  Simulating a depositional (or stratigraphic) sequence conditionally on
borehole data is a long-standing problem in hydrogeology and in petroleum
geostatistics. This paper presents a new rule-based approach for simulating
depositional sequences of surfaces conditionally on lithofacies thickness data.
The thickness of each layer is modeled by a transformed latent Gaussian random
field allowing for null thickness thanks to a truncation process. Layers are
sequentially stacked above each other following the regional stratigraphic
sequence. By choosing adequately the variograms of these random fields, the
simulated surfaces separating two layers can be continuous and smooth. Borehole
information is often incomplete in the sense that it does not provide direct
information as to the exact layer some observed thickness belongs to. The
latent Gaussian model proposed in this paper offers a natural solution to this
problem by means of a Bayesian setting with a Markov Chain Monte Carlo (MCMC)
algorithm that can explore all possible configurations compatible with the
data. The model and the associated MCMC algorithm are validated on synthetic
data and then applied to a subsoil in the Venetian Plain with a moderately
dense network of cored boreholes.
