Data Sheet 1_Preliminary analysis of response spectra, energy spectra, and energy-input directionality for the 2026 Kumamoto earthquake.pdf

For a damping ratio of 0.05, the pseudo-acceleration remains above 5.0 m/s² while the displacement reaches approximately 1.3 m. The cumulative input energy spectrum reaches a maximum value of 3.59 m/s at T = 3.14 s, while the maximum momentary input energy spectrum reaches 1.95 m/s at T = 2.50 s, indicating large energy input to structures with relatively long natural periods. Strong directionality is also observed: at T = 3.14 s, the ratio of the minor-to major-axis cumulative input energy spectra is 0.222, corresponding to an energy ratio of approximately 0.222² ≈ 0.049.

In the period range where the energy input is large, the major-axis direction of cumulative input energy is predominantly southeast to east-southeast, while the displacement increments associated with the maximum momentary input energy are concentrated predominantly in the southeast direction. These findings demonstrate that KMM012 can impose large and strongly directional energy demands on long-period structures.</p>