Bathymetry is the measurement of the water depth similar to underwater topography. Gravity anomaly and vertical gravity gradient are important data used to inverse bathymetry. In this study, we investigate the sensitivities of the gravity anomalies and vertical gravity gradient data to bathymetry inversion. Firstly, the formulas of the gravity anomaly and vertical gravity gradient signals produced by the seabed terrain are derived, and then a series of numerical studies are designed to investigate the sensitivities. The results show that gravity anomalies and vertical gravity gradients have different sensitive bands to bathymetry inversion. Therefore, accuracy requirements for the gravity anomaly and vertical gravity gradient data are different for bathymetry inversion with different spatial resolutions and accuracies. With decreasing resolution, the accuracy requirement of the gravity anomaly gradually decreases, whereas the accuracy requirement of the vertical gravity gradient first decreases and then increases, indicating that the vertical gravity gradient is more sensitive to the short-wavelength signal than the gravity anomaly, especially in the 0–20 km wavelength ranges. In addition, we perform a theoretical analysis that shows that the vertical gravity gradient has a band that is most sensitive to the seafloor topography. This study is capable to provide a reference for the design of future satellites to retrieve the bathymetry.

中文翻译：

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测深法反演的重力异常和垂直重力梯度数据的敏感性分析

测深法是类似于水下地形的水深测量。重力异常和垂直重力梯度是用于反测深的重要数据。在这项研究中，我们调查了重力异常和垂直重力梯度数据对测深法反演的敏感性。首先推导了海床地形产生的重力异常和垂直重力梯度信号的公式，然后进行了一系列数值研究，以研究其敏感性。结果表明，重力异常和垂直重力梯度对测深法的反演具有不同的敏感带。因此，对于具有不同空间分辨率和精度的测深法反演，重力异常和垂直重力梯度数据的精度要求是不同的。随着分辨率的降低，重力异常的精度要求逐渐降低，而垂直重力梯度的精度要求先降低然后升高，这表明垂直重力梯度比重力异常对短波信号更敏感，尤其是在0– 20 km波长范围。此外，我们进行了理论分析，结果表明垂直重力梯度具有一个对海底地形最敏感的波段。这项研究能够为将来检索测深仪的卫星设计提供参考。表明垂直重力梯度比重力异常对短波信号更敏感，特别是在0-20 km波长范围内。此外，我们进行了理论分析，结果表明垂直重力梯度具有一个对海底地形最敏感的波段。这项研究能够为将来检索测深仪的卫星设计提供参考。表明垂直重力梯度比重力异常对短波信号更敏感，特别是在0-20 km波长范围内。此外，我们进行了理论分析，结果表明垂直重力梯度具有一个对海底地形最敏感的波段。这项研究能够为将来检索测深仪的卫星设计提供参考。