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

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 (

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.