Markov chains and embedded Markov chains in geology

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.     

Modelling of cyclical stratigraphy using Markov chains

Summary State-of-the-art on modelling of cyclical stratigraphy using first-order Markov chains is reviewed. Shortcomings of the presently available procedures are identified. A procedure which eliminates all the identified shortcomings is presented. Required statistical tests to perform this modelling are given in detail. An example is given to illustrate the presented procedure.     

Occurrence and impact of characteristic earthquakes in northern Algeria

Earthquakes constitute the natural hazard that is one of the main natural threats to the northern part of Algeria because of its geographical setting at the Eurasia–Africa plate boundary. Several active multi-segment reverse faults have been identified near urban areas that may rupture during characteristic earthquakes and produce earthquakes of magnitudes ≥7.0. Characteristic earthquakes are extreme seismic events characterized by long return periods, which can have great societal impact. Earthquakes in northern Algeria are destructive for two main reasons: firstly, the shallow character of the faults and secondly, the vulnerability of the building stock built essentially prior to the implementation of seismic design codes that take into account the level of the seismic hazard. That is why even moderate earthquakes are disastrous in this area.     

Dynamic monitoring of drought using HJ-1 and MODIS time series data in northern China

From early November 2008 to February 2009, lack of rainfall led to severe drought in northern China. More than 9.3 million ha of wheat in six major crop production provinces, including Henan, Anhui, Shandong, Shanxi, Gansu, and Shaanxi, were hit by drought. Supported by Chinese HJ-1 satellite images together with NASA Moderate Resolution Imaging Spectroradiometer (MODIS) data, dynamic monitoring of the drought was conducted. HJ-1 CCD data with 30-m resolution were used to identify cropland information. Spatial–temporal variation of drought was detected using Vegetation Index and Water Index time series data derived from MODIS visible, infrared, and short-wave infrared bands. The influences of drought were classified into five levels based on MODIS-derived 8-day composite Anomaly Water Index (AWI) and field survey data. The results indicated that the drought deteriorated beginning in November 2008 and became most serious in late January 2009. HJ-1 data together with MODIS data proved to be valuable data sources for monitoring soil moisture and drought at a both regional and national scale.     

模糊马尔科夫链状模型在斜坡稳定性预测中的应用

滑坡灾害的突发特征和滑坡运动的不确定性,使得斜坡稳定状态预测成为岩土工程领域内的一个难点。模糊马尔科夫链状模型能够预测序列从某种模糊状态出发转移到其它状态的概率,非常适合斜坡工程的稳定状态预测。文章首先介绍了模糊马尔科夫链的概念、特点及该方法的原理、算法,之后将其应用到实际的边坡稳定状态预测分析中。实际边坡滑动经过稳定状态、基本稳定状态、临界状态、失稳状态,应用模糊马尔科夫原理分析边坡稳定状态变化,进行斜坡变形-失稳过程预测预报。通过实例应用表明,预测结果与实际情况吻合较好。为此,该模型能够准确地对斜坡稳定状态进行预测。     

Entropy in Markov chains and discrimination of cyclic patterns in lithologic successions

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.     

Hydrochemical method of prospecting in northern swamp areas

Presented here are the results of the study of surface (hypergenous) migration of a number of chemical elements in a swampy area of the northwestern Siberian Platform. The migration mode of a number of chemical elements, and their relationship with the ore bodies, were determined from a study of various natural objects (water, peat, iron gels, etc.). Geochemical exploration criteria for the bornite-chalcocite ores are cited. -- Author.     

Neogene rotations of the Chenoua massif,northern Algeria,from remagnetizations

The tectonics of the Chenoua massif suggests block rotations of Neogene nappes associated with the African–European plate convergence. To estimate the extent of these rotations, a Paleomagnetic study on rhyolites and andesites of Langhian–Serravallian age and sandstones of Burdigalian age was carried out on 23 sites (200 specimens). The sites are distributed in the northwestern, southeastern and southern Chenoua massif. One or two components of magnetization, mainly carried by magnetite, pyrrhotite and/or hematite, were isolated in sandstones and volcanics. The sandstone sites reveal magnetizations in sandstones from the Cap Blanc syncline that are post-folding. However, both polarities are found, which is consistent with data from Africa during the Upper Miocene. Clockwise and counterclockwise rotations were recorded, dating back to the Neogene times in volcanics and sediments. From the faulted Cap Blanc syncline counterclockwise rotations of 1?±?4° to 18?±?28° around a vertical axis occurred in sediments since the Miocene with respect to Africa. In fact, remagnetizations occurred at several periods of time and in different sites, providing information on the evolution of post-tectonic rotations. Some volcanics record counterclockwise rotations of about 30° since the Miocene, whereas others do not show any significant rotation. This can be explained by the direction of the principal compressive stress axis σ ₁ and by lateral extrusions related to an indentation model, in which we expect both clockwise and counterclockwise rotations.     

