Transient signal-based quantification of earthquake triggering effects on nearby faults using rate and state friction

Both numerical simulations and observational pieces of evidence suggest that the earthquake triggering mechanism depends non-linearly on time. The rate and state friction (RSF) demonstrate these dependencies with a changing weight of healing and weakening terms during its state's evolution. A clock advance due to a nearby rupture using the RSF models either agrees well with the Coulomb's static failure during the fault healing stage or becomes highly susceptible to velocity changes when the failure is imminent. Here we aim to formulate an analytical relation for earthquake triggering effects on nearby faults using transient signals. The dynamic mechanical weakening on the fault interface is quantified as a function of a transient oscillatory signal's peak ground velocity (PGV) and peak spectral frequency (PSF), elastic properties of the fault, and different state weakening terms. So far, the tested numerical simulations show a good agreement with our proposed analytical approach. As a case study, nearby seismic waveforms recorded during the M6.4 (04.07.2019) event that preceded the larger  M7.1 (06.07.2019) Ridgecrest earthquake are used to calculate mechanical weakening, which correlates well with the computed PGV values attenuating with distance. The results support that if inadequate instrumentation exists, those dynamic weakening effects can be approximated empirically using the source parameter of the triggering event as a function of distance and directivity. Derivation of this analytical relation with additional verifications from numerical simulations will contribute to simultaneously including dynamic and static effects. This may lead to a more realistic estimation of increased seismic risk on nearby faults after an earthquake.