利用标量和矢量Slepian函数从卫星数据估计位场
Potential-field estimation from satellite data using scalar and vector Slepian functions
摘要：
在过去的几十年里，一系列日益复杂的卫星任务为我们带来了质量不断提高的重力和磁力数据。为了充分利用地球和其他天体结构的丰富信息来源，我们的计算算法应该与数据的特定属性相匹配。特别是，如果数据仅在本地可用，其质量在空间上变化，或者如果我们只对特定空间区域的模型恢复感兴趣，则反演方法需要专门的适应。在这里，我们提出了两种方法来估计球形地球上的位场，从卫星高度收集的梯度数据。我们的背景是，从矢量值测量的重力或磁位的估计。我们的两种方法都利用球面Slepian函数来产生卫星高度的本地数据的近似，随后将其转换为地球的球面参考表面。第一种方法仅针对径向分量数据设计，并使用标量Slepian函数。第二种方法使用梯度数据的所有三个组成部分，并结合了一种新型的矢量球面Slepian函数，我们将在本章中介绍。
英文摘要：
In the last few decades a series of increasingly sophisticated satellite missions has brought us gravity and magnetometry data of ever improving quality. To make optimal use of this rich source of information on the structure of Earth and other celestial bodies, our computational algorithms should be well matched to the specific properties of the data. In particular, inversion methods require specialized adaptation if the data are only locally available, their quality varies spatially, or if we are interested in model recovery only for a specific spatial region. Here, we present two approaches to estimate potential fields on a spherical Earth, from gradient data collected at satellite altitude. Our context is that of the estimation of the gravitational or magnetic potential from vector-valued measurements. Both of our approaches utilize spherical Slepian functions to produce an approximation of local data at satellite altitude, which is subsequently transformed to the Earth's spherical reference surface. The first approach is designed for radial-component data only, and uses scalar Slepian functions. The second approach uses all three components of the gradient data and incorporates a new type of vectorial spherical Slepian functions which we introduce in this chapter.
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