TEMPORAL AND SPATIAL VARIATIONS IN TSUNAMI CODA ENERGY IN MEDIUM- TO LONG-TERM DECAY PROCESSES

Abstract

Temporal and spatial variations in tsunami coda waves in medium- to long-term decay processes were investigated based on theoretical analysis and observations. In this paper, medium- and long-term were defined as approximately τ ≤ t ≤ 2τ and t ≥ 2τ, respectively, where t is elapsed time from the earthquake origin time, and τ is the coda energy e-folding decay time. In the medium- to long-term decay processes, the energy and amplitude of tsunami coda waves may become small so that the energy dissipation due to turbulent friction can be negligible compared to the directional spectrum of coda waves. It was found that the energy balance equation without dissipation for the directional spectrum, D(f,θ), should be approximately satisfied in a quasi-steady state, and the quantity CCgD(f,θ) should hold for any two points, where C and Cg are the wave phase speed and group velocity, respectively. The latter relationship indicates the inverse proportion of the tsunami coda energy to the water depth, and the similarity of the frequency spectrum of coda waves between any two points. The water depth dependency of tsunami coda was confirmed over a wide frequency range by using the 2011 Tohoku Earthquake Tsunami data. However, the tsunami coda energy with periods of 30–70 min did not follow the h-1 law, because continental seiche and edge waves were generated at Kochi, and the amplitude of tsunami coda waves at other stations did not show exponential decay in time. The estimated frequency spectra of coda waves at depths larger than 100 m were found to be inversely proportional to frequency squared, f2, for a wide frequency range. The f-2 law of frequency spectrum was theoretically derived by using linear shallow water equations with linear friction and dispersion terms. The effects of linear friction and dispersion on the frequency spectrum were deduced from the spectral solutions.