A non-parametric approach to inverse atmospheric dispersion problems

Using measure theoretic arguments, we provide a general framework for describing and studying the general inverse dispersion problem where no a priori assumptions on the source function has been made. Using this framework we derive necessary and sufficient conditions for a source to be detectable and non-detectable. 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.