Research in Underwater Acoustics

本研究解决了水下声学中的逆问题，并展示了如何解决具有深度变化折射率的有限海洋的情况。有两个困难必须解决。第一个与海洋表面和海底的相互作用有关。初步的计算和图形表明，使用我们的远场函数阵列已经处理好了这个问题。为了获得更高的分辨率，我们建议使用更多的传播模式。但是，该过程将需要增加cpu时间。为了考虑可变折射率的影响，我们使用了嬗变法，这是一种把复杂微分方程的解与简单微分方程的解联系起来的方法。我们已经展示了如何使用嬗变来计算“扰动模态”和传播格林函数。小波数的初步计算是有希望的。

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.