|Authors||S. Clark, A. M. Bruaset, T. O. Sømme and T. M. Løseth|
|Editors||R. Anderssen, R. Braddock and L. Newham|
|Title||A Flexible Stochastic Approach to Constraining Uncertainty in Forward Stratigraphic Models|
|Afilliation||Center for Biomedical Computing (SFF), Scientific Computing|
|Project(s)||Center for Biomedical Computing (SFF)|
|Publication Type||Proceedings, refereed|
|Year of Publication||2009|
|Conference Name||18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation|
|Publisher||Modelling and Simulation Society of Australia and New Zealand and International Association for Mathematics and Computers in Simulation|
Pinpointing the location of reservoir rocks and stratigraphic traps is crucial to the cost-effective extraction of oil. Forward stratigraphic models have been used to aid interpretations of these rocks and traps by determining their potential sand, shale and silt content. These stratigraphic models often rely on diffusion as a basis for simulating the processes of rock-erosion and the deposition of sediment, which forms the basis for rock formation. Diffusion-based modelling is consistent with observations in sedimentary environments over long time-scales. However, a persistent problem with these models is the determination of coefficients that specify the effectiveness of diffusion for each sediment type.
These coefficients, the so-called transport coefficients, are usually determined by a manual inversion to fit the data. In many cases, varying the transport coefficients by orders of magnitude can still achieve consistency with observations of sediment thickness from seismic data. By mapping the uncertainty in these transport coefficients to probability distributions, a probabilistic method can be used to determine the uncertainty in the output of the model, the basin bathymetry and the location of rocks and their original sediment compositions. We provide an example from the Ebro Basin, located off the east coast of the Iberian Peninsula.
The stochastic approach consists of generating a surface response of the stratigraphic forward model for each point in the domain. The building blocks, in our case, are Hermite polynomials, an orthogonal set. The surface response is a function of the uncertain parameters in the stratigraphic model, the most prominent of which are the diffusion coefficients. Assigning probability distributions to the uncertain parameters then determines the statistical properties of the surface response model. We show the time-dependent development of uncertainty in the Ebro Basin in the sand, silt and shale content of deposited sediment using this methodology.