Estimation of subsurface geomodels by multi-objective stochastic optimization

• We present a new method to estimate subsurface geomodels.
• The method combines geostatistics and multi-objective optimization.
• It improves geomodel estimation by simultaneous incorporation of multiple datasets.
• Incorporation of seismic data in the process improves the performance of the method.
• The method produces robust solutions even in presence of realistic noise in data.

We present a new method to estimate subsurface geomodels using a multi-objective stochastic search technique that allows a variety of direct and indirect measurements to simultaneously constrain the earth model. Inherent uncertainties and noise in real data measurements may result in conflicting geological and geophysical datasets for a given area; a realistic earth model can then only be produced by combining the datasets in a defined optimal manner. One approach to solving this problem is by joint inversion of the various geological and/or geophysical datasets, and estimating an optimal model by optimizing a weighted linear combination of several separate objective functions which compare simulated and observed datasets. In the present work, we consider the joint inversion of multiple datasets for geomodel estimation, as a multi-objective optimization problem in which separate objective functions for each subset of the observed data are defined, followed by an unweighted simultaneous stochastic optimization to find the set of best compromise model solutions that fits the defined objectives, along the so-called “Pareto front”. We demonstrate that geostatistically constrained initializations of the algorithm improves convergence speed and produces superior geomodel solutions. We apply our method to a 3D reservoir lithofacies model estimation problem which is constrained by a set of geological and geophysical data measurements and attributes, and assess the sensitivity of the resulting geomodels to changes in the parameters of the stochastic optimization algorithm and the presence of realistic seismic noise conditions.