We present a rigorous theoretical framework that allows one to assess the range of applicability of the spatial autocorrelation (SPAC) method, a technique of microtremor exploration that is widely used to infer phase velocities of Rayleigh waves using vertical-motion records from a circular array of seismic sensors. The magnitude of systematic errors (biases) that depend on the number of seismic sensors deployed around the circle, and the magnitude of systematic errors that arise from the presence of incoherent noise, are both evaluated analytically, and their general properties are discussed. The relationship between the magnitude of stochastic errors, inherent in the analysis results, and the duration of measurement (or to put it more accurately, the data's degree of freedom) is also elucidated. The validity of our theory is corroborated by checks against the results of both real data analysis and numerical experiments, and an example is given of how the theory can be adapted to account for practical situations encountered in the field. Discussions on the range of applicability of the SPAC method, which have heretofore often fallen back on empirical observations, have now obtained a theoretical ground on which to stand, providing a basis for strategies to make maximal use of the SPAC method's capabilities.