# A New Ground-Motion Prediction Model for Shallow Crustal Earthquakes in Turkiye
## 3 Ground-Motion Prediction Models (GMPMs)
### Regression Coefficients and Residuals  
The full set of GMPE coefficients (variable names starting with the letter \(c\) or others) obtained from the regression analysis is listed in Tables 2 and 3. Residual plots are shown in Figure 10 to help us to explore the degree of agreement between the ground-motion estimates of our GMPE and the empirical observations obtained from the Turkiye dataset. The distributions are displayed in the left, middle, and right panels for periods of 0.01 s, 0.2 s, and 1 s, respectively. However, the residuals are separated into between-events, single-site, and site-to-site terms plotted versus \(M_{W}\), \(R_{JB}\), and \(V_{530}\), respectively. In Figure 10, each parameter is divided into specific intervals, with the means and standard deviations of each interval represented by the error bars. The between-event residuals, located at the top of the figure, generally show no significant trend; however, it is observed that the records of the Van earthquake (\(M_{W}\) 7.1) fall below the median. This inconsistency can be explained as the possible interaction of the variable stress drop and the kappa term (16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42). The Van earthquake exhibits very weak ground motions that are inconsistent with finite-fault distance metrics. The means of the site-to-site residuals and single-site within-event residuals suggest that the proposed model accurately represents the observed data without any bias. These plots show that the model fits the data well and there are no significant trends in the residuals. \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline
**Period (s)** & \(\mathbf{c_{1}}\) & \(\mathbf{c_{2}}\) & \(\mathbf{c_{3}}\) & \(\mathbf{c_{4}}\) & \(\mathbf{c_{5}}\) & \(\mathbf{c_{6}}\) & \(\mathbf{c_{7}}\) & \(\mathbf{c_{8}}\) & \(\mathbf{d_{1}}\) & \(\mathbf{d_{2}}\) & \(\mathbf{d_{3}}\) \\ \hline PGV & 7.4200 & \(-\)4.1159 & 1.0709 & \(-\)1.0385 & \(-\)1.1349 & 0.0108 & \(-\)0.0120 & 0.0200 & \(-\)0.8183 & 0.2000 & \(-\)0.0026 \\ PGA & 2.4717 & \(-\)2.7927 & 0.7180 & \(-\)0.6765 & \(-\)0.9615 & 0.0163 & \(-\)0.0120 & 0.0200 & \(-\)1.0108 & 0.2000 & \(-\)0.0054 \\
0.01 & 2.4722 & \(-\)2.7671 & 0.7171 & \(-\)0.6708 & \(-\)0.9463 & 0.0163 & \(-\)0.0120 & 0.0200 & \(-\)1.0138 & 0.2000 & \(-\)0.0054 \\
0.03 & 2.5008 & \(-\)2.6916 & 0.6982 & \(-\)0.6520 & \(-\)0.8853 & 0.0161 & \(-\)0.0120 & 0.0200 & \(-\)1.0305 & 0.2000 & \(-\)0.0053 \\
0.04 & 2.8840 & \(-\)2.7779 & 0.6495 & \(-\)0.6660 & \(-\)0.8936 & 0.0163 & \(-\)0.0120 & 0.0200 & \(-\)1.0980 & 0.2000 & \(-\)0.0051 \\
0.05 & 3.2209 & \(-\)2.8597 & 0.6079 & \(-\)0.6822 & \(-\)0.9234 & 0.0163 & \(-\)0.0120 & 0.0200 & \(-\)1.1488 & 0.2000 & \(-\)0.0051 \\
0.07 & 3.5751 & \(-\)2.8716 & 0.5338 & \(-\)0.6851 & \(-\)0.9305 & 0.0167 & \(-\)0.0120 & 0.0200 & \(-\)1.1931 & 0.2000 & \(-\)0.0057 \\
0.10 & 3.3146 & \(-\)2.3686 & 0.5264 & \(-\)0.5778 & \(-\)0.7252 & 0.0184 & \(-\)0.0120 & 0.0200 & \(-\)1.1605 & 0.2000 & \(-\)0.0067 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Period-dependent regression coefficients of the GMPMs. A trilinear model dependent on magnitude is established for the between-event component (see Figure 11). This model remains constant below \(M_{1}\) (\(\tau_{1}\)) and above \(M_{2}\) (\(\tau_{2}\)), with \(M_{1}\) and \(M_{2}\) set at 5.5 and 6.75, respectively. Fixed thresholds were selected to ensure  
Figure 10: Residual distributions for between-event, single-site, and site-to-site variations in the developed model across three different periods. The error bars represent the mean and standard deviation of the binned residuals.