Stochastic Simulation of Patterns Using Distance-Based Pattern Modeling

The advent of multiple-point geostatistics (MPS) gave rise to the integration of complex subsurface geological structures and features into the model by the concept of training images. Initial algorithms generate geologically realistic realizations by using these training images to obtain conditional probabilities needed in a stochastic simulation framework. More recent pattern-based geostatistical algorithms attempt to improve the accuracy of the training image pattern reproduction. In these approaches, the training image is used to construct a pattern database. Consequently, sequential simulation will be carried out by selecting a pattern from the database and pasting it onto the simulation grid. One of the shortcomings of the present algorithms is the lack of a unifying framework for classifying and modeling the patterns from the training image. In this paper, an entirely different approach will be taken toward geostatistical modeling. A novel, principled and unified technique for pattern analysis and generation that ensures computational efficiency and enables a straightforward incorporation of domain knowledge will be presented.     

Modeling Conditional Distributions of Facies from Seismic Using Neural Nets

We present a general, flexible, and fast neural network approach to the modeling of a conditional distribution of a discrete random variable, given a continuous or discrete random vector. Although many more applications of the neural net technique could be envisioned, the aim is to apply the developed methodology to the integration of seismic data into reservoir models. Many geostatistical methods for integrating seismic data rely on a screening assumption of further away seismic events by the colocated seismic datum. Such assumption makes the task of modeling cross-covariances and local conditional distributions much easier. In many cases, however, the seismic data exhibit distinct and locally varying spatial patterns of continuity related to geological events such as channels, shale bodies, or fractures. The previous screening assumption prevents recognizing and hence utilizing these patterns of seismic data. In this paper we propose to relate seismic data to facies or petrophysical properties through a colocated window of seismic information instead of the single colocated seismic datum. The variation of seismic data from one window to another is accounted for. Several examples demonstrate that using such a window improves the predictive power of seismic data.     

Adding Local Accuracy to Direct Sequential Simulation

Geostatistical simulations are globally accurate in the sense that they reproduce global statistics such as variograms and histograms. Kriging is locally accurate in the minimum local error variance sense. Building on the concept of direct sequential simulation, we propose a fast simulation method that can share these opposing objectives. It is shown that the multiple-point entropy of the resulting simulation is related to the univariate entropy of the local conditional distributions used to draw simulated values. Adding local accuracy to conditional simulations does not detract much from variogram reproduction and can be used to increase multiple-point entropy. The methods developed are illustrated using a case study.     

Best Paper Award 2010

Announcement

Best Paper Award 2010     

Dr. Lawrence Drew—International Association for Mathematical Geosciences Krumbein Medalist 2010

Association Announcement

Dr. Lawrence Drew—International Association for Mathematical Geosciences Krumbein Medalist 2010     

Predicting changes in alluvial channel patterns in North-European Russia under conditions of global warming

Global climate change may have a noticeable impact on the northern environment, leading to changes in permafrost, vegetation and fluvial morphology. In this paper we compare the results from three geomorphological models and study the potential effects of changing climatic factors on the river channel types in North-European Russia. Two of the selected models by Romashin [Romashin, V.V., 1968. Variations of the river channel types under governing factors, Annals of the Hydrological Institute, vol. 155. Hydrometeoizdat, Leningrad, pp. 56–63.] and Leopold and Wolman [Leopold, L.B., Wolman, M.G., 1957. River channel pattern: braided, meandering and straight, Physiographic and hydraulic studies of rivers. USA Geological Survey Professional Paper 252, pp. 85–98.] are conventional QS-type models, which predict the existence of either multi-thread or single-tread channel types using data on discharge and channel slope. The more advanced model by Van den Berg [Van den Berg, J.H., 1995. Prediction of alluvial channel pattern of perennial rivers. Geomorphology 12, 259–270.] takes into account the size of the sediment material.We used data from 16 runoff gauges to validate the models and predict the channel types at selected locations under modern and predicted for the future climatic conditions. Two of the three models successfully replicated the currently existing channel types in all but one of the studied sites. Predictive calculations under the hypothetical scenarios of 10%, 15%, 20% and 35% runoff increase gave different results. Van den Berg's model predicted potential transformation of the channel types, from single- to multi-thread, at 4 of 16 selected locations in the next few decades, and at 5 locations by the middle of the 21st century. Each of the QS-type models predicted such transformation at one site only.Results of the study indicate that climatic warming in combination with other environmental changes may lead to transformation of the river channel types at selected locations in north-western Russia. Further efforts are needed to improve the performance of the fluvial geomorphological models and their ability to predict such changes.     

