Collaborative Research: Localized Analysis of Geophysical Signals Acquired by Satellites: Making the most of GRACE

几乎所有的地球物理过程都会在地球重力场或重力场的变化中留下痕迹。如果这个过程足够“大”，它可以被GRACE测量，这是一个对地球时变重力场敏感的双卫星使命，它已经产生了大约七年的数据。在它的许多其他成就中，基于GRACE的模型提供了地球极地地区由于冰盖逐渐融化而失去质量的证据，GRACE建模也有助于限制大地震引起的地壳变形，从而开创了一个新的地震观测时代。GRACE数据是嘈杂的，需要大量的处理，过滤和统计分析，以产生这种信号，这些信号深埋在噪音之下，并受到洋流，水文循环或冰后反弹的地球物理特征的污染。 我们的方法开发将使我们和科学界能够充分利用当今可用的GRACE数据。来自地球极地地区的质量通量率及其误差，以及对大地震同震变形的强大检测，分析和建模将作为科学成果独立存在，但它们也将反馈到气候研究，冰川学，地震学和大地测量学中。更广泛地说，我们解决的问题是相关的噪声和不完整的数据分布在一个球体上提供新的估计方法，在最普遍的意义上，例如，用于生物医学和统计研究，在物理学，宇宙学和计算机science.We开发一个新的数学技术的GRACE数据，这是噪声和不完整的反演。这项工作的核心是开发“噪声识别Slepian函数”，这是一种函数基础，可替代球面谐波，非常适合于表示和分析球面上的地理定位、带宽限制的信号。不再只产生信号的空间平均值，也不基于球谐函数重新处理全球模型，我们直接在此基础上对来自GRACE的卫星间电势差的时间序列进行反演。从这一点，我们恢复估计的整个空间依赖性的质量增益/损失在冰雪覆盖的地区和水文流域，以及伴随着大地震的重力扰动的估计。前者对科学和社会本身都很重要，后者在GPS测量或地震数据的基础上增加了不同时间和空间尺度的信息，该项目得到地球物理学、北极自然科学和南极地球科学方案的支持。

Almost every geophysical process leaves it signature in the terrestrial gravity field or its changes. If the process is "big'' enough, it can be measured by GRACE, a twin satellite mission that is sensitive to the Earth's time-variable gravity field, which has been yielding data for about seven years now. Among its many other accomplishments, models based on GRACE have provided evidence that the Earth's polar regions are losing mass due to progressive melting of their ice cover, and GRACE modeling has also helped constrain crustal deformation resulting from large earthquakes, thereby inaugurating an era of a new class of earthquake observations. The GRACE data are noisy and require extensive processing, filtering, and statistical analysis to yield signals of this kind, which are buried deeply beneath the noise and contaminated by the geophysical signatures of ocean currents, the hydrological cycle, or post-glacial rebound. Our methods development will enable us, and the scientific community, to make the most of today's available GRACE data. Well-constrained mass flux rates from Earth's polar regions, and their errors, and the robust detection, analysis and modeling of the coseismic deformation from large earthquakes will stand alone as scientific results, but they will also feed back into climate research, glaciology, seismology, and geodesy. Even more broadly than that, the problems we solve are relevant in providing new estimation methods for noisy and incomplete data distributed on a sphere, in the most general sense, e.g. as used in biomedical and statistical research, in physics, cosmology and computer science.We develop a new mathematical technique for the inversion of GRACE data, which are noisy and incomplete. Central to this effort is the development of "noise-cognizant Slepian functions'', a function basis, alternative to spherical harmonics, that is eminently suited to represent and analyze geographically localized, bandlimited, signals on the sphere. No longer producing only spatial averages of the signal, nor reprocessing global models based on spherical harmonics, we perform inversions on time series of the inter-satellite potential difference derived from GRACE, directly in this basis. From this we recover estimates of the entire spatial dependence of the mass gain/loss in ice-covered regions and hydrological basins, as well as estimates of the gravity perturbations accompanying large earthquakes. The former are important to science and society per se, the latter add information on a different temporal and spatial scale to that which can be had from GPS measurements or seismological data.This project is supported by the Geophysics, Arctic Natural Sciences, and Antarctic Earth Sciences Programs.