A recent passive seismic technology in the oil industry, sometimes referred to as hydrocarbon microtremor analysis (also low-frequency spectroscopy), claims high correlation in some instances between the presence of hydrocarbons and low-frequency spectral anomalies (elevated spectral energy levels) computed from passively recorded seismic data. These observations have been reported for a number of different geographic locations. One of the difficulties in assessing this method is the lack of a physical basis for explaining the empirically observed effects. A potential explanation that has appeared in the literature can be referred to as the resonant amplification model. The main idea of the model is that, because of capillary effects, an oil drop in a rockpore will oscillate at a resonant frequency when driven by the ambient noise field of the earth. This resonance phenomenon is interpreted as a possible source of the spectral anomaly. I examined this model by numerical simulation but was unable to reproduce the amplification effect. I then considered one of the main input parameters, the resonant frequency itself. By computing resonant frequencies using theoretical models from the literature, I found that the resulting values are too high to be consistent with the frequency range of hydrocarbon microtremor analysis. Furthermore, I found that such resonances only exist for little or no viscous damping. When realistic damping is considered, there is no oil-drop resonance effect. The model, at least in its current form, does not appear to provide a promising direction for establishing a physical basis for hydrocarbon microtremor analysis.