Propagation and reverberation of acoustic fields in continental-shelf waters depend strongly on the spatial variability of seabed geoacoustic parameters (propagation velocity of sound waves, density, sound attenuation, and layering structure), and lack of knowledge of seabed variability is often a limiting factor in modeling acoustic propagation. However, direct sampling (e.g., coring) of ... [Show full abstract] vertical and lateral variability is expensive, laborious, and provides only limited lateral resolution. This work develops probabilistic (Bayesian) inference methods for seabed reflectivity data to investigate and quantify spatial variability of seabed sediments in two and three dimensions. Typical experimental configurations (Fig. 1) involve ship-towed sound sources and hydrophone arrays that provide high-resolution sampling of the seabed and minimize the impact of complicated processes in the water column (currents, internal waves, internal tides, changes in sound-velocity structure). The data recorded by such systems are similar to data recorded in seismic surveys but are processed further to give the seabed reflection coefficient as a function of frequency and angle (Fig. 2 shows an example of a simulated experiment). For proper quantitative examination of spatial sediment variability, it is important to differentiate between parameter estimate uncertainty, model parameterization effects (due to limited knowledge about the optimal seabed model), and actual spatial variability (changes of seabed parameters within sediment layers, changes of layer thicknesses, and changes in the number of layers). A sequential trans-dimensional Monte Carlo algorithm is used here to efficiently analyze the data for long survey tracks during which the seabed environment changes significantly. The algorithm applies advanced Markov chain Monte Carlo methods in combination with sequential techniques (particle filters) to carry out geoacoustic parameter inference for consecutive data sets acquired along these track. Changes in model parametrization along the track (e.g., number of sediment layers) are accounted for with trans-dimensional partition modeling which intrinsically determines the amount of structure supported by the data information content. Challenging issues such as rapid environmental change between consecutive data sets and high information content (peaked likelihood) are addressed by bridging distributions implemented using annealed importance sampling. This provides an efficient method to locate high-likelihood regions for new data which are distant and/or disjoint from previous high-likelihood regions.