Fitting the Linear Model of Coregionalization by Generalized Least Squares

In geostatistical studies, the fitting of the linear model of coregionalization (LMC) to direct and cross experimental semivariograms is usually performed with a weighted least-squares (WLS) procedure based on the number of pairs of observations at each lag. So far, no study has investigated the efficiency of other least-squares procedures, such as ordinary least squares (OLS), generalized least squares (GLS), and WLS with other weighing functions, in the context of the LMC. In this article, we compare the statistical properties of the sill estimators obtained with eight least-squares procedures for fitting the LMC: OLS, four WLS, and three GLS. The WLS procedures are based on approximations of the variance of semivariogram estimates at each distance lag. The GLS procedures use a variance–covariance matrix of semivariogram estimates that is (i) estimated using the fourth-order moments with sill estimates (GLS₁), (ii) calculated using the fourth-order moments with the theoretical sills (GLS₂), and (iii) based on an approximation using the correlation between semivariogram estimates in the case of spatial independence of the observations (GLS₃). The current algorithm for fitting the LMC by WLS while ensuring the positive semidefiniteness of sill matrix estimates is modified to include any least-squares procedure. A Monte Carlo study is performed for 16 scenarios corresponding to different combinations of the number of variables, number of spatial structures, values of ranges, and scale dependence of the correlations among variables. Simulation results show that the mean square error is accounted for mostly by the variance of the sill estimators instead of their squared bias. Overall, the estimated GLS₁ and theoretical GLS₂ are the most efficient, followed by the WLS procedure that is based on the number of pairs of observations and the average distance at each lag. On that basis, GLS₁ can be recommended for future studies using the LMC.     

Numerical model of convection in sills

The numerical model of convection in magma sills is developed. The model is based on a full system of equations of fluid dynamics and includes heat transfer, buoyancy effects and diffusion of some minor component (marker). Solidification is treated as a phase transition. The results indicate that there are some qualitative differences between very thin sills with Rayleigh number Ra = 10⁵ and thin sills with Ra = 10⁶. For a basaltic magma the first case corresponds to the thickness of the sills of approximately 30 cm and the second case corresponds to the thickness of 60 cm. In the first case mixing is inefficient and conduction is the dominant form of heat transfer. In the second case mixing is efficient and convection is the dominant form of heat transfer. Some of the results can be scaled for the more viscous magmas in thicker sills.     

Early Eocene leucocratic sill/dike swarms in the Gangdese belt,southern Tibet: Tectonic implications for Indo-Asian collision

The timing of the initial Indo-Asian collision is a subject of debate for a long time. Besides, the magmatic trace of the collisional process is also unclear. In the present study, the authors report Early Eocene leucocratic sill/dike swarms in the northern edge of the Nymo intrusive complex of the Gangdese belt, southern Tibet. The Nymo intrusive complex was emplaced at ca. 50 –47 Ma and surrounded by the metamorphosed Jurassic-aged Bima Formation volcano-sedimentary sequence along its northern side. At outcrops, the leucocratic sills/dikes intruded along or truncated the deformed foliations of the host Bima Formation, which has been subject to high-temperature amphibolite-facies metamorphism at ca. 50 –47 Ma. Detailed cathodoluminescence image analyses reveal that the zircon grains of the leucocratic sills/dikes have core-mantle textures. The cores yield the Jurassic ages comparable to the protolith ages of the Bima Formation. In contrast, the mantles of zircon grains yield weighted mean ages of ca. 49–47 Ma, representing the crystallization timing of these leucocratic sills/dikes. The coeval ages for the Nymo intrusive complex, the high-temperature metamorphism, and the leucocratic sills/dikes indicate that a close relationship exists among them. The authors tentatively suggest that these leucocratic sills/dikes were generated from partial melting of the Jurassic-aged Bima Formation volcanic rocks, triggered by the high heat from the magma chamber of the Nymo intrusive complex. This Early Eocene tectono-thermal event of coeval magmatism, metamorphism and partial melting was most likely formed during the Indo-Asian collisional setting.©2021 China Geology Editorial Office.     

The variogram sill and the sample variance

The relationship between the sill of the variogram and the sample variance is explored. The common practice of using the sample variance as an estimate of the variogram sill is questioned, and a conceptual framework for determining the appropriateness of this heuristic is constructed.     

Petrology and geochemistry of the Karaj Dam basement sill: Implications for geodynamic evolution of the Alborz magmatic belt

