Форум » ПЕТРОФИЗИЧЕСКИЙ СОФТ - PETROPHYSICAL SOFTWARE » Cкрытые марковские цепи и их применение » Ответить
Cкрытые марковские цепи и их применение
bne: В свое время я первым сообразил как сформулировать принцип упорядоченности математико-статистически через ММП для цепей Маркова Теперь понятие скрытых цепей широко используется в распозновании (люди пришли к этому независимо за последние десятки лет) Но последнее сообщение в Nature на тему реализации этой идеи (во всяком случае я так это понял) впечатлило... click here
Ответов - 16
bne: Application of Markov chain and entropy analysis to lithologic succession – an example from the early Permian Barakar Formation, Bellampalli coalfield, Andhra Pradesh, India Ram Chandra Tewari1,∗, D P Singh2,∗∗ and Z A Khan3,† 1Department of Geology, Sri J.N.P.G. College, Lucknow 226 001, India. 2SMEC India Pvt. Ltd., 5th Floor, Tower C, DLF Building 8, Cyber City, Phase II, Gurgaon 122 002, Haryana, India. A statistical approach by a modified Markov process model and entropy function is used to prove that the early Permian Barakar Formation of the Bellampalli coalfield developed distinct cyclicities during deposition. From results, the transition path of lithological states typical for the Bellampalli basin is as: coarse to medium-grained sandstone → interbedded fine-grained sandstone/shale → shale → coal and again shale. The majority of cycles are symmetrical but asymmetrical cycles are present as well. The chi-square stationarity test implies that these cycles are stationary in space and time. The cycles are interpreted in terms of in-channel, point bar and overbank facies association in a fluvial system. The randomness in the occurrence of facies within a cycle is evaluated in terms of entropy, which can be calculated from the Markov matrices. Two types of entropies are calculated for every facies state; entropy after deposition E(post) and entropy before deposition E(pre), which together form entropy set; the entropy for the whole system is also calculated. These values are plotted and compared with Hattori’s idealized plots, which indicate that the sequence is essentially a symmetrical cycle (type-B of Hattroi). The symmetrical cyclical deposition of early Permian Barakar Formation is explained by the lateral migration of stream channels in response to varying discharge and rate of deposition across the alluvial plain. In addition, the fining upward cycles in the upper part enclosing thick beds of fine clastics, as well as coal may represent differential subsidence of depositional basin. http://www.ias.ac.in/jess/oct2009/d8j-79.pdf
PVI: кто и где в каротаже такие алгоритмы сейчас применяет?
BorisE: Впервые в каротаже она появилась с подачи Губермана и Чуриновой У Губермана стояла задача научить алгоритмы распознавания использовать ту же априорную информацию, что и человек А в массивных залежах информация о расположении ВНК критична Им (вместе с Чуриновой - это ее кандидатская 1971 года) был предложен ряд эвристических способов учета такой упорядоченности Позже алгоритмы такого рода разрабатывали Кулинкович, Ингерман, Шапиро Лично мне повезло обнаружить (1978), что они просто рассматриваются как задача с переключением марковской цепи в состояние "нефть" из состояния "вода" Отсюда выписывается очень простой вычислительный алгоритм Фокус только в том как определить понятие вероятности насыщения по имеющимся данным И по хорошему это требует применения вероятностно-статистического подхода ко всей интерпретации Расширенный вариант применения алгоритмов такого рода - задачи корреляции (этим много занимался эмигрировавший в начале перестройки Я.М.Вайнберг, работавший тогда у Швидлера) Сейчас разного рода алгоритмы того же типа также применяются и при интерпретации сейсморазведки и как часть алгоритмов геостатистики
bne: Вайнберг, А.М. Математическое моделирование процессов переноса. Решение нелинейных краевых. - М.: Иерусалим, 2009. - 209c. Похоже в России читатели не нашлись Жаль
