Using Simultaneous Diagonalization to Identify a Space–Time Linear Coregionalization Model

Although there are multiple methods for modeling matrix covariance functions and matrix variograms in the geostatistical literature, the linear coregionalization model is still widely used. In particular it is easy to check to ensure whether the matrix covariance function is positive definite or that the matrix variogram is conditionally negative definite. One of the difficulties in using a linear coregionalization model is in determining the number of basic structures and the corresponding covariance functions or variograms. In this paper, a new procedure is given for identifying the basic structures of the space–time linear coregionalization model and modeling the matrix variogram. This procedure is based on the near simultaneous diagonalization of the sample matrix variograms computed for a set of spatiotemporal lags. A case study using a multivariate spatiotemporal data set provided by the Environmental Protection Agency of Lombardy, Italy, illustrates how nearly simultaneous diagonalization of the empirical matrix variograms simplifies modeling of the matrix variograms. The new methodology is compared with a previous one by analyzing various indices and statistics.     

Estimation of Sill Matrices in the Linear Model of Coregionalization

When using least squares to fit the linear model of coregionalization to multivariate geostatistical data, the sill matrices for the different regions must be estimated, subject to the constraint that they be non-negative definite. In 1992, Goulard and Voltz proposed and empirically examined an iterative algorithm for doing this. Although no proof was given for its convergence or for the uniqueness of the solution to the problem, the algorithm has subsequently been extensively and successfully used. In this paper, we prove that the minimization problem, in fact, has a unique solution and that the algorithm is guaranteed to converge to it from any starting point. We also discuss the effect of the starting point on the speed of convergence.     

Relativistic Metrology of Near-Earth Space–Time and Its Practical Applications

Astronomy Reports - Results of studies of relativistic effects for the time and frequency shifts for an Earth–satellite system of atomic clocks, and also for moving clocks on the Earth, are...     

Geostatistical Space–Time Models: A Review

Geostatistical space–time models are used increasingly for addressing environmental problems, such as monitoring acid deposition or global warming, and forecasting precipitation or stream flow. Each discipline approaches the problem of joint space–time modeling from its own perspective, a fact leading to a significant amount of overlapping models and, possibly, confusion. This paper attempts an annotated survey of models proposed in the literature, stating contributions and pinpointing shortcomings. Stochastic models that extend spatial statistics (geostatistics) to include the additional time dimension are presented with a common notation to facilitate comparison. Two conceptual viewpoints are distinguished: (1) approaches involving a single spatiotemporal random function model, and (2) approaches involving vectors of space random functions or vectors of time series. Links between these two viewpoints are then revealed; advantages and shortcomings are highlighted. Inference from space–time data is revisited, and assessment of joint space–time uncertainty via stochastic imaging is suggested.     

Space–Time Mathematical Framework for Sedimentary Geology

Interpolating physical properties in the subsurface is a recurrent problem in geology. In sedimentary geology, the geometry of the layers is generally known with a precision much superior to that which one can reasonably expect for the properties. The geometry of the layers is affected by folding and faulting since the time of deposition, whereas the distribution of properties is, to a certain extent, determined at the time of deposition. As a consequence, it may be wise to model first the geometry of the layers and then, simplify the geologic equation by removing the influence of that geometry. Inspired from the work of H. E. Wheeler on Time-Stratigraphy, we define, mathematically, a new space where all horizons are horizontal planes and where faults, if any, have disappeared. We surmise that this new space, however approximative, is better to model physical properties of the subsurface whatever the subsequent interpolation method used. The proposed mathematical framework also provides solutions to complex problems such as determination of strains resulting from tectonic events and up-scaling of permeabilities on structured and unstructured 3D grids.     

The Hissar–Alay and the Pamirs: Deep-Seated Structure,Geodynamic Model,and Experimental Evidence

The structural and geodynamic features of the Pamirs and the Hissar–Alay have been revealed based on geological and geophysical evidence supplemented by experimental data. It has been shown that both the Pamirs and the Hissar–Alay are geodynamic systems, the formation of which is related to interference of two geodynamic regimes: (i) global orogeny covering extensive territories of Eurasia and determining their similarity and (ii) regional regimes differing for the Pamirs and the Alay, which act independently within Central Asian and Apline–Himalayan mobile belts, respectively. The Pamirs do not act as an indentor during the formation of structure of the Hissar–Alay and areas to the north. It is stated that the Pamir–Alay segment of Asia is a reflection of the geodynamic countermotion setting (3D flow of mountain masses) of several distinct segments of the continental lithosphere, while the Pamirs are an intracontinental subduction domain at the surface, which represents a special tectonic–geodynamic type of structures.     

