# Seismic Risk in Alborz: Insights from Geological Moment Rate Estimation and Fault Activity Analysis
## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c} \hline
**a** & **b** & **Ms** & **log N** & **N** & **T (Year)** \\ \hline  & & 3 & \(-\)0.255856 & 0.55481 & 1.8 \\  & & 3.2 & \(-\)0.394216 & 0.403445 & 2.4 \\  & & 3.4 & \(-\)0.532576 & 0.293376 & 3.4 \\  & & 3.6 & \(-\)0.670936 & 0.213336 & 4.6 \\  & & 3.8 & \(-\)0.809296 & 0.155133 & 6.4 \\  & & 4 & \(-\)0.947656 & 0.112089 & 8.8 \\  & & 4.4 & \(-\)1.224376 & 0.059652 & 16.7 \\  & & 4.6 & \(-\)1.362736 & 0.043377 & 23.0 \\  & & 4.8 & \(-\)1.501096 & 0.031543 & 31.7 \\  & & 5 & \(-\)1.639456 & 0.022937 & 43.5 \\  & & 5.2 & \(-\)1.777816 & 0.01668 & 59.9 \\
1.832508913 & 0.6918 & 5.4 & \(-\)1.916176 & 0.012129 & 82.4 \\  & & 5.6 & \(-\)2.054536 & 0.00882 & 113.3 \\  & & 5.8 & \(-\)2.192896 & 0.006414 & 155.9 \\  & & 6 & \(-\)2.331256 & 0.004664 & 214.4 \\  & & 6.2 & \(-\)2.469616 & 0.003391 & 294.8 \\  & & 6.4 & \(-\)2.607976 & 0.002466 & 405.4 \\  & & 6.6 & \(-\)2.746336 & 0.001793 & 557.6 \\  & & 6.8 & \(-\)2.884696 & 0.001304 & 766.8 \\  & & 7.2 & \(-\)3.161416 & 0.00069 & 1450.1 \\  & & 7.4 & \(-\)3.299776 & 0.000501 & 1994.2 \\  & & 7.6 & \(-\)3.438136 & 0.000365 & 2742.4 \\  & & 7.7 & \(-\)3.507316 & 0.000311 & 3216.0 \\ \hline \end{tabular}
\end{table} 
Table 3: Estimates of the earthquake return period (T) with different magnitudes (Ms) in the region (based on [30]). N represents the cumulative frequency of earthquakes, while a and b are constant coefficients. The ground motion parameters, such as velocity, acceleration, and displacement in the vertical and horizontal directions at the earthquake epicenter, were estimated using the formulas proposed by [31]. Additionally, various formulas, including some from [30; 32; 33; 34], were used to calculate the relationship between fault length (L) and earthquake magnitude (Ms) in the study area. These formulas were employed to estimate the seismic potential of the faults, and the calculations are presented in Table 5. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**a** & **b** & **MS** & \begin{tabular}{c} **Earthquake** \\ **Return Period** \\ \end{tabular} & \begin{tabular}{c} **Useful Life** \\ **(T)** \\ \end{tabular} & \
\begin{tabular}{c} **DBE** \\ **(R = 64\%)** \\ \end{tabular} &
\begin{tabular}{c} **MCE** \\ **(R = 90\%)** \\ \end{tabular} \\ \hline  & & 3 & 1.8 & 10 & 4.08 & 5.51 \\  & & 3.2 & 2.4 & 20 & 4.52 & 5.94 \\  & & 3.4 & 3.4 & 30 & 4.77 & 6.2 \\  & & 3.6 & 4.6 & 40 & 4.95 & 6.38 \\  & & 3.8 & 6.4 & 50 & 5.09 & 6.52 \\  & & 4 & 8.8 & 60 & 5.21 & 6.63 \\  & & 4.4 & 16.7 & 70 & 5.3 & 6.73 \\  & & 4.6 & 23.0 & 80 & 5.39 & 6.81 \\  & & 4.8 & 31.7 & 90 & 5.46 & 6.89 \\  & & 5 & 43.5 & 100 & 5.53 & 6.95 \\  & & 5.2 & 59.9 & 110 & 5.59 & 7.01 \\
1.832509 & 0/6918 & 5.4 & 82.4 & 120 & 5.64 & 7.07 \\  & & 5.6 & 113.3 & 130 & 5.69 & 7.12 \\  & & 5.8 & 155.9 & 140 & 5.74 & 7.16 \\  & & 6 & 214.4 & 150 & 5.78 & 7.21 \\  & & 6.2 & 294.8 & 160 & 5.82 & 7.25 \\  & & 6.4 & 405.4 & 170 & 5.86 & 7.29 \\  & & 6.6 & 557.6 & 180 & 5.9 & 7.32 \\  & & 6.8 & 766.8 & 190 & 5.93 & 7.36 \\  & & 7.2 & 1450.1 & 200 & 5.96 & 7.39 \\  & & 7.4 & 1994.2 & 210 & 5.99 & 7.42 \\  & & 7.6 & 2742.4 & 220 & 6.02 & 7.45 \\  & & 7.7 & 3216.0 & 230 & 6.05 & 7.48 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Estimates of DBE and MCE for a useful life of 10 to 230 years.