Topological uncertainties in structural geology and assimilation of dynamic data: parametrization and sampling.

@inproceedings{Cherpeau2GM2011,
 abstract = { This paper focuses on fault-related uncertainties in the subsurface, which can significantly affect fluid flow predictions. Because flow curves do not provide direct information about fault characteristics, a stochastic 3D fault model is integrated within a stochastic inversion scheme in order to reduce uncertainties about fault characteristics and fault zone layout, by minimizing the mismatch between observed and simulated flow response.
The stochastic fault model uses a priori information such as fault orientation, localization, size and roughness, to sample both geometrical and topological uncertainties with realistic fault descriptions. Faults are simulated sequentially, and each fault object is fully parameterized by the random vector used to simulate the fault features. Then, during inversion, the random vector of the current model is stochastically perturbed, producing a new parameter vector. This new vector is used as input by the stochastic fault model to produce a new model. Then, a flow simulation, i.e. the forward problem, is run on the new model which is accepted or rejected according to the Metropolis rule. Even if the topology varies from one model to another, the algorithm produces correlated models so that their flow responses evolve quite smoothly.
The methodology is applicable in general and illustrated on a synthetic two-phase flow example. A first set of models is generated to sample the prior uncertainty space. Then, models that minimize reference water-saturation data misfit are selected from this set. Each selected model is then used as a seed to generate a continuous Markov chain of models with discrete states. Local minima of these Markov chains represent a part of the posterior probability density. These models minimize the misfit criterion, reduce uncertainties about fault location, while the topology varies from one model to another. A second synthetic example highlights the interest of the parameterization for analyzing geological scenarios and falsifying those that do not match two-phase flow observations. },
 author = { Cherpeau, Nicolas AND Caumon, Guillaume AND Caers, Jef AND Levy, Bruno },
 booktitle = { Proc. 31st Gocad Meeting, Nancy },
 title = { Topological uncertainties in structural geology and assimilation of dynamic data: parametrization and sampling. },
 year = { 2011 }
}