# Seismic Hazard Evaluation and Strain Dynamics in the
## 3 Methodology and Implementation
### Gutenberg-Richter Law  
#### 3.2.1 Seismic Hazard Parameters  
In seismology, the Gutenberg-Richter law, the most well-known empirical relationship used for evaluating earthquake magnitudes and seismic hazard, is a method based on establishing a linear magnitude-frequency relationship between the number of past earth  
Figure 4: Histograms created based on magnitude (Mw) and years for the dataset used (KOERI). \begin{table}
\begin{tabular}{c c c c c c} \hline
**Mag.** & \multirow{2}{*}{**Const**} & \multirow{2}{*}{**Magnitude**} & \multicolumn{2}{c}{**Relationship**} & **Data** \\
**Type** & & & & **(\%)** & **Count** \\ \hline  & **Coef** & **Std Err.** & **Coef** & **Std Err.** & & \\ \hline Md & 0.2061 & \(\pm\)0.069 & 0.9980 & \(\pm\)0.015 & 98 & 88 \\ Ml & \(-\)0.1554 & \(\pm\)0.047 & 1.0483 & \(\pm\)0.012 & 95 & 411 \\ Ms & 1.3900 & \(\pm\)0.063 & 0.7521 & \(\pm\)0.013 & 97 & 92 \\ Mb & \(-\)0.3018 & \(\pm\)0.080 & 1.1007 & \(\pm\)0.017 & 98 & 93 \\ \hline \end{tabular}
\end{table} 
Table 3: The coefficients obtained for magnitude scaling along with standard deviations, correlation percentages, and data counts. quakes in a region and their magnitudes to estimate the potential magnitudes of future events [87; 88]. One of the key relationships used to reflect the seismic activity of a relevant region, the G-R law method, defines the relationship between earthquake magnitudes and their frequencies of occurrence through the equation provided in Equation (1):  
\[\log\text{N(M)}=a-b.\text{M} \tag{1}\]  
Here, N(M) represents the number of earthquake events in the study area during a specific time period with magnitudes equal to or greater than M, while the values of \(a\) and \(b\) refer to the regression coefficients assumed to be constant for the region. While the \(a\) parameter is a value that depends on the seismic activity level of the study area, which may vary significantly from different regions, the \(b\) parameter is accepted as a parameter representing the tectonic features of the region [89; 90; 91; 92]. The \(a\) parameter, which represents the annual average seismic activity, can vary depending on the time period under study, the area size, and the earthquake frequency. The \(b\) parameter, which is inversely proportional to the stress in the crust and is related to the physics of earthquake occurrence, is crucial for earthquake occurrence probability evaluation. It is also associated with or reflects the stress conditions in the region [93; 94]. While the \(a\)-value represents the overall earthquake rate, the \(b\)-value indicates the ratio between small and large earthquakes. A higher \(b\)-value suggests that smaller magnitude earthquakes occur more frequently than larger ones, whereas a lower \(b\)-value indicates that larger magnitude earthquakes are more common, reflecting a region with higher stress [8; 95; 96; 97]. In the early studies conducted on seismic hazard analysis, it was assumed that the \(b\)-value was the same across all regions. However, subsequent studies have shown that the \(b\) parameter can vary between regions, as demonstrated in several studies, examples of which are provided below [98]. In a seismically active region, the \(b\) parameter is generally assumed to be very close to 1, but changes in this value can be observed depending on the estimation method, the catalogue used, and the magnitude range of the selected earthquakes, and the slightest difference in the \(b\) parameter notably affects the results [99]. [PERSON] and [PERSON] [100] presented \(b\) = 0.90 \(\pm\) 0.02 for shallow earthquakes in the M = 6 to 6.5 range and \(b\) = 1.2 \(\pm\) 0.2 for intermediate and deep earthquakes. They also suggested that the \(b\) parameter varies between 0.45 and 1.5 for other regions. [PERSON] [101] proposed that the \(b\)-value ranges between 0.4 and 1.8 for different tectonic regions, suggesting that it is related to the geological age of the tectonic region. [PERSON] [102], on the other hand, stated that the \(b\)-value varies between 1.0 and 1.6.