Collaborative Research: CMG: Multi-Resolution Inversion of Tectonically Driven Spatio-Temporal Gravity Signals Using Wavelets and Satellite Data

Ohio State University Research Foundation -Do Not Use, Columbus OH

Investigators

Abstract

The primary objectives of this investigation include interdisciplinary studies of tectonically driven spatio-temporal signals resulting from complex geophysical processes. These processes include convergent plate boundaries, earthquake deformation cycle, mantle convection, intra-plate deformations and Glacial Isostatic Adjustment (GIA). At present, these processes generate small but measurable signals in the form of surface deformations, which at present can only be detected over land by either point measurements using GPS, or on small spatial scales (<100 km) using InSAR. These "slow deformation" signals have spatial scales longer than hundreds of km to continental and planetary scales, and temporal scales of a year to decades, and millennia. The Earth's gravity field and its spatio-temporal variations, providing insight on the integrated mass redistributions within the Earth's systems, represent a unique fundamental measurable quantity to directly study mechanisms which drive these complex processes with many degrees of freedom. For the first time ever, dedicated satellite gravity missions like CHAMP, GRACE and GOCE are anticipated to measure these small, broad-scale tectonically driven signals in the form of integrated mass change and vertical deformations. However, the contemporary mathematical functions to represent the geopotential are conventionally spherical harmonics which do not allow spatial localization. 3-D wavelets have notable advantages over spherical harmonics, e.g. for multi-resolution representation and localization, however, would have to satisfy the so-called "boundary-value problem". The overarching scientific goal is to develop multi-resolution based 3-D wavelet tools to enhance the tectonically driven spatio-temporal gravity signals for improved analyses and to make progress towards addressing the major open scientific questions of understanding the driving mechanisms of these "slow deformation" over land, ocean and ice-covered surfaces. The investigators propose to develop mathematical tools based on two wavelet approaches: (1) the rotational invariant spherical wavelet function, and (2) the non-separable compactly supported tensor-product wavelets to represent the spatio-temporal gravity field signals and perform geophysical "inversions" to enhance the signals. The "inversion" of these gravity signals represents stringent mathematical and numerical challenges, especially in light of the need for multi-resolution representation to enhance localized signals and to consider extending wavelets to include the time dimension. The broader impacts and anticipated results include the development of 3-D wavelet tools capable of solving the boundary value problem and inversion of gravity signals using satellite data and to demonstrate and apply the technique in the Nazca and South American plate region. The developed mathematical tools are intended to be among the first steps to "popularize" the use of 3-D wavelets for teaching and research, and are applicable to numerous interdisciplinary scientific studies and engineering problems.