The northeastward subduction of the Neo-Tethyan oceanic lithosphere beneath the Iranian block produced vast volcanic and plutonic rocks that now outcrop in central (Urumieh–Dokhtar magmatic assemblage) and north–northeastern Iran (Alborz Magmatic Belt), with peak magmatism occurring during the Eocene. The Karaj Dam basement sill (KDBS), situated in the Alborz Magmatic Belt, comprises gabbro, monzogabbro, monzodiorite, and monzonite with a shoshonitic affinity. These plutonic rocks are intruded into the Karaj Formation, which comprise pyroclastic rocks dating to the lower–upper Eocene. The geochemical and isotopic signatures of the KDBS rocks indicate that they are cogenetic and evolved through fractional crystallization. They are characterized by an enrichment in LREEs relative to HREEs, with negative Nb–Ta anomalies. Geochemical modeling using Sm/Yb versus La/Yb and La/Sm ratios suggests a low-degree of partial melting of a phlogopite–spinel peridotite source to generate the KDBS rocks. Their low I_Sr = 0.70453–0.70535, ɛNd (37.2 Ma) = 1.54–1.9, and T_DM ages ranging from 0.65 to 0.86 Ga are consistent with the melting of a Cadomian enriched lithospheric mantle source, metasomatized by fluids derived from the subducted slab or sediments during magma generation. These interpretations are consistent with high ratios of ²⁰⁶Pb/²⁰⁴Pb = 18.43–18.67, ²⁰⁷Pb/²⁰⁴Pb = 15.59, and ²⁰⁸Pb/²⁰⁴Pb = 38.42–38.71, indicating the involvement of subducted sediments or continental crust. The sill is considered to have been emplaced in an environment of lithospheric extension due to the slab rollback in the lower Eocene. This extension led to localized upwelling of the asthenosphere, providing the heat required for partial melting of the subduction-contaminated subcontinental lithospheric mantle beneath the Alborz magmatic belt. Then, the shoshonitic melt generates the entire spectrum of KDBS rocks through assimilation and fractional crystallization during the ascent of the magma.     

Episodic fluid flow as a trigger for Miocene‐Pliocene slope instability on the Utgard High,Norwegian Sea

Mass wasting is triggered on many continental slopes by a number of mechanisms, including seismic shaking, high sedimentation rates, the presence of weak geological units and gas hydrate dissociation. In this study, the morphology of a Late Miocene–Early Pliocene mass‐transport complex (MTC) on the Utgard High is unravelled and discussed in relation to possible trigger mechanisms. The approach used here includes 3D seismic interpretation and the analysis of variance attribute maps. The interpreted MTC is located on the crest and flanks of the Utgard High and is composed of three mass‐transport deposits with seismic characters varying from transparent and chaotic seismic facies at the base to slightly deformed layers composed of mounds and rafted blocks in the middle and chaotic to transparent reflections at the top. Lithologically, the MTC consists predominantly of claystone with high gamma ray and low density and resistivity values, demonstrating that the associated mounds represent remobilized ooze sediments. A vertical stack of six magmatic sills emplaced from 55.6 to 56.3 Ma into the Upper Cretaceous shales is interpreted at depths of 3,000–5,500 ms two‐way travel time (TWTT). In association with these magmatic sills are several hydrothermal vent complexes that interacted with the top MTC horizon, signifying that episodic and secondary fluid‐venting events might be the principal mechanism facilitating mass wasting in the study area. In addition, the remobilization of ooze sediments into mounds is hypothesized to be dependent on fluids and clayey layers. As a corollary of this work, the importance of relict and recurrent episodes of fluid flow in the Vøring Basin and their influence on the geotechnical integrity of the overburden and later mass wasting is established.     

武当地块基性岩席群及其地质意义

侵位于武当地块内部的大量的板状为基性侵入体近年来一直被认为是800Ma左右发生的扬子古大陆裂解的重要依据。然而作者在武当地块北缘与西南部所做的1：5万地质填图以及相应的构造学和同位素年代学研究表明，它们与武当地块顺层伸展滑脱构造主滑脱面之顺层韧性一韧性变形带有密切的空间关系，是被褶皱了的岩席群。最新获得的岩体单颗粒锆石U－Pb年龄为401－407Ma，结合已有的地球化学研究成果，并考虑到邻区同时代碱性岩浆的侵位，作者认为，这套基性岩群代表了泥盆纪时南秦岭地区曾发生过大规模的上地幔岩浆的底侵作用，并因此导致南秦岭上部地壳的伸展减薄。     

1891–1883 Ma Southern Bastar–Cuddapah mafic igneous events, India: A newly recognized large igneous province

A newly recognized remnant of a Paleoproterozoic Large Igneous Province has been identified in the southern Bastar craton and nearby Cuddapah basin from the adjacent Dharwar craton, India. High precision U–Pb dates of 1891.1 ± 0.9 Ma (baddeleyite) and 1883.0 ± 1.4 Ma (baddeleyite and zircon) for two SE-trending mafic dykes from the BD2 dyke swarm, southern Bastar craton, and 1885.4 ± 3.1 Ma (baddeleyite) for a mafic sill from the Cuddapah basin, indicate the existence of 1891–1883 Ma mafic magmatism that spans an area of at least 90,000 km² in the south Indian shield.This record of 1.9 Ga mafic/ultramafic magmatism associated with concomitant intracontinental rifting and basin development preserved along much of the south-eastern margin of the south Indian shield is a widespread geologic phenomenon on Earth. Similar periods of intraplate mafic/ultramafic magmatism occur along the margin of the Superior craton in North America (1.88 Ga Molson large igneous province) and in southern Africa along the northern margin of the Kaapvaal craton (1.88–1.87 Ga dolerite sills intruding the Waterberg Group). Existing paleomagnetic data for the Molson and Waterberg 1.88 Ga large igneous provinces indicate that the Superior and Kalahari cratons were at similar paleolatitudes at 1.88 Ga but a paleocontinental reconstruction at this time involving these cratons is impeded by the lack of a robust geological pin such as a Limpopo-like 2.0 Ga deformation zone in the Superior Province. The widespread occurrence of 1.88 Ga intraplate and plate margin mafic magmatism and basin development in numerous Archean cratons worldwide likely reflects a period of global-scale mantle upwelling or enhanced mantle plume activity at this time.