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1.
Conditioning complex subsurface flow models on nonlinear data is complicated by the need to preserve the expected geological connectivity patterns to maintain solution plausibility. Generative adversarial networks (GANs) have recently been proposed as a promising approach for low-dimensional representation of complex high-dimensional images. The method has also been adopted for low-rank parameterization of complex geologic models to facilitate uncertainty quantification workflows. A difficulty in adopting these methods for subsurface flow modeling is the complexity associated with nonlinear flow data conditioning. While conditional GAN (CGAN) can condition simulated images on labels, application to subsurface problems requires efficient conditioning workflows for nonlinear data, which is far more complex. We present two approaches for generating flow-conditioned models with complex spatial patterns using GAN. The first method is through conditional GAN, whereby a production response label is used as an auxiliary input during the training stage of GAN. The production label is derived from clustering of the flow responses of the prior model realizations (i.e., training data). The underlying assumption of this approach is that GAN can learn the association between the spatial features corresponding to the production responses within each cluster. An alternative method is to use a subset of samples from the training data that are within a certain distance from the observed flow responses and use them as training data within GAN to generate new model realizations. In this case, GAN is not required to learn the nonlinear relation between production responses and spatial patterns. Instead, it is tasked to learn the patterns in the selected realizations that provide a close match to the observed data. The conditional low-dimensional parameterization for complex geologic models with diverse spatial features (i.e., when multiple geologic scenarios are plausible) performed by GAN allows for exploring the spatial variability in the conditional realizations, which can be critical for decision-making. We present and discuss the important properties of GAN for data conditioning using several examples with increasing complexity. 相似文献
2.
Spatial inverse problems in the Earth Sciences are often ill-posed, requiring the specification of a prior model to constrain
the nature of the inverse solutions. Otherwise, inverted model realizations lack geological realism. In spatial modeling,
such prior model determines the spatial variability of the inverse solution, for example as constrained by a variogram, a
Boolean model, or a training image-based model. In many cases, particularly in subsurface modeling, one lacks the amount of
data to fully determine the nature of the spatial variability. For example, many different training images could be proposed
for a given study area. Such alternative training images or scenarios relate to the different possible geological concepts
each exhibiting a distinctive geological architecture. Many inverse methods rely on priors that represent a single subjectively
chosen geological concept (a single variogram within a multi-Gaussian model or a single training image). This paper proposes
a novel and practical parameterization of the prior model allowing several discrete choices of geological architectures within
the prior. This method does not attempt to parameterize the possibly complex architectures by a set of model parameters. Instead,
a large set of prior model realizations is provided in advance, by means of Monte Carlo simulation, where the training image
is randomized. The parameterization is achieved by defining a metric space which accommodates this large set of model realizations.
This metric space is equipped with a “similarity distance” function or a distance function that measures the similarity of
geometry between any two model realizations relevant to the problem at hand. Through examples, inverse solutions can be efficiently
found in this metric space using a simple stochastic search method. 相似文献
3.
Direct push (DP) technologies are typically used for cost-effective geotechnical characterization of unconsolidated soils and sediments. In more recent developments, DP technologies have been used for efficient hydraulic conductivity ( K) characterization along vertical profiles with sampling resolutions of up to a few centimetres. Until date, however, only a limited number of studies document high-resolution in situ DP data for three-dimensional conceptual hydrogeological model development and groundwater flow model parameterization. This study demonstrates how DP technologies improve building of a conceptual hydrogeological model. We further evaluate the degree to which the DP-derived hydrogeological parameter K, measured across different spatial scales, improves performance of a regional groundwater flow model. The study area covers an area of ~60 km 2 with two overlying, mainly unconsolidated sand aquifers separated by a 5–7 m thick highly heterogeneous clay layer (in north-eastern Belgium). The hydrostratigraphy was obtained from an analysis of cored boreholes and about 265 cone penetration tests (CPTs). The hydrogeological parameter K was derived from a combined analysis of core and CPT data and also from hydraulic direct push tests. A total of 50 three-dimensional realizations of K were generated using a non-stationary multivariate geostatistical approach. To preserve the measured K values in the stochastic realizations, the groundwater model K realizations were conditioned on the borehole and direct push data. Optimization was performed to select the best performing model parameterization out of the 50 realizations. This model outperformed a previously developed reference model with homogeneous K fields for all hydrogeological layers. Comparison of particle tracking simulations, based either on the optimal heterogeneous or reference homogeneous groundwater model flow fields, demonstrate the impact DP-derived subsurface heterogeneity in K can have on groundwater flow and solute transport. We demonstrated that DP technologies, especially when calibrated with site-specific data, provide high-resolution 3D subsurface data for building more reliable conceptual models and increasing groundwater flow model performance. 相似文献
4.
