Variational method for computing ray trajectories and fronts of tsunami waves generated by a localized source. (English. Russian original) Zbl 1450.35257
Comput. Math. Math. Phys. 60, No. 8, 1392-1401 (2020); translation from Zh. Vychisl. Mat. Mat. Fiz. 60, No. 8, 1439-1448 (2020).
Summary: A variational approach for solving the boundary value problem of computing ray trajectories and fronts of ocean waves is presented. The solution method is based on Fermat’s principle (of stationary time). A distinctive feature of the proposed approach is that the Fermat functional is optimized directly without solving the Euler-Lagrange equation; moreover, the locations of the wave source and receiver are fixed. Multipath propagation in the boundary value problem is addressed by finding various types of stationary points of the Fermat functional. The technique is numerically tested by applying the method of bicharacteristics with the use of analytical seabed models. The advantages of the variational approach and the prospects of its further development as applied to ocean wave computation are described. The relations between various types of stationary points of the travel time functional, caustics, and foci are discussed.
MSC:
| 35Q86 | PDEs in connection with geophysics |
| 35Q35 | PDEs in connection with fluid mechanics |
| 86A15 | Seismology (including tsunami modeling), earthquakes |
| 86A05 | Hydrology, hydrography, oceanography |
| 76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
| 65M25 | Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs |
Keywords:
ocean waves; tsunami; rays; fronts; Fermat’s principle; functional; method of bicharacteristicsReferences:
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