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

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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.