The inverse problem of finding the structure of the solar interior from the observed frequencies can be written as

where, δωi is the difference in frequency of the ith mode between the solar data and the reference model, f1 and f2 are an appropriate pair of model parameters (e.g. sound speed squared c2, and density ρ), Ei is the mode kinetic energy, K(1) and K(2) are known functions of the reference model, and F(ω) is the unknown function added to account for uncertainties associated with the physics of the surface layers.