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

Abstract

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.

Uncertainty analysis of gravity disturbance for geothermal exploration in the Geneva Basin (Switzerland)

“…It is not surprising that the aforementioned anomalies show high variability, due to the heteroscedastic nature of geological parameters that commonly show a higher variability for high values and a lower variability for low values (Linsel et al, 2020). This is illustrated in single stochastic realizations ( Fig.…”

“…In fact, since stochastic simulation preserves both the mean and the variance observed in the data, they can reproduce the extreme value encountered in the variable distribution. And since the higher variability (uncertainty) is encountered in the extreme values of the data distributions (Linsel et al, 2020), stochastic techniques are best fitted to quantify this variability through variance (or standard deviation) maps. Instead, classical interpolation techniques, preserve only the mean value observed in the data and tends to produce images that are smoothed in which the interpolated value is close to the mean value, and in which the extreme values are underrepresented.…”

3D geological modeling of deep fractured low porosity sandstone gas reservoir in the Kuqa Depression, Tarim Basin

“…Similar to the facies modeling simulation methods, petrophysical modeling of the reservoir involves techniques such as sequential Gaussian simulation, Gaussian random function simulation, Kriging simulation, and moving average simulation (Linsel et al, 2020;Yong et al, 2020;Giraud et al, 2021;Ursegov et al, 2021). In line with the geological features of the study area, sequential Gaussian simulation is utilized to stochastically model the reservoir properties, including porosity, permeability, and gas saturation under facies constraints.…”

Informed Local Smoothing in 3D Implicit Geological Modeling

“…In this work, we only consider the measurement error portion of the nugget effect, allowing us to only adjust the behavior at zero lag distance. In practice this is achieved by manipulating the diagonal of the redundancy kriging matrix (compare [18,33]):…”

“…In the context of geosciences, varying methods have been proposed to relax the assumption of second-order stationarity by applying a non-stationary covariance structure [29][30][31]. Other suggested methods alter the diagonal entries of the covariance matrix, analogue to the concept of classical heteroscedasticity, with additional information of the variances of the modeled process [32,33]. This is equivalent to locally changing portion of the nugget effect attributed to measurement error and has also been named kriging with known measurement error or filtered kriging [18,34,35].…”