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Markov processes

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Journal Article
Journal: The Leading Edge
Published: 01 November 2024
The Leading Edge (2024) 43 (11): 765–773.
... processes within sedimentary basins. Combining mathematical precision with geologic insights, the approach simulates and visualizes the formation and evolution of sedimentary basins, moving beyond traditional deterministic models. The methodology employs Markov chain models to capture the stochastic nature...
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Journal Article
Journal: Geophysics
Published: 03 May 2019
Geophysics (2019) 84 (4): A37–A42.
...Erasmus Kofi Oware; James Irving; Thomas Hermans ABSTRACT Bayesian Markov-chain Monte Carlo (McMC) techniques are increasingly being used in geophysical estimation of hydrogeologic processes due to their ability to produce multiple estimates that enable comprehensive assessment of uncertainty...
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The LTFM as a hidden Markov process. (a) Example with three earthquakes. (b) Representation of (a) as a Markov model with the probability space discretized into 11 states. (c) Transition probability matrix indicating probability of transition from state j to state k for this set of model parameters. The color version of this figure is available only in the electronic edition.
Published: 27 December 2022
Figure 2. The LTFM as a hidden Markov process. (a) Example with three earthquakes. (b) Representation of (a) as a Markov model with the probability space discretized into 11 states. (c) Transition probability matrix indicating probability of transition from state j to state k for this set
Journal Article
Published: 01 September 1982
Journal of Sedimentary Research (1982) 52 (3): 905–912.
...Timothy R. Carr Abstract Quantitative techniques employing Markovian processes have been used by a number of investigators to test stratigraphic sections against a null hypothesis of a random succession of sedimentary facies. Rejection of the null hypothesis is used to imply presence of a Markov...
Journal Article
Published: 01 February 1980
Bulletin of the Seismological Society of America (1980) 70 (1): 323–347.
...Ashok S. Patwardhan; Ram B. Kulkarni; Don Tocher abstract A semi-Markov model estimating the waiting times and magnitudes of large earthquakes is proposed. The model defines a discrete-time, discrete-state process in which successive state occupancies are governed by the transition probabilities...
Journal Article
Published: 01 June 1971
Journal of Sedimentary Research (1971) 41 (2): 444–449.
... of lithologic transitions observed is likely governed by a first-order Markov process as opposed to an independent-events model. The fixed probability vector computed for the Kope and Fairview composite data provides the following estimates for the frequency of occurrence of each lithology: shale, 49.27...
Journal Article
Published: 01 August 1969
Canadian Journal of Earth Sciences (1969) 6 (4): 625–652.
... are eliminated, both the silt and clay residual thickness data satisfy a Markov model of the second order. This model is shown to be related to variations in the rate of retreat of the icefront. Besides the second-order Markov process, two weakly-developed short-term cycles have also been detected. non...
Journal Article
Journal: AAPG Bulletin
Published: 01 April 1973
AAPG Bulletin (1973) 57 (4): 793.
... distributed. The lack of correlation in thickness between successive sandstone-shale, shale-sandstone, and shale-shale beds is indicative of a renewal rather than a Markov process. The process is nonstationary, however, in that the sandstone/shale ratio decreases systematically from a value of approximately 2...
Series: SEPM Special Publication
Published: 01 January 2004
DOI: 10.2110/pec.04.79.0085
EISBN: 9781565762152
... to moderate sediment supply. Emphasis is placed upon determining how changes in the rate of Holocene sea-level rise (fast, slow, punctuated) effect incised-valley fill and deposition. Stochastic models were generated from Q-mode factor analysis, ANOVA, and binomial Markov process analysis to identify...
Series: SEPM Gulf Coast Section Publications
Published: 01 November 1999
DOI: 10.5724/gcs.99.14.0233
EISBN: 978-0-9836097-1-1
... and interfluves by using Repeated Measures ANOVA, Q-Mode Factor Analysis, and Binomial Markov process analysis. The Oxygen Isotope Stage 2 lowstand led to bifurcation of the Mobile-Tensaw River system and yielded two distinct incised valleys, eastern and western. These major incised valleys have very different...
