Estimating gas saturation in a thin layer by using frequency-dependent amplitude versus offset modelling

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 have typically been limited to single interface models. Here we propose a modelling technique which allows us to incorporate frequency-dependent reflectivity into convolutional modelling. With this modelling framework, seismic data can be synthesized 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 constrains, gas saturation and layer thickness can both theoretically be estimated in the case of interfering reflections.