New Validity Conditions for the Multivariate Matérn Coregionalization Model,with an Application to Exploration Geochemistry

Mathematical Geosciences - This paper addresses the problem of finding parametric constraints that ensure the validity of the multivariate Matérn covariance for modeling the spatial...     

Calculation of the CO2 Degassing during Contact Metamorphism and Its Geological Significance: The Model and Example from the Shuanshan Area of the South Tan–Lu Fault Belt

The paper studies CO2 degassing and controlling factors under the condition of contact metamorphism in the Shuangshan area, southern Tan-Lu fault belt and the method of calculating the amount of CO2 degassing. The results show that the amount of CO2 degassing is controlled by the characteristics of the country rocks, including the thermal conductivity, penetrability, porosity and connectivity. Compositions, size and depth of intrusive rock also have an important influence on CO2 degassing, i.e., they generated numerous cracks in the country rocks, and thus allowed the easy flow and accumulation of fluids. The amount of CO2 flux in contact metamorphism is calculated quantitatively based on the metamorphic reaction and time-integrated fluid flux. The value （0.729- 2.446×10^4 mol/cm^2） of CO2 flux suggests that CO2 was provided mainly by the contact metamorphic reaction. The generation and releasing of CO2 are positively correlated with the degree of metamorphism, and XCO2 in fluids gradually increases from dolomite zone to calcite zone, but in the zone of grossular, fluid flux is the largest and XCO2 sharply decreases due to involvement of magmatic water. This study presents evidence that a large amount of industrial-scale CO2 can be produced during contact metamorphism. On the basis of theoretical and practical studies, a cone model has been proposed to response CO2 degassing for the contact metamorphism, and it can be used to explore CO2 accumulations beyond the oil-gas basins. This model can also be applied to the study of inorganic genesis of CO2 accumulations.     

Time scales and length scales in magma flow pathways and the origin of magmatic Ni–Cu–PGE ore deposits

Ore forming processes involve the redistribution of heat, mass and momentum by a wide range of processes operating at different time and length scales. The fastest process at any given length scale tends to be the dominant control. Applying this principle to the array of physical processes that operate within magma flow pathways leads to some key insights into the origins of magmatic Ni–Cu–PGE sulfide ore deposits. A high proportion of mineralised systems, including those in the super-giant Noril'sk-Talnakh camp, are formed in small conduit intrusions where assimilation of country rock has played a major role. Evidence of this process is reflected in the common association of sulfides with vari-textured contaminated host rocks containing xenoliths in varying stages of assimilation. Direct incorporation of S-bearing country rock xenoliths is likely to be the dominant mechanism for generating sulfide liquids in this setting. However, the processes of melting or dissolving these xenoliths is relatively slow compared with magma flow rates and, depending on xenolith lithology and the composition of the carrier magma, slow compared with settling and accumulation rates. Chemical equilibration between sulfide droplets and silicate magma is slower still, as is the process of dissolving sulfide liquid into initially undersaturated silicate magmas. Much of the transport and deposition of sulfide in the carrier magmas may occur while sulfide is still incorporated in the xenoliths, accounting for the common association of magmatic sulfide-matrix ore breccias and contaminated “taxitic” host rocks. Effective upgrading of so-formed sulfide liquids would require repetitive recycling by processes such as re-entrainment, back flow or gravity flow operating over the lifetime of the magma transport system as a whole. In contrast to mafic-hosted systems, komatiite-hosted ores only rarely show an association with externally-derived xenoliths, an observation which is partially due to the predominant formation of ores in lava flows rather than deep-seated intrusions, but also to the much shorter timescales of key component systems in hotter, less viscous magmas. Nonetheless, multiple cycles of deposition and entrainment are necessary to account for the metal contents of komatiite-hosted sulfides. More generally, the time and length scale approach introduced here may be of value in understanding other igneous processes as well as non-magmatic mineral systems.     

The tectonics and stages of the geological history of the Yenisei–Khatanga Basin and the conjugate Taimyr Orogen

A new interpretation of the seismic profile series for the Taimyr Orogen and the Yenisei–Khatanga Basin is given in terms of their tectonics and geological history. The tectonics and tectonostratigraphy of the Yenisei–Khatanga and the Khatanga–Lena basins are considered. In the Late Vendian and Early Paleozoic, a passive continental margin and postrift shelf basin existed in Taimyr and the Yenisei–Khatanga Basin. From the Early Carboniferous to the Mid-Permian, the North and Central Taimyr zones were involved in orogeny. The Late Paleozoic foredeep was formed in the contemporary South Taimyr Zone. In the Middle to Late Triassic, a new orogeny took place in the large territory of Taimyr and the Noril’sk district of the Siberian Platform. A synorogenic foredeep has been recognized for the first time close to the Yenisei–Khatanga Basin. In the Jurassic and Early Cretaceous, this basin was subsided under transpressional conditions. Thereby, anticlinal swells were formed from the Callovian to the Aptian. Their growth continued in the Cenozoic. The Taimyr Orogen underwent tectonic reactivation and apparently right-lateral transpression from Carboniferous to Cenozoic.     

