The influence of local equilibrium parameters on the Alfven spectrum is studied. The aim is to solve the inverse problem: identification of the plasma profiles, and especially the safety factor profile, using measurements of magnetohydrodynamic (MHD) waves. A study case is presented to determine what the possible uses of MHD spectroscopy are. The dependence of the TAE (Toroidicity induced Alfven Eigenmode) frequency on the safety factor at the edge is shown. The possible use of Alfven continuum modes near the edge is investigated. A very accurate determination of the safety factor on axis will be presented for plasmas where core-localized TAE's are present. It will be shown how measurements of mode structures can provide information on plasma parameters at particular points in the plasma. The numerical findings will be compared to experimental results from the Joint European Torus (JET) [P. ii. Rebut and the JET Team, Plasma Physics and Controlled Nuclear Fusion Research 1984 (International Atomic Energy Agency,Vienna, 1985), Vol. 1, p. 11] active Alfven wave diagnostic.