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

几乎每一次地球物理过程都会在地球重力场或其变化中留下印记。如果这个过程“足够大”，它可以由Grace来测量，Grace是一颗对地球时变重力场非常敏感的双星任务，到目前为止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的模型提供了证据，表明由于冰盖的逐渐融化，地球极地地区正在失去质量，GRACE模型还帮助限制了大地震造成的地壳变形，从而开创了地震观测的新时代。GRACE数据有噪声，需要广泛的处理、过滤和统计分析才能产生这类信号，这些信号深埋在噪声之下，受到洋流、水文循环或冰川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最大限度地利用今天可用的GRACE数据。来自地球极地地区的严格约束的质量通量速率及其误差，以及对大地震同震变形的稳健检测、分析和建模将作为科学成果单独存在，但它们也将反馈到气候研究、冰川学、地震学和大地测量学。更广泛地说，我们解决的问题与为球面上分布的噪声和不完整数据提供新的估计方法有关，在最一般的意义上，例如在生物医学和统计学研究中使用的，在物理学、宇宙学和计算机科学中使用的。我们开发了一种新的数学方法来反演GRACE数据，这些数据是噪声和不完整的。这项工作的核心是开发“识别噪声的Slepian函数”，这是一种函数基础，可以替代球面调和，非常适合表示和分析球面上地理上局部的、带宽有限的信号。我们不再只产生信号的空间平均，也不再重新处理基于球谐函数的全球模型，而是直接在此基础上对GRACE得出的卫星间电势差的时间序列进行反演。由此，我们恢复了对冰盖地区和水文盆地质量增减的整个空间相关性的估计，以及对伴随着大地震的重力扰动的估计。前者对科学和社会本身很重要，后者增加了从GPS测量或地震数据获得的不同时间和空间尺度的信息。该项目得到地球物理、北极自然科学和南极地球科学计划的支持。

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.