Abstract
Ray tracing, which has been widely used for seismic waves, was also applied to tsunamis to examine the bathymetry effects during propagation, but it was limited to linear shallow-water waves. Green’s law, which is based on the conservation of energy flux, has been used to estimate tsunami amplitude on ray paths. In this study, we first propose a new ray tracing method extended to dispersive tsunamis. By using an iterative algorithm to map two-dimensional tsunami velocity fields at different frequencies, ray paths at each frequency can be traced. We then show that Green’s law is valid only outside the source region and that extension of Green’s law is needed for source amplitude estimation. As an application example, we analyzed tsunami waves generated by an earthquake that occurred at a submarine volcano, Smith Caldera, near Torishima, Japan, in 2015. The ray-tracing results reveal that the ray paths are very dependent on its frequency, particularly at deep oceans. The validity of our frequency-dependent ray tracing is confirmed by the comparison of arrival angles and travel times with those of observed tsunami waveforms at an array of ocean bottom pressure gauges. The tsunami amplitude at the source is nearly twice or more of that just outside the source estimated from the array tsunami data by Green’s law.
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Acknowledgements
We used the bathymetry data, JTOPO30, provided by the Marine Information Research Center of the Japan Hydrographic Association. The earthquake information data are obtained from the Global Centroid Moment Tensor catalog. The information of tsunami at Hachijo Island is reported in Japanese by Japan Meteorological Agency (http://www.jma.go.jp/jma/press/1505/13a/1504recently-eq.pdf). We generated figures with the Generic Mapping Tools (GMT) data processing and package and Gnuplot. We also used Mathematica to analyze and plot the solutions of the wave equations. The simulation parts are supported by the JSPS KAKENHI Grant number JP17J02919. The observation was supported by JSPS KAKENHI Grant number 25247074. We appreciate to T. Maeda, R. Geller and T. Furumura for providing valuable comments. We thank four anonymous reviewers whose comments helped us to improve our paper.
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Sandanbata, O., Watada, S., Satake, K. et al. Ray Tracing for Dispersive Tsunamis and Source Amplitude Estimation Based on Green’s Law: Application to the 2015 Volcanic Tsunami Earthquake Near Torishima, South of Japan. Pure Appl. Geophys. 175, 1371–1385 (2018). https://doi.org/10.1007/s00024-017-1746-0
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DOI: https://doi.org/10.1007/s00024-017-1746-0