Conditional stability for an inverse source problem and an application to the estimation of air dose rate radioactive substances by drone data

TL;DR

This paper establishes a theoretical conditional stability estimate for inverse source problems, specifically applied to estimating air dose rates of radioactive substances using drone data, based on harmonic analysis techniques.

Contribution

It provides a new conditional stability estimate for inverse source problems with applications to environmental radiation monitoring using drone data.

Findings

Proves a Hölder-type stability estimate for the inverse problem.

Provides a theoretical foundation for drone-based air dose rate estimation.

Utilizes harmonic extension and unique continuation principles.

Abstract

We consider the density field $f(x)$ generated by a volume source $\mu(y)$ in $D$ which is a domain in $\R^3$. For two disjoint segments $\gamma, \Gamma_1$ on a straight line in $\R^3 \setminus \ooo{D}$, we establish a conditional stability estimate of H\"older type in determining $f$ on $\Gamma_1$ by data $f$ on $\gamma$. This is a theoretical background for real-use solutions for the determination of air dose rates of radioactive substance at the human height level by high-altitude data. The proof of the stability estimate is based on the harmonic extension and the stability for line unique continuation of a harmonic function.