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首页> 外文期刊>European Journal of Mechanics, B. Fluids >Detection of ocean bathymetry from surface wave measurements
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Detection of ocean bathymetry from surface wave measurements

机译：从表面波测量中检测海洋测深

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摘要

The detection of ocean bathymetry is one of the most important and difficult problems in oceanography. On the theoretical side it is a classical inverse problem which features severe ill-posedness found in similar problems from a wide array of applied sciences. From a practical standpoint, standard procedures based upon "Underwater Acoustics" are quite dangerous and expensive as the desired surface is separated from measuring devices by (at least) the entire ocean layer providing a very hostile and unpredictable sampling environment. In this research we take a rather different approach to this inverse problem as we rely upon nonlinear features of the governing fluid mechanical equations to detect information about the ocean bathymetry. This is also in contrast to similar methods in the literature which rely solely upon the variations in the dispersion relation. Using a formulation of the water wave problem due to Zakharov, and Craig and Sulem, and the analyticity of the "Dirichlet-Neumann operator" we find surprisingly convenient formulas involving the ocean bathymetry. Of course, these formulas are ill-conditioned and nonlinear, however, we have found that application of standard techniques from the theory of inverse problems allow us to predict the shape of bottom topography with excellent precision.
机译：海洋测深的检测是海洋学中最重要和最困难的问题之一。从理论上讲，这是一个经典的逆问题，其特征是在广泛的应用科学领域的类似问题中发现了严重的不适定性。从实践的角度来看，基于“水下声学”的标准程序非常危险且昂贵，因为所需的表面与（至少）整个海洋层与测量设备分开，从而提供了非常不利和不可预测的采样环境。在这项研究中，我们采用了一种截然不同的方法来解决这一反问题，因为我们依靠控制流体力学方程的非线性特征来检测有关海洋测深的信息。这也与文献中类似的方法相反，后者仅依赖于色散关系的变化。使用Zakharov，Craig和Sulem提出的水波问题的公式以及“ Dirichlet-Neumann算子”的解析性，我们发现了涉及海洋测深的令人惊讶的方便公式。当然，这些公式是病态的并且是非线性的，但是，我们发现从反问题理论中应用标准技术可以使我们以极高的精度预测底部地形的形状。

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