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 i th mode between the solar data and the reference model, f 1 and f 2 are an appropriate pair of model parameters (e.g. sound speed squared c 2, and density ρ), E i 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.