A parameter quantifying radiation damping of bay oscillations excited by incident tsunamis

The transient response of a bay with a narrow mouth to incident tsunamis is interpreted as the convolution of the input signal with the impulse response obtained by an inverse Fourier transform of the response curve of the oscillatory system with one degree of freedom. The rate of radiation damping associated with energy escaping seaward through the bay mouth is expressed in terms of the quality factor Q, which determines the decaying envelope of the impulse response. The value of Q of the resonant peak is approximated by the ratio of the resonant frequency ω₀ to the bandwidth between frequencies at which the power spectral density of sea level within the bay drops to half of the peak value. Since the shape of the frequency power spectrum during the tsunami event is almost similar to that in the normal state in the neighborhood of ω₀, Q can be estimated from sea level datasets in the normal state. Although the amplitude and phase of the impulse response need to be adjusted using the first crest or trough of the observed leading wave, this approach proves to work well in examining the transient responses of Miyako Bay and Kushimoto Bay on the Japanese Pacific coast to incident tsunamis.