A Bayesian linear inversion methodology based on Gaussian mixture models and its application to geophysical inverse problems are presented in this paper. The proposed inverse method is based on a Bayesian approach under the assumptions of a Gaussian mixture random field for the prior model and a Gaussian linear likelihood function. The model for the latent discrete variable is defined to be a stationary first-order Markov chain. In this approach, a recursive exact solution to an approximation of the posterior distribution of the inverse problem is proposed. A Markov chain Monte Carlo algorithm can be used to efficiently simulate realizations from the correct posterior model. Two inversion studies based on real well log data are presented, and the main results are the posterior distributions of the reservoir properties of interest, the corresponding predictions and prediction intervals, and a set of conditional realizations. The first application is a seismic inversion study for the prediction of lithological facies, P- and S-impedance, where an improvement of 30% in the root-mean-square error of the predictions compared to the traditional Gaussian inversion is obtained. The second application is a rock physics inversion study for the prediction of lithological facies, porosity, and clay volume, where predictions slightly improve compared to the Gaussian inversion approach. 相似文献
6.
Reservoir characterization needs the integration of various data through history matching, especially dynamic information
such as production or 4D seismic data. Although reservoir heterogeneities are commonly generated using geostatistical models,
random realizations cannot generally match observed dynamic data. To constrain model realizations to reproduce measured dynamic
data, an optimization procedure may be applied in an attempt to minimize an objective function, which quantifies the mismatch
between real and simulated data. Such assisted history matching methods require a parameterization of the geostatistical model
to allow the updating of an initial model realization. However, there are only a few parameterization methods available to
update geostatistical models in a way consistent with the underlying geostatistical properties. This paper presents a local
domain parameterization technique that updates geostatistical realizations using assisted history matching. This technique
allows us to locally change model realizations through the variation of geometrical domains whose geometry and size can be
easily controlled and parameterized. This approach provides a new way to parameterize geostatistical realizations in order
to improve history matching efficiency. 相似文献
7.
An adequate representation of the detailed spatial variation of subsurface parameters for underground flow and mass transport
simulation entails heterogeneous models. Uncertainty characterization generally calls for a Monte Carlo analysis of many equally
likely realizations that honor both direct information (e.g., conductivity data) and information about the state of the system
(e.g., piezometric head or concentration data). Thus, the problems faced is how to generate multiple realizations conditioned
to parameter data, and inverse-conditioned to dependent state data. We propose using Markov chain Monte Carlo approach (MCMC)
with block updating and combined with upscaling to achieve this purpose. Our proposal presents an alternative block updating
scheme that permits the application of MCMC to inverse stochastic simulation of heterogeneous fields and incorporates upscaling
in a multi-grid approach to speed up the generation of the realizations. The main advantage of MCMC, compared to other methods
capable of generating inverse-conditioned realizations (such as the self-calibrating or the pilot point methods), is that
it does not require the solution of a complex optimization inverse problem, although it requires the solution of the direct
problem many times. 相似文献
8.
