Conditional Simulation of Multi-Type Non Stationary Markov Object Models Respecting Specified Proportions

Although Boolean model simulation has been widely used during the last two decades to simulate sedimentary bodies (especially in fluvio-deltaic environments), a key issue has subsisted. One of the most important parameter for object model simulation, namely the (non stationary) intensity of the underlying object process, is not a parameter provided by the end user but must instead be computed from other input parameters, such as local proportions of lithofacies, erosion rule between objects of different types and interaction between objects. This paper revisits a birth and death algorithm for simulating conditional, non stationary, multi-type objects models with interaction. It provides workable approximations for computing the local intensity of the underlying point process to respect proportion maps. Simulated examples show that this algorithm is able to reproduce the desired proportions. Important issues for implementing this algorithm are discussed.