Modeling seismicity rate changes during the 1997 Umbria-Marche sequence (central Italy) through a rate- and state-dependent model

We model the spatial and temporal pattern of seismicity during a sequence of moderate-magnitude normal faulting earthquakes, which struck in 1997 the Umbria-Marche sector of Northern Apennines (Italy), by applying the Dieterich (1994) rate- and state-dependent constitutive approach. The goal is to investigate the rate of earthquake production caused by repeated coseismic stress changes computed through a 3-D elastic dislocation model in a homogeneous half-space. The reference seismicity rate is assumed time independent, and it is estimated by smoothing the seismicity that occurred in the previous decade without declustering. We propose an analytical relation for deriving the stressing rate directly from the reference seismicity rate. This allows us to perform a tuning of the constitutive parameter A sigma (where A accounts for the direct effect of friction in the rate- and state-dependent model and sigma is the effective normal stress) into the Dieterich model through a maximum likelihood method, which yields for this seismic sequence a best fitting value equal to 0.004 Mpa. Our computations show that, although seven out of eight main shocks are located in areas of increased rate of earthquake production, numerous aftershocks are located in seismicity shadows. Our simulations point out that the adopted value of A sigma strongly affects the pattern of both seismicity shadow and areas enhanced rate of earthquake production. We conclude that solely accounting for static stress changes caused by the main shocks of this seismic sequence is not sufficient to forecast the complex spatial and temporal evolution of seismicity.