In the analysis of petroleum reservoirs, one of the most challenging problems is to use inverse theory in the search for an optimal parameterization of the reservoir. Generally, scientists approach this problem by computing a sensitivity matrix and then perform a singular value decomposition in order to determine the number of degrees of freedom i.e. the number of independent parameters necessary to specify the configuration of the system. Here we propose a complementary approach: it uses the concept of refinement indicators to select those degrees which have the greatest sensitivity to an objective function quantifying the mismatch between measured and simulated data. We apply this approach to the problem of data integration for petrophysical reservoir charaterization where geoscientists are currently working with multimillion cell geological models. Data integration may be performed by gradually deforming (by a linear combination) a set of these multimillion grid geostatistical realizations during the optimization process. The inversion parameters are then reduced to the number of coefficients of this linear combination. However, there is an infinity of geostatistical realizations to choose from which may not be efficient regarding operational constraints. Following our new approach, we are able through a single objective function evaluation to compute refinement indicators that indicate which realizations might improve the iterative geological model in a significant way. This computation is extremely fast as it implies a single gradient computation through the adjoint state approach and dot products. Using only the most sensitive realizations from a given set, we are able to resolve quicker the optimization problem case. We applied this methodology to the integration of interference test data into 3D geostatistical models. 相似文献
9.
Ensemble methods present a practical framework for parameter estimation, performance prediction, and uncertainty quantification in subsurface flow and transport modeling. In particular, the ensemble Kalman filter (EnKF) has received significant attention for its promising performance in calibrating heterogeneous subsurface flow models. Since an ensemble of model realizations is used to compute the statistical moments needed to perform the EnKF updates, large ensemble sizes are needed to provide accurate updates and uncertainty assessment. However, for realistic problems that involve large-scale models with computationally demanding flow simulation runs, the EnKF implementation is limited to small-sized ensembles. As a result, spurious numerical correlations can develop and lead to inaccurate EnKF updates, which tend to underestimate or even eliminate the ensemble spread. Ad hoc practical remedies, such as localization, local analysis, and covariance inflation schemes, have been developed and applied to reduce the effect of sampling errors due to small ensemble sizes. In this paper, a fast linear approximate forecast method is proposed as an alternative approach to enable the use of large ensemble sizes in operational settings to obtain more improved sample statistics and EnKF updates. The proposed method first clusters a large number of initial geologic model realizations into a small number of groups. A representative member from each group is used to run a full forward flow simulation. The flow predictions for the remaining realizations in each group are approximated by a linearization around the full simulation results of the representative model (centroid) of the respective cluster. The linearization can be performed using either adjoint-based or ensemble-based gradients. Results from several numerical experiments with two-phase and three-phase flow systems in this paper suggest that the proposed method can be applied to improve the EnKF performance in large-scale problems where the number of full simulation is constrained. 相似文献
10.
Construction of predictive reservoir models invariably involves interpretation and interpolation between limited available data and adoption of imperfect modeling assumptions that introduce significant subjectivity and uncertainty into the modeling process. In particular, uncertainty in the geologic continuity model can significantly degrade the quality of fluid displacement patterns and predictive modeling outcomes. Here, we address a standing challenge in flow model calibration under uncertainty in geologic continuity by developing an adaptive sparse representation formulation for prior model identification (PMI) during model calibration. We develop a flow-data-driven sparsity-promoting inversion to discriminate against distinct prior geologic continuity models (e.g., variograms). Realizations of reservoir properties from each geologic continuity model are used to generate sparse geologic dictionaries that compactly represent models from each respective prior. For inversion initially the same number of elements from each prior dictionary is used to construct a diverse geologic dictionary that reflects a wide range of variability and uncertainty in the prior continuity. The inversion is formulated as a sparse reconstruction problem that inverts the flow data to identify and linearly combine the relevant elements from the large and diverse set of geologic dictionary elements to reconstruct the solution. We develop an adaptive sparse reconstruction algorithm in which, at every iteration, the contribution of each dictionary to the solution is monitored to replace irrelevant (insignificant) elements with more geologically relevant (significant) elements to improve the solution quality. Several numerical examples are used to illustrate the effectiveness of the proposed approach for identification of geologic continuity in practical model calibration problems where the uncertainty in the prior geologic continuity model can lead to biased inversion results and prediction. 相似文献
11.
