Types,composition and diagenetic evolution of authigenic clay minerals in argillaceous limestone of sepiolite-bearing strata:A case study of Mao-1 Member of Middle Permian Maokou Formation,eastern Sichuan Basin,SW China

The types,occurrence and composition of authigenic clay minerals in argillaceous limestone of sepiolite-bearing strata of the first member of the Middle Permian Maokou Formation(Mao-1 Member)in eastern Sichuan Basin were investigated through outcrop section measurement,core observation,thin section identification,argon ion polishing,X-ray diffraction,scanning electron microscope,energy spectrum analysis and laser ablation-inductively coupled plasma-mass spectrometry.The diagenetic evolution sequence of clay minerals was clarified,and the sedimentary-diagenetic evolution model of clay minerals was established.The results show that authigenic sepiolite minerals were precipitated in the Si4+and Mg2+-rich cool aragonite sea and sepiolite-bearing strata were formed in the Mao-1 Member.During burial diagenesis,authigenic clay minerals undergo two possible evolution sequences.First,from the early diagenetic stage A to the middle diagenetic stage A1,the sepiolite kept stable in the shallow-buried environment lack of Al3+.It began to transform into stevensite in the middle diagenetic stage A2,and then evolved into disordered talc in the middle diagenetic stage B1and finally into talc in the period from the middle diagenetic stage B2to the late diagenetic stage.Thus,the primary diagenetic evolution sequence of authigenic clay minerals,i.e.sepiolite-stevensite-disordered talc-talc,was formed in the Mao-1 Member.Second,in the early diagenetic stage A,as Al3+carried by the storm and upwelling currents was involved in the diagenetic process,trace of sepiolite started to evolve into smectite,and a part of smectite turned into chlorite.From the early diagenetic stage B to the middle diagenesis stage A1,a part of smectite evolved to illite/smectite mixed layer(I/S).The I/S evolved initially into illite from the middle diagenesis stage A2to the middle diagenesis stage B2,and then totally into illite in the late diagenesis stage.Thus,the secondary diagenetic evolution sequence of authigenic clay minerals,i.e.sepiolite-smectite-chlorite/illite,was formed in the Mao-1 Member.The types and evolution of authigenic clay minerals in argillaceous limestone of sepiolite-bearing strata are significant for petroleum geology in two aspects.First,sepiolite can adsorb and accumulate a large amount of organic matters,thereby effectively improving the quality and hydrocarbon generation potential of the source rocks of the Mao-1 Member.Second,the evolution from sepiolite to talc is accompanied by the formation of numerous organic matter pores and clay shrinkage pores/fractures,as well as the releasing of the Mg2+-rich diagenetic fluid,which allows for the dolomitization of limestone within or around the sag.As a result,the new assemblages of self-generation and self-accumulation,and lower/side source and upper/lateral reservoir,are created in the Middle Permian,enhancing the hydrocarbon accumulation efficiency.

Physical Experiments and Mechanism Study on the Occurrence State of Hydrogen in Clay Minerals

In recent years,natural hydrogen has been discovered in various geological environments both domestically and internationally,which has sparked a global interest among geologists and led to a surge in the exploration of hydrogen gas(Klein et al.,2019;Prinzhofer et al.,2019;Moretti and Webber,2021;Scott,2021;Bezruchko,2022).However,there is a lack of research on the occurrence state of natural hydrogen gas,which hinders a deeper understanding of its behavior in underground storage and migration.

Wettability of different clay mineral surfaces in shale:Implications from molecular dynamics simulations

