Calculation of maximum earthquake accelerations in a semi-empirical way for southern Gulf of California extensional province, Mexico

The Gulf of California (GoC) is an extensional province where the North America and Pacific plates limit. The boundary is an echelon set of normal and transform faults that produce low and moderate seismicity (M $$\sim$$ ∼ 5). Castro et al. (J S Am Earth Sci: 106:103087, 2021) reports a Gutenberg–Richter law with a minimum magnitude catalog completeness of 3.6 and b value of 0.86 that are typical for active regions. However, earthquakes with magnitude 7.1 (e.g., 2012/04/12 earthquake) have been reported in the Pescadero transform fault (Sumy et al. in Bull Seismol Soc Am: 103(1):487–506, 2013; Huesca-Pérez et al. in Bull Seismol Soc Am, 2022). The importance of applying a maximum acceleration analysis in this region is to assess the danger associated with earthquakes and their destructive potential. In this work, a semiempirical methodology for making maximum acceleration maps is proposed by using Green’s function method and Brune’s source time function model. It has the advantages of being physical, as opposed to probabilistic, and a method that is deterministic and based on first principles, as well as open to improvement. A consequence of this model is that the effective stress of the rupture is directly proportional to the scalar moment. We show observed accelerations minus predicted accelerations calculated by both methods: the semiempirical and the probabilistic methods. Numerically, the probabilistic method gives a slightly better numerical result due to the fact that the attenuation relationships are more accurate to represent the rupture process but it is obtained using regression analysis. Then, we compare it with the traditional probabilistic seismic hazard analysis (PSHA). Differences are observed, which makes it evident that the probabilistic hazard analysis includes a fluctuating part of the maximum acceleration. We see that both methods have particular advantages.