Conditional facies modeling combines geological spatial patterns with different types of observed data, to build earth models for predictions of subsurface resources. Recently, researchers have used generative adversarial networks (GANs) for conditional facies modeling, where an unconditional GAN is first trained to learn the geological patterns using the original GAN’s loss function, then appropriate latent vectors are searched to generate facies models that are consistent with the observed conditioning data. A problem with this approach is that the time-consuming search process needs to be conducted for every new conditioning data. As an alternative, we improve GANs for conditional facies simulation (called GANSim) by introducing an extra condition-based loss function and adjusting the architecture of the generator to take the conditioning data as inputs, based on progressive growing of GANs. The condition-based loss function is defined as the inconsistency between the input conditioning value and the corresponding characteristics exhibited by the output facies model, and forces the generator to learn the ability of being consistent with the input conditioning data, together with the learning of geological patterns. Our input conditioning factors include global features (e.g., the mud facies proportion) alone, local features such as sparse well facies data alone, and joint combination of global features and well facies data. After training, we evaluate both the quality of generated facies models and the conditioning ability of the generators, by manual inspection and quantitative assessment. The trained generators are quite robust in generating high-quality facies models conditioned to various types of input conditioning information.
相似文献
12.
Uncertainty quantification for subsurface flow problems is typically accomplished through model-based inversion procedures in which multiple posterior (history-matched) geological models are generated and used for flow predictions. These procedures can be demanding computationally, however, and it is not always straightforward to maintain geological realism in the resulting history-matched models. In some applications, it is the flow predictions themselves (and the uncertainty associated with these predictions), rather than the posterior geological models, that are of primary interest. This is the motivation for the data-space inversion (DSI) procedure developed in this paper. In the DSI approach, an ensemble of prior model realizations, honoring prior geostatistical information and hard data at wells, are generated and then (flow) simulated. The resulting production data are assembled into data vectors that represent prior ‘realizations’ in the data space. Pattern-based mapping operations and principal component analysis are applied to transform non-Gaussian data variables into lower-dimensional variables that are closer to multivariate Gaussian. The data-space inversion is posed within a Bayesian framework, and a data-space randomized maximum likelihood method is introduced to sample the conditional distribution of data variables given observed data. Extensive numerical results are presented for two example cases involving oil–water flow in a bimodal channelized system and oil–water–gas flow in a Gaussian permeability system. For both cases, DSI results for uncertainty quantification (e.g., P10, P50, P90 posterior predictions) are compared with those obtained from a strict rejection sampling (RS) procedure. Close agreement between the DSI and RS results is consistently achieved, even when the (synthetic) true data to be matched fall near the edge of the prior distribution. Computational savings using DSI are very substantial in that RS requires \(O(10^5\)– \(10^6)\) flow simulations, in contrast to 500 for DSI, for the cases considered. 相似文献
14.
We analyze the results of a mathematical simulation of pulsed electromagnetic fields in geologic media with dipping near-vertical boundaries as well as interpretations within approximating block models and a layered homogeneous conducting model. We consider the possibilities and limitations of these approaches to the inversion of data from pulsed soundings of actual geologic media. 相似文献
15.
