Abstract

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.

中文翻译：

---

计算局部源产生的海啸波的射线轨迹和前沿的变分方法

摘要

提出了一种求解射线轨迹和海浪前沿的边值问题的变分方法。解决方法基于费马原理（固定时间）。所提出方法的一个显着特点是，无需求解Euler-Lagrange方程即可直接优化Fermat函数。此外，波源和接收器的位置是固定的。边界值问题中的多径传播通过找到Fermat函数的各种固定点来解决。通过使用分析海床模型应用双特征方法对该技术进行了数值测试。描述了变分方法的优点及其在海浪计算中的进一步发展前景。