Abstract

The strong noise of satellite-based Time-Variable Gravity (TVG) field is often suppressed by applying the averaging filters. However, how to appropriately compromise the data blurring and de-noising remains as a challenge. In our hypothesis, the optimum spatial averaging filter expects to contain averaging kernels that capture the same amount of orbital samples everywhere, to avoid introducing excessive data blurring. To achieve the goal, we take advantages of the spherical convolution and introduce extra spatial constraints into a Gaussian kernel: (1) its half-width radius adapts to the global inhomogeneity of satellite orbit, and (2) the kernel is reshaped as an ellipsoid to adapt to the regional anisotropy. In this way, we designed optimal filters that contain a spatially-Varying non-isotropic Gaussian-based Convolution (VGC) kernel. The VGC-based filter is compared against three most popular filters through real TVG fields and another closed-loop simulation. In both scenarios, VGC-based filters retain more realistic secular trend and seasonal characteristics, in particular at high latitudes. The spatial correlation between the VGC estimates and the simulated ground truth is found to be 0.95 and 0.86 over Greenland and Antarctica, which is found to be 10% better than other tested filters. Temporal correlations with the ground truth are also found to be considerably better than the other filters over 90% of the globally distributed river basin. Besides, the VGC-based filters provide tolerable efficiency (3.5 s per month) and sufficient accuracy (integral error less than 3%). The method can be extended to the next generation gravity mission as well.

Plain Language Summary

Time-Variable Gravity (TVG) fields of the Gravity Recovery and Climate Experiment (GRACE) and its Follow-On mission (GRACE-FO) need proper filtering to suppress the noise before being applied for intended geophysical studies. Existing filters are generally designed in the spectral domain. Though they are numerically efficient, they can hardly treat the noise in fairness, globally. As a result, the TVG fields may get over-smoothed after applying those filters, particularly in regions with high-latitudes. However, it would be mathematically simple to design a filter by applying a spherical convolution, whose kernels can be easily constrained and tuned in the spatial domain. This study introduces filters with spatially-Varying non-isotropic Gaussian-based Convolution kernel (VGC) that is enforced to comply with the spatial distribution of the TVG noise. The proposed filter is found to preserve a finer spatial resolution of TVG fields, and at the same time, to be able to de-noise them at a comparable level as the existing techniques. Geophysical applications that use GRACE-like TVG fields might have benefits from this practical filtering technique.

中文翻译：

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用于平滑类 GRACE 时间重力场的空间变化非各向同性高斯卷积滤波器

 抽象的

基于卫星的时变重力（TVG）场的强噪声通常通过应用平均滤波器来抑制。然而，如何适当地折衷数据模糊和去噪仍然是一个挑战。在我们的假设中，最佳空间平均滤波器期望包含在各处捕获相同数量的轨道样本的平均内核，以避免引入过多的数据模糊。为了实现这一目标，我们利用球面卷积的优势，并向高斯核引入额外的空间约束：（1）其半宽半径适应卫星轨道的全局不均匀性，（2）将核重塑为椭球体适应区域各向异性。通过这种方式，我们设计了包含空间变化的非各向同性的基于高斯的卷积（VGC）内核的最佳滤波器。通过真实 TVG 场和另一个闭环仿真，将基于 VGC 的滤波器与三种最流行的滤波器进行比较。在这两种情况下，基于 VGC 的滤波器保留了更现实的长期趋势和季节特征，特别是在高纬度地区。在格陵兰岛和南极洲，VGC 估计值与模拟地面实况之间的空间相关性为 0.95 和 0.86，比其他测试的滤波器好 10%。还发现与地面实况的时间相关性比全球分布的 90% 河流流域的其他过滤器要好得多。此外，基于 VGC 的滤波器提供了可容忍的效率（每月 3.5 秒）和足够的精度（积分误差小于 3%）。该方法也可以扩展到下一代重力任务。

 通俗易懂的语言总结

重力恢复和气候实验 (GRACE) 及其后续任务 (GRACE-FO) 的时变重力 (TVG) 场在应用于预期的地球物理研究之前需要适当的滤波来抑制噪声。现有的滤波器通常是在谱域中设计的。尽管它们在数量上是高效的，但它们很难在全球范围内公平地对待噪音。因此，应用这些滤波器后，TVG 场可能会变得过度平滑，特别是在高纬度地区。然而，通过应用球形卷积来设计滤波器在数学上很简单，其内核可以在空间域中轻松约束和调整。本研究引入了具有空间变化的非各向同性基于高斯的卷积核 (VGC) 的滤波器，该卷积核被强制遵守 TVG 噪声的空间分布。研究发现，所提出的滤波器可以保留 TVG 场的更精细的空间分辨率，同时能够以与现有技术相当的水平对其进行降噪。使用类 GRACE TVG 场的地球物理应用可能会受益于这种实用的滤波技术。