Traveltime delay and initial phase reversal of distant tsunamis coupled with the self‐gravitating elastic Earth

Abstract

Systematic tsunami traveltime delays of up to 15 min relative to the numerically simulated long waves from the 2010 Chilean and 2011 Tohoku-Oki earthquakes were widely observed at deep ocean tsunamimeters. Enigmatic small negative phases appearing before the main peak were commonly found only at the trans-oceanic locations. The frequency dependence of the measured tsunami phase velocities shows reverse dispersions at long periods, i.e., the tsunami speed becomes slower at periods beyond 1000 s. This is consistent with the phase velocities of a tsunami mode coupled with a self-gravitating elastic Earth, suggesting that the effects of compression and dilatation of seawater, elastic tsunami loadings on a solid Earth, and the geopotential variations associated with the motion of mass during tsunami propagation are responsible for the traveltime delays and the initial negative phases. Simple 1-D tsunami propagation tests confirm that the reverse dispersion creates a small negative phase that precedes the main peak at large distances. A new method to simulate tsunami waveforms on real ocean bathymetry that takes into account seawater compressibility, the elasticity of the Earth, and geopotential perturbations has been developed by applying a phase correction to the simulated long waves. The simulated waveforms, in which phase corrections are applied for the dispersion effects, accurately reproduce the observed waveforms, including a small initial negative phase that appears at distant locations. The traveltime difference between the observed and simulated waveforms has been decreased to less than 5 min and the waveform difference between them remarkably diminishes.

A long source area of the 1906 Colombia–Ecuador earthquake estimated from observed tsunami waveforms

“…Both the high and the low frequency dispersion effects are expected to significantly influence the waveforms at Honolulu. Thus, all dispersion effects are introduced into the waveforms simulated by the linear long wave model based on the phase correction method developed by Watada et al (2014). In contrast, only the high frequency dispersion effect is expected to influence the waveforms of Naos Island with respect to distance relations.…”

“…Here, the phase correction method requires a propagation distance and average water depth during tsunami propagation. The distance was assumed to be the arc distance along the great-circle path through the subfault location and the tide gauge station, as defined by Watada et al (2014), who used a depth of 4 km as the average water depth during the propagation. However, arrival times of the waveforms simulated by the linear long wave model at the Honolulu station assumed a range of approximately 12-13 h. When the tsunami propagated following the linear long wave theory over distance and time, the equal average depth was comparable to 1.5-1.7 km with respect to the dispersion relation in the long wave condition.…”

“…Therefore, the equal average depth for the phase correction was estimated and applied based on the relationship between the simulated arrival times of waveforms and the propagation distance using the dispersion relation in the long wave condition. Furthermore, modified dispersion relation curves corresponding to the equal average water depth were estimated by linear interpolation based on the dispersion relation curves with depths of 2, 4, and 6 km shown in Watada et al (2014). Table 1 and Fig.…”

Acoustic-gravity waves in the atmosphere generated by infragravity waves in the ocean

“…IGW phase speed c = ω/k does not exceed (gH) 1/2 and is much smaller than sound speed in water and compressional and shear wave speeds in the ocean bottom. Therefore, corrections to the dispersion equation due to water compressibility and seafloor compliance are rather small (Tsai et al 2013;Watada et al 2014) and do not change the nature of IGWs as horizontally propagating surface waves, where both k and ω are real-valued (Brekhovskikh and Godin 1998).…”

Advances in earthquake and tsunami sciences and disaster risk reduction since the 2004 Indian ocean tsunami

“…A small reduction of the tsunami phase velocity at very long period (>1000 seconds), caused by the coupling of seawater and self-gravitating elastic Earth, is considered to be responsible for these delays [65].…”