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1.
Conditional Simulation with Patterns   总被引:12,自引:0,他引:12  
An entirely new approach to stochastic simulation is proposed through the direct simulation of patterns. Unlike pixel-based (single grid cells) or object-based stochastic simulation, pattern-based simulation simulates by pasting patterns directly onto the simulation grid. A pattern is a multi-pixel configuration identifying a meaningful entity (a puzzle piece) of the underlying spatial continuity. The methodology relies on the use of a training image from which the pattern set (database) is extracted. The use of training images is not new. The concept of a training image is extensively used in simulating Markov random fields or for sequentially simulating structures using multiple-point statistics. Both these approaches rely on extracting statistics from the training image, then reproducing these statistics in multiple stochastic realizations, at the same time conditioning to any available data. The proposed approach does not rely, explicitly, on either a statistical or probabilistic methodology. Instead, a sequential simulation method is proposed that borrows heavily from the pattern recognition literature and simulates by pasting at each visited location along a random path a pattern that is compatible with the available local data and any previously simulated patterns. This paper discusses the various implementation details to accomplish this idea. Several 2D illustrative as well as realistic and complex 3D examples are presented to showcase the versatility of the proposed algorithm.  相似文献
2.
Direct Pattern-Based Simulation of Non-stationary Geostatistical Models   总被引:3,自引:2,他引:1  
Non-stationary models often capture better spatial variation of real world spatial phenomena than stationary ones. However, the construction of such models can be tedious as it requires modeling both statistical trend and stationary stochastic component. Non-stationary models are an important issue in the recent development of multiple-point geostatistical models. This new modeling paradigm, with its reliance on the training image as the source for spatial statistics or patterns, has had considerable practical appeal. However, the role and construction of the training image in the non-stationary case remains a problematic issue from both a modeling and practical point of view. In this paper, we provide an easy to use, computationally efficient methodology for creating non-stationary multiple-point geostatistical models, for both discrete and continuous variables, based on a distance-based modeling and simulation of patterns. In that regard, the paper builds on pattern-based modeling previously published by the authors, whereby a geostatistical realization is created by laying down patterns as puzzle pieces on the simulation grid, such that the simulated patterns are consistent (in terms of a similarity definition) with any previously simulated ones. In this paper we add the spatial coordinate to the pattern similarity calculation, thereby only borrowing patterns locally from the training image instead of globally. The latter would entail a stationary assumption. Two ways of adding the geographical coordinate are presented, (1) based on a functional that decreases gradually away from the location where the pattern is simulated and (2) based on an automatic segmentation of the training image into stationary regions. Using ample two-dimensional and three-dimensional case studies we study the behavior in terms of spatial and ensemble uncertainty of the generated realizations.  相似文献
3.
Adding Local Accuracy to Direct Sequential Simulation   总被引:3,自引:0,他引:3  
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.  相似文献
4.
Conditioning Surface-Based Geological Models to Well and Thickness Data   总被引:2,自引:1,他引:1  
Geostatistical simulation methods aim to represent spatial uncertainty through realizations that reflect a certain geological concept by means of a spatial continuity model. Most common spatial continuity models are either variogram, training image, or Boolean based. In this paper, a more recent spatial model of geological continuity is developed, termed the event, or surface-based model, which is specifically applicable to modeling cases with complex stratigraphy, such as in sedimentary systems. These methods rely on a rule-based stacking of events, which are mathematically represented by two-dimensional thickness variations over the domain, where positive thickness is associated with deposition and negative thickness with erosion. Although it has been demonstrated that the surface-based models accurately represent the geological variation present in complex layered systems, they are more difficult to constrain to hard and soft data as is typically required of practical geostatistical techniques. In this paper, we develop a practical methodology for constraining such models to hard data from wells and thickness data interpreted from geophysics, such as seismic data. Our iterative methodology relies on a decomposition of the parameter optimization problem into smaller, manageable problems that are solved sequentially. We demonstrate this method on a real case study of a turbidite sedimentary basin.  相似文献
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In this paper, a new generalized sensitivity analysis is developed with a focus on parameter interaction. The proposed method is developed to apply to complex reservoir systems. Most critical in many engineering applications is to find which model parameters and parameter combinations have a significant impact on the decision variables. There are many types of parameters used in reservoir modeling, e.g., geophysical, geological and engineering. Some parameters are continuous, others discrete, and others have no numerical value and are scenario-based. The proposed generalized sensitivity analysis approach classifies the response/decision variables into a limited set of discrete classes. The analysis is based on the following principle: if the parameter frequency distribution is the same in each class, then the model response is insensitive to the parameter, while differences in the frequency distributions indicate that the model response is sensitive to the parameter. Based on this simple idea, a new general measure of sensitivity is developed. This sensitivity measure quantifies the sensitivity to parameter interactions, and incorporates the possibility that these interactions can be asymmetric for complex reservoir modeling. The approach is illustrated using a case study of a West Africa offshore oil reservoir.  相似文献
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This paper focuses on fault-related uncertainties in the subsurface, which can significantly affect the numerical simulation of physical processes. Our goal is to use dynamic data and process-based simulation to update structural uncertainty in a Bayesian inverse approach. We propose a stochastic fault model where the number and features of faults are made variable. In particular, this model samples uncertainties about connectivity between the faults. The stochastic three dimensional fault model is integrated within a stochastic inversion scheme in order to reduce uncertainties about fault characteristics and fault zone layout, by minimizing the mismatch between observed and simulated data.  相似文献
9.
Building of models in the Earth Sciences often requires the solution of an inverse problem: some unknown model parameters need to be calibrated with actual measurements. In most cases, the set of measurements cannot completely and uniquely determine the model parameters; hence multiple models can describe the same data set. Bayesian inverse theory provides a framework for solving this problem. Bayesian methods rely on the fact that the conditional probability of the model parameters given the data (the posterior) is proportional to the likelihood of observing the data and a prior belief expressed as a prior distribution of the model parameters. In case the prior distribution is not Gaussian and the relation between data and parameters (forward model) is strongly non-linear, one has to resort to iterative samplers, often Markov chain Monte Carlo methods, for generating samples that fit the data likelihood and reflect the prior model statistics. While theoretically sound, such methods can be slow to converge, and are often impractical when the forward model is CPU demanding. In this paper, we propose a new sampling method that allows to sample from a variety of priors and condition model parameters to a variety of data types. The method does not rely on the traditional Bayesian decomposition of posterior into likelihood and prior, instead it uses so-called pre-posterior distributions, i.e. the probability of the model parameters given some subset of the data. The use of pre-posterior allows to decompose the data into so-called, “easy data” (or linear data) and “difficult data” (or nonlinear data). The method relies on fast non-iterative sequential simulation to generate model realizations. The difficult data is matched by perturbing an initial realization using a perturbation mechanism termed “probability perturbation.” The probability perturbation method moves the initial guess closer to matching the difficult data, while maintaining the prior model statistics and the conditioning to the linear data. Several examples are used to illustrate the properties of this method.  相似文献
10.
Modeling Conditional Distributions of Facies from Seismic Using Neural Nets   总被引:1,自引:0,他引:1  
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.  相似文献
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