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1.
Isamu Hattori 《Mathematical Geology》1976,8(4):477-497
The concept of Markov chains, applied to stratigraphic sections, is reliable in analyzing cyclic patterns in lithologic successions. Randomness in the occurrence of lithologies repeating in a succession is evaluated generally in terms of entropies which can be calculated for the Markov matrix equated with the succession. Two types of entropies pertain to every state; one is relevant to the Markov matrix expressing the upward transitions, and the other, relevant to the matrix expressing the downward transitions. The latter and the former with respect to a certain state, making an entropy set, correspond to the degree of randomness in its linking with the others which occur as the precursor and the successor, respectively. It is obvious that the entropy sets which are calculated for all state variables serve as a reliable criterion in the discrimination of cyclic pattern of the succession. We are able based on the entropy sets to classify the various patterns into asymmetric, symmetric, and random cycles, which are exhibited also in actual lithologic successions. The entropy sets are calculated for Markov matrices which have been reported from a number of areas in the world, and compared with the cyclic patterns supposed there. Entropy for the whole system of sedimentation also is introduced to discuss variability of the condition in the depositional processes. 相似文献
2.
The succession of lithofacies of a part of the Barren Measures Formation of the Talchir Gondwana basin has been studied by
statistical techniques. The lithologies have been grouped under five facies states viz coarse-, medium-, and fine-grained
sandstones, shale and coal for statistical analyses. Markov chain analysis indicates the arrangement of Barren Measures lithofacies
in the form of fining upward cycles. A complete cycle consists of conglomerate or coarse-grained sandstone at the base sequentially
succeeded by medium-and fine-grained sandstones, shales and coal at the top. The entropy analysis puts the Barren Measures
cycles into A-4 type cyclicity, which consists of different proportions of lower, upper and side truncated cycles of lithologic
states. Regression analysis indicates a sympathetic relationship between total thickness of strata (net subsidence) and number
of cycles and an antipathic relationship between average thickness and number of sedimentary cycles. The cyclic sedimentation
of the Barren Measures Formation was controlled by autocyclic process which occurred due to the lateral migration of streams
triggered by intrabasinal differential subsidence. In many instances, the clastic sediments from the laterally migrating rivers
interrupted the cyclic sedimentation resulting in thinner cycles in areas where the number of cycles are more. Principal component
and multivariate regression analyses suggest that the net subsidence of the basin is mostly controlled by the thickness of
sandstones, shale beds and coal stringers. 相似文献
3.
ANDREW D. MIALL 《Sedimentology》1973,20(3):347-364
Markov chain analysis is a comparatively simple statistical technique for the detection of repetitive processes in space or time. Coal measure cyclothems or fluvial fining-upward cycles are good examples of sedimentary successions laid down under the control of Markovian processes. Analyses of stratigraphic sections commence with a transition count matrix, a two-dimensional array in which all possible vertical lithologic transitions are tabulated. Various probability matrices may be derived from this raw data, and these are then subjected to chi-square tests to determine the presence or absence of the Markov property. This technique is applied to four types of stratigraphic succession which occur in the Devonian rocks of Prince of Wales Island, Arctic Canada. (1) A conglomerate succession of alluvial fan origin. Markov analysis is of little or no assistance in the interpretation of these rocks, in which only two principal lithologies are present. (2) A conglomerate-sandstone succession. Fluvial fining-upward cycles are detectable by visual examination of the sections and are strongly indicated by Markov analysis. (3) A sandstone-carbonate succession, of marginal marine origin, and including both marine and non-marine strata. Cyclicity is weak in these rocks, but analysis suggests that regressions took place much more rapidly than transgressions during their period of deposition. (4) A succession in which the relative proportions of the various lithologies vary markedly with age. The varying nature of the cyclic tendencies is emphasized in this case by dividing the succession into two subintervals, for the purpose of analysis. 相似文献
4.
William Alfred Read 《Mathematical Geology》1969,1(2):199-219
Many difficulties inherent in analyzing cyclical successions in terms of an idealized cycle and, to a lesser extent, in terms of the modal cycle and composite sequence can be overcome by structuring data in terms of probabilities of upward transitions from one lithology to another. This enables a finite Markov-process model to be used. Transition probability matrices have been constructed from two versions of the same borehole section through paralic Namurian (Pendleian Stage, E
1
) sediments east of Stirling. The first version does not allow, but the second allows, adjacent items to be of the same lithology. The matrix derived from the first version indicates the following preferred upward succession of lithologies: coal, mudstone, siltstone, sandstone, seatclay, silty and sandy rooty beds, coal. A version of the Chi-square test strongly rejects the hypothesis that the lithologies were deposited in random order. The second matrix is used as computer input forTestmark, Stochex, andMarchain programs, the last of which stimulates a realistic vertical succession. The transition probability data fit readily into the broad framework of deltaic cycles.Published with permission of the Director, Institute of Geological Sciences. 相似文献
5.