bne: Статья Моттля-Мучника-Ивановой-Блинова http://www.tvp.ru/ourizd/oppm/1996/1/htmmottl.pdf Первая часть статьи по теме ранее развиваемой Вайнбергом и немного мной
bne: Markov chains and embedded Markov chains in geology Mathematical Geology Springer Netherlands ISSN 0882-8121 (Print) 1573-8868 (Online) Volume 1, Number 1 / Март 1969 г. DOI 10.1007/BF02047072 Страницы 79-96 Markov chains and embedded Markov chains in geology W. C. Krumbein1 and Michael F. Dacey2 (1) Department of Geology, Northwestern University, USA (2) Department of Geography, Northwestern University, USA Received: 30 June 1969 Abstract Geological data are structured as first-order, discrete-state discrete-time Markov chains in two main ways. In one, observations are spaced equally in time or space to yield transition probability matrices with nonzero elements in the main diagonal; in the other, only state transitions are recorded, to yield matrices with diagonal elements exactly equal to zero. The mathematical differences in these two approaches are reviewed here, using stratigraphic data as an example. Simulations from chains with diagonal elements greater than zero always yield geometric distributions of lithologic unit thickness, and their use is recommended only if the input data have the same distribution. For thickness distributions lognormally or otherwise distributed, the embedded chain is preferable. The mathematical portions of this paper are well known, but are not readily available in publications normally used by geologists. One purpose of this paper is to provide an explicit treatment of the mathematical foundations on which applications of Markov processes in geology depend. -------------------------------------------------------------------------------- References Allegre, C., 1964, Vers une logique mathematique des series sedimentaires: Bull. Soc. Geol. de France, Series 7, Tome 6, p. 214–218. Anderson, T. W., and Goodman, L. A., 1957, Statistical inference about Markov chains: Ann. Math. Stat., v. 28, p. 89–110. Billingsley, P., 1961, Statistical methods in Markov chains: Ann. Math. Stat., v. 32, p. 12–40. Carr, D. D., and others, 1966, Stratigraphic sections, bedding sequences, and random processes: Science, v. 154, no. 3753, p. 1162–1164. Feller, W., 1968, An introduction to probability theory and its applications (3rd ed.): John Wiley & Sons, New York, 509 p. Gingerich, P. D., 1969, Markov analysis of cyclic alluvial sediments: Jour. Sed. Pet., v. 39, no. 1, p. 330–332. Karlin, S., 1966, A first course in stochastic processes: Academic Press, New York, 502 p. Kolmogorov, A. N., 1951, Solution of a problem in probability theory connected with the problem of the mechanism of stratification: Am. Math. Society Trans., no. 53, 8 p. Krumbein, W. C., 1967,fortran iv computer programs for Markov chain experiments in geology: Kansas Geol. Survey Computer Contr. 13, 38 p. Krumbein, W. C., 1968a, Computer simulation of transgressive and regressive deposits with a discrete-state, continuous-time Markov model,in Computer applications in the earth sciences: Colloquium on simulation, D. F. Merriam, ed.: Kansas Geol. Survey Computer Contr. 22, p. 11–18. Krumbein, W. C., 1968b,fortran iv computer program for simulation of transgression and regression with continuous-time Markov models: Kansas Geol. Survey Computer Contr. 