Second kind Chebyshev operational matrix algorithm for solving differential equations of Lane–Emden type

In this paper, we present a new second kind Chebyshev (S2KC) operational matrix of derivatives. With the aid of S2KC, an algorithm is described to obtain numerical solutions of a class of linear and nonlinear Lane–Emden type singular initial value problems (IVPs). The idea of obtaining such solutions is essentially based on reducing the differential equation with its initial conditions to a system of algebraic equations. Two illustrative examples concern relevant physical problems (the Lane–Emden equations of the first and second kind) are discussed to demonstrate the validity and applicability of the suggested algorithm. Numerical results obtained are comparing favorably with the analytical known solutions.     

Hemispheric asymmetry of sunspot area in solar cycle 23 and rising phase of solar cycle 24: Comparison of three data sets

Analysis of long-term solar data from different observatories is required to compare and confirm the various level of solar activity in depth. In this paper, we study the north–south asymmetry of monthly mean sunspot area distribution during the cycle-23 and rising phase of cycle-24 using the data from Kodaikanal Observatory (KO), Michelson Doppler Imager (MDI) and Solar Optical Observing Network (SOON). Our analysis confirmed the double peak behavior of solar cycle-23 and the dominance of southern hemisphere in all the sunspot area data obtained from three different resources. The analysis also showed that there is a 5–6 months time delay in the activity levels of two hemispheres. Furthermore, the wavelet analysis carried on the same data sets showed several known periodicities (e.g., 170–180 days, 2.1 year) in the north–south difference of sunspot area data. The temporal occurrence of these periods is also the same in all the three data sets. These results could help in understanding the underlying mechanism of north–south asymmetry of solar activity.     

Glacier change in Garibaldi Provincial Park, southern Coast Mountains, British Columbia, since the Little Ice Age

Fluctuations of glaciers during the 20th century in Garibaldi Provincial Park, in the southern Coast Mountains of British Columbia, were reconstructed from historical documents, aerial photographs, and fieldwork. Over 505 km², or 26%, of the park, was covered by glacier ice at the beginning of the 18th century. Ice cover decreased to 297 km² by 1987–1988 and to 245 km² (49% of the early 18th century value) by 2005. Glacier recession was greatest between the 1920s and 1950s, with typical frontal retreat rates of 30 m/a. Many glaciers advanced between the 1960s and 1970s, but all glaciers retreated over the last 20 years. Times of glacier recession coincide with warm and relatively dry periods, whereas advances occurred during relatively cold periods. Rapid recession between 1925 and 1946, and since 1977, coincided with the positive phase of the Pacific Decadal Oscillation (PDO), whereas glaciers advanced during its negative phase (1890–1924 and 1947–1976). The record of 20th century glacier fluctuations in Garibaldi Park is similar to that in southern Europe, South America, and New Zealand, suggesting a common, global climatic cause. We conclude that global temperature change in the 20th century explains much of the behaviour of glaciers in Garibaldi Park and elsewhere.     

Investigation of inner-basin variation: Impact of large reservoirs on water regimes of downstream water bodies

Large dams and reservoirs alter not only the natural flow regimes of streams and rivers but also their flooding cycles and flood magnitudes. Although the effect of dams and reservoirs has been reported for some vulnerable locations, the understanding of the inner-basin variation with respect to the effects remains limited. In this study, we analyse the Three Gorges Dam (TGD) built on the Changjiang mainstream (Yangtze River) to investigate the dam effect variations in the system of interconnected water bodies located downstream. We investigated the effect of flow alterations along the downstream river network using discharge time series at different gauging stations. The river–lake interactions (referring to the interactions between the Changjiang mainstream and its tributary lakes i.e. the Dongting and Poyang lakes) and their roles in modifying the TGD effect intensity were also investigated in the large-scale river–lake system. The results show that the water storage of the tributary lakes decreased after the activation of the TGD. Severe droughts occurred in the lakes, weakening their ability to recharge the Changjiang mainstream. As a consequence, the effect of the TGD on the Changjiang flow increase during the dry season diminished quickly downstream of the dam, whereas its impact on the flow decrease during the wet season gradually exacerbated along the mainstream, especially at sites located downstream of the lake outlets. Therefore, when assessing dam-induced hydrological changes, special attention should be paid to the changes in the storage of tributary lakes and the associated effects in the mainstream. This is of high importance for managing the water resource trade-offs between different water bodies in dam-affected riverine systems.     

