共查询到10条相似文献，搜索用时 124 毫秒
1.
Comparing the Gradual Deformation with the Probability Perturbation Method for Solving Inverse Problems 总被引：1，自引：0，他引：1
Jef Caers 《Mathematical Geology》2007,39(1):27-52
Inverse problems are ubiquitous in the Earth Sciences. Many such problems are ill-posed in the sense that multiple solutions
can be found that match the data to be inverted. To impose restrictions on these solutions, a prior distribution of the model
parameters is required. In a spatial context this prior model can be as simple as a Multi-Gaussian law with prior covariance
matrix, or could come in the form of a complex training image describing the prior statistics of the model parameters. In
this paper, two methods for generating inverse solutions constrained to such prior model are compared. The gradual deformation
method treats the problem of finding inverse solution as an optimization problem. Using a perturbation mechanism, the gradual
deformation method searches (optimizes) in the prior model space for those solutions that match the data to be inverted. The
perturbation mechanism guarantees that the prior model statistics are honored. However, it is shown with a simple example
that this perturbation method does not necessarily draw accurately samples from a given posterior distribution when the inverse
problem is framed within a Bayesian context. On the other hand, the probability perturbation method approaches the inverse
problem as a data integration problem. This method explicitly deals with the problem of combining prior probabilities with
pre-posterior probabilities derived from the data. It is shown that the sampling properties of the probability perturbation
method approach the accuracy of well-known Markov chain Monte Carlo samplers such as the rejection sampler. The paper uses
simple examples to illustrate the clear differences between these two methods 相似文献
2.
Comparison of Mathematical Methods of Potential Modeling 总被引：1，自引：0，他引：1
Helmut Schaeben 《Mathematical Geosciences》2012,44(1):101-129
Various attempts are known to turn the “catalogue” of mineral deposit models compiled by Cox and Singer (1986) operational, and have initiated activities called “potential mapping”, “potential modeling”, or “targeting”. The common
ultimate objective is to estimate the probability for a given location that a mineralization of a given type occurred. The
mathematics range from “weights of evidence” and others featuring a Bayesian approach to logistic regression by maximum likelihood,
and include other realizations by means of fuzzy methods, genetic programming, and artificial neural nets. Once developed
and coded, applications are not restricted to mineral prospection and exploration but include any kind of occurrences and
their estimated probabilities, e.g., risk assessment of land slides and many others. 相似文献
3.
受工程勘察成本及试验场地限制，可获得的试验数据通常有限，基于有限的试验数据难以准确估计岩土参数统计特征和边坡可靠度。贝叶斯方法可以融合有限的场地信息降低对岩土参数不确定性的估计进而提高边坡可靠度水平。但是，目前的贝叶斯更新研究大多假定参数先验概率分布为正态、对数正态和均匀分布，似然函数为多维正态分布，这种做法的合理性有待进一步验证。总结了岩土工程贝叶斯分析常用的参数先验概率分布及似然函数模型，以一个不排水黏土边坡为例，采用自适应贝叶斯更新方法系统探讨了参数先验概率分布和似然函数对空间变异边坡参数后验概率分布推断及可靠度更新的影响。计算结果表明：参数先验概率分布对空间变异边坡参数后验概率分布推断及可靠度更新均有一定的影响，选用对数正态和极值I型分布作为先验概率分布推断的参数后验概率分布离散性较小。选用Beta分布和极值I型分布获得的边坡可靠度计算结果分别偏于保守和危险，选用对数正态分布获得的边坡可靠度计算结果居中。相比之下，似然函数的影响更加显著。与其他类型似然函数相比，由多维联合正态分布构建的似然函数可在降低对岩土参数不确定性估计的同时，获得与场地信息更为吻合的计算结果。另外，构建似然函数时不同位置处测量误差之间的自相关性对边坡后验失效概率也具有一定的影响。 相似文献
4.
