Lack of Excitation by Tsunamis of Normal Modes of Sea-surface Oscillations in Bays

We conducted a spectral analysis of records of tsunamis following the 1993 Hokkaido Nansei-Oki earthquake and the 1983 Nihonkai-Chubu earthquake, at two tide-gauge stations in Maizuru Bay, Kyoto Prefecture. Having solved the eigenvalue problem of the proper oscillations for the bay, we compared spectral peaks between the records and theory. The fundamental mode with a theoretical period of 76 min and the third mode with 19 min were clearly identified in the observed records, however, the second mode with a theoretical period of 38 min was not detected, and there was little evidence for the fourth mode with 15 min. We conducted the same analysis for the 1993 tsunami in Saigo Bay, Shimane Prefecture, and found the third mode to be missing.¶By introducing "a water-exchange ratio" defined as the ratio of sea-water volume exchanged between the bay and the outer sea to the sum of the absolute volume of sea-surface displacement for each theoretical mode, we find that the excitation of a mode of proper oscillation depends on the value of this water-exchange ratio.