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  • Articles  (38)
  • Mathematics  (27)
  • Architecture, Civil Engineering, Surveying  (11)
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  • Articles  (38)
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  • 1
    Electronic Resource
    Electronic Resource
    Infinitely divisible stochastic processes (1967)
    Springer
    Probability theory and related fields 7 (1967), S. 147-160 
    Details
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary It often happens that a stochastic process may be approximated by a sum of a large number of independent components no one of which contributes a significant proportion of the whole. For example the depth of water in a lake with many small rivers flowing into it from distant sources, or the point process of calls entering a telephone exchange (considered as the sum of a number of point processes of calls made by individual subscribers) may approximately fulfil these hypotheses. In the present work we formulate and solve the problem of characterizing stochastic processes all of whose finite-dimensional distributions are infinitely divisible. Although some of our results could be derived from known theorems on probabilities on general algebraic structures, many could not and it seems preferable to take the vector-valued infinitely divisible laws as our starting point. We emphasize that an infinitely divisible process (in our sense) on the real line is not necessarily a decomposable process in the sense of Lévy (cf. § 4) though decomposable processes are particular cases. In § 1 a representation theorem for non-negative (and possibly infinite) stochastic processes is derived, while an analogous theorem in the real-valued case is to be found in § 2. § 3 is devoted to the statement of a “central limit theorem” and the investigation of some of the properties of infinitely divisible processes. The investigation is continued in § 4 by an examination of processes on the real line giving, for example, a representation theorem under weak conditions for infinitely divisible processes which are a.s. sample continuous. Finally in § 5 a study is made of infinitely divisible point processes and random measures.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00536328
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  • 2
    Electronic Resource
    Electronic Resource
    Bivariate non-central negative binomial distribution: Another generalisation (1986)
    Springer
    Metrika 33 (1986), S. 29-46 
    Details
    ISSN: 1435-926X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Another bivariate generalisation (Type V) of the non-central negative binomial distribution is considered. This generalisation is constructed (i) as a latent structure model; (ii) as an extension of an accident proneness model investigated by Edwards/Gurland (1961); and (iii) as a reversible stochastic counter model. The third construction gives, as a result, an apparently new formulation of the Edwards/Gurland model. The probabilities, moments, recurrence formulas and some properties are given. An application to the data used by Holgate (1966) is considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01894724
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  • 3
    Electronic Resource
    Electronic Resource
    The bivariate non-central negative binomial distributions (1986)
    Springer
    Metrika 33 (1986), S. 1-28 
    Details
    ISSN: 1435-926X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Four bivariate generalisations (Type I–IV) of the non-central negative binomial distribution (Ong/Lee) are considered. The Type I generalisation is constructed using the “latent structure model” scheme (Goodman) while the Type II generalisation arises from a variation of this scheme. The Type III generalisation is formed by using the method of random elements in common (Mardia). The Type IV is an extension of the Type I generalisation. Properties of these bivariate distributions including joint central and factorial moments are discussed; several recurrence formulae of the probabilities are given. An application to the childhood accident data of Mellinger et al. is considered with the precision of the Type I maximum likelihood estimates computed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01894723
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  • 4
    Electronic Resource
    Electronic Resource
    Probabilistic formulation of a method for the evaluation of petroleum resources (1983)
    Springer
    Mathematical geology 15 (1983), S. 163-181 
    Details
    ISSN: 1573-8868
    Keywords: oil ; gas ; resources evaluation ; subjective probability ; multivariate lognormal ; exploration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Since 1973 the Geological Survey of Canada has been making estimates of the petroleum resources for Canadian sedimentary basins. The purpose of this activity has been to provide a systematic approach to making an inventory of petroleum resources for departmental planning purposes. The resource evaluation was processed by the Hydrocarbon Assessment System Processor (HASP), devised by the Geological Survey of Canada. Since then, demands on the evaluation capability have increased and at the same time evaluation data have been increasingly applied to economic analyses. HASP can no longer be adapted to handle the new challenges. This study contains a probabilistic formulation for HASP and establishes a framework from which the following may be calculated: (1)distribution of number of pools; (2)expected rth largest pool size and its distribution; and (3)generation of reservoir parameters for a given pool size. Play 10 from the East Coast of Canada was used as an example to illustrate the applications of the analytical approach presented. This paper demonstrates that the analytical approach has more to offer than HASP.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01030081
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  • 5
    Electronic Resource
    Electronic Resource
    Conditional analysis for petroleum resource evaluations (1983)
    Springer
    Mathematical geology 15 (1983), S. 349-361 
    Details
    ISSN: 1573-8868
    Keywords: oil ; gas ; play potential distribution ; rth largest pool size ; conditional probability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Conditional analysis is an essential component for evaluation of petroleum resources. Such analysis attempts to answer the questions: for the input data and a given play potential, what is the most likely number of pools and their sizes? An example is provided to illustrate the usage and application of this conditional method of analysis. This example demonstrates that the method can be used as a feedback mechanism to challenge the underlying geological concepts of the play; and to yield more certain predictions if additional information is given. Consequently, the method will enhance the reliability of the estimates of petroleum resources.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01036075
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  • 6
    Electronic Resource
    Electronic Resource
    Prediction of oil or gas pool sizes when discovery record is available (1985)
    Springer
    Mathematical geology 17 (1985), S. 95-113 
    Details
    ISSN: 1573-8868
    Keywords: evaluation of petroleum resources ; pool size distribution ; Upper Devonian Leduc reefs ; sampling process
