This study investigates the relationship between earthquake magnitude and the amplitude–duration characteristics of the initial few seconds of the P-wave using 21,069 waveforms from 867 events recorded at 1,545 stations of the Japanese strong-motion network operated by the National Research Institute for Earth Science and Disaster Resilience (NIED), Japan. High-precision hypocentral information and associated displacement magnitudes were used, and P-phase arrivals were carefully picked using five different algorithms and validated against a velocity model. Four amplitude-based parameters, Peak Acceleration ( \(\:{P}_{a}\) ), Peak Velocity ( \(\:{P}_{v}\) ), Peak Displacement ( \(\:{P}_{d}\) ), and Peak Abasement ( \(\:{{P}_{a}}^{*}\) ), were considered in the analysis along with three amplitude-duration-based parameters, Cumulative Absolute Velocity (CAV), Cumulative Absolute Displacement (CAD), and Cumulative Absolute Abasement (CAA). Each parameter was computed over time windows ranging from 1 to 7 s. Outliers were removed using magnitude–distance binning with statistical methods appropriate for normally distributed and skewed datasets. The results show that parameters sensitive to high frequencies (CAV, \(\:{P}_{a}\) , \(\:{P}_{v}\) ) exhibit lower standard deviations with strong ground motion parameters, but show weaker correlation with magnitude. In contrast, parameters influenced by lower frequencies ( \(\:{P}_{d}\) , \(\:{{P}_{a}}^{*}\) , CAD, CAA) demonstrate strong and consistent linear relationships with magnitude, with the threshold magnitude increasing with longer time windows. Among all tested parameters, \(\:{{P}_{a}}^{*}\) and CAA consistently provide the most stable correlations for a given time window. These findings highlight that low-frequency amplitude–duration parameters are more suitable for robust magnitude estimation in EEW systems, while magnitude saturation is progressively postponed with increasing P-wave time window length rather than completely eliminated.
