# Hazard Model: Epidemic-Type Aftershock Sequence (ETAS) Model for Hungary
## 2 Data
This suggests an inhomogeneity of the merger of the primary sources underlying the Romanian part of catalogue C. Therefore, the affected area is excluded from the ETAS parameter fitting due to concerns of data quality. The boundary of the excluded area follows the area source zone boundaries of the SHARE project [26]. Therefore, the exclusion affects a strip within Hungary along the Romanian border. Magnitude-frequency distributions suggest that the completeness threshold of the remaining catalogue on the core window is \(M\geq 2.8\) at the beginning in 1996, which has gradually improved to \(M\geq 2.5\) by 2000 and to \(M\geq 2.2\) by 2013. The sensitivity contours of the Hungarian seismograph network indicate completeness for \(M\geq 2.5\) on most of the modelled area in the core window with some lower-sensitivity areas on the periphery and with gradually improving coverage over time [19]. The catalogue is considered complete for \(M\geq 2.5\) in the extended window only since 2018, except for a completeness gap immediately after the Petrinja 2020 mainshock: the detection of early aftershocks after a large earthquake is typically incomplete since the seismograms in this initial period are saturated with overlapping waves from multiple events [18]. Given the trade-off between completeness and the size of the catalogue, we find that the optimal choice of the threshold for this study is \(M\geq 2.5\). A threshold increase would marginalize the part of the catalogue within Hungary itself and would sharply reduce the number of events for estimating the spatial distribution of the background process. For the model parameterization, completeness is assumed on the core window since 2000 and on the extended window since 2018, except for a 1-day period after the Petrinja mainshock. Figure 1: Schematic diagram of the coverage and overlaps of the source catalogues used in the study. After merging catalogues B, C, and X, applying the \(M\geq 2.5\) threshold, removing duplications, removing events outside the completeness periods, and removing events in the excluded area, the remaining size of the target catalogue for ETAS parameter fitting is 1978. An additional 236 events reaching \(M\geq 2.5\) are used as auxiliary trigger events; this includes 27 events from year 1999 and 209 events from the Petrinja completeness gap. A map of the fitting catalogue is shown in Figure 2. Another 218 events from catalogues B, C, and X outside the completeness periods are used as additional epicenter nodes for the kernel density estimation of the spatial distribution of background events. For model calculations, geographical latitude-longitude coordinates \((\varphi,\lambda)\) are converted to an \((x,y)\) kilometre grid via the following transformation:  
\[x=R\cdot\cos\varphi\cdot\tan(\lambda-\lambda_{0}),\;\;y=R\cdot(\varphi-\varphi _{0}), \tag{1}\]  
where \(R=6\;371.01\) is the mean radius of the Earth in kilometres. This corresponds to a tangent transverse cylindrical projection whose central meridian is at \(\lambda_{0}\) and that transforms parallels into straight lines. The point \((\varphi_{0},\lambda_{0})\) is set at (47.5\({}^{\circ}\), 19\({}^{\circ}\)), i.e., the rounded coordinates of Budapest, which are transformed into \((x,y)=(0,0)\) in the kilometre grid. Figure 2: (**a**) Location of the model area within Europe. (**b**) Plot of the earthquake catalogue for Hungary used for epidemic-type aftershock sequence (ETAS) model parameterization—target catalogue plus auxiliary events, 1999–2021. The map covers the extended window. The boundaries of the core window (dashed black line) and excluded area (red line) are marked. Events reaching \(M\geq 4.0\) are highlighted.