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An Uncertainty Model for Fault Shape and Location Per Røe · Frode Georgsen · Petter Abrahamsen

Received: 31 May 2013 / Accepted: 11 April 2014 © The Author(s) 2014. This article is published with open access at Springerlink.com

Abstract Fault models are often based on interpretations of seismic data that are constrained by observations of faults and associated strata in wells. Because of uncertainties in depth migration, seismic interpretations and well data, there often is significant uncertainty in the geometry and position of the faults. Fault uncertainty impacts determinations of reservoir volume, flow properties and well planning. Stochastic simulation of the faults is important for quantifying the uncertainties and minimizing the impacts. In this paper, a framework for representing and modeling uncertainty in fault location and geometry is presented. This framework can be used for prediction and stochastic simulation of fault surfaces, visualization of fault location uncertainty, and assessments of the sensitivity of fault location on reservoir performance. The uncertainty in fault location is represented by a fault uncertainty envelope and a marginal probability distribution. To be able to use standard geostatistical methods, quantile mapping is employed to construct a transformation from the fault surface domain to a transformed domain. Well conditioning is undertaken in the transformed domain using kriging or conditional simulations. The final fault surface is obtained by transforming back to the fault surface domain. Fault location uncertainty can be visualized by transforming the surfaces associated with a given quantile back to the fault surface domain. Keywords Structural uncertainty · Uncertainty envelope · Fault geometry realizations · Well conditioning

P. Røe (B) · F. Georgsen · P. Abrahamsen Norwegian Computing Center, PO Box 114, Blindern, 0314 Oslo, Norway e-mail: [email protected]

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Math Geosci

1 Introduction In petroleum reservoirs, faults are generally modeled using seismic data, well data and a knowledge of the local geology. Thore et al. (2002) list several sources of uncertainty when modeling faults based on seismic data, but conclude that the main sources are uncertainty in the seismic interpretation combined with vertical and lateral uncertainty arising from the time-depth migration of the seismic data. The interpretation uncertainty is often a consequence of the poor quality of seismic data near faults, together with the fact that faults are usually represented as surfaces, even though they are three-dimensional zones of deformation. The interpretation uncertainty encompasses both the existence of faults, and the location and local shape of the faults. The depth migration uncertainty is due to uncertainties in the velocity model and the actual seismic signal path due to non-horizontal velocity contrasts. The interpretation error is assumed to be independent for each fault, whereas the error introduced by the time-depth migration is correlated between nearby faults. Although the faul