This paper presents a unified exposition of methods which permit the quantitative study of turbulent motions within interstellar clouds; it is a companion to the accompanying work on the velocity field of the Taurus molecular cloud complex. The basic method discussed here- which is at least some 30 years old- involves mapping a source in an optically thin spectral line, and studying the spatial correlation properties of the resulting velocity centroid map. We first establish the relationship between the centroid of an optically thin spectral transition and the average velocity of gas along the line formation path. We then show how the correlation length and amplitude of turbulence in a source are reflected in the statistical behavior of spectral line centroids. Some useful general relations, which basically stem from simple dimensional arguments, are noted in this context. Finally, we also consider the impact of data noise on derived velocity field parameters, and describe methods for assessing its magnitude and correcting for its influence.
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Dickman et al. (1985) studied this question.