Journal Article
Journal: AAPG Bulletin
Published: 01 February 1985
AAPG Bulletin (1985) 69 (2): 240.
... containing full curve logs, lithology, oil and gas shows, geologic markers, interpreted dipmeters, and structural relationships. Contouring and the use of color will also be demonstrated as interpretive aids. Two of the methods used in preparing geologic data—the polynominal regression and the Markov process...
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Markov chain process for estimating the optimal size of the source. First iteration: (a) observed (blue solid line) and calculated (red dots) gravity anomalies. (b) Inverted model and (c) estimated boundary (the white boxes highlight the dimensions used for the different prisms). (d-f) and (g-i) are the same as (a-c) for, respectively, 5th iteration and 10th iteration.
Published: 28 December 2017
Figure 5. Markov chain process for estimating the optimal size of the source. First iteration: (a) observed (blue solid line) and calculated (red dots) gravity anomalies. (b) Inverted model and (c) estimated boundary (the white boxes highlight the dimensions used for the different prisms). (d-f
Series: Special Publications of IAVCEI
Published: 01 January 2006
DOI: 10.1144/IAVCEI001.13
EISBN: 9781862396234
... (white) to one (black). About Markov models Fig. 5. Trellis diagram of a generic two-states Markov model. The evolution of the Markov process over time is plotted by repeating the state diagram at every time unit. S 1...
Journal Article
Published: 01 May 2024
Jour. Geol. Soc. India (2024) 100 (5): 707–720.
... of excavation. The study aims at developing a model that would predict the ground class ahead of the tunnel face. This in turn can help in better decision-making and efficient execution of work. The objective is to build a hybrid model that would combine the analytical capabilities of the Markov process...
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Journal Article
Journal: Geophysics
Published: 01 January 2002
Geophysics (2002) 67 (3): 770–776.
... of stochastic gravity modeling, two types of models—a Gauss-Markov process and a trigonometric expansion—are selected for each component of the gravity disturbance vector. In both cases, one must augment the design matrix and system dynamics equations accordingly. We choose the third-order Gauss-Markov...
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Journal Article
Published: 01 April 2012
Journal of Sedimentary Research (2012) 82 (4): 232–243.
... transition tendencies. Statistical interrogation of the 3-D model output reveals the simulation to contain realistic facies associations compared to the outcrop. This suggests that the reconstruction process, based on Markov chains, produces a useful representation of 3-D heterogeneity in this Lower...
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Journal Article
Published: 01 August 1995
Bulletin of the Seismological Society of America (1995) 85 (4): 1177–1189.
... for the nature of fault segmentation , in Proc. Fault Segmentation and Controls of Rupture Initiation and Termination , U.S. Geol. Surv. Open-File Rept. 89-215 , 193 - 228 . Lutz K. A. (1993) . A generalized semi-Markov process...
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Sample simulation of stochastic building expansion over time based on Markov chain process.
Published: 01 November 2017
Figure 6. Sample simulation of stochastic building expansion over time based on Markov chain process.
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Flow chart showing the numerous decisions users are required to make during the process of modeling thermochronometric data. MCMC—Markov-Chain Monte Carlo algorithm.
Published: 27 January 2023
Figure 2. Flow chart showing the numerous decisions users are required to make during the process of modeling thermochronometric data. MCMC—Markov-Chain Monte Carlo algorithm.
Journal Article
Journal: AAPG Bulletin
Published: 01 March 1969
AAPG Bulletin (1969) 53 (3): 728.
...Graham Lea Abstract When preceding events influence succeeding events, a certain probability can be calculated for the process, which is said to possess the Markov property. An increasing number of geologic processes have been described that demonstrate this property, and the behavior...