A significant component of Earth's surface topography is maintained by stresses induced by underlying mantle flow. This “dynamic” topography cannot be directly observed, but it can be approximated—particularly at longer wavelengths—from measurements of residual topography, which are obtained by removing isostatic effects from the observed topography. However, as these measurements are made at discrete, unevenly distributed locations on Earth's surface, inferences about global properties can be challenging. In this paper, we present and apply a new approach to transforming pointwise measurements into a continuous global representation. The approach, based upon the statistical theory of Gaussian processes, is markedly more stable than existing approaches—especially for small data sets. We are therefore able to infer the spatial pattern, wavelength, and amplitude of residual topography using only the highest quality oceanic spot measurements within the database of Hoggard et al. (2017, https://doi.org/10.1002/2016JB013457). Our results indicate that the associated spherical harmonic power spectrum peaks at l = 2, with power likely in the range 0.46–0.76 km². This decreases by over an order of magnitude to around 0.02 km² at l = 30. Around 85% of the total power is concentrated in degrees 1–3. Our results therefore confirm previous findings: Earth's residual topography expression is principally driven by deep mantle flow, but shallow processes are also crucial in explaining the general form of the power spectrum. Finally, our approach allows us to determine the locations where collection of new data would most impact our knowledge of the spectrum.

中文翻译：

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稀疏数据的全球模型：对地球残余地形谱的鲁棒估计

地球表面形貌的重要组成部分是由地幔流动引起的应力维持的。无法直接观察到这种“动态”形貌，但是可以通过测量残余形貌来近似估计（尤其是在更长的波长下），而残余形貌的测量是通过从观察到的形貌中去除静力效应而获得的。但是，由于这些测量是在地球表面的离散且分布不均匀的位置进行的，因此对全局特性的推论可能具有挑战性。在本文中，我们提出并应用了一种新方法将点状度量转换为连续的全局表示。该方法基于高斯过程的统计理论，比现有方法明显更稳定-特别是对于小型数据集。因此，我们能够推断出空间格局，在Hoggard等人的数据库中，仅使用最高质量的海洋斑测量结果，即可确定残留地形的波长和幅度。（2017，https://doi.org/10.1002/2016JB013457）。我们的结果表明，相关的球谐功率谱在l  = 2，功率可能在0.46-0.76 km ²的范围内。在l  = 30时，它减小了一个数量级，达到0.02 km ²左右。总功率的85％集中在1-3度。因此，我们的结果证实了先前的发现：地球的剩余地形表达主要由深地幔流驱动，但是浅层过程对于解释功率谱的一般形式也至关重要。最后，我们的方法使我们能够确定新数据收集将对我们的频谱知识产生最大影响的位置。