Shale contains a lot of clay minerals. Clay minerals mainly exist in nano- and micro-meter sized particles, and the pore structure is complex, which leads to its extremely complex wettability. The surface wettability of clay minerals significantly affects the oil and gas-bearing capacity of shale reservoirs. Therefore, studying the wettability of common clay minerals in shale at the nanoscale is of great significance for shale hydrocarbon exploration and development. In this study, the wetting behavior of water in n-hexane and toluene on different clay mineral surfaces at the nanoscale was systematically studied using Molecular dynamics (MD) simulation. And the influencing factors of wettability were analyzed. Through the analysis of the morphological changes of water, relative concentration of water, RDF and interaction energy, it is concluded that the following order of water wettability on the surfaces of clay minerals: montmorillonite > chlorite > kaolinite > illite. Through the analysis of interaction energy, it is concluded that the hydrophilicity of four clay minerals is stronger than that of lipophilicity. And the main interactions between water and oil and the mineral surfaces were van der Waals force and electrostatic force. In addition, the temperature, liquid hydrocarbon type, and mineralization of water affected the wettability of clay minerals. The concentration of water on the surfaces of montmorillonite, kaolinite, and illite decreased with increasing temperature, and the water wettability decreased. At 298 K, the hydrophilicity of the surfaces of the clay minerals in toluene follows the order montmorillonite > chlorite > kaolinite > illite. The higher the NaHCO3 concentration in water, the weaker the wettability of the clay mineral surfaces to water. By comparing the previous experimental results with the MD simulation results, similar wetting characteristics were obtained, and the reliability of the simulation results was verified. MD simulation was used to explore the water wetting of the surfaces of four clay minerals in a shale reservoir from the micro level. This makes up for the lack of experimental means for clarifying the flow and production mechanisms of shale oil and gas and effectively improves the evaluation technology of shale.

Rheological mechanical properties and its constitutive relation of soft rock considering influence of clay mineral composition and content

Rheological mechanical properties of the soft rock are afected signifcantly by its main physical characteristics-clay mineral.In this study,taking the mudstone on the roof and foor in four typical mining regions as the research object,frstly,the clay mineral characteristic was analyzed by the X-ray difraction test.Subsequently,rheological mechanical properties of mudstone samples under diferent confning pressures are studied through triaxial compression and creep tests.The results show that the clay mineral content of mudstone in diferent regions is diferent,which leads to signifcant diferences in its rheological properties,and these diferences have a good correlation with the content of montmorillonite and illite-montmorillonite mixed layer.Taking the montmorillonite content as an example,compared with the sample with 3.56%under the lower stress level,the initial creep deformation of the sample with 11.19%increased by 3.25 times,the viscosity coefcient and longterm strength decreased by 80.59%and 53.94%,respectively.Furthermore,based on the test results,the damage variation is constructed considering the montmorillonite content and stress level,and the M–S creep damage constitutive model of soft rock is established.Finally,the test results can be ftted with determination coefcients ranging from 0.9020 to 0.9741,which proves that the constitutive relation can refect the infuence of the clay mineral content in the samples preferably.This study has an important reference for revealing the long-term stability control mechanism of soft rock roadway rich in clay minerals.

Distribution of clay minerals in surface sediments off Yangtze River estuary

Based on the clay minerals, content analysis from 187 stations in the surface sediments, this paper dealt with the assemblages and the distributions of clay minerals in the surface sediments off the Yangtze River estuary. The research results showed that the illite dominates the surface sediments off the Yangtze River estuary with the smectite or kaolinite the second rank and chlorite the third rank; the illite-smectite-kaolinite-chlorite-assemblage is the main type of the clay minerals assemblage in the area, with the illite-kaolinite-chlorite-smectite-type as the second rank; the source of clay mineral is mainly from the Yellow River and the Yangtze River. The Q-type cluster analysis show that sediments from both recent and ancient Yellow River were deposited mainly in the northeast part of the study area to the north of 29°30′. Substance from the Yangtze River was deposited mainly in the western and middle parts off the Yangtze River estuary.

Advances in interaction mechanism of water(gas) on clay minerals in China

Dealing with large-scale deformations in soft-rock tunnels is a very important issue in soft-rock tunnel engineering. The mechanism of this large-scale deformation is closely related to the physical and chemical properties of soft rock, interaction between soft rock and water, and interaction between soft rock and gas contained in soft rock. In order to gain a better predictive understanding of the governing principles associated with this phenomenon, we used experimental and theoretical methods to study the effects of point defect on physical and chemical properties of soft rock and mechanism of interaction between water(gas) and soft rock. Firstly, we calculated the impurity formation energies and transition energy levels of defects by using the first-principle calculation, the results showed the microscopic mechanism of defects substitution in kaolinite and effects of defects on the structure of kaolinite. Moreover,comparing the experimental and theoretical results, we found the mechanism of interaction between water and soft rock. The results show that water is one of the most important factors which can induce various kinds of geological disasters. At last, the interaction between soft rock and surrounding gas as CO2, CH4 and CO is disused, the influence of surrounding gas on soft rock should not be ignored.