Preliminary 3–D geological model of the Kalgoorlie region,Yilgarn Craton,Western Australia,based on deep seismic‐reflection and potential‐field data

The granite‐greenstone terranes of the Eastern Goldfields Province, Yilgarn Craton, Western Australia, are a major Australian and world gold and nickel source. The Kalgoorlie region, in particular, hosts several world‐class gold deposits. To attempt to understand why these deposits occur where they do, it is important to understand the crustal architecture in the region and how the major mineral systems operate in this architecture. One way to understand these relationships is to develop a detailed 3–D geological model for the region. The best method to map the 3–D geometry of major geological structures is by acquisition and interpretation of seismic‐reflection profiles. To contribute to this aim, a grid of deep seismic‐reflection traverses was acquired in 1999 to examine the 3–D geometry of the region in an area including the Kalgoorlie mineral region and mineral fields to the north and west. This grid was tied to the 1991 regional deep seismic traverse and 1997 high‐resolution seismic profiles in the same region. The grid covers an area measuring approximately 50 km wide by 50 km long and extended to a depth of approximately 50 km (below the base of the crust in this region). The resulting 3–D geological model was further constrained by both surface geological data and geophysical interpretations, with the seismic interpretations themselves also constrained by gravity and magnetic modelling. The 3–D model was used to investigate the geometric relationships between the major faults and shear zones in the area, the relationship between the granite‐greenstone succession and the basement, and the spatial relationships between the greenstones and the granites. Interpretation of the grid of seismic lines and construction of the 3–D geological model confirmed the existence of the detachment surface and led to the recognition that the granite‐greenstone contact usually occurs at a much shallower level than the detachment. Also, west‐dipping faults in the vicinity of the Golden Mile, including the Abattoir Shear through to Boulder‐Lefroy Fault, appear to be more important than previously thought in controlling the structure of that area. An antiformal thrust stack occurs beneath a triangle zone centred on the Golden Mile. The Black Flag Group was deposited in a probable extensional setting, and late extension was also probably more important than previously thought. The granite‐gneiss domes were uplifted by the formation of antiformal thrust stacks at depth beneath them.     

The magmatic history of the Vetas-California mining district,Santander Massif,Eastern Cordillera,Colombia

The Vetas-California Mining District (VCMD), located in the central part of the Santander Massif (Colombian Eastern Cordillera), based on U–Pb dating of zircons, records the following principal tectono-magmatic events: (1) the Grenville Orogenic event and high grade metamorphism and migmatitization between ∼1240 and 957 Ma; (2) early Ordovician calc–alkalic magmatism, which was synchronous with the Caparonensis–Famatinian Orogeny (∼477 Ma); (3) middle to late Ordovician post-collisional calc–alkalic magmatism (∼466–436 Ma); (4) late Triassic to early Jurassic magmatism between ∼204 and 196 Ma, characterized by both S- and I-type calc–alkalic intrusions and; (5) a late Miocene shallowly emplaced intermediate calc–alkaline intrusions (10.9 ± 0.2 and 8.4 ± 0.2 Ma). The presence of even younger igneous rocks is possible, given the widespread magmatic–hydrothermal alteration affecting all rock units in the area.The igneous rocks from the late Triassic–early Jurassic magmatic episodes are the volumetrically most important igneous rocks in the study area and in the Colombian Eastern Cordillera. They can be divided into three groups based on their field relationships, whole rock geochemistry and geochronology. These are early leucogranites herein termed Alaskites-I (204–199 Ma), Intermediate rocks (199–198 Ma), and late leucogranites, herein referred to as Alaskites-II (198–196 Ma). This Mesozoic magmatism is reflecting subtle changes in the crustal stress in a setting above an oblique subduction of the Panthalassa plate beneath Pangea.The lower Cretaceous siliciclastic Tambor Formation has detrital zircons of the same age populations as the metamorphic and igneous rocks present in the study area, suggesting that the provenance is related to the erosion of these local rocks during the late Jurassic or early Cretaceous, implying a local supply of sediments to the local depositional basins.     

东昆仑东段到木提岩体成因及构造意义：来自年代学及地球化学的约束

到木提岩体位于东昆仑造山带东段,主要岩性有二长花岗岩、花岗闪长岩及闪长岩。笔者对新发现的闪长岩进行了锆石U–Pb测年和岩石地球化学测试,以确定其形成时代及岩石成因,结合二长花岗岩和花岗闪长岩的岩石地球化学特征,综合探讨到木提岩体的侵位时代、岩石成因及构造演化程。LA–ICP–MS锆石U–Pb测年获得的闪长岩206Pb/238U年龄为（244.6±1.8）Ma,到木提闪长岩体结晶时代为早三叠世。二长花岗岩和花岗闪长岩的地球化学特征显示：里特曼指数小于3.3,具钙碱性–高钾钙碱性特征;铝饱和指数A/CNK值均小于1.1;岩石中P2O5含量普遍较低,且与SiO2含量呈负相关性;富集K、Rb、La等LILE,亏损Nb、Ta、Ti、P等HFSE。地球化学特征表明,到木提岩体属于I型花岗岩。综合分析认为,东昆仑东段到木提岩体是下地壳岩石发生部分熔融形成的火山弧花岗岩,阿尼玛卿洋俯冲作用可以持续到早—中三叠世,俯冲过程中形成区域性的地幔岩浆底侵就是导致下地壳熔融的热源,且幔源岩浆不同程度混入到到木提岩浆演化中,岩浆演化中伴有一定的结晶分异发生。     

Paleoproterozoic juvenile magmatism within the northeastern sector of the São Francisco paleocontinent: Insights from the shoshonitic high Ba–Sr Montezuma granitoids