Some aspects of the spatial characteristics of drought in northern Nigeria

A long-period instrumental data set (1916–1987) of monthly growing season (April–October) rainfall totals for 34 stations in northern Nigeria is used to quantify drought following the method of H. N. Bhalme and D. A. Mooley. It is established that there are remarkable seasonal changes in the patterns of wetness and dryness over the region with no consistent recurrent spatial patterns in the moisture anomalies. In general, large-scale droughts only rarely cover the region as a whole, and there are distinct spatial differences dominating the wet and dry years. The length and severity of drought varies from sub-area to sub-area with very low interannual persistence. Although discrete areas do catch the brunt of drought on a year-by-year basis, drought occurrence in the region is largely sporadic in its spatial distribution. The rather noisy spatial characteristics of drought in northern Nigeria suggests that the seasonal shift in the Intertropical Discontinuity (ITD) is not likely the most important causal mechanism of drought in the region.     

Application of factor analysis in defining drought prone areas in Lake Urmia Basin

Data reduction methods such as principal components analysis and factor analysis can be used to define drought prone areas of a basin. In this study, factor analysis method applied for the purpose of projecting the information space on the few dominant axes. The main aim of this study is regionalization of Lake Urmia Basin from the view of drought using factor analysis. For this purpose, monthly precipitation data of 30 weather stations in the period 1972–2009 were used. For each of the selected stations, 3- and 12-month Standardized Precipitation Index (SPI) values were calculated. Factor analysis conducted on SPI values to delineate the study area with respect to drought characteristics. Homogeneity of obtained regions tested using the S statistics proposed by Wiltshire. Results of factor analysis of 3- and 12-month SPI values showed that 5 (6) factors having eigenvalues >1 accounted for 68.08 (78.88) % of total variance. The Lake Urmia Basin was delineated into the five distinct homogeneous regions using the 3-month SPI time series. This was six in the case of the 12-month SPI time series. It can be concluded that there are different distinct regions in Lake Urmia Basin according to drought characteristics. The map of regions defined using the 3- and 6-month SPI time series presented in this paper for Lake Urmia Basin.     

陕北黄土丘陵区威胁窑洞民居的地质灾害问题—以陕西延安地区为例

窑洞是陕北黄土丘陵区民居的一种主要形式。在介绍区内窑洞的类型、分布的基础上,阐述了滑坡、崩塌、塌窑、窑洞透水等主要窑洞民居地质灾害的发育特征。从沟谷发育期、斜坡结构类型、地形特征等方面分析了窑洞灾害形成的主要原因,认为黄土的工程地质特性是灾害发育的物质基础,人类工程活动和降雨是灾害形成的主要诱发因素。最后从窑洞的选址、斜坡的设计、窑洞的防水等几个方面提出了灾害的防治措施。     

A test of independence for stratigraphic sequences with respect to embedded Markov chains

Identification of cyclic sequences gives valuable insight into depositional associations of stratigraphic facies. An embedded Markov chain is a reasonable general model for facies transitions. But a model with independent random occurrences of facies is not an appropriate null hypothesis to be tested to show the presence of cycles because of definitional restriction in transition observations to only those between different facies. This is a common stratigraphic situation and the problem has been raised recently by several authors. We present here a test statistic for null hypothesis derived from the concept of partial independence and inherent to the model of embedded Markov processes.     

潍坊市北部漏斗区的含水层调蓄库容研究

近年来,由于过量开采地下水,潍坊市北部地区形成了大范围的地下水降落漏斗,而漏斗区产生了连续的储水空间。本研究收集了潍坊市北部水文地质条件资料,分析了研究区地质构造,并划分了水文地质单元。同时,选取研究区有代表性的钻孔,绘制了水文地质剖面图,刻画地下含水层的空间分布状态。然后根据土壤粒级将地下空间划分为透水层、弱透水层和不透水层。其中,透水层再细分为潜水含水层、微承压水含水层和承压水含水层。最后,利用松散岩型地下水调蓄公式计算研究区调蓄库容。本研究还利用GMS空间建模,绘制了地下水库三维实体模型。研究结果表明,潍坊调蓄区段内地下水补给源条件及调蓄条件良好,具有很好的储蓄水能力。研究区的调蓄库容为11.81亿m3,可开采量为9.44亿m3。这些研究结果为潍坊市利用地下空间储存水资源提供了数据支持。     

Measurement of soil-gas radon in some areas of northern Rajasthan,India

The health hazards of the radioactive gas radon on general public are well known. In order to understand the level and distribution of ²²²Rn concentrations in soil-gas in Sri Ganganagar district of Rajasthan, a ²²²Rn survey was carried out for the first time using RAD7, an electronic radon detector manufactured by Durridge Company (USA), at different locations covering a total area of 10,978 km ², having a population of approximately 20 lakh. The measurement of ²²²Rn concentration in soil-gas was carried out at four different depths (10, 40, 70, and 100 cm). The radon concentration in soil-gas for 10, 40, 70, and 100 cm depths ranged from 0.09–4.25, 0.15–6.30, 0.50–9.18, and 0.72–10.40 kBq m ^?3, respectively. The minimum value of radon concentration is observed in 33 GB village at 10 cm depth and maximum for Mohanpura village at 100 cm depth. As expected, our data show an increase of soil-gas radon concentration levels with depth. The present results are compared with the available radon data from other studies.     

