## 4 Ground Motion Parameters  
Ground motion generated by an earthquake is complicated, and multiple parameters rather than a single parameter are used to quantitatively reflect the characteristics of ground motion. The amplitude, frequency content, and duration are the most significant characteristics in the engineering community [39]. Some ground motion parameters, such as PGA and PGV, provide information on amplitude, while other parameters, such as acceleration spectrum intensity and Arias intensity, reflect the above two or three characteristics. A total of 16 ground motion parameters are used to characterize the recorded ground motion in the relationship study. The single amplitude parameters include PGA and PGV. Peak ground displacement (PGD) is not included, due to its sensitiveness to long period noise, and different choices of baseline correction and filtering of acceleration may give quite different displacements. The individual frequency content parameters include central frequency, which measures the frequency where the power spectral density is most concentrated, and the ratio \(v_{\text{max}}/a_{\text{max}}\), which gives the period where the ground motion is most significant. The individual duration parameters include bracketed duration and significant duration. Bracketed duration is the total time elapsed between the first and the last excursions of a given level. Absolute level 5 gal and relative level 5% PGA are both considered. Significant duration is defined as the interval time when a proportion of the total Arias intensity is accumulated, and the interval between 5% and 95% thresholds is chosen here. The ground motion parameters reflecting more than one characteristic include derivations of accelerations, such as the root mean square of acceleration, cumulative absolute velocity, Arias intensity, characteristic intensity, JMA equivalent peak acceleration, and destructive index. Spectrum-based intensities, such as the acceleration spectrum intensity, velocity spectrum intensity, and Housner intensity, are considered. For the completeness and readability of the paper, the definitions, explanations, and calculation formulas of the above ground motions are given as follows [39; 40; 41]. The root mean square of acceleration (\(a_{\text{RMS}}\)) stands for the effective average acceleration in the significant duration, given by  
\[a_{\text{RMS}}=\sqrt{\frac{1}{T_{s}}\int_{t_{1}}^{t_{2}}[a(t)]^{2}dt} \tag{1}\]  
where \(T_{s}\) is significant duration and \(t_{1}\) and \(t_{2}\) are the start and end time instants, respectively. The cumulative absolute velocity (CAV) is proposed by U.S. Electrical Power Research Institute for indicating the onset of structural damage caused by an earthquake, and is given by  
\[\text{CAV}=\int_{t_{1}}^{t_{2}}\bigl{|}a(t)\bigr{|}dt \tag{2}\]  
The Arias intensity (AI) is proposed for indicating the damage potential to nuclear power plants, and is given by  
\[\text{AI}=\frac{\pi}{2g}\int_{t_{1}}^{t_{2}}[a(t)]^{2}dt \tag{3}\]  
The characteristic intensity (\(I_{c}\)) is proposed to indicate structural damage caused by maximal deformation and dissipative hysteretic energy, and is given by  
\[I_{c}=a_{\text{RMS}}^{1.5}T_{s}^{0.5} \tag{4}\]  
The JMA equivalent peak acceleration is used to calculate JMA seismic intensity. It is the value of vector composition of three component band-pass accelerations, each of which is filtered by a compound filter composed of a amplitude filter, a high-cut filter, and a low-cut filter, such that the total duration when the vector composite acceleration is larger than this value is longer than 0.3 s, as shown in Equation (5). The schematic diagram of JMA equivalent peak acceleration, compound filter, andtotal duration with respect to peak values are shown in [11].