Inverse Random Source Problems for the Helmholtz and Navier Equations

.In this paper, we study the inverse random source problems for the three-dimensional Helmholtz and Navier equations. The driven source is assumed to be a generalized Gaussian random function whose covariance operator is a classical pseudodifferential operator. We present stability in determining the principal symbol of the covariance operator by using far-field patterns at multiple frequencies in the presence of a potential. The key ingredient in the analysis is employing scattering theory to obtain the analytic domain and an upper bound for the resolvent of the elliptic operator. The analysis only requires data in a finite interval of frequencies.Keywordsinverse source problemgeneralized Gaussian random fieldpotential functionstabilityHelmholtz and Navier equationsGaussian random functionsMSC codes35R3035R6078A46