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Aki (1969) first modeled coda waves of a local earthquake as a superposition of scattered surface waves. This paper attempts to clarify the constituents of surface-wave coda at long periods at very long lapse times. For a large earthquake of magnitude 7 or larger, vertical component oscillation in periods from 90 to 180 s persists for more than 20 hours from the earthquake origin time. Although the early portion of the coda envelope is successfully modeled by assuming incoherent scattered Rayleigh waves by heterogeneities distributed all over the Earth, the later potion of the observed coda envelope (roughly later than 35,000 s) has systematically larger amplitude than theoretical prediction. To clarify the cause of this discrepancy, we studied the constituents of vertical-component seismograms of three large earthquakes recorded by the F-net in Japan using the f- k power spectral analysis. We found that the direct and scattered fundamental-mode Rayleigh waves of velocity about 3.7 km/s are dominant in the earlier part of each envelope. It justifies the use of a scattering model of the fundamental Rayleigh waves for synthesizing the envelope. At lapse times later than 20,000 s–35,000 s, higher modes with phase velocities around 20 km/s become dominant. The transition time to the dominance of higher modes is found to become earlier for a deeper focus earthquake. The small coda attenuation factor from (1.90±0.23) × 10−3 to (2.38±0.32) × 10−3 estimated from later coda envelopes recorded at IRIS stations distributed worldwide also agrees with the attenuation factor of spheroidal modes according to PREM. We may interpret that higher mode waves are uniformly distributed at large lapse time due to large velocity dispersion and/or scattering and they dominate over the fundamental mode waves because of smaller attenuation in the lower mantle. The coda attenuation measurement proposed by Aki is found to be useful even for long periods and at very large lapse times. [ABSTRACT FROM AUTHOR]