The map R^{2T} to W^T via C^T factorization is continuous in operator topologies, so R_j^{2T} converging implies the potential q_j converging to q in H^{-2}(Ω^T).
A Non-Iterative Reconstruction Algorithm for the Acoustic Inverse Boundary Value Problem.arXiv: 2009.00641v1 [math.AP] 1 Sep 2020
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On a stability of time-optimal version of the Boundary Control method
The map R^{2T} to W^T via C^T factorization is continuous in operator topologies, so R_j^{2T} converging implies the potential q_j converging to q in H^{-2}(Ω^T).