In this article, we propose an inverse technique that accurately reconstructs the ocean's density stratification profile simply from free surface elevation data. Satellite observations suggest that ocean surface contains the signature of internal tides, which are internal gravity waves generated by the barotropic tides. Since internal tides contain the information of ocean's density stratification, the latter can in principle be reconstructed from the free surface signature. We consider a simple theoretical model that approximates a continuously stratified ocean as discrete layers of constant buoyancy frequency; this facilitates the derivation of a closed-form dispersion relation. First, we numerically simulate internal tide generation for toy ocean scenarios and subsequently perform Space-Time Fourier Transform (STFT) of the free surface, which yields internal tide spectra with wavenumbers corresponding to the tidal frequency. The density profile is reconstructed by substituting these wavenumbers into the dispersion relation. Finally, we consider a more realistic situation with rotation, bottom topography, shear and density profiles representative of the Strait of Gibraltar. Density reconstruction in the presence and absence of shear are respectively found to be $90.2\%$ and $94.2\%$ accurate.

中文翻译：

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一种从表面数据重建海洋密度分层的逆技术

在本文中，我们提出了一种逆向技术，该技术可以简单地根据自由表面高程数据准确重建海洋的密度分层剖面。卫星观测表明，海洋表面包含内部潮汐的特征，这是由正压潮汐产生的内部重力波。由于内部潮汐包含海洋密度分层的信息，后者原则上可以从自由表面特征重建。我们考虑一个简单的理论模型，该模型将连续分层的海洋近似为具有恒定浮力频率的离散层；这有助于推导出封闭形式的色散关系。首先，我们对玩具海洋场景的内部潮汐生成进行数值模拟，然后对自由表面进行时空傅立叶变换（STFT），其产生具有对应于潮汐频率的波数的内部潮汐谱。通过将这些波数代入色散关系来重建密度分布。最后，我们考虑更现实的情况，包括直布罗陀海峡的旋转、底部地形、剪切和密度剖面。分别发现在存在和​​不存在剪切的情况下密度重建的准确度为 $90.2\%$ 和 $94.2\%$。