The Ordovician Gabbro–Tonalite–Trondhjemite Complex and Associated Volcanic Rocks in the Paleozoic Suture between the Urals and Kazakhstan

Doklady Earth Sciences - This paper reports new data on the Early Ordovician age established for granitoids of the gabbro—tonalite–trondhjemite complex in the Denisovka ophiolite zone...     

The Ni–Antimonide Mineral Assemblage: A Product of Recrystallization of Sn–Pb–Zn Ores of the Yuzhnoe Deposit,Sikhote-Alin,Russia

Doklady Earth Sciences - A mineral assemblage with nisbite NiSb2 and breithauptite NiSb unique for a Mesozoic (Sn)–Pb–Zn vein deposit is found during mineralogical–geochemical...     

The seismicity of the Gunning and surrounding areas, 1958–1961

Between October 1958 and August 1961, 98 tremors were located within 100 km. of Yass, New South Wales, of which 52 were in the vicinity of Gunning. Many of the epicentres appear to be closely associated with granite boundaries and with known faults in the area. The Gunning epicentres form two arms of a wedge, and activity oscillates between these arms. Temporary cessation of activity at Gunning is often accompanied by an increase in the frequency of events in the surrounding areas, which suggests that the wedge acts as a “safety valve” for the region.

Only one tremor was observed in the vicinity of Lake George. Fault plane analysis of the tremor gave a solution consistent with movement on a meridional high angle fault. It is inferred that recent movement on the Lake George Fault has been largely eliminated by the formation of the Gunning wedge.     

Space–time analysis, faulting and triggering of the 2010 earthquake doublet in western Corinth Gulf

Two moderate magnitude earthquakes (M5.5 and M5.4) occurred in January 2010 with their epicenters at a distance of about 5?km between them, in the western part of the Corinth Gulf. The recordings of the regional seismological network, which is dense locally, were used for the location of the two main events and aftershocks, which are concentrated in three clusters beneath the northern coasts of the Gulf. The first two clusters accompany each one of the two stronger earthquakes, whereas the third cluster comprises only low magnitude aftershocks, located westward of the two stronger events. Seismic excitation started in January 18, 2010, with the M?=?5.5 earthquake in the area occupied by the central cluster. Seismicity immediately jumped to the east with numerous aftershocks and the M?=?5.4 earthquake which occurred four days later (January 22, 2010). Cross sections normal to the long axis of each cluster show ruptures on north dipping faults at depths of 7?C11?km. Focal mechanisms of the stronger events of the sequence support the results obtained from the spatial distribution of the aftershocks that three different fault segments activated in this excitation. The slip vectors of all the events have an NNW?CSSE to NNE?CSSW orientation almost parallel to the direction of extension along the Corinth Gulf. Calculation of the Coulomb stress changes supports an interaction between the different clusters, with the major activity being coincided with the area of positive induced stress changes after the first earthquake.     

Experiment and Pitzer Model Prediction for the Solid + Liquid Equilibria of the Ternary System LiCl–CaCl2–H2O

正1 Introduction Lithium resources are widely distributed in the oilfield brine from the Nanyishan district in the Qaidam Basin(Fan et al.,2007).The investigation of the thermodynamics and phase diagram of the brine system is valuable in providing the theoretic foundation and scientific guidance in the comprehensive exploitation of the mixture salts effectively.Comprehensive     

The Thakkhola–Mustang graben in Nepal and the late Cenozoic extension in the Higher Himalayas

The Thakkhola–Mustang graben is located at the northern side of the Dhaulagiri and Annapurna ranges in North Central Nepal. The structural pattern is mainly characterised by the N020–040° Thakkhola Fault system responsible for the development of the half-graben. A detailed study of the substrate and the sedimentary fill in several outcrops indicates polyphased faulting:-pre-sedimentation faulting (Miocene), with a mainly NNW–SSE to N–S compressional stress expressed in the substratum by N020–040° and N180–N010° sinistral and N130–140° dextral conjugate strike-slip faults;-syn-sedimentation faulting (Pliocene–Pleistocene), characterised by a W–E to WNW–ESE extensional stress and tectonic subsidence of the half-graben during the Tetang period (Pliocene probably), followed by a doming of the Tetang deposits and a short period of erosion (cf. Pliocene planation surface and unconformity between the Tetang and Thakkhola Formations); the Thakkhola period (Pleistocene) is characterized by a W–E to WNW–ESE extensional stress and a major subsidence of the half graben;-post-sedimentation recurrent extensional faulting and N–S and NE–SW normal faults in the late Quaternary terrace formations.Geodynamic interpretation of the faulting is discussed in relation to the following:

