The magnetizations of thin film disk-shaped type-II superconductors in perpendicular magnetic fields are considered by aid of Mikheenko's critical state model which has been corrected by Zhu for the case of a time-varying periodic field. This paper presents the application of this scheme to an arbitrary nonperiodic time dependence H(t). We calculate the influence of field inhomogeneities in a magnetometer on the current density distribution of a disk-shaped type-II superconductor. The resulting SQUID pickup signals and magnetic moments are compared to measurements performed on a 200 nm thick YBa2Cu3O7 film in the irreversible regime of the phase diagram. Theory and experiment show good agreement, even for heavily distorted SQUID signals.