A multiscale adjoint method to compute sensitivity coefficients for flow in heterogeneous porous media

A multiscale adjoint (MSADJ) method is developed to compute high-resolution sensitivity coefficients for subsurface flow in large-scale heterogeneous geologic formations. In this method, the original fine-scale problem is partitioned into a set of coupled subgrid problems, such that the global adjoint problem can be efficiently solved on a coarse grid. Then, the coarse-scale sensitivities are interpolated to the local fine grid by reconstructing the local variability of the model parameters with the aid of solving embedded adjoint subproblems. The approach employs the multiscale finite-volume (MSFV) formulation to accurately and efficiently solve the highly detailed flow problem. The MSFV method couples a global coarse-scale solution with local fine-scale reconstruction operators, hence yielding model responses that are quite accurate at both scales. The MSADJ method is equally efficient in computing the gradient of the objective function with respect to model parameters. Several examples demonstrate that the approach is accurate and computationally efficient. The accuracy of our multiscale method for inverse problems is twofold: the sensitivity coefficients computed by this approach are more accurate than the traditional finite-difference-based numerical method for computing derivatives, and the calibrated models after history matching honor the available dynamic data on the fine scale. In other words, the multiscale based adjoint scheme can be used to history match fine-scale models quite effectively.     

Representing Spatial Uncertainty Using Distances and Kernels

Assessing uncertainty of a spatial phenomenon requires the analysis of a large number of parameters which must be processed by a transfer function. To capture the possibly of a wide range of uncertainty in the transfer function response, a large set of geostatistical model realizations needs to be processed. Stochastic spatial simulation can rapidly provide multiple, equally probable realizations. However, since the transfer function is often computationally demanding, only a small number of models can be evaluated in practice, and are usually selected through a ranking procedure. Traditional ranking techniques for selection of probabilistic ranges of response (P10, P50 and P90) are highly dependent on the static property used. In this paper, we propose to parameterize the spatial uncertainty represented by a large set of geostatistical realizations through a distance function measuring “dissimilarity” between any two geostatistical realizations. The distance function allows a mapping of the space of uncertainty. The distance can be tailored to the particular problem. The multi-dimensional space of uncertainty can be modeled using kernel techniques, such as kernel principal component analysis (KPCA) or kernel clustering. These tools allow for the selection of a subset of representative realizations containing similar properties to the larger set. Without losing accuracy, decisions and strategies can then be performed applying a transfer function on the subset without the need to exhaustively evaluate each realization. This method is applied to a synthetic oil reservoir, where spatial uncertainty of channel facies is modeled through multiple realizations generated using a multi-point geostatistical algorithm and several training images.     

Migration dynamics of clupeoids in the Schelde estuary: A stable isotope approach

Large numbers of young of the year herring (Clupea harengus L.) and sprat (Sprattus sprattus (L.)) typically enter and remain within North Sea estuaries during the winter months. The main purpose of this study was to examine their migration dynamics between the North Sea and the Schelde estuary using C and N stable isotopes. Prior to this, stomach contents were used to verify the isotopic differences between the food sources at the sampling stations. From May 2000 to April 2001 fish were collected monthly in the upper and lower estuary. Muscle tissue and stomach contents were analyzed for δ¹³C and δ¹⁵N using an EA-IRMS. Based on the stomach contents, it was demonstrated that δ¹⁵N could not be used as a tracer for fish migration because the longitudinal estuarine δ¹⁵N gradient had reversed completely during autumn. The δ¹³C gradient, however, was found to be reliable for studying fish movement in the Schelde estuary.Seasonal movements of clupeoids in the Schelde estuary were analyzed by separating the temporal abundance patterns into migration groups based on their muscle isotopic composition. Immigration and emigration seem to occur continuously throughout the year. Most exchange occurred in November. During winter, immigration remained high but gradually decreased. Although the herring and sprat abundance further declined in the estuary during February and March, large seaward emigration was not fully demonstrated. As temporal overlap between immigration and emigration is concluded the results support the hypothesis that migration to estuarine nurseries is individually based.