The spectra of earthquake waveforms can provide important insight into rupture processes, but the analysis and interpretation of these spectra is rarely straightforward. Here we develop a Bayesian framework that embraces the inherent data and modeling uncertainties of spectral analysis to infer key source properties. The method uses a spectral ratio approach to correct the observed S‐wave spectra of nearby earthquakes for path and site attenuation. The objective then is to solve for a joint posterior probability distribution of three source parameters—seismic moment, corner frequency, and high‐frequency falloff rate—for each earthquake in the sequence, as well as a measure of rupture directivity for select target events with good azimuthal station coverage. While computationally intensive, this technique provides a quantitative understanding of parameter tradeoffs and uncertainties and allows one to impose physical constraints through prior distributions on all source parameters, which guide the inversion when data is limited. We demonstrate the method by analyzing in detail the source properties of 14 different target events of magnitude M5 in southern California that span a wide range of tectonic regimes and fault systems. These prominent earthquakes, while comparable in size, exhibit marked diversity in their source properties and directivity, with clear spatial patterns, depth‐dependent trends, and a preference for unilateral directivity. These coherent spatial variations source properties suggest that regional differences in tectonic setting, hypocentral depth or fault zone characteristics may drive variability in rupture processes, with important implications for our understanding of earthquake physics and its relation to hazard. Plain Language Summary The frequency content of seismic waveforms contains important information about the physics of earthquakes. However, measuring earthquake properties in this way is notoriously difficult and the resulting source parameter estimates are often highly uncertain. In this work we develop a technique based on Bayesian probability theory to reliably characterize earthquake source parameters and fully quantify their uncertainties. We apply this method to study 14 widely felt earthquakes in southern California. While these earthquakes are comparable in size, we show that the events can have large differences in their rupture behavior and in the frequency content of their waveforms. These findings have important implications both for our physical understanding of earthquakes and their influence on regional seismic hazard. Key Points We describe a Bayesian technique for analyzing earthquake spectra to infer key source parameters and rupture directivity We apply the method to characterize 14 earthquake sequences in southern California, each with a M5 target event We observe systematic regional and depth‐dependent variations in stress drop, with most events exhibiting unilateral rupture