An Uncertainty Model for Fault Shape and Location

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, flowproperties 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.