Patterns of Clay Minerals Transformation in Clay Gouge, with Examples from Revers Fault Rocks in Devonina Niqiuhe Formation in The Dayangshu Basin

The role of authigenic clay growth in clay gouge is increasingly recognized as a key to understanding the mechanics of berittle faulting and fault zone processes,including creep and seismogenesis,and providing new insights into the ongoing debate about the frictional strength of brittle fault(Haines and van der Pluijm,2012).However,neither the conditions nor the processes which

The distribution characteristics of clay minerals in the northern South China Sea

The clay minearals are composed of illite, chlorite, kaolinite, montmorillonite and mixed-layer minerals in the submarine sediments of the northern South China Sea. Three types of clay mineral zone can be recognized on the basis of the distributive regularity of clay minerals, submarine relief, hydrodynamic conditions and depositional characteristics in this region. Apart from the northern mainland source, kaolinites carried from the Philippines volcanic arc in the east and Malaysia in the south are also assumed to be one of the sources of the clay minerals in the deep sea. The increase of chlorites to the abyssal direction in the west of 116° E might be associated with the residual chlorites carried from the ancient Zhujiang River during the glacial period and the conversion of kaolinite into chlorite submarine volcanoes appear to be one of the sources of the increment of montmorillonite and chlorite around the Huangyan Island. From the distribution pattern of clay minerals in the whole area, it is known that the types of clay mineral assemblage in the study area are mainly controlled by climate and rock types of the source are-

Characteristics and genesis of clay minerals in the northern margin of the Qaidam Basin

In order to develop appropriate reservoir protection measures in the northern margin of the Qaidam Basin and improve its oil and gas recovery efficiency,characteristics of clay minerals from eleven clay rock samples from the northern margin of the Qaidam Basin were investigated using X-ray diffraction analysis,the Scanning Electron Microscope（SEM）and energy spectrum analysis.Clay mineral composition and distribution characteristics of the main hydrocarbon reservoirs,i.e.,from the Jurassic and Paleogene-Neogene,were explored.We analyzed the main factors which affected these attributes.The results show that the major clay minerals in the northern margin are chlorite,kaolinite,illite,smectite and illite/smectite inter-stratified minerals.Illite is the most widely spread clay mineral in this area. Chlorite is mainly found in the entire Neogene and in shallow horizons of the Paleogene.Smectite is enriched in the shallow Paleogene-Neogene.There are large amounts of kaolinite and illite/smectite inter-stratified minerals in the Jurassic.The major factors affecting the different development of clay minerals in the region are properties of parent rocks,paleoclimate and paleowater media conditions, diagenesis transformation,tectonic and terrain conditions.

Residual Effect of Long Term Application of Organic and Mineral Fertilizers on Selected Chemical Properties of a Savanna Alfisol

The residual effect of organic and mineral fertilizers on selected chemical properties of an Alfisol in the long term soil fertility trial established in 1950 at Samaru, Nigerian savanna was assessed. The trial was left fallow for fourteen years due to lack of funds. Topsoil was collected from plots that received three levels of cow dung （D）, nitrogen （N） and phosphorus （P） in all possible combinations. The soils were analyzed for selected chemical properties. Except for significant effect of applied P on available P, sole application of cow dung, N or P had no significant effect on all the measured soil properties. The interaction of D and P significantly affected the mean values of exchangeable Ca, Mg, K and ECEC in the range of 1.12-1.96, 0.62-1.11, 0.37-0.64 and 2.82-4.11 cmol/kg respectively. The most important results were the ability of the plot that received neither D nor P to significantly increase these parameters than the plots that received only one of the treatments. The results show that the fallow period has changed the effects of application of organic and mineral fertilizers on the soil chemical properties under continuous cultivation by modifying them towards those of a native savanna Alfisol.

