## 4 Results and Discussion
For the parameter associated with the logarithm of tremor energy, the minimum value of the estimator was 0.4763 for a direction equal to \(39^{\circ}\), while the maximum value was 0.5848 for a direction equal to \(296^{\circ}\). For the parameter associated with the geometric scattering of the wave front, the limiting values were \(-0.3736\) and \(-0.048\) for directions equal to \(71^{\circ}\) and \(334^{\circ}\), respectively. The minimum value of the estimator associated with damping was \(-0.00028\) for the \(271^{\circ}\) direction, while the maximum value was \(-0.00012\) for the \(8^{\circ}\) direction. The coefficients of variation of the parameters \(\alpha_{0}\), \(\alpha_{1}\), \(\alpha_{2}\) and \(\alpha_{3}\) were 7%, 6%, 26% and 20%. This means that the dispersion of parameters related to free expression and tremor energy is relatively small, while the dispersion of estimators related to distance from the source shows moderate heterogeneity. This may mean that the variability of the predictions of the maximum resultant vibration accelerations, taking into account the \(\gamma\) direction, can be traced to the variability of the distance-related parameters. The estimation of regression estimators of models of vibration attenuation relations for directions \(\gamma_{\rm i}\) made it possible to determine isolines of PGA for a hypothetical tremor with energy equal to \(5\times 10^{6}\) J. The results are presented in Figure 5. The isolines shown are in fact contour lines of the function f(E,R)--vibration attenuation relations. In order to determine the dominant direction of the fastest increase in the value of the parameter describing the intensity of vibration attenuation, the gradient properties of the function and the vector field concept were used. Figure 3: Dependence of the minimum subsample size on the assumed penetration angle. Figure 4: Estimation of GMPE parameters for the rotational model assuming a penetration angle of 180\({}^{\circ}\). Figure 5: Vibration acceleration predictions estimated on the basis of the analyzed models for a tremor with an energy equal to \(5\times 10^{6}\) J. The gradient of the function f(E,R) at the point \((E_{0},\ R_{0})\) is the vector defined by Equation (7):  
\[\
abla f(E_{0},\ R_{0})=\left(\frac{\partial f}{\partial E}(E_{0},\ R_{0}),\ \frac{ \partial f}{\partial R}(E_{0},\ R_{0})\right) \tag{7}\]  
where:  
\[ \begin{array}{c}\frac{\partial f}{\partial E}=\lim_{\Delta E\to 0}\frac{f(E_{0}+\Delta E,\ R_{0})-f(E_{0},\ R_{0})}{\Delta E};\\ \frac{\partial f}{\partial R}=\lim_{\Delta r\to 0}\frac{f(E_{0},\ R_{0}+\Delta R)-f(E_{0}, \ R_{0})}{\Delta R}.\end{array} \]  
Figure 6 shows the vector field of the function f(E,R) in two-dimensional space at a fixed energy of \(5\times 10^{6}\) J. For clarity, Figure 6 presents only those vectors whose origin is at points 1000 m, 1500 m, 2000 m, 2500 m and 3000 m away from the measurement station. The lengths of the vectors for given distances from the measuring station are proportional to the value of the growth rate of the ground vibration intensity parameter. The yellow color indicates those vectors whose lengths for a given distance from the site are relatively small. The values of vibration acceleration increase most rapidly from the NNE direction for an angle \(\gamma\) equal to \(67^{\circ}\), and most slowly from the ESE direction for an angle \(\gamma\) equal to \(331^{\circ}\).