• 1.the geographic situation of the Thakkhola–Mustang half-graben in the southern part of Tibet and its setting in the Tethyan series above the South Tibetan Detachment System (STDS);
• 2.the geodynamic conditions of the convergence between India and Eurasia and the dextral east–west shearing between the High Himalayas and south Tibet;
• 3.the possible relations between the sinistral Thakkhola and the dextral Karakorum strike-slip faults in a N–S compressional stress regime during the Miocene.

     

The Verkhoyansk–Chukchi area of the recent orogeny: zoning and the main formation stages

The Verkhoyansk–Chukchi orogenic area formed on the vast land mass that had appeared as a result of collision in the Early Cretaceous and that had consolidated the Mesozoic protoorogenic structures in northeastern Asia. This heterostructural land mass was the basis on which spatially and structurally coupled orogens developed in the late Mesozoic and Cenozoic. The protoorogenic stages in the evolution of the Verkhoyansk–Chukchi area were followed by several large orogenic stages: Albian–Cenomanian, Eocene, and Pliocene–Quaternary. The Okhotsk–Chukchi volcanic-block and the Yana–Kolyma fold-block orogenic systems formed at stage 1. The Taui–Anadyr continental-margin rift system formed at stage 2. This shaped the structure of the Verkhoyansk–Chukchi area. The internal structure of the orogenic systems formed through the Pliocene–Quaternary (neotectonic) stage, which was dominated by uplifting throughout the Verkhoyansk–Chukchi area. The neotectonic structure was mostly inherited from the previous orogenic stages.     

The Early Mesozoic NE–SW Extensional Model and Exhumation Processes at the Southeastern Margin of the Central Asian Orogenic Belt: Insights from the Strain and Kinematic Vorticity Analysis of the Sonid Zuoqi Ductile Detachment Zone

The Sonid Zuoqi ductile detachment zone is located at the southeastern margin of the Central Asian orogenic belt (CAOB), striking EW and dipping to the S. The major rock type of the Sonid Zuoqi ductile detachment zone is mylonite derived from granite. The sequence of mylonite features is: (1) S and C foliations of mylonite, and (2) extensional crenulation cleavage (ecc) or C′ and the kinematic vorticity (Wk) value changed from 0.70 to 0.95 and from 0.37 to 0.69, respectively; the strain type of the mylonites within the Sonid Zuoqi ductile detachment zone is compressional to planar strain. The strong deformation mylonite and Halatu plutons yielded a zircon U-Pb age of 244 Ma and a zircon (U-Th)/He age of 214 Ma, respectively. Based on the strain and kinematic vorticity analysis, together with the zircon U-Pb and zircon (U-Th)/He ages and the regional tectonic background, the study area experienced three stage evolution: tangential simple-shear (244 Ma), simple-shear-dominated general shear represented by upper crustal extension (224 Ma) and pure–shear–dominated general shear represented by the Halatu pluton doming (214 Ma), which constrained the early Mesozoic NE–SW crustal extension at the southeastern margin of the CAOB. This NE–SW extension probably originated from the post-orogenic extensional collapse of the CAOB, subsequent exhumation being controlled by the far afield effects of the closure of the Mongol–Okhotsk belt.     

Time constraints on the closure of the Paleo–South China Ocean and the Neoproterozoic assembly of the Yangtze and Cathaysia blocks: Insight from new detrital zircon analyses

The South China Block was built up by the assembly of the Yangtze and Cathaysia blocks along the Neoproterozoic Jiangnan Orogenic Belt. The timing of the Jiangnan Orogeny remains controversial. The widespread orogeny–related Neoproterozoic angular unconformity that separates the underlying folded Sibao (ca.1000–820 Ma) and overlying Danzhou (ca.800–720 Ma) Groups was investigated. Six sedimentary samples, below and above the unconformity in three distal localities (Fanjingshan, Madiyi, and Sibao) yield detrital zircon with UPb ages ranging from 779 ± 16 Ma to 3006 ± 36 Ma, with a prominent peak at ca. 852 Ma. The youngest ages of 832 ± 11 Ma and 779 ± 16 Ma are revealed for the underlying Sibao and overlