In this work, we use a parametrized theory-agnostic approach that connects the observation of black hole quasinormal modes with the underlying perturbation equations, with the goal of reconstructing the potential and the coupling functions appearing in the latter. The fundamental quasinormal mode frequency and its first two overtones are modeled through a second order expansion in the deviations from general relativity, which are assumed to be small but otherwise generic. By using a principal component analysis, we demonstrate that percent-level measurements of the fundamental mode and its overtones can be used to constrain the effective potential of tensor perturbations and the coupling functions between tensor modes and ones of different helicity, without assuming an underlying theory. We also apply our theory-agnostic reconstruction framework to analyze simulated quasinormal mode data produced within specific theories extending general relativity, such as Chern-Simons gravity.