26, 38 p. Krumbein, W. C., and Sloss, L. L., 1963, Stratigraphy and sedimentation (2nd ed.): W. H. Freeman and Co., San Francisco, 660 p. Pettijohn, F. P., 1957, Sedimentary rocks: Harper and Bros., New York, 718 p. Potter, P. E., and Blakely, R. F., 1967, Generation of a synthetic vertical profile of a fluvial sandstone body: Jour. Soc. Petroleum Engineers, v. 6, p. 243–251. Potter, P. E., and Blakely, R. F., 1968, Random processes and lithologic transitions: Jour. Geology, v. 76, no. 2, p. 154–170. Potter, P. E., and Siever, R., 1955, A comparative study of Upper Chester and Lower Pennsylvanian stratigraphic variability: Jour. Geology, v. 63, no. 5, p. 429–451. Pyke, R., 1961a, Markov renewal processes: definitions and preliminary properties: Ann. Math. Stat., v. 32, p. 1231–1242. Pyke, R., 1961b, Markov renewal processes with finitely many states: Ann. Math. Stat., v. 32, p. 1243–1259. Scherer, W., 1968, Applications of Markov chains to cyclical sedimentation in the Oficina Formation, eastern Venezuela: Unpubl. master's thesis, Northwestern Univ., 93 p. Schwarzacher, W., 1964, An application of statistical time-series analysis of a limestone-shale sequence: Jour. Geology, v. 72, no. 2, p. 195–213. Schwarzacher, W., 1967, Some experiments to simulate the Pennsylvanian rock sequence of Kansas,in Computer applications in the earth sciences: Colloquium on simulation, D. F. Merriam, ed.: Kansas Geol. Survey Computer Contr. 18, p. 5–14. Smart, J. S., 1968, Statistical properties of stream lengths: Water Resources Res., v. 4, p. 1001–1014. Vistelius, A. B., 1949, On the question of the mechanism of the formation of strata: Doklady Akad. Nauk SSSR, v. 65, p. 191–194. Zeller, E. J., 1964, Cycles and psychology,in Symposium on cyclic sedimentation: Kansas Geol. Survey Bull. 169, p. 631–636. Additional references Agterberg, F. P., 1966a, The use of multivariate Markov schemes in geology: Jour. Geology, v. 74, no. 5, pt. 2, p. 764–785. Agterberg, F. P., 1966b, Markov schemes for multivariate well data: Min. Ind. Experiment Sta., Pennsylvania State Univ. Sp. Publ. 2–65, p. Y1-Y18. Conover, W. J., and Matalas, N. C., in press, A statistical model of turbulence applicable to sediment laden streams: ASCE, Jour. Engineering Mechanics. Graf, D. L., Blyth, C. R., and Stemmler, R. S., 1967, One-dimensional disorder in carbonates: Illinois Geol. Survey Circ. 408, 61 p. Griffiths, J. C., 1966, Future trends in geomathematics: Pennsylvania State Univ., Mineral Industries, v. 35, p. 1–8. Harbaugh, J. W., 1966, Mathematical simulation of marine sedimentation with IBM 7090/7094 computers: Kansas Geol. Survey Computer Contr. 1, 52 p. James, W. R., and Krumbein, W. C., 1969, Frequency distributions of stream link lengths: Jour. Geology, v. 77, no. 5, p. 544–565. Kemeny, J. G., and Snell, J. L., 1960, Finite Markov chains: D. Van Nostrand Co., Inc., Princeton, New Jersey, 210 p. Leopold, L. B., and Langbein, W. B., 1962, The concept of entropy in landscape evolution: U.S. Geol. Survey Prof. Paper 500-A, p. A1–A20. Matalas, N. C., 1967a, Mathematical assessment of synthetic hydrology: Water Resources Res., v. 3, p. 937–946. Matalas, N. C., 1967b, Some distribution problems in time series simulation,in Computer applications in the earth sciences: Colloquium on time-series analysis, D. F. Merriam, ed.: Kansas Geol. Survey Computer Contr. 18, p. 37–40. Scheidegger, A. E., 1966, Stochastic branching processes and the law of stream orders: Water Resources Res., v. 2, p. 199–203. Scheidegger, A. E., and Langbein, W. B., 1966, Probability concepts in geomorphology: U.S. Geol. Survey Prof. Paper 500-C, p. C1–C14. Schwarzacher, W., 1968, Experiments with variable sedimentation rates,in Computer applications in the earth sciences: Colloquium on simulation, D. F. Merriam, ed.: Kansas Geol. Survey Computer Contr. 22, p. 19–21. Vistelius, A. B., 1966, Genesis of the Mt. Belaya granodiorite, Kamchatka (an experiment in stochastic modeling): Doklady Akad. Nauk SSSR, v. 167, p. 1115–1118. Vistelius, A. B., and Faas, A. V., 1965, On the character of the alternation of strata in certain sedimentary rock masses: Doklady Akad. Nauk SSSR, v. 164, p. 629–632. Vistelius, A. B., and Feigel'son, T. S., 1965, On the theory of bed formation: Doklady Akad. Nauk SSSR, v. 164, p. 158–160. Wickman, F. E., 1966, Repose period patterns of volcanoes, V. General discussion and a tentative stochastic model: Arkiv for Mineralogi och Geologi, v. 4, p. 351–367.