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The Upper Devonian Bashaw reef play of the Western Canada Basin was used to demonstrate: (1) estimation of pool size distribution by means of a discovery model, (2) the usefulness of a feedback mechanism in petroleum resources evaluations, and (3) enhancement of reliability by reducing uncertainty associated with estimates. The feedback mechanism presented herein allows us to challenge geological interpretations. For example, given the second largest pool size, the largest pool size can be estimated, and vice versa. In evaluations of petroleum resources, the uncertainty inherited from superpopulations is inevitably associated with the estimates. This type of uncertainty can be reduced to a certain extent if additional information is included in the estimation procedures and, consequently, the reliability of the estimates is enhanced. The additional information used may, for example, be the geological interpretation of a particular play. To achieve maximum effectiveness, resource evaluation methods should possess these types of flexibility. This study also estimated, with a 90% probability, that the remaining potential in the Bashaw reef play ranges from 32 to 50 millions of cubic meters (200 to 300 MM bbl) of oil in place.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01033149
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  • 7
    Electronic Resource
    Electronic Resource
    A study on one-dimensional consolidation of layered systems (1992)
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 16 (1992), S. 815-831 
    Details
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A general analytical solution, which is more explicit than the one given by Schiffman and Stein,1 for the problem of one-dimensional consolidation of layered soils is presented. A relevant computer program is developed and the computed results on some examples are included. From these results, an in-depth study on the one-dimensional consolidation behaviour of layered systems is then made. It is demonstrated through these examples that both the solution technique and the computer program developed are very efficient. It is found that the effects of coefficients of permeability and volume compressibility of soil on the consolidation of layered systems are different and cannot be embodied into the coefficient of consolidation of soil. The stiffness of soil layer also plays an important role on the rate of consolidation.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nag.1610161104
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  • 8
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    Bayesian inversion with total variation prior for discrete geologic structure identification (2013)
    Wiley
    Details
    Publication Date: 2013-10-23
    Description: The characterization of geologic heterogeneity that affects flow and transport phenomena in the subsurface is essential for cost-effective and reliable decision-making in applications such as groundwater supply and contaminant cleanup. In the last decades, geostatistical inversion approaches have been widely used to tackle subsurface characterization problems and quantify their corresponding uncertainty. Some well-established geostatistical methods use models that assume gradually varying parameters. However, in many cases, the subsurface can often be better represented as consisting of a few relatively uniform geologic facies or zones with abrupt changes at their boundaries. We advance a Bayesian inversion approach with the gradient represented not through a Gaussian but a Laplace prior, also known as total variation prior, for the case that there are reasons to believe that discrete geologic structures with relatively homogeneous properties predominate in the subsurface but their number, locations, and shapes are unknown a priori. Structural parameters (or hyperparameters of the inversion scheme) are determined in a Bayesian framework by maximizing the marginal distribution of these parameters using an expectation-maximization approach; this allows proper weighting of prior versus data information and produces results with realistic uncertainty quantification. We present here three applications of the method: a time-varying extraction rate estimation at a well, a linear cross-well seismic tomography, and a nonlinear hydraulic tomography. These results are compared with those achieved in the classical geostatistical method and it is shown that the Bayesian inversion approach with total variation prior can be a useful tool to identify discrete geologic structures.
    Print ISSN: 0043-1397
    Electronic ISSN: 1944-7973
    Topics: Architecture, Civil Engineering, Surveying , Geography
    Published by Wiley on behalf of American Geophysical Union (AGU).
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  • 9
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    Large-scale hydraulic tomography and joint inversion of head and tracer data using the Principal Component Geostatistical Approach (PCGA) (2014)
    Wiley
    Details
    Publication Date: 2014-06-14
    Description: The stochastic geostatistical inversion approach is widely used in subsurface inverse problems to estimate unknown parameter fields and corresponding uncertainty from noisy observations. However, the approach requires a large number of forward model runs to determine the Jacobian or sensitivity matrix, thus the computational and storage costs become prohibitive when the number of unknowns, m , and the number of observations, n increase. To overcome this challenge in large-scale geostatistical inversion, the Principal Component Geostatistical Approach (PCGA) has recently been developed as a “matrix-free” geostatistical inversion strategy that avoids the direct evaluation of the Jacobian matrix through the principal components (low-rank approximation) of the prior covariance and the drift matrix with a finite-difference approximation. As a result, the proposed method requires about K runs of the forward problem in each iteration independently of m and n , where K is the number of principal components and can be much less than m and n for large-scale inverse problems. Furthermore, the PCGA is easily adaptable to different forward simulation models and various data types for which the adjoint-state method may not be implemented suitably. In this paper, we apply the PCGA to representative subsurface inverse problems to illustrate its efficiency and scalability. The low-rank approximation of the large-dimensional dense prior covariance matrix is computed through a randomized eigen-decomposition. A hydraulic tomography problem in which the number of observations is typically large is investigated first to validate the accuracy of the PCGA compared with the conventional geostatistical approach. Then the method is applied to a large-scale hydraulic tomography with 3 million unknowns and it is shown that underlying subsurface structures are characterized successfully through an inversion that involves an affordable number of forward simulation runs. Lastly, we present a joint inversion of head and tracer test data using MODFLOW and MT3DMS as coupled black-box forward simulation solvers. These applications demonstrate the advantages of the PCGA, i.e. , the scalability to high-dimensional inverse problems and the ability to utilize multiple forward models as black boxes.
    Print ISSN: 0043-1397
    Electronic ISSN: 1944-7973
    Topics: Architecture, Civil Engineering, Surveying , Geography
    Published by Wiley on behalf of American Geophysical Union (AGU).
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  • 10
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    On prime ideals and radicals of polynomial rings and graded rings (2014)
    Elsevier
    Details
    Publication Date: 2014-02-01
    Print ISSN: 0022-4049
    Electronic ISSN: 1873-1376
    Topics: Mathematics
    Published by Elsevier
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