The Kappa model of probability and higher-order rock sequences 总被引：2，自引：0，他引：2
J. A. Vargas-Guzmán 《Computational Geosciences》2011,15(4):661-671
In any depositional environment, the sequence of sediments follows specific high- and low-frequency patterns of rock occurrences
or events. The occurrence of a rock in a spatial location is conditional to a prior rock event at a distant location. Subsequently,
a third rock occurs between the two locations. This third event is conditional to both prior events and is driven by a third-order
conditional probability P(C ∣ (A ∩ B)). Such probability has to be characterized beyond the classic conditional independence model, and this research has found
that exact computation requires a third-order co-cumulant term. The co-cumulants provide the higher-order redundancy among
multiple indicator variables. A Bayesian analysis has been performed with “known” numerical co-cumulants yielding a novel
model of conditional probability that is called the “Kappa model.” This model was applied to three-point variables, and the
concept has been extended for multiple events P(G ∣ A ∩ B ∩ C ∩ D... ∩ N), allowing the reproduction of complex transitions of rocks in sequence stratigraphy. The Kappa model and co-cumulants have
been illustrated with simple numerical examples for clastic rock sequences. In addition, the co-cumulant has been used to
discover an extension of the variogram called the indicator cumulogram. In this way, multiple prior events are no longer ignored
for evaluating the probability of a posterior event with higher-order co-cumulant considerations. 相似文献
5.
Spatial data are often sparse by nature. However, in many instances, information may exist in the form of soft data, such as expert opinion. Scientists in the field often have a good understanding of the phenomenon under study and may be able to provide valuable information on its likely behavior. It is thus useful to have a sensible mechanism that incorporates expert opinion in inference. The Bayesian paradigm suffers from an inherent subjectivity that is unacceptable to many scientists. Aside from this philosophical problem, elicitation of prior distributions is a difficult task. Moreover, an intentionally misleading expert can have substantial influence on Bayesian inference. In our experience, eliciting data is much more natural to the experts than eliciting prior distributions on the parameters of a probability model that is a purely statistical construct. In this paper we elicit data, i.e., guess values for the realization of the process, from the experts. Utilizing a hierarchical modeling framework, we combine elicited data and actual observed data for inferential purposes. A distinguishing feature of this approach is that even an intentionally misleading expert proves to be useful. Theoretical results and simulations illustrate that incorporating expert opinion via elicited data substantially improves the estimation, prediction, and design aspects of statistical inference for spatial data. 相似文献
6.
Summary
The feasibility and safety of a mining project or the choice among alternative mining methods could depend on the joint densities
and orientations within the rock mass. The accurate determination of the orientation of all joints is technically difficult
and often economically unrealistic. This study presents a new approach in classifying joints found in exploration boreholes
as joint sets, whose statistical distribution is determined from a few hundred oriented joints in boreholes. Each non-oriented
joint is classified as belonging to a set based on its “a posteriori” probability of membership in a Bayesian framework. The
theoretical rate of success of the classification can be computed for each possible borehole orientation and plotted on a
stereonet to determine the optimal orientation of new boreholes. The performance and limitations of this approach are investigated.
An application example at the Mont Porphyre's large scale block-caving project at Gaspé Mines, Quebec, Canada, is studied. 相似文献
7.
Mine gas disaster prediction and prevention are based on gas content measurement, which results in initial stage loss when determining coal gas desorption contents in engineering applications. We propose a Bayesian probability statistical method in the coal gas desorption model on the basis of constrained prior information. First, we use a self-made coal sample gas desorption device to test initial stage gas desorption data of tectonic coal and undeformed coal. Second, we calculate the initial stage loss of different coal samples with the power exponential function parameters by using Bayesian probability statistics and least squares estimation. Results show that Bayesian probability statistics and least squares estimation can be used to obtain regression and desorption coefficients, thereby illustrating the Bayesian estimation method’s validity and reliability. Given that the Bayesian probability method can apply prior information to constrain the model’s posterior parameters, it provides results that are statistically significant in the initial stage loss of coal gas desorption by connecting observation data and prior information.
相似文献8.
