  The Sunyaev-Zeldovich (SZ) effect is a promising tool to study physical
properties of the hot X-ray emitting intracluster medium (ICM) in galaxy
clusters. To date, most SZ observations have been interpreted in combination
with X-ray follow-up measurements in order to determine the ICM temperature and
estimate the cluster mass. Future high-resolution, multifrequency SZ
observations promise to enable detailed studies of the ICM structures, by
measuring the ICM temperature through the temperature-dependent relativistic
corrections. In this work we develop a non-parametric method to derive
three-dimensional physical quantities, including temperature, pressure, total
mass, and peculiar velocities, of galaxy clusters from SZ observations alone.
We test the performance of this method using hydrodynamical simulations of
galaxy clusters, in order to assess systematic uncertainties in the
reconstructed physical parameters. In particular, we analyze mock Cerro
Chajnantor Atacama Telescope (CCAT) SZ observations, taking into account
various sources of systematic uncertainties associated with instrumental
effects and astrophysical foregrounds. We show that our method enables accurate
reconstruction of the three-dimensional ICM profiles, while retaining full
information about the gas distribution. We discuss the application of this
technique for ongoing and future multifrequency SZ observations.