New,integrated petrographic,mineral chemistry,whole rock geochemical,zircon and titanite UPb geochronology,and zircon Hf isotopic data from the Montezuma granitoids,as well as new geochemical results for its host rocks represented by the Corrego Tingui Complex,provides new insights into the late-to post-collisional evolution of the northeastern Sao Francisco paleocontinent.U-Pb zircon dates from the Montezuma granitoids spread along the Concordia between ca.2.2 Ga to 1.8 Ga and comprise distinct groups.Group I have crystallization ages between ca.2.15 Ga and 2.05 Ga and are interpreted as inherited grains.Group II zircon dates vary from 2.04 Ga to1.9 Ga and corresponds to the crystallization of the Montezuma granitoids,which were constrained at ca.2.03 Ga by the titanite U-Pb age.Inverse age zoning is common within the ca.1.8 Ga Group III zircon ages,being related to fluid isotopic re-setting during the Espinhaco rifiting event.Zircon ε_(Hf)(t) analysis show dominantly positive values for both Group I(-4 to+9) and Ⅱ(-3 to+8) zircons and T_(DM2) model ages of 2.7-2.1 Ga and 2.5-1.95 Ga,respectively.Geochemically,the Montezuma granitoids are weakly peraluminous to metaluminous magnesian granitoids,enriched in LILES and LREE,with high to moderate Mg#and depleted in some of the HFSE.Their lithochemical signature,added to the juvenile signature of both inherited and crystallized zircons,allowed its classification as a shoshonitic high Ba-Sr granitoid related to a late-to post-collisional lithosphere delamination followed by asthenospheric upwelling.In this scenario,the partial melting of the lithospheric mantle interacted with the roots of an accreted juvenile intra-oceanic arc,being these hybrid magma interpreted as the source of the Montezuma granitoids.The Corrego Tingui Complex host rocks are akin to a syn-to late-collisional volcanic arc granitoids originated from the partial melting of ancient crustal rocks.The results presented in this study have revealed the occurrence of juvenile rocks,probably related to an island arc environment,that are exotic in relation to the Paleo-to Neoarchean crust from the Sao Francisco paleocontinent's core.     

Late Pleistocene paleoclimatic history documented by an oxygen isotope record from carbonate sediments in Qarhan Salt Lake,NE Qinghai–Tibetan Plateau

Late Pleistocene paleoclimatic variability on the northeastern Qinghai–Tibetan Plateau (NE QTP) was reconstructed using a chronology based on AMS ¹⁴C and ²³⁰Th dating results and a stable oxygen isotopic record. These are derived from lake carbonates in a 102-m-long Qarhan sediment core (ISL1A) collected from the eastern Qaidam Basin. Previous research indicates that the δ¹⁸O values of lacustrine carbonates are mainly controlled by the isotopic composition of lake water, which in turn is a function of regional P/E balance and the proportion of precipitation that is monsoon-derived on the NE QTP. Modern isotopic observations indicate that the δ¹⁸O values of lake carbonates in hyper-arid Qaidam Basin are more positive during the warm and wet period. Due to strong evaporation and continental effect in this basin, the positive δ¹⁸O values in the arid region indicate drier climatic conditions. Based on this interpretation and the δ¹⁸O record of fine-grained lake carbonates and dating results in ISL1A, the results imply that drier climatic conditions in the Qarhan region occurred in three intervals, around 90–80 ka, 52–38 ka and 10–9 ka, which could correspond to late MIS 5, middle MIS 3 and early Holocene, respectively. These three phases were almost coincided with low lake level periods of Gahai, Toson and Qinghai Lakes (to the east of Qarhan Lake) influenced by ASM on the orbital timescales. Meanwhile, there was an episode of relatively high δ¹⁸O value during late MIS 3, suggesting that relatively dry climatic condition in this period, rather than “a uniform Qarhan mega-paleolake” spanning the ∼44 to 22 ka period. These results insight into the understanding of “the Greatest Lake Period” on the QTP.     

Artificial neural network model for prediction of rock properties from sound level produced during drilling

In many rock engineering applications such as foundations, slopes and tunnels, the intact rock properties are not actually determined by laboratory tests, due to the requirements of high quality core samples and sophisticated test equipments. Thus, predicting the rock properties by using empirical equations has been an attractive research topic relating to rock engineering practice for many years. Soft computing techniques are now being used as alternative statistical tools. In this study, artificial neural network models were developed to predict the rock properties of the intact rock, by using sound level produced during rock drilling. A database of 832 datasets, including drill bit diameter, drill bit speed, penetration rate of the drill bit and equivalent sound level (L_eq) produced during drilling for input parameters, and uniaxial compressive strength (UCS), Schmidt rebound number (SRN), dry density (ρ), P-wave velocity (V_p), tensile strength (TS), modulus of elasticity (E) and percentage porosity (n) of intact rock for output, was established. The constructed models were checked using various prediction performance indices. Goodness of the fit measures revealed that recommended ANN model fitted the data as accurately as experimental results, indicating the usefulness of artificial neural networks in predicting rock properties.