# Seismic Hazard Evaluation and Strain Dynamics in the
## 3 Methodology and Implementation
### Spatiotemporal Distribution of Earthquake Energy  
Identifying areas where earthquakes are concentrated is important for seismic hazard analysis and subsequent risk management in a region. Determining regions with frequent earthquake occurrences allows for the examination of active faults/zones and their associated seismic hazards, and through comprehensive interpretation of the results, potential epicenters and impacted areas of future earthquakes can be forecasted. For this reason, there are studies in the literature where spatial density analyses have been conducted using earthquake catalogs [116; 117]. Through the obtained dataset, a spatial density analysis was conducted for the SFZ and its surrounding area (Figure 7). Kernel Density Estimation (KDE) has been used for the density analysis. KDE is a statistical method used to estimate the probability density function for a dataset. This method defines a kernel function (Gaussian) around each data point and then sums the effects of these kernels to smoothly represent the density of the data. The results of the spatial density analysis conducted in this study indicate intense seismic activity to the northwest of the Gelenbe Fault Zone (GFZ) and approximately to the north of the Simav segment. The spatial density analysis highlights the areas where events are concentrated in terms of frequency. These densities are obtained by applying a kernel with a specific  
Figure 6: The recurrence periods of earthquakes with magnitudes ranging from M 5 to M 7.1 in the study area (The texts indicated by the arrows represent the maximum earthquake magnitude that the segment can generate according to the Wells and Coppersmith [42] relationship). Figure 7: Spatial density results calculated using Kernel Density Estimation for the study area (the black dashed line represents the main zone examined in this study, the SFZ, while the red lines indicate other active faults in the region). bandwidth around each point, calculating the increase in density in the region where the point is located. The bandwidth controls the degree of spread of the kernels, with a smaller bandwidth creating a more detailed density pattern, while a larger bandwidth results in a more general density pattern. The bandwidth factor was determined according to [PERSON]'s Rule of Thumb, as proposed by [PERSON] [118], and was obtained as 0.64643 in this study. Although spatial density analyses provide valuable insights into areas with concentrated events, one disadvantage of spatial density analysis is the assumption that all events used for the analysis are considered equally significant. In other words, the impact of two earthquakes, one with a magnitude of M = 6 and the other with a magnitude of M = 3, is considered equal in the spatial density analysis. However, the magnitudes of actual or potential earthquakes are critically important for seismic hazard analyses as they play a distinctive role in assessing the risk. The energy released during earthquakes, which is closely linked to their destructive potential, increases logarithmically. \[E=10^{1.5~{}x~{}M+4.8} \tag{3}\]  
For the reasons mentioned above, it is necessary to weight the earthquakes according to their magnitudes in seismic hazard analysis spatial density maps. The most appropriate method for weighting the occurred earthquakes is to use the energy released as a result of the earthquakes. Therefore, the earthquakes in the dataset have been converted into energy using the formula in Equation (3). In this equation, E represents the energy released by the earthquake (Joule) and M (Mw) denotes the magnitude of the earthquake (Figure 8). The results show that the energy released by the earthquakes that occurred and were recorded during the instrumental period was mostly concentrated at the intersection of the Sundrigi and Simav segments. Additionally, high energy was also released to the north of the Abide segment.