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

The linear shallow-water approximation is commonly used to describe tsunami propagation, where the wave is assumed as a long surface gravity wave. The evolution of wave height during its propagation from offshore to onshore is a classic problem. When arriving at a shoreline, the increased wave height causes severe destruction on infrastructures and fatalities. This problem has then been an important issue within the context of disaster risk reduction as it gives rise to the importance of tsunami run-up prediction. Using maximum run-up data from past events, we tested the applicability of the Green’s law based on shoaling only to calculate run-ups and found that the basic Green’s law was in doubt. Then, we examined energy density conservation involving refraction effect but no dissipation and derived a simple formula for parameterizing run-up height. Detailed descriptions on factors affecting run-ups, such as complex bathymetry and topography are not yet considered in the current study. The aim of this study is therefore to determine whether the modified Green’s law is applicable for tsunami run-up prediction using local water depths as external parameters and ray spacing widths in the normal direction of wave fronts related to refraction. The results are consistent with the measured run-ups, where approximately 70% of total points of observations confirm the modified Green’s law with a reasonable accuracy.

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Long waves approaching the coast: Green’s law generalization

Journal of Ocean Engineering and Marine Energy ◽

10.1007/s40722-019-00152-9 ◽

2019 ◽

Vol 5 (4) ◽

pp. 385-402 ◽

Cited By ~ 1

Author(s):

Francesco Lalli ◽

Matteo Postacchini ◽

Maurizio Brocchini

Keyword(s):

Long Waves ◽

Green’S Law ◽

Green's Law

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Shoaling on Steep Continental Slopes: Relating Transmission and Reflection Coefficients to Green’s Law

Pure and Applied Geophysics ◽

10.1007/s00024-019-02316-y ◽

2019 ◽

Vol 177 (3) ◽

pp. 1659-1674 ◽

Cited By ~ 1

Author(s):

Jithin George ◽

David I. Ketcheson ◽

Randall J. LeVeque

Keyword(s):

Reflection Coefficients ◽

Transmission And Reflection Coefficients ◽

Continental Slopes ◽

Green’S Law ◽

Green's Law ◽

Transmission And Reflection

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Traveltime and amplitude estimation using wavefront construction

Geophysics ◽

10.1190/1.1443499 ◽

1993 ◽

Vol 58 (8) ◽

pp. 1157-1166 ◽

Cited By ~ 190

Author(s):

Vetle Vinje ◽

Einar Iversen ◽

Håvar Gjøystdal

Keyword(s):

Ray Tracing ◽

Incidence Angle ◽

New Method ◽

Two Dimensional ◽

Time Step ◽

Amplitude Estimation ◽

Large Velocity ◽

Ray Cells ◽

D Model ◽

Critical Incidence

We have developed and implemented a new method for estimating traveltimes and amplitudes in a general smooth two‐dimensional (2-D) model. The basic idea of this wavefront (WF) construction approach is to use ray tracing to estimate a new WF from the old one. The WF is defined as a curve (in 2-D) of constant traveltime from the source. The ray direction and amplitude will then be a function of s, the distance along the front. To maintain a sufficiently small sampling distance along the WF, it is scanned at every time step and new rays are interpolated whenever the distance between two rays becomes larger than a predefined limit. As the wavefronts are constructed, the data (i.e. traveltimes, amplitude coefficients, etc.) are transferred to the receivers by interpolation within the ray cells. Advantages of the WF construction method are its flexibility, robustness, and accuracy. First, second, and later arrivals may be found at any point in the model. Any shape of the initial wavefront is possible. The drawbacks of the method are the same as for conventional ray tracing: large velocity contrasts, caustics and near‐critical incidence angle of rays onto interfaces will give less accurate solutions.

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TRANSFORMATION OF NONLINEAR LONG WAVES

Coastal Engineering Proceedings ◽

10.9753/icce.v15.23 ◽

1976 ◽

Vol 1 (15) ◽

pp. 23

Author(s):

Nobuo Shuto

Keyword(s):

Friction Coefficient ◽

Bottom Friction ◽

Wave Profile ◽

Experimental Results ◽

Constant Depth ◽

Cnoidal Waves ◽

Wave Characteristics ◽

Green’S Law ◽

Green's Law ◽

Nonlinearity Dispersion

Kakutani's equation is extended to include the effects of variable width of the channel and the bottom friction. Based on the equation, several solutions are derived and compared with experimental results. For example, Green's law is obtained if the nonlinearity, dispersion and bottom friction are neglected. With the nonlinearity included, it is shown that the wave amplitude follows Green's law and at the same time the wave profile deforms due to the nonlinear effect. Discussion of the present paper is mainly focused on the effect of the bottom friction. From the experimental results of cnoidal waves in a channel of constant depth and width, on the bottom of which artificial roughnesses are planted, it is shown that the friction coefficient estimated from Kajiura's theories gives good agreements, thus confirming the validity of the method of conversion, proposed in the present paper, between sinusoidal and cnoidal wave motions. Change in height of cnoidal waves on a slope is also solved. The friction coefficient determined from wave characteristics and bottom conditions, by means of Kajiura's theories and the method of conversion stated above, is used in the comparison with experimental results. Theoretical prediction agrees very well with experimental results.

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