A sequential Monte Carlo framework for the physical modeling of post-seismic transients

Post-seismic deformation encompasses the complex adjustment of the crust and upper mantle following large earthquakes, often continuing for years to decades. Accurately modeling these transients remains challenging due to nonlinear processes, observational noise, and incomplete data. We present a Sequential Monte Carlo (SMC) framework for estimating post-seismic deformation that uses particle filtering (PF) to track the evolving deformation signal and the associated parameters in a fully stochastic setting. Using synthetic GNSS time series spanning logarithmic, exponential, mixed logarithmic-exponential and stretched exponential transient behaviors, we assess model performance under realistic noise levels and data gaps. Compared with a grid-based method and standard MCMC, our approach yields systematically lower fitting errors and more stable parameter estimates, with the true synthetic values recovered within narrower 95% credible intervals. The PF scheme further enables online estimation of both the latent deformation state and the time-varying parameters, maintaining robust performance even when only truncated segments of the time series are available. From a statistical perspective, the logarithmic-exponential model shows the best fitting performance, whereas the stretched exponential formulation offers a compact and physically interpretable alternative. Application to long-term GNSS observations after the 2011 M_W9.0 Tohoku earthquake demonstrates that the proposed framework successfully captures complex, multi-timescale post-seismic signals in a heterogeneous tectonic setting. Finally, the results highlight PF as a promising tool for the robust estimation of post-seismic deformation in both real-time and retrospective analyses.