A measure theoretic approach to linear inverse atmospheric dispersion problems

TL;DR

This paper introduces a measure theoretic framework for linear inverse atmospheric dispersion problems, establishing solvability conditions for least-squares solutions without prior assumptions on the source function.

Contribution

It provides a rigorous measure theoretic approach to describe and analyze the inverse dispersion problem, including conditions for the well-posedness of least-squares solutions.

Findings

Derived solvability conditions for the inverse problem

Established when the least-squares method is well-defined

Provided a general framework applicable without prior source assumptions

Abstract

Using measure theoretic arguments, we provide a general framework for describing and studying the general linear inverse dispersion problem where no a priori assumptions on the source function has been made. We investigate the source-sensor relationship and rigorously state solvability conditions for when the inverse problem can be solved using a least-squares optimisation method. That is, we derive conditions for when the least-squares problem is well-defined.