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

Abstract

We consider the density field $ f(x) $ generated by a volume source $ \mu(y) $ in $ D $ which is a domain in $ \mathbb{R}^3 $. For two disjoint segments $ \gamma, \Gamma_1 $ on a straight line in $ \mathbb{R}^3 \setminus \overline{D} $, we establish a conditional stability estimate of Holder 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.