Exploring Monte Carlo Simulation Strategies for Geoscience Applications (original) (raw)
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Computer simulations are an increasingly important area of geoscience research and development. At the core of stochastic or Monte Carlo simulations are the random number sequences that are assumed to be distributed with specific characteristics. Computer-generated random numbers, uniformly distributed on (0, 1), can be very different depending on the selection of pseudo-random number (PRN) or chaotic random number (CRN) generators. In the evaluation of some definite integrals, the resulting error variances can even be of different orders of magnitude. Furthermore, practical techniques for variance reduction such as importance sampling and stratified sampling can be applied in most Monte Carlo simulations and significantly improve the results. A comparative analysis of these strategies has been carried out for computational applications in planar and spatial contexts. Based on these experiments, and on some practical examples of geodetic direct and inverse problems, conclusions and recommendations concerning their performance and general applicability are included.
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Central European Geology, 2018
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Advances in Water Resources, 2007
ABSTRACT A covariance-based model-fitting approach is often considered valid to represent field spatial variability of hydraulic properties. This study examines the representation of geologic heterogeneity in two types of geostatistical models under the same mean and spatial covariance structure, and subsequently its effect on the hydraulic response to a pumping test based on 3D high-resolution numerical simulation and field data. Two geostatistical simulation methods, sequential Gaussian simulation (SGS) and transition probability indicator simulation (TPROGS) were applied to create conditional realizations of alluvial fan aquifer systems in the Lawrence Livermore National Laboratory (LLNL) area. The simulated K fields were then used in a numerical groundwater flow model to simulate a pumping test performed at the LLNL site. Spatial connectivity measures of high-K materials (channel facies) captured connectivity characteristics of each geostatistical model and revealed that the TPROGS model created an aquifer (channel) network having greater lateral connectivity. SGS realizations neglected important geologic structures associated with channel and overbank (levee) facies, even though the covariance model used to create these realizations provided excellent fits to sample covariances computed from exhaustive samplings of TPROGS realizations. Observed drawdown response in monitoring wells during a pumping test and its numerical simulation shows that in an aquifer system with strongly connected network of high-K materials, the Gaussian approach could not reproduce a similar behavior in simulated drawdown response found in TPROGS case. Overall, the simulated drawdown responses demonstrate significant disagreement between TPROGS and SGS realizations. This study showed that important geologic characteristics may not be captured by a spatial covariance model, even if that model is exhaustively determined and closely fits the exponential function.
In this study we introduce a new approach named importance sampling or quick simulations. The method has been extensively used in communication theory in estimating probability of rare events. The basic idea behind importance sampling techniques is that certain values of the input random variables (or vectors) have more important impact on the parameters being estimated than others, and if these ''important'' values are sampled more frequently than others, i.e., sampled from a biased density function, the variance of the estimator can be reduced. The outputs from simulations are then weighted to correct such biased sampling. Two illustrative examples are given to show the general procedure of the importance sampling approach as well as its applicability to subsurface flow and transport problems. In one example we estimated the mean and variance of hydraulic head for one-dimensional flow, and in the other we estimated the probability of a particle's travel time t less than a given critical value T . In both examples, we compared results from analytical solutions, the conventional Monte Carlo (CMC) simulations, and the importance sampling approach. It is shown that when an importance density function is chosen appropriately, importance sampling techniques may be many orders of magnitude more efficient than the CMC simulations and have a great potential in simulating subsurface flow and transport. Published by Elsevier Ltd.