bne: Estimation of Geological Attributes from a Well Log: An Application of Hidden Markov Chains Mathematical Geology Springer Netherlands ISSN 0882-8121 (Print) 1573-8868 (Online) Volume 36, Number 3 / Апрель 2004 г. DOI 10.1023/B:MATG.0000028443.75501.d9 pp. 379-397 Estimation of Geological Attributes from a Well Log: An Application of Hidden Markov Chains Jo Eidsvik1 , Tapan Mukerji2 and Paul Switzer3 (1) Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway (2) Department of Geophysics, Stanford Rock Physics Laboratory, Stanford University, California (3) Department of Statistics, Stanford University, California Abstract Geophysical well logs used in petroleum exploration consist of measurements of physical properties (such as radioactivity, density, and acoustic velocity) that are digitally recorded at a fixed interval (typically half a foot) along the length of the exploratory well. The measurements are informative of the unobserved rock type alternations along the well, which is critical for the assessment of petroleum reservoirs. The well log data that are analyzed here are from a North Sea petroleum reservoir where two distinct strata have been identified from large scale seismic data. We apply a hidden Markov chain model to infer properties of the rock type alternations, separately for each stratum. The hidden Markov chain uses Dirichlet prior distributions for the Markov transition probabilities between rock types. The well log measurements, conditional on the unobserved rock types, are modeled using Gaussian distributions. Our analysis provides likelihood estimates of the parameters of the Dirichlet prior and the parameters of the measurement model. For fixed values of the parameter estimates we calculate the posterior distributions for the rock type transition probabilities, given the well log measurement data. We then propagate the model parameter uncertainty into the posterior distributions using resampling from the maximum likelihood model. The resulting distributions can be used to characterize the two reservoir strata and possible differences between them. We believe that our approach to modeling and analysis is novel and well suited to the problem. Our approach has elements in common with empirical Bayes methods in that unspecified parameters are estimated using marginal likelihoods. Additionally, we propagate the parameter uncertainty into the final posterior distributions. petrophysical logs - marginal likelihood estimation - forward–backward recursion - Gibbs sampling - pseudo-logs - sequence stratigraphy
bne: Image Analysis, Random Fields and Dynamic Monte Carlo Methods: A Mathematical Introduction (Applications of Mathematics, 27) Publisher: Springer | ISBN: 0387570691 | edition 1995 |360 pages | This second edition of G. Winkler's successful book on random field approaches to image analysis, related Markov Chain Monte Carlo methods, and statistical inference with emphasis on Bayesian image analysis concentrates more on general principles and models and less on details of concrete applications. Addressed to students and scientists from mathematics, statistics, physics, engineering, and computer science, it will serve as an introduction to the mathematical aspects rather than a survey. Basically no prior knowledge of mathematics or statistics is required. The second edition is in many parts completely rewritten and improved, and most figures are new. The topics of exact sampling and global optimization of likelihood functions have been added. This second edition comes with a CD-ROM by F. Friedrich,containing a host of (live) illustrations for each chapter. In an interactive environment, readers can perform their own experiments to consolidate the subject.
bne: Estimation of a Stochastic Discontinuous Permeability Using a Multidimensional Markov Chain S. Zein, V. Rath and C. Clauser January 19, 2009 Abstract In this paper, we are interested in estimating a stochastic permeability distribution by considering the steady flow inverse problem (Poisson problem) over a two-dimensional domain. The permeability is discretised over a regular rectangular gird and considered to be constant by cell but it can take randomly a finite number of values. Such permeability is modeled using a multidimensional Markov chain and it is constrained by some permeability measures and some pressure measures at some points of the domain. The difficulty of this inverse problem is the non-uniqueness of the solution, in the classical least-squares sens. To overcome this difficulty we propose a solution for this inverse problem, in a probabilistic sens, by coupling the MCMC sampling technique with the multidimensional Markov chain model. Keywords: Discontinuous Parameter Estimation, Poisson Problem, Multidimensional Markov Chain, MCMC. http://www.geophysik.rwth-aachen.de/Downloads/pdf/ZeinRathClauser_InverseProblemsInScienceAndEngineering_2009.pdf
bne: Hidden Markov Models for Time Series Walter Zucchini, Iain L. MacDonald | Chapman & Hall/CRC | 2009-04-28 | ISBN:1584885734 | Pages: 269 | This book illustrates the wonderful flexibility of HMMs as general-purpose models for time series data. It presents an accessible overview of HMMs for analyzing time series data, from continuous-valued, circular, and multivariate series to binary data, bounded and unbounded counts, and categorical observations. It explores a variety of applications in animal behavior, finance, epidemiology, climatology, and sociology. The authors discuss how to employ the freely available computing environment R to carry out computations for parameter estimation, model selection and checking, decoding, and forecasting. They provide all of the data sets analyzed in the text online.
