New Source Duration Relationships for Mexican Earthquakes: Practical Application to Stochastic Summation Methods

From the gathering of 127 source time functions (STFs) of seismic events in Mexico, relationships have been developed between the seismic moment (M₀) and the total source rupture duration (τ_d), for normal-faulting inslab, interplate and strike-slipe mechanisms. This relationship has been explored by different authors like Furomoto and Nakanishi (J Geophys Res 88:2191–2198, 1983), Tanioka and Ruff (Seismol Res Lett 68:386–400, 1997), Singh et al. (Bull Seismol Soc Ame 90:468–482, 2000), among others; the latter authors present a similar general relationship for Mexico, considering 53 STFs and with information until 1998. In this research, complementary databases have been integrated, and the available functions updated base on recent research works about the SCARDEC method are used (Vallée et al. in Geophys J Int 184:338–358, 2011; Vallée and Douet in Phys Earth Planet Interiors 257:149–157, 2016). With the proposed expressions, it is possible to estimate reasonably, the main parameters of interest for algorithms of stochastic summation, such as the corner frequencies or stress drops in order to simulate strong ground motions, commonly used for source-rupture studies, site-amplification analysis, or for earthquake-resistant design. Besides, a new flexible model of stochastic summation is presented, which allows considering several ways to generate more realistic motions, according to the spectral behavior, both for low and for intermediate frequencies, under earthquakes with moderate and high magnitude; this model was compared with results from a two-stage alternative method considering two corner frequencies.