Research in Underwater Acoustics

这项研究解决了水下声学中的反问题，并展示了如何在有限的海洋和深度变化的折射率的情况下求解该问题。有两个困难必须解决。第一个问题与海洋表面和海底的相互作用有关。初步计算和图形显示，使用我们版本的远场函数阵列已经解决了这个问题。为了获得更高的分辨率，我们建议使用更多的传播模式。然而，该过程将需要增加的CPU时间。为了考虑可变折射率的影响，我们利用了变形，这是一种将复杂微分方程解与较简单微分方程解联系起来的过程。我们已经展示了如何利用变形来计算“微扰模”和传播的格林函数。波数较小的初始计算结果令人满意。

This research addresses the inverse problem in underwater acoustics and shows how it may be solved for the case of finite oceans with depth varying index of refraction. There are two difficulties which must be resolved. The first has to do with the interaction of the ocean surface and bottom. Preliminary computations and graphics show that this problem has been taken care of using our version of the far-field function array. For more resolution we propose using more propagating modes. The procedure will require, however, an increased cpu time. To take into account the effects of a variable index of refraction, we make use of transmutation, a procedure which relates solutions of complicated differential equations to simpler ones. We have shown how, using transmutation, we may compute the "perturbed modes", and the propagating Green's function. Initial computations with small wave number were promising.