The cyclic arrangement of lithofacies of the Karharbari Formation of the Damuda Group from a part of the Talchir Gondwana
basin has been examined by statistical techniques. The lithologies have been condensed into five facies states viz. coarse-,
medium-, fine-grained sandstones, shale and coal for the convenience of statistical analyses. Markov chain analysis indicates
the arrangement of Karharbari lithofacies in form of fining upward cycles. A complete cycle consists of conglomerate or coarse-grained
sandstone at the base sequentially succeeded by medium-and fine-grained sandstones, shale and coal at the top. The entropy
analysis categorizes the Karharbari cycles into the C-type cyclicity, which is essentially a random sequence of lithologic
states. Regression analysis undertaken in the present study indicates the existence of sympathetic relationship between total
thickness of strata (net subsidence) and number and average thickness of sedimentary cycle and antipathic relationship between
number and average thickness of sedimentary cycle. These observations suggest that cyclic sedimentation of the Karharbari
Formation was controlled by autocyclic process by means of lateral migration of streams activated by intrabasinal differential
subsidence, which operated within the depositional basin and the channels carrying coarse grade clastic sediments, which make
the cycles thicker, tend to be more common in the areas of maximum subsidence. Clastic sediments issued from the laterally
migrating rivers interrupted the cyclic sedimentation of the Karharbari Formation in many instances. 相似文献
6.
Markov chains and embedded Markov chains in geology 总被引：2，自引：0，他引：2
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. 相似文献
7.
A stratigraphic section may be divided into lithologic units which in turn may be divided into beds. This paper gives a mathematical
formulation of stratigraphic sections that takes these two levels into account and uses bed properties to yield the thickness
and number of beds in lithologic units. The model is a semiMarkov chain in which the succession of lithologic bed types forms
a Markov chain and is an independent random variable. The model is tested against stratigraphic data obtained from micrologs.
There is close agreement between the observed and calculated thicknesses of lithologic units. Tests for the degree of agreement
between observed and calculated numbers of beds in lithologic units are hampered by inability to observe thin beds on micrologs.
Some implications of this limitation to stratigraphic analysis are noted. 相似文献
8.
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. 相似文献
9.
The Antola Formation of Upper Cretaceous age crops out extensively in the Northern Apennines and consists of graded units of calcareous sandstones, sandstones, marlstones, and shales. It can be subdivided into the Cerreto, Antola Marlstone, Bruggi, and S. Donato Members on the basis of bed thicknesses and percentage of shales. Although the whole formation is interpreted as a deep-sea basin plain deposit, the members constitute lateral facies subdivisions which range from proximal, thick-bedded turbidities that show a prevalence of thinning upward cycles in bed thicknesses to distal turbidites that show predominantly thickening upward cycles and have a high percentage of shale. Repetitive patterns in the lithological sequence of the turbidite association are generally distinctive and are satisfactorily described as first order Markov chains. Only the Antola Marlstone Member has an additional second order Markov property. Imaginary eigenvalues of the transition probability matrices of all but the Bruggi Member demonstrate a strong cyclic character in the lithologic ordering within the formation. The behaviour of the Antola Marlstone and of the Bruggi may reflect the influence of a secondary ophiolitic intra-basinal source of clastics that contributed sandy turbidites and olistostromes. Systematic long-term variations in the sequence of bed thickness development in some sections of the Antola Formation are often subtle and equivocal, and pose special problems in interpretation. Fourier analysis was applied to the task of partitioning fundamental wavelengths from “background noise” introduced by essentially random depositional processes. In all members there is (1) strong short-term wavelength of two to three beds indicative of alternating thin and thick beds and judged to be typical of turbidite sequences; (2) an intermediate wavelength ranging from about five beds (proximal facies), eight beds (distal) to nine beds (very distal), which have both thinning and thickening upward trends, interpreted respectively as valley fill due to shifting talwegs of low density turbidity currents, and to progradational, flat turbidite lobes; (3) a poorly defined long-term wave-length of from thirty to greater than sixty beds that may be related to an unspecified trend in the evolution of the sedimentary basin. Phase angles associated with the coniputed power spectra give indications as to the asymmetry (thickening or thinning upward) or symmetry of the representative units. 相似文献
10.