The chemical zoning profile in metamorphic minerals is often used to deduce the pressure–temperature (P–T) history of rock. However, it remains difficult to restore detailed paths from zoned minerals because thermobarometric evaluation
of metamorphic conditions involves several uncertainties, including measurement errors and geological noise. We propose a
new stochastic framework for estimating precise P–T paths from a chemical zoning structure using the Markov random field (MRF) model, which is a type of Bayesian stochastic
method that is often applied to image analysis. The continuity of pressure and temperature during mineral growth is incorporated
by Gaussian Markov chains as prior probabilities in order to apply the MRF model to the P–T path inversion. The most probable P–T path can be obtained by maximizing the posterior probability of the sequential set of P and T given the observed compositions of zoned minerals. Synthetic P–T inversion tests were conducted in order to investigate the effectiveness and validity of the proposed model from zoned Mg–Fe–Ca
garnet in the divariant KNCFMASH system. In the present study, the steepest descent method was implemented in order to maximize
the posterior probability using the Markov chain Monte Carlo algorithm. The proposed method successfully reproduced the detailed
shape of the synthetic P–T path by eliminating appropriately the statistical compositional noises without operator’s subjectivity and prior knowledge.
It was also used to simultaneously evaluate the uncertainty of pressure, temperature, and mineral compositions for all measurement
points. The MRF method may have potential to deal with several geological uncertainties, which cause cumbersome systematic
errors, by its Bayesian approach and flexible formalism, so that it comprises potentially powerful tools for various inverse
problems in petrology. 相似文献
9.
Groundwater is a very important natural resource in Khanyounis Governorate (the study area) for water supply and development.
Historically, the exploitation of aquifers in Khanyounis Governorate has been undertaken without proper concern for environmental
impact. In view of the importance of quality groundwater, it might be expected that aquifer protection to prevent groundwater
quality deterioration would have received due attention. In the long term, however, protection of groundwater resources is
of direct practical importance because, once pollution of groundwater has been allowed to occur, the scale and persistence
of such pollution makes restoration technically difficult and costly. In order to maintain basin aquifer as a source of water
for the area, it is necessary to find out, whether certain locations in this groundwater basin are susceptible to receive
and transmit contamination. This study aims to: (1) assess the vulnerability of the aquifer to contamination in Khanyounis
governorate, (2) find out the groundwater vulnerable zones to contamination in the aquifer of the study area, and (3) provide
a spatial analysis of the parameters and conditions under which groundwater may become contaminate. To achieve that, DRASTIC
model within geographic information system (GIS) environment was applied. The model uses seven environmental parameters: depth
of water table, net recharge, aquifer media, soil media, topography, impact of vadose zone, and hydraulic conductivity to
evaluate aquifer vulnerability. Based on this model and by using ArcGIS 9.3 software, an attempt was made to create vulnerability
maps for the study area. According to the DRASTIC model index, the study has shown that in the western part of the study area
the vulnerability to contamination ranges between high and very high due to the relatively shallow water table with moderate
to high recharge potential, and permeable soils. To the east of the previous part and in the south-eastern part, vulnerability
to contamination is moderate. In the central and the eastern part, vulnerability to contamination is low due to depth of water
table. Vulnerability analysis of the DRASTIC Model indicates that the highest risk of contamination of groundwater in the
study area originates from the soil media. The impact of vadose zone, depth to water level, and hydraulic conductivity imply
moderate risks of contamination, while net recharge, aquifer media, and topography impose a low risk of aquifer contamination.
The coefficient of variation indicates that a high contribution to the variation of vulnerability index is made by the topography.
Moderate contribution is made by the depth to water level, and net recharge, while impact of vadose zone, hydraulic conductivity,
soil media, and Aquifer media are the least variable parameters. The low variability of the parameters implies a smaller contribution
to the variation of the vulnerability index across the study area. Moreover, the “effective” weights of the DRASTIC parameters
obtained in this study exhibited some deviation from that of the “theoretical” weights. Soil media and the impact of vadose
zone were the most effective parameters in the vulnerability assessment because their mean “effective” weights were higher
than their respective “theoretical” weights. The depth of water table showed that both “effective” and “theoretical” weights
were equal. The rest of the parameters exhibit lower “effective” weights compared with the “theoretical” weights. This explains
the importance of soil media and vadose layers in the DRASTIC model. Therefore, it is important to get the accurate and detailed
information of these two specific parameters. The GIS technique has provided an efficient environment for analysis and high
capabilities of handling large spatial data. Considering these results, DRASTIC model highlights as a useful tool that can
be used by national authorities and decision makers especially in the agricultural areas applying chemicals and pesticides
which are most likely to contaminate groundwater resources. 相似文献
10.
A Distance-based Prior Model Parameterization for Constraining Solutions of Spatial Inverse Problems 总被引：4，自引：3，他引：1
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