Study of the Stacking Sequences of an Irregular Mixed-Layer Illite/Smectite (I/S) Clay Mineral—with a Discussion on the Existence of Minerals with Two-Dimentional Lattice and One-Dimentional Quasi-Lattice

There are two aspects in the study of irregular mixed-layer clay minerals: one is the kinds and ratios of their basic structural unit layers and the other is the junction probabilities of the unit layers. Irregular mixed-layer illite/smectite clay minerals (I/S) are widespread in nature. While studying the clay minerals from the Permian-Triassic (P/T) boundary bed, the authors found that I/S clay minerals are developed in all P/T boundary clay layers in areas from the northwest to southeast of China. Systematic mineralogical studies of the I/S clay minerals from Hunan, Hubei, Sichuan and Zhejiang were made by means of X-ray, infrared spectroscopic, electron microscopic and chemical analyses and a deepened study of the stacking sequences of their structural unit layers was conducted by the MacEwan one—dimentional direct Fourier transform. It was found that the stacking of the illite and smectite crystal layers along the c axis can be derived from Fibonacci sequences. Hence, the authors propose that such I/S clay minerals are possessed of two—dimentional crystal lattice and one—dimentional quasicrystal lattice.

Kinetics and Thermodynamic Parameters of the CopperExchange on Na-montmorillonite Clay Mineral inSelected Solvents

The kinetics of Cu ion exchange on Na-montmorillonite clay mineral has been investigated at three temperatures, in three solvents: H2O, ethylene glycol and glycerol. Solvent effects on the reaction rate have been discussed. The thermodynamic activation parameters were calculated and discussed in terms of solvation effects. The determined isokinetic temperature indicates that the reaction is enthalpy controlled where the interaction between solvent and clay surface plays an important role. A reaction mechanism which describes the solvent effect on the rate of Cu ion exchange is proposed.

Bio-Mobilization of Potassium from Clay Minerals: I. By Ectomycorrhizas

A pot experiment was carried out to investigate effect of ectomycorrhizal fungi on eucalyptus growth and K bio-mobilization from soils and clay minerals. In the experiment, sands mixed with soil, KCI-saturated vermiculate and mica, respectively, were used to nurse eucalyptus seedlings which were nonectomycorrhized or ectomycorrhized by an ectomycorrhizal fungus Pisolithus tinctorius strain XCI (Pt XC1) isolated from a forest soil from Xichang, Sichuan Province, China, and a worldwide well-known ectomycorrhizal fungus Pisolithus tinctorius strain 2144 (Pt 2144) obtained in Australia. More depletion of HCl-soluble K by mycorrhizas from the soil and minerals than nonmycorrhizas suggested that mycorrhizas had a great ability to mobilize K present in the interlayer and feldspar. Mycorrhizal seedlings depressed greatly K digested with HF-HCIO4 from substrates after consecutive extractions of soils and minerals by water, ammonium cetate and boiling HCl, while nonmycorrhizal seedlings reduced it little if any, showing that the mycorrhizal seedlings could mobilize and then utilize the structural K in mineral lattice. Ectomycorrhizal fungi played a very important role not only in promoting the growth of eucalyptus seedlings but also in mobilizing K in soils and minerals. The infection of Pt XC1 led to a better growth of eucalyptus seedlings and more K accumulation in the seedlings than that of Pt 2144. The large differences in K accumulation by the seedlings might be due to different abilities of the two ectomycorrhizal fungi to mobilize K in interlayer and lattice pools in the clay minerals.

The Sources and Transport Patterns of Modern Sediments in Hangzhou Bay: Evidence from Clay Minerals

Clay mineral compositions of 199 offshore surface sediment samples collected from the Hangzhou Bay have been analyzed. The clay minerals in the sediments from the Hangzhou Bay are dominated by illite(58.7%, on average), followed by chlorite(20.3%), kaolinite(16.9%) and smectite(4.1%). Two provinces were classified by Q-mode cluster analysis. Class Ⅰ with relatively low amounts of illite and smectite is widely distributed in the Hangzhou Bay, especially concentrated in the top and mouth of the bay, and the northern and southern nearshore areas. Class Ⅱ with comparatively high amounts of illite and smectite is mainly concentrated in the central part of the bay with the water depth of 8–10 m. By comparing clay mineral compositions with the neighbouring regions, we can find that the sediments in the Hangzhou Bay are mainly influenced by the resuspension and repeated deposition of particles from the Yangtze River due to the strong dynamic environment. In particular, the clay fraction of Class Ⅰ is mainly supplied by the Yangtze River, while the sediments of Class Ⅱ are mixture of the clay minerals carried by the Yangtze River and Qiantang River. In general, the distributions of clay minerals in the northern bay are affected by Yangtze River runoff, coastal current and flood tide together, and in the southern they are mainly affected by the Qiantang River runoff and ebb tide.

