Inference of Multiple Earthquake-Cycle Relaxation Timescales from Irregular Geodetic Sampling of Interseismic Deformation

Characterizing surface deformation throughout a full earthquake cycle is a challenge due to the lack of high-resolution geodetic observations of duration comparable to that of characteristic earthquake recurrence intervals (250-10,000 years). Here we approach this problem by comparing long-term geologic slip rates with geodetically derived fault slip rates by sampling only a short fraction (0.001%-0.1%) of a complete earthquake cycle along 15 continental strike-slip faults. Geodetic observations provide snapshots of surface deformation from different times through the earthquake cycle. The timing of the last earthquake on many of these faults is poorly known, and may vary greatly from fault to fault. Assuming that the underlying mechanics of the seismic cycle are similar for all faults, geodetic observations from different faults may be interpreted as samples over a significantly larger fraction of the earthquake cycle than could be obtained from the geodetic record along any one fault alone. As an ensemble, we find that geologically and geodetically inferred slip rates agree well with a linear relation of 0.94 +/- 0.09. To simultaneously explain both the ensemble agreement between geologic and geodetic slip-rate estimates with observations of rapid postseismic deformation, we consider the predictions from simple two-layer earthquake-cycle models with both Maxwell and Burgers viscoelastic rheologies. We find that a two-layer Burgers model, with two relaxation timescales, is consistent with observations of deformation throughout the earthquake cycle, whereas the widely used two-layer Maxwell model with a single relaxation timescale, is not, suggesting that the earthquake cycle is effectively characterized by a largely stress-recoverable rapid postseismic stage and a much more slowly varying interseismic stage.