Inference of multiple earthquake cycle relaxation time scales from irregular geodetic sampling of interseismic deformation

Characterizing and understanding the earthquake cycle is difficult due to the lack of high-resolution geodetic observations of duration comparable to that of characteristic earthquake recurrence intervals (100-10,000 years). Here we approach this problem by comparing long-term geologic slip rates with geodetically derived fault slip rates 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 varies greatly from fault to fault. Assuming that the underlying mechanics of the seismic cycle are similar for many faults, taken as a whole, observations nearby different faults may be interpreted as stochastic samples over a significantly larger fraction of the earthquake cycle than could be obtained from the geodetic record at any one fault alone. As an ensemble, we find that geologic and geodetically inferred slip rates agree well with a linear relation of 0.94±0.05. 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 the two-layer Burgers model (with two relaxation timescales) is consistent with observations of deformation throughout the earthquake cycle while the widely used two-layer Maxwell model (single relaxation timescale) is not, suggesting that the earthquake cycle is effectively characterized by rapid postseismic stage and a much more slowly varying interseismic stage.