The inverse problem of seawater intrusion (SWI) is reviewed. It represents a challenge because of both conceptual and computational difficulties and because coastal aquifer models display many singularities: (1) head measurements need to be complemented with density information; (2) salinity concentration data are very sensitive to flow within the borehole. Data problems can be reduced by incorporating the measurement process within model calibration; (3) SWI models are extremely sensitive to aquifer bottom topography; (4) the initial conditions may be far from steady state and depend on the location and type of sea-aquifer connection. Problems with aquifer geometry and initial conditions can be addressed by parameterization, which allows for modification during inversion. The four sets of difficulties can be partly overcome by using tidal response and electrical conductivity data, which are highly informative and provide extensive coverage. Still, SWI inversion is extremely demanding from a computation point of view. Computational improvements are discussed. 相似文献
17.
A new low-dimensional parameterization based on principal component analysis (PCA) and convolutional neural networks (CNN) is developed to represent complex geological models. The CNN–PCA method is inspired by recent developments in computer vision using deep learning. CNN–PCA can be viewed as a generalization of an existing optimization-based PCA (O-PCA) method. Both CNN–PCA and O-PCA entail post-processing a PCA model to better honor complex geological features. In CNN–PCA, rather than use a histogram-based regularization as in O-PCA, a new regularization involving a set of metrics for multipoint statistics is introduced. The metrics are based on summary statistics of the nonlinear filter responses of geological models to a pre-trained deep CNN. In addition, in the CNN–PCA formulation presented here, a convolutional neural network is trained as an explicit transform function that can post-process PCA models quickly. CNN–PCA is shown to provide both unconditional and conditional realizations that honor the geological features present in reference SGeMS geostatistical realizations for a binary channelized system. Flow statistics obtained through simulation of random CNN–PCA models closely match results for random SGeMS models for a demanding case in which O-PCA models lead to significant discrepancies. Results for history matching are also presented. In this assessment CNN–PCA is applied with derivative-free optimization, and a subspace randomized maximum likelihood method is used to provide multiple posterior models. Data assimilation and significant uncertainty reduction are achieved for existing wells, and physically reasonable predictions are also obtained for new wells. Finally, the CNN–PCA method is extended to a more complex nonstationary bimodal deltaic fan system, and is shown to provide high-quality realizations for this challenging example. 相似文献
18.
The non-linear apparent resistivity problem in the subsurface study of the earth takes into account the model parameters in terms of resistivity and thickness of individual subsurface layers using the trained synthetic data by means of Artificial Neural Networks (ANN). Here we used a single layer feed-forward neural network with fast back propagation learning algorithm. So on proper training of back propagation networks it tends to give the resistivity and thickness of the subsurface layer model of the field resistivity data with reference to the synthetic data trained in the appropriate network. During training, the weights and biases of the network are iteratively adjusted to make network performance function level more efficient. On adequate training, errors are minimized and the best result is obtained using the artificial neural networks. The network is trained with more number of VES data and this trained network is demonstrated by the field data. The accuracy of inversion depends upon the number of data trained. In this novel and specially designed algorithm, the interpretation of the vertical electrical sounding has been done successfully with the more accurate layer model. 相似文献
19.
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
20.
三维地质模型精度评估与误差修正问题已成为制约三维地质模拟技术深入发展应用的瓶颈。在综合国内外研究现状与发展趋势的基础上,提出了三维地质结构模型精度评估、误差检测、动态修正的总体研究框架。在模型精度评估方面,提出分别构建三维地质结构模型精度评估的一般理论模型、面向特定地质体的实际操作模型和地质结构构造不确定性的三维空间分布模型的研究思路,指出应重点研究地质实体自身特性、三维地质建模方法对三维地质结构模型精度的影响,解决由一般地质界面的内插误差和特殊地质体的外推误差引起的精度评估问题。在模型误差修正方面,提出基于建模初始数据的模型误差修正方法和基于建模中间结果的模型误差修正方法,在具体实现时,引入“数据 模型的可视化交互技术”。这些研究成果为建立一套完整的三维地质结构模型精度评估与误差修正的理论体系和方法体系奠定了基础,有助于完善复杂地质条件下三维地质模拟的方法与技术。 相似文献
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