bne: GEOPHYSICS, VOL 45, NO. 9 (SEPTEMBER 1980): P. 1351-1372. 19 FIGS. Modeling seismic impedance with Markov chains Robert Godfrey*, Francis Muir& and Fabio Rocca# Acoustic impedance is modeled as a special type of Markov chain. one which is constrained to have a purely exponential correlation function. The stochastic model is parsimoniously described by M parameters. where M is the number of states or rocks composing an impedance well log. The probability mass function of the states provides M-l parameters. and the “blockiness” of the log determines the remaining degree of freedom. Synthetic impedance and reflectivity logs constructed using the Markov model mimic the blockiness of the original logs. Both synthetic impedance and reflectivity are shown to be Bussgang, i.e.. if the sequenceis input into an instantaneous nonlinear device. then the correlation of input and output is proportional to the autocorrelation of the input. The final part of the paper uses the stochastic model in formulating an algorithm that transforms a deconvolved seismogram into acoustic impedance. The resulting function is blocky and free of random walks or sags. Low-frequency information. as provided by moveout velocities. can be easily incorporated into the algorithm
bne: Preprint UCRL-JC-155048 Stochastic Inversion of Electrical Resistivity Changes Using a Markov Chain, Monte Carlo Approach Abelardo L. Ramirez John J. Nitao William G. Hanley Roger D. Aines Ronald E. Glaser Sailes K. Sengupta Kathleen M. Dyer Tracy L. Hickling William D. Daily This article was submitted to the Journal of Geophysical Research August 2003
bne: Сейсмика и марковские поля Норвежцы в это влезли http://www.math.ntnu.no/~joeid/ure/public_list.html Характерно, что ни на Вайнберга ни на Моттля ссылок нет (хотя они печатались на английском) Про себя я и вовсе молчу
bne: A Markov Chain Model for Subsurface Characterization: Theory and Applications Mathematical Geology Springer Netherlands ISSN 0882-8121 (Print) 1573-8868 (Online) Volume 33, Number 5 / Июль 2001 г. DOI 10.1023/A:1011044812133 pp 569-589 A Markov Chain Model for Subsurface Characterization: Theory and Applications Amro Elfeki and Michel Dekking1 (1) Thomas Stieltjes Institute for Mathematics and Faculty of ITS, Department of Probability, Statistics and Operation Research, Delft University of Technology, P. O. Box 5031, 2600GA Delft, The Netherlands Abstract This paper proposes an extension of a single coupled Markov chain model to characterize heterogeneity of geological formations, and to make conditioning on any number of well data possible. The methodology is based on the concept of conditioning a Markov chain on the future states. Because the conditioning is performed in an explicit way, the methodology is efficient in terms of computer time and storage. Applications to synthetic and field data show good results. Markov chains - geostatistics - geological heterogeneity - reservoir characterization - conditioning
bne: Я отчасти и давно слежу за работами в этой области и сам немного крутился по теме и потому несколько слов Строго говоря функциональная постановка не новая - снова эквивалентна задачи поиска максимума апостериорной вероятности Обычно для этого применяли метод динамического программирования но основные трудности в заданиях априорных вероятностей и структуре ограничений на пространственные взаимосвязи А вот в реализации идеи публика пошла разными путями С одной стороны Губерман и его последователи 1970 - 1990 Бабенышева и др приблизительно 1978-1990 Вайнберг ЯМ 1980 -1989 Моттль 1989-2000 С другой - Гутман и его команды (во многом идеологически Губерман) 1989 - 2011 С третьей - Ковалевский 1992 - 2011 В последние годы та же тема активна рассматривается в сейсмике на Западе и к ней подступаются через концепцию частично наблюдаемых марковских полей У меня впечатление, что основная проблема в алгоритме, в удобном интерфейсе и в хорошей рекламной компании (Гутман возится с этим более 10 лет)
БНЕ_Gurg: Наверное осмысленно таки попробовать упорядоченность на условиях наличия правил неправомерного чередования типов (скажем коллектор-глина) для выделения пачек и мощностей В качестве начального можно брать просто кластерные результаты (с введением глубины?)
полная версия страницы