Testing the best modeling techniques for earthquake-related long-term geodetic transients

Major earthquakes can produce evident offsets in geodetic time series up to dozens of kilometres far from their epicentres. Moreover, the viscoelastic relaxation along faults and within the adjoining crustal volumes foster slow geodetic transients called ‘afterslip’. They usually last for months or even years and are usually modelled using exponentials (Montillet & Bos, 2020). Recently, evidence has been collected that the seismic cycle can affect GNSS time series for decades (e.g., Carafa et al., 2024). These observations challenge the idea that geodetic recordings can be considered stationary over human-life time intervals and only affected by periodic modulations induced by seasonal loading, tides and anthropic activities. Here, we compare three different models for dozens of long-term afterslips in suitably pre-processed GNSS daily data series: exponential, power law and stretched exponential functions. The exponential arises from a purely viscoelastic behavior of faults, a power-law attenuation can be produced by a suitable sum of exponential relaxation process or power-law fault rheology (Ingleby & Wright, 2017), while the stretched exponential can be derived assuming geodetic contributions from crustal volumes with heterogeneous rheology. We prove that stretched exponentials can be used for the reliable prediction of future developments of afterslip in GNSS time series being comparable or even superior to both exponentials and power laws in fitting both in the short- and long-term trends. We also provide a physical motivation to support their occurrence in terms of stress redistribution in the crustal volumes surrounding major faults. References Carafa M. M., Bird P., Verdecchia A., Taroni M. and Doglioni C.; 2024: Empirical evidence for multi-decadal transients affecting geodetic velocity fields and derived seismicity forecasts in Italy. Sci. Rep., 14(1), 19941. Ingleby, T., & Wright, T. J. (2017). Omori‐like decay of postseismic velocities following continental earthquakes. Geophysical Research Letters, 44(7), 3119-3130. Montillet, J. P., & Bos, M. S. (Eds.). (2019). Geodetic time series analysis in earth sciences. Springer.