An increase in Coulomb stress could not only trigger aftershocks but also enhance the probability of the next larger earthquake. The Pasaman Earthquake took place in the Sumatran Fault system, where there was a potential for devastating earthquakes (Sieh and Natawidjaja, 2000). To evaluate the seismic hazard of the Pasaman Earthquake, we considered the ∆CFS imparted by the Pasaman Earthquake and the fault parameters of the Sumatran Fault.

A map view of the ∆CFS (Fig. 4) illustrates a general pattern of stress change on the Sumatran Fault. According to this map view, stress in the Sumpur, Sianok, Sumani, and Angkola segments was promoted while stress in the Barumun segment was dropped. To specify the stress change in these segments, their mechanisms (Table 2) and alignments were implemented in the ∆CFS calculation (Fig. 5). The stresses in the Sumpur and Sianok segments were significantly enhanced, with a maximum ∆CFS of 0.1 bar, and the stresses in the Sumani and Angkola segments were slightly enhanced, with a maximum ∆CFS of 0.03 and 0.01 bars, respectively. To quantify the impact of the seismicity rate based on ∆CFS, we implemented the rate-and-state friction model (Dieterich, 1994). This model evaluates seismicity rate evolution \(\varDelta R\left(t\right)\) using ∆CFS and is expressed as:

$$\varDelta R\left(t\right)=\frac{\lambda }{\left[exp\right(-\frac{\varDelta CFS}{A\sigma })-1]exp(-\frac{t-{t}_{n}}{{t}_{na}})+1}$$

,

where \(\lambda\) represents long-term seismicity rate; \(A\sigma\) represents a constitutive parameter of the model, assumed to be 0.3 (Chan et al., 2017); \({t}_{n}\) represents the occurrence time of the earthquake that caused the ∆CFS; and \({t}_{na}\) represents aftershock duration, obtained from our Omori’s model (Fig. 3).

Based on the rate-and-state friction model and stress change, the rate perturbation by the Pasaman Earthquake could be evaluated at each segment of the Sumatran Fault (Table 2). Due to a significant stress increase in the Sumpur and Sianok segments, we expected a seismicity rate increase of ca. 40%. The seismicity rates in the Sumani and Angkola could rise by 10.5% and 3.4%, respectively, whereas the Barumum segment could be farther from the next earthquake due to coseismic stress drop.

The short-term rate perturbation imparted by the Pasaman event has been evaluated for the Sumatran fault. To quantify its long-term rupture probability, we considered the recurrence interval of each fault segment (Table 2). The rupture probability could be quantified using a Poisson process, which is widely applied for probabilistic seismic hazard assessment (Cornell, 1968), expressed as follows:

$$P=1-{e}^{-\nu \bullet t}$$

,

where \(P\) represents the rupture probability of a fault, \(\nu\) represents the annual seismicity rate of the fault segment, and t represents the time period of interest.

Using this model, each segment’s rupture probability in the coming 50 years could be quantified (Table 2). A high rupture probability of ca. 60% was obtained for the Sumpur segment due to its short recurrence interval (55 years). Generally, the earthquake probabilities on all these segments are rather high, due to their high slip rates (14 mm/year).

In addition to the stationary probability based on the assumption of the Poisson process mentioned above, for segments where data from at least one previous earthquake were recorded, evaluation of rupture probability can be further improved by including the record of the previous earthquake(s). The time elapsed since the previous event could be incorporated into the time-dependent Brownian Passage Time (BPT) model (Ellsworth et al., 1999). The BPT model has been applied to many probabilistic seismic hazard assessments (e.g., Fujiwara, 2014), and its credibility has been confirmed by comparing it to paleo-seismic data (Gao et al., 2022). The density function (DF) of this model can be expressed as:

$$DF={\left(\frac{\mu }{2\pi {\alpha }^{2}{t}^{3}}\right)}^{1/2}\text{e}\text{x}\text{p}(-\frac{{(t-\mu )}^{2}}{2{\alpha }^{2}\mu t})$$

,

where *µ* represents the mean recurrence interval, *t* represents the time elapsed since last earthquake, and \(\alpha\) represents the aperiodicity, whose value is usually between 0.3 and 0.7 and is assumed to be 0.5 (Chan et al., 2019). Based on this model, the rupture probabilities for the Angkola, Sianok, and Sumani segments (with records of previous events) were evaluated (shown in Fig. 6). A high rupture probability is expected for a segment with a short recurrence interval and/or long time elapsed since the last earthquake. The earthquake probability at the Sumani segment in the coming 50 years could be 72.0%. Based on the BPT model, these three segments obtained higher rupture probabilities compared to the probabilities obtained via the time-dependent Poisson process, which can be attributed to a long time elapsed since the last earthquake.