Randomness in the occurrence of lithologies in a cyclical succession is evaluated in terms of entropies which can be calculated from a Markov chain matrix. Two types of entropies are linked with every lithologic state; one is the entropy before deposition E
(pre)
and the other is that after deposition E
(post),which together form an entropy set. The entropy sets for pebbly sandstone, sandstone, shale, and coal for the Karharbari coal measures, and sandstone, shale, carbonaceous shale, and coal for the Barakar coal measures were plotted separately and compared with Hattori's idealized plots. These coal measures probably were essentially of symmetrical cyclical pattern (Type-B)of Hattori. The entropy of the whole sedimentation unit readily fits under the broad framework of fluvial cycles. 相似文献
11.
Dr. Satyendra M. Casshyap 《International Journal of Earth Sciences》1975,64(1):610-640
Regional patterns of sandstone distribution were examined in the coal-bearing Bochumer Formation with the help of fence diagrams and isolith (thickness) maps. In addition, isolith maps and cross-sections were drawn for some well defined sandstone bodies, like Dickebank sandstone (Lower), Röttgersbank sandstone (Middle), and Matthias sandstone (Upper), and sand-mud ratio maps were prepared, on which isolith contours showing the total thickness of coal were superimposed. Most sandstone bodies are oriented west-southwest; they are elongate, straight to sinuous, show bifurcation and branching, and closely resemble sand-bodies designated as belt and dendroid. The area with greater thickness (50 m or more) of sandstone and poorer in mudstone (sand-mud ratio > 1.0) is linearly distributed to the north in the Lower unit, but shifts toward the south in the Middle and Upper units. Interrelationship between certain stratigraphic variables was investigated statistically, and it is concluded that the total thickness of strata or net subsidence of the basin exhibits direct relationship with the number and thickness of sandstone, rooty bed, and coal. A synthesis of integrated results reveals that the sediments of the Bochumer Formation were transported to and across the basin down the regional paleoslope toward west-southwest, and partly toward northwest; that it was a longitudinal marginal basin; and that the depositional environment consisted mainly of a high-constructive delta plain, in which distributary and tributary channels and their subenvironments including natural levees and coal-forming swamps developed and migrated constantly across the plain to give rise to characteristic interbedded (cyclic) sequence. 相似文献
12.
Quantitative relationships between numbers of fluvial cycles, bulk lithological composition and net subsidence in a Scottish Namurian basin 总被引：1，自引：0，他引：1
This detailed quantitative basin analysis of fluvial deposits in a subsiding Namurian structural basin is aimed at discovering underlying statistical relationships between numbers of fluvial cycles, bulk lithological composition and net subsidence which could be used as a background to future sophisticated computer simulation experiments and would also facilitate comparison with other ancient basins. The succession studied lies between two widespread marine bands, one of Arnsbergian (E2) and one of Kinderscoutian (R1) age, and is dominated by upward-fining cycles: 94% of the semi-cycles containing sand, here termed grain-size cycles, are upward-fining and the ratio of fine members (mudstone+siltstone) to coarse members ranges from 0·23 to 5·0. Trend-surface analysis reveals basement structures, which influenced sedimentation, including a Caledonoid graben. Correlation coefficient values and results of principal component analysis demonstrate that the numbers of rooty horizons and grain-size cycles, together with the total thicknesses of sandstone and of mudstone+siltstone, all tend significantly towards a linear relationship with the total thickness of strata and hence net subsidence. The average thickness of grain-size cycles tends towards an inverse linear relationship with net subsidence. This probably reflects the presence of stacked, relatively thin, channel-fills within persistent channel belts. These belts tend to be localized in the areas of greatest subsidence within the basin and follow courses basically similar to channels already discovered in the underlying deltaic sediments. The highest concentrations of mudstone+siltstone tend to lie on the flanks of the basin, but high local sand concentrations found at points on the margin where channels entered the basin from the NW and NE and left to the SW, effectively disrupt any significant relationship between net subsidence and the proportion of sand. Coal has been selectively preserved on the flanks of the basin and the number of rooty horizons is greatest in an area of low subsidence which lay somewhat remote from the main channel belts. 相似文献
13.