Hydrogeochemical processes and multivariate analysis for groundwater quality in the arid Maadher region of Hodna,northern Algeria

Acta Geochimica - This study focused on water quality and hydro-geochemical processes (evolution, origin) in the Maadher region, central Hodna in Algeria. In recent decades, the excessive...     

Multivariate statistical analysis of the groundwater flow in shallow aquifers: a case of the basins of northern Algeria

Water resources in Algeria are mainly controlled by climate change which creates enormous problems in its planning, management and distribution. While the surface water resources are perfectly managed and operated by means of dams and small dams built for several years, the groundwater resources remain long unknown and unusable because of the lack of relevant working tools (e.g., methods, formulas, maps, etc.) for planners and engineers working in the field of water resources exploration. To highlight the hydrodynamic processes of groundwater in shallow aquifers of the basins of northern Algeria, we conducted a study using 81 subwatersheds collected from different locations at the basins; taking into account the climatic and geomorphological factors, to understand water usage trends, analyse patterns, tap good shallow aquifers and ensure long lasting supplies of water through arid periods, mapping and modelling of groundwater are fundamental to problem resolution. Multivariate statistical techniques as well as cluster and principal component analysis were applied to the data on groundwater flow, with the objective of defining the main controls on the groundwater flows at the basins. These statistical techniques showed the presence of three groundwater flow groups with increasing importance according to precipitation. The first group was mainly influenced by climatic factors, the second was more controlled by the communication between the surface and underground flows and the third group revealed the influence of geomorphological factors on groundwater flows.     

Simulation of water resources management scenarios in western Algeria watersheds using WEAP model

The question of water constitutes a permanent challenge for the countries of North Africa in general and Algeria in particular. For over 20 years, western Algeria region had significant rainfall deficits that resulted in severe droughts, which seriously affected the water resources in terms of quality and quantity. This research presents one of the Water Evaluation and Planning (WEAP) model applications in watersheds of western Algeria. The model is applied to evaluate and analyze the existing balance and expected future water resources management scenarios by taking into account the different operating policies and factors that may affect demand until 2030. The results showed that neither domestic demand nor agricultural demand is met for the basis year 2006. The results also showed that domestic demand can be satisfied for the considered scenarios. Demand management and development of standard of living are the necessary procedures for proper management of the available resources. However, agricultural demand cannot be satisfied for Development of Large Irrigation System scenarios. The results confirmed that WEAP software offers a solid basis to assist planners in developing recommendations for future water resource management by revealing hot spots of action.     

Hydrogeochemistry and sensitivity to acidification of streamwaters in crystalline areas of northern Fennoscandia

About 6,400 water samples were collected from small catchments in northern Finland and Norway above 66° N latitude as a part of the Nordkalott Project carried out jointly by the Geological Surveys of Finland, Norway, and Sweden. Electrical conductivity (EC) was measured in situ and Ca, Mg, Sr, Ba, Na, K, Si, Fe, Mn, Al, and Zn concentrations were determined from filtered and acidified samples by the ICAP method. The relative abundance of mafic, ultramafic, and carbonate rock components in the catchments is the most influential factor controlling the EC values and the main cation concentrations (Ca, Mg, Sr). These components also determine the HCO₃ alkalinity or acid-neutralizing capacity (ANC) of streamwater. In the northern coastal belt, Na is derived largely from airborne sea salts, but in the southwestern corner of the research area it may be derived partly from relict sea salts in sediments. The concentrations of Na, K, and Si do not depend solely on the lithological environment. Fe and, to a lesser extent, Mn and Al occur in the highest abundances in the low-lying, intensely paludified southern part of the area, suggesting that these metals tend to go into solution and are transported in complexed forms with dissolved and colloidic humic matter. The areal distribution patterns of the main cations (Ca, Mg, Sr) and of some heavy metals (Fe, Mn) in streamwater are fairly consistent with those of till and minerogenic stream sediments, although, in a statistical approach, only a few significant correlation coefficients were established.     

Detecting hydro-climatic change using spatiotemporal analysis of rainfall time series in Western Algeria

The knowledge of the climatic behavior especially that one of semi-arid regions is required to optimize the management of water resources. Here climate variability is directly related to water resources that are of a high socio-economic and environmental significance. This work deals mainly with a statistical analysis of the precipitation regime to assess its spatial distribution and temporal variation in north-western Algeria. For this, a time series and a principal component analysis are performed on rainfall series representing annual precipitations of twenty-one meteorological stations for the period 1914 to 2004, the most complete and longest of West Algeria, in order to detect patterns and trends in the region. A spectral analysis of the time series revealed the existence of a period of roughly 30 years for all stations. Furthermore, the trend of a wide part of the obtained spectra suggests the existence of another period longer than the samples size.