Crustal magnetic field estimation from local vectorial data: using Slepian functions for varying satellite altitude

Speaker: 
Alain Plattner - Princeton University - Geoscience Dept
Date: 
Nov 13 2013 - 3:00pm
Event type: 
IDeAS
Room: 
110 Fine Hall
Abstract: 

When estimating a planet's crustal magnetic field from satellite data the sources of the field are assumed to be contained within a thin shell on the planet's surface while the space between the surface and the satellite is considered source-free. This conceptualization renders the field outside of
the planet harmonic, and the inversion a reevaluation of the field at a different altitude. If we express the field in a bandlimited spherical-harmonics basis, the reevaluation on the planet's surface from a single satellite altitude can be expressed as a linear transformation that is intrinsically poorly conditioned. For satellite data of homogenous quality covering the entire planet, this reevaluation presents a viable method for the field inversion. If the data is of strongly varying quality or only locally available, the above mentioned method will become unstable and we need to find an alternative procedure. In this presentation we show how we can use the spatiospectral concentration concept by Slepian, Landau, and Pollak to construct a potential-field inversion method for vector data on a sphere. In order to account for the poorly conditioned reevaluation of the field on the planet's surface we incorporate the transformation in the construction of these so-called Slepian functions. We present how the potential-field inversion emerging from this concept can stably estimate a crustal field within a target region from data only within that region while accounting for varying satellite altitude.