Małgorzata Pisarska‐Jamroży Tomasz Zieliński 《Boreas: An International Journal of Quaternary Research》2014,43(2):330-348
The Drawa sandur, which is the largest, coarse‐grained sandur in Poland, dates from the Pomeranian phase of the Weichselian glaciation (c. 16 ka BP). Using Markov chain analysis we infer that five cycles and five rhythms occur in its proximal part. The cycles dominated by Gt and St lithofacies in the lower part of the sandur succession and by a GDm lithofacies in the upper part, are fining‐upward cycles deposited in braided channels during large ablation floods. Three groups of cycles are distinguished based on their genesis: (i) cycles due to channel‐sheet evolution during large floods; (ii) cycles due to braid‐bar development during initial and advanced diminishing of floods; and (iii) cycles developed in the thalweg or interbar channels. The succession as a whole forms a large‐scale coarsening‐up megacycle (‘sandur megacycle’) which corresponds to a phase of ice‐sheet advance. Because the cyclicity was evident from Markov chain analysis of the sedimentary succession, we suggest that this statistical tool is valuable for reconstruction of glacifluvial sedimentary conditions, particularly as it can shed new light on the palaeogeographical development of sandar. 相似文献
14.
The Moodies Group in the Dycedale Syncline, Barberton Greenstone Belt consists of a 100–130 m-thick upward-fining succession that exhibits a transition from fluvial to tide-modified sedimentation. A basal, 10–30 m-thick conglomerate–sandstone interval of alluvial origin is overlain by stacked upward-fining, decimeter- to meter-scale cycles within which three facies are recognized: 1) conglomerate lag; 2) cross-bedded sandstone; and 3) interlaminated sandstone–siltstone and mudstone. Within the cycles, the abundance of mudstone drapes increases upwards. Structureless conglomerates and cross-beds lacking mudstone drapes record braided-alluvial processes. In contrast, cross-beds with mudstone drapes and interlaminated sandstone–siltstone and mudstone are products of flows modified by various tidal beats. Sand and/or silt transport took place during the ebb and flood stages and mudstone accumulated during slack water phases. Alternating thick–thin laminations reflect dominant and subordinate, twice-daily tides. Thicker groupings of foresets and thicker intervals of vertically stacked sandstone–siltstone and mudstone laminations are interpreted as spring tide deposits whereas thinner groupings of foresets and thinner laminations record neap tides. Desiccated mudstone drapes on foresets indicate that bedforms rarely were locally exposed during some portion of the tidal cycle. Abundant exposure structures in the interlaminated sandstone–siltstone and mudstone facies indicate that the cycles are upward shoaling. The stacked upward-fining cycles are attributed to alternating subaerial exposure and fluvial influx followed by marine inundation, probably related to absolute sea level fluctuations. Lack of high-order vegetation on the Archean landscape promoted rapid lateral migration or avulsion of tidally influenced fluvial channels.
The association of facies within the 100–130 m-thick upward-fining succession is comparable to Holocene and ancient paleovalley fills characterized by basal alluvial gradational upwards into estuarine facies. However, in the absence of vegetation, the land–ocean interface in the Archean probably consisted of laterally extensive fan or braid deltas rather than point sources of sediment characteristic of most modern rivers. The abrupt up-section change from syntectonic, high-energy, alluvial–fluvial flash flood deposits to tide-influenced sedimentation implies a proximal source that provided sediment to a shoreline influenced by strong tidal action. Possible Holocene analogues are orogenic settings such as the Canterbury Plains of New Zealand, the Indo-Gangetic Plains of India and strike-slip settings such as the Gulf of Aqaba but all three examples lack a direct transition to tidally influenced sedimentation. 相似文献
15.
Rabindra Nath Hota 《Mathematical Geosciences》2010,42(2):223-242
Total thickness of strata and coal cycle parameters of the three formations, i.e. Karharbari, Barakar, and Barren Measures
of the Damuda Group of the Talchir Gondwana basin were subjected to bivariate and multivariate statistical analyses. Polynomial
regression lines were fitted to data sets consisting of total thickness of strata, number of coal cycles, and average thickness
of coal cycles of the three formations of the Damuda Group. A significant direct relationship is observed between total thickness
(net subsidence) of strata and number of coal cycles, while a significant inverse relationship exists between the number of
coal cycles and their average thickness. Principal component and multiple regression analyses suggest that lithological parameters
of the coal bearing strata reflect the dynamic of the basin subsidence. The sedimentary distributive mechanism in the form
of lateral migration of streams or drainage diversion caused in response to differential subsidence of the depositional surface
seem to be appropriate mechanisms for the development of coal cycles and peat swamps in the Talchir basin. Often during Karharbari
sedimentation, peat accumulated in abandoned channels was scoured away by high energy migrating channels. On the other hand,
Barakar peat swamps developed in a distal part of the flood plain, as a result of which many of the coal seams could be of
appreciable thickness. The advent of arid climatic condition retarded the growth of vegetation to a larger extent that prevented
profuse development of coal seams during the Barren Measures Formation. 相似文献
16.
本文应用沉积学与测井学理论,对山东聊城煤矿区太原组的沉积环境进行了研究,认为太原组是以陆源碎屑潮坪及泻湖为主体的海退沉积与潮下带海进沉积所组成的多施回沉积体系,主采煤层M9,M10形成于泻湖泥遄沼泽化环境。在分析M9、M10煤聚煤特点的基础上,运用灰色系统理论,建立了M9、M10煤GM（1,1）灰色数学横型,并对煤厚进行了灰色预测。 相似文献
17.
多元统计分析在矿井断层预测中的应用 总被引：1，自引：0，他引：1
矿井小构造预测是一个难度极大的研究课题,根据岩层厚度、岩层组合关系,运用判别分析、地质统计学等数学方法预测矿井小构造,是一种全新的思想方法。本次研究选取我国西部某一煤矿作为研究对象,研究主采煤层上下岩性变化特征,根据岩石的不同抗压强度,确定五个变量;将已采区的钻孔分为含有断层的钻孔和不含有断层的钻孔,统计这两类钻孔中五个变量的值,建立判别函数,对未采区的钻孔进行判别分类。对每个钻孔的岩层在可采煤层的上下划分成10个层段,判别出每个层段中未知钻孔的归属,从而得到钻孔属于有断层的概率,即断层分布的概率等值线图。经实例验证,精确度达70%以上,对生产矿井具有一定经济效益和实用价值。 相似文献
18.
We define a distance between sedimentary successions to compare their dissimilarity formally. Distance definition is based on attributed syntactic representation. One-dimensional successions can be represented by a string of lithofacies symbols sequentially or vertically. Each symbol can also have a vector of attributes that can provide other information on lithofacies such as thickness. The distance of any two successions is then defined consisting of its syntactic and attribute subdistances. Syntactic distance measures difference of vertical lithofacies change between two successions and attribute distance measures difference of thickness of corresponding lithofacies. Clustering is used to test validity of distance definition and its potential application to analysis of cycle-dominated sedimentary successions. Example is from the Namurian-A succession in Kincardine basin, central Scotland. There are 56 cycles in intervals of about 300 m each in two boreholes. Recognition of intermediate cycles depends on correctly determining of types of these short cycles and their vertical stacking pattern. Intermediate cycles have better potential in high-resolution stratal correlation regionally. Syntactic clustering results show that 56 short cycles can be classified into four groups with distinctive geological interpretation, which further helps reveal hierarchical cyclic architecture of the whole succession. 相似文献
19.
Cyclic characteristics of a sequence of Permian coal-measure sediments have been studied using Markov chain analysis on borehole data. Fining-upwards and oscillating sequences can be distinguished, and depositional regimes are proposed to explain the observed sequences. However, there is no clearly defined relationship of sequence type to tectonosedimentary environment. The relationship of the number of coal-defined and fining-upwards cycles to total thickness and mean cycle thickness is examined using linear regression. The relationships for coal-defined and fining-upwards cycles are essentially the same. Significant positive correlations are present between the number of cycles and total thickness and significant inverse relationships are present for the number of cycles and the mean cycle thickness. 相似文献
20.
措勤盆地是西藏近年来矿产勘查的重要地区之一,其北部川巴地区是目前的煤炭资源调查远景地区。川巴地区下白垩统由下而上可划分为则弄群、多尼组和郎山组。在对川巴地区下白垩统露头剖面沉积特征研究的基础上,结合区域地质资料,共识别出浅海泥质陆棚、碳酸盐岩台地、混积台地、潮坪、辫状河三角洲、扇三角洲和辫状河7种沉积相。则弄群岩性主要为火山碎屑岩、细砾岩、含砾粗砂岩、砂岩,发育扇三角洲相;多尼组岩性主要为细砾岩、含砾粗砂岩、砂岩、泥岩及灰岩,夹炭质泥岩和薄煤层,发育辫状河、辫状河三角洲、混积台地和浅海泥质陆棚相;郎山组岩性主要为灰岩,夹细砂岩、粉砂岩及泥岩,发育潮坪、混积台地和碳酸盐岩台地相。基于沉积相分析的聚煤规律研究,指出川巴地区主要成煤环境为多尼组辫状河三角洲平原分流间湾,阿格桑至川巴一线及其以东一带地区,是本区主要的聚煤作用带。 相似文献