Unified Explanation of Long-Period Ground Motion Using the Basin Sloshing Index (BSI): A Dimensionless Analysis of Large-Scale Sloshing Phenomena in Sedimentary Basins

Yoshikazu Hiraoka 

This study introduces a new dimensionless index, the Basin Sloshing Index (BSI), to provide a unified explanation for long-period ground motion and persistent shaking observed in large sedimentary basins. Inspired by fluid sloshing dynamics, BSI is defined using three fundamental parameters—the basin scale L, seismic wavelength λ, and attenuation factor Q —and takes the simplified form:
BSI=2πQ(L/λ)
Applying representative values for the Kanto Basin yields BSI ≈ 12,500 (≈10⁴), indicating an extremely high level of inertial dominance comparable to strongly resonant fluid sloshing systems. This high BSI naturally explains key features of long-period ground motion in the Kanto Basin, including amplification in the 5–10 s band, double peaks, prolonged shaking exceeding 100 s, and sensitivity to distant earthquakes, all of which arise as consequences of dynamic flattening.
Using the analogy of cake batter in a baking pan (BSI ≈ 12,500), the study illustrates that solid Earth behaves fluid-like in the long-period regime, enabling intuitive understanding of basin-scale resonance. Furthermore, dynamic flattening induced by repeated deep large earthquakes may have contributed to maintaining the anomalously flat geomorphology of the Kanto Basin for over one million years, a process that can be quantitatively interpreted through BSI.
Finally, the free oscillation of the Earth following great earthquakes—characterized by BSI ≈ 2,500—is shown to lie on the same dimensionless “worldline” as basin-scale sloshing, suggesting that BSI provides a unified framework applicable continuously from basin-scale dynamics to whole-Earth oscillations.