We introduce a new method for post-stack seismic inversion using Bayesian transdimensional methods in layered media. We employ a reversible jump Markov chain Monte Carlo algorithm, defined within a parsimonious Bayesian framework, to infer not only the values of the model parameters but also the optimal number of layers required to describe the data. The parameterization includes a layer inclination angle to locally infer the stratigraphy from a group of adjacent seismic traces. The forward method generates a set of synthetic seismic traces using a classical convolution model. These synthetic traces are then compared with actual seismic traces to infer the geological model parameters that are layer acoustic impedances, interface depths, and dipping angles. We run the inversion on synthetic data obtained from a two-dimensional reference geometry and show its ability to recover the reference model parameters. This suggests the potential of the method to discover stratigraphic gaps in seismic reservoir characterization tasks. More generally, this demonstrates the capability of transdimensional inversion in quantitative interpretation tasks. It opens opportunities for inversion of entire post-stack seismic sections, accommodating lateral variability with relatively low computational time.