Paleoclimate and Paleoenvironment of Gonghe Basin, Qinghai-Tibet Plateau, During the Lastdeglacial: Weathering, Erosion and Vegetation Cover Affect Clay Mineral Formation

With the analysis of the sources and formation mechanism of the clay minerals in the sediment core from the Dalianhai lake in the Gonghe Basin,northeastern Tibet-Qinghai Plateau,clay mineral composition proxies,grain-size and carbonate contents have been employed for high-resolution study in order to reconstruct East Asian Summer Monsoon （EASM） over the northeastern Tibet-Qinghai Plateau during the lastdeglacial.The study also extended to establish a relationship between vegetation cover changes and erosion during the last 14.5 ka with pollen record and clay mineral proxies.Smectite/kaolinite and smectite/（illite＋chlorite） ratios allow us to assess hydrolysis conditions in lowlands and/or physical erosion process in highlands of the Gonghe Basin.Before 12.9 Cal ka BP,both mineralogical ratios show low values indicative of strong physical erosion in the basin with a dominant cold and dry phase.After 12.9 Cal ka BP,an increase in both mineralogical ratios indicates enhanced chemical weathering in the basin associated with a warm and humid climate.The beginning of Holocene is characterized by high smectite/（illite＋chlorite） and smectite/kaolinite ratios that is synchronous as with deposition of many peat laminae,implying the best warm and humid conditions specifically between 8.0 to 5.5 Cal ka BP.The time interval after 5.0 Cai ka BP is characterized by a return to high physical erosion and low chemical weathering with dry climate conditions in the basin.Comparing variations of clay mineral assemblages with previous pollen results,we observe a rapid response in terms of chemical weathering and physical erosion intensity to a modification of the vegetation cover in the basin.

Effects of Organic Anions on Phosphate Adsorption and Desorption from Variable-Charge Clay Minerals and Soil

Effects of citrate and tartrate on phosphate adsorption and desorption from kaolinite, goethite, amorphous Al-oxide and Ultisol were studied. P adsorption was significantly decreased as the concentration of the organic anions increased from 10-5 to 10-1 M. At 0.1 M and pH 7.0, tartrate decreased P adsorption by 27.6% - 50.6% and citrate by 37.9 - 80.4%, depending on the kinds of adsorbent. Little Al and/ or Fe were detected in the equilibrium solutions, even at the highest concentration of the organic anions. Effects of the organic anions on phosphate adsorption follow essentially the competitive adsorption mechanism.The selectivity coefficients for competitive adsorption can be used to compare the effectiveness of different organic anions in reducing P adsorption under given conditions.Phosphate desorption was increased by 3 to 100 times in the presence of 0.001 M citrate or tartrate compared to that in 0.02 M KC1 solution alone. However, for all the soil and clay minerals studied the amount of P desorbed by citrate or tartrate was generally lower than or close to that of isotopically exchangeable P. The effect of organic anions on phosphate desorption arises primarily from ligand exchange.

Characteristics of Clay Minerals in the Northern South China Sea and Its Implications for Evolution of East Asian Monsoon since Miocene

Clay mineral assemblages, crystallinity, chemistry, and micromorphology of clay particles in sediments from ODP Site 1146 in the northern South China Sea （SCS） were analyzed, and used to trace sediment sources and obtain proxy records of the past changes in the East Asian monsoon climate since the Miocene, based on a multi-approach, including X-ray diffraction （XRD） and scanning electron microscopy combined with energy dispersive X-ray spectrometry （SEM-EDS）. Clay minerals consist mainly of illite and smectite, with associated chlorite and kaolinite. The illite at ODP Site 1146 has very well-to-well crystallinity, and smectite has moderate-to-poor crystallinity. In SEM the smectite particles at ODP Site 1146 often appear cauliflower-like, a typical micromorphology of volcanic smecites. The smectite at ODP Site 1146 is relatively rich in Si element, but poor in Fe, very similar to the smectite from the West Philippine Sea. In contrast, the chemical composition of illite at ODP Site 1146 has no obvious differences from those of the Loess plateau, Yellow River, Yangtze River, and Pearl River. A further study on sediment source indicates that smectite originates mainly from Luzon, kaolinite from the Pearl River, and illite and chlorite from the Pearl River, Taiwan and/or the Yangtze River. The clay mineral assemblages at ODP Site 1146 were not only controlled by continental eathering regimes surrounding the SCS, but also by the changing strength of the transport processes. The ratios of （illite＋chlorite）/smectite at ODP Site 1146 were adopted as proxies for the East Asian monsoon evolution. Relatively higher ratios reflect strongly intensified winter monsoon relative to summer monsoon, in contrast, lower ratios indicate a strengthened summer monsoon relative to winter monsoon. The consistent variation of this clay proxy from those of Loess plateau, eolian deposition in the North Pacific, planktonic, benthic foraminifera, and black carbon in the SCS since 20 Ma shows that three profound shifts of the East Asian winter monsoon intensity, and aridity in the Asian inland and the intensity of winter monsoon relative to summer monsoon, occurred at about 15 Ma, 8 Ma, and the younger at about 3 Ma. The phased uplift of the Himalaya-Tibetan plateau may have played a significant role in strengthening the Asian monsoon at 15 Ma, 8 Ma, and 3 Ma.

Distribution and dispersal pattern of clay minerals in surface sediments,eastern Beibu Gulf,South China Sea

Clay minerology of sediments are useful in determining distribution, sources and dispersal routes of fine-grained sediments. In the present paper, clay minerals of surface sediments throughout the eastern part of Beibu Gulf has been investigated to reveal sources and transport of detrital fine- grained sediments. Four distinct clay mineral suites were observed from cluster analysis of clay mineral compositions of the samples. From the distribution pattern of clay minerals, we conclude that kaolinte in the eastern gulf is mainly derived from South China Landmass; Smectite could not be transported mainly by surface current from north-western Hainan Island, and maybe minor portion of it from Red River; Illite is mainly transported by the currents fl＇om South China Sea. Chlorite has two sources, namely South China Sea and South China Landmass. The Zhujiang River derived sediments could not be one of the sources for the clay mineral here, because of very different composition and ratios. The distribution pattern of clay minerals in the eastern Beibu Gulf is mainly controlled by fine-grained sediment source and local currents. The Silt/Clay, Smectite/Kaolinte, and Smetite/（Chlorite＋Illite） ratios could be used as indicators of fine-grained sediment dispersal in the gulf.

Characteristics of Lead Sorption on Clay Minerals in Relation to Metal Oxides

Difference of montmorillonite (Mt), illite (It) and kaolinite (Kt) in lead sorption characteristics and the effects of amorphous Fe and Al oxide coatings on the characteristics were experimentally studied with logistic model. The sorption curves had sigmoid feature due to use of acetate-type buffer solution. With the model the sorption process could be divided into four stages and the sorption characteristics at the stages were discussed. The results showed that, after Mt, It and Kt were coated by amorphous Fe oxide, their maximum sorption capacity (MSC) and percentage of high-SSC concentration scope (HCS) of Pb2+ increased markedly, but the specific sorption capacity (SSC) decreased. With regard to effects of amorphous Al oxide coating, except for It+AI, the SSC of other samples showed a downtrend, despite that their MSC remained unchanged. Eventually, the gray correlation degrees to Pb2+ sorption for different physicochemical characteristics of the clay minerals were indicated to be higher for hydronium, zero point of surface charge and hydroxy, but lower for specific surface area, density of surface charge and amount of surface charges.

Study of Adsorption Properties and Enriching RE on Clay Minerals by Ouantum Chemical Calculation

The order of adsorbability of three kinds of clay minerals and their selectivity of adsorption to common cations and RE ions have been studied by quantum chemical calculation.They are as follows: montmorilionite>halloysite>kaolinite,RE^(3+)>Al^(3+)>Ca^(2+)>Mg^(2+)>K^+>NH_4^+>Na^+,Sc^(3+)>La^(3+)> Ce^(3+)>Pr^(3+)>Nd^(3+)>Sm^(3+)>Eu^(3+)>Gd^(3+)>Tb^(3+)>Dy^(3+)>Ho^(3+)>Y^(3+)>Er^(3+)>Tm^(3+)>Yb^(3+)>Lu^(3+).Based on these orders,the facts that RE is preferentially adsorbed in weathered residual type of clay mineral and light RE and heavy RE are enriched at the upper layer and at the lower layer respectively in ore body have been explained.