCs. Two criteria (root mean square (RMS) misfit and the Akaike Information Criterion (AIC), a posterior measure of log-likelihood) are used to gauge the goodness of fit. Validation was performed on synthetic data and eight daily GPS coordinate time series subject to the 2011 Tohoku-Oki earthquake in Japan. We find that the temporally correlated noise, optimization strategy and the tradeoffs among sub-models of station trajectory jointly govern the identification of decay function form and the accuracy of inferred RTCs. The double logarithmic model can fit the post-seismic data well and exhibits more uniform RTCs, making it more practical for PSD modeling. Significant trajectory misfit is evident during the initial weeks to months after the earthquake, with millimeter-level discrepancies observed between the RMS and AIC criteria. Incorrect RTC assignments further exacerbate these discrepancies and introduce biases into PSD modeling and co-seismic offset estimation, risking misleading post-seismic predictions.