Various models have been proposed to link partial gas saturation to seismic attenuation and dispersion, suggesting that the reflection coefficient should be frequency-dependent in many cases of practical importance. Previous approaches to studying this phenomenon typically have been limited to single-interface models. Here, we propose a modelling technique that allows us to incorporate frequency-dependent reflectivity into convolutional modelling. With this modelling framework, seismic data can be synthesised from well logs of velocity, density, porosity, and water saturation. This forward modelling could act as a basis for inversion schemes aimed at recovering gas saturation variations with depth. We present a Bayesian inversion scheme for a simple thin-layer case and a particular rock physics model and show that, although the method is very sensitive to prior information and constraints, both gas saturation and layer thickness theoretically can be estimated in the case of interfering reflections.