# Accounting for Local Geological Variability in Sequential Simulations—Concept and Application

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Department of Applied Sedimentary Geology, Institute of Applied Geosciences, Technische Universität Darmstadt, 64287 Darmstadt, Germany

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Department of Applied Geothermal Science and Technology, Institute of Applied Geosciences, Technische Universität Darmstadt, 64287 Darmstadt, Germany

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Author to whom correspondence should be addressed.

Received: 11 May 2020 / Revised: 23 June 2020 / Accepted: 23 June 2020 / Published: 26 June 2020

(This article belongs to the Special Issue Uncertainty Modeling in Spatial Data Analysis)

Heterogeneity-preserving property models of subsurface regions are commonly constructed by means of sequential simulations. Sequential Gaussian simulation (SGS) and direct sequential simulation (DSS) draw values from a local probability density function that is described by the simple kriging estimate and the local simple kriging variance at unsampled locations. The local simple kriging variance, however, does not necessarily reflect the geological variability being present at subsets of the target domain. In order to address that issue, we propose a new workflow that implements two modified versions of the popular SGS and DSS algorithms. Both modifications, namely, LVM-DSS and LVM-SGS, aim at simulating values by means of introducing a local variance model (LVM). The LVM is a measurement-constrained and geology-driven global representation of the locally observable variance of a property. The proposed modified algorithms construct the local probability density function with the LVM instead of using the simple kriging variance, while still using the simple kriging estimate as the best linear unbiased estimator. In an outcrop analog study, we can demonstrate that the local simple kriging variance in sequential simulations tends to underestimate the locally observed geological variability in the target domain and certainly does not account for the spatial distribution of the geological heterogeneity. The proposed simulation algorithms reproduce the global histogram, the global heterogeneity, and the considered variogram model in the range of ergodic fluctuations. LVM-SGS outperforms the other algorithms regarding the reproduction of the variogram model. While DSS and SGS generate a randomly distributed heterogeneity, the modified algorithms reproduce a geologically reasonable spatial distribution of heterogeneity instead. The new workflow allows for the integration of continuous geological trends into sequential simulations rather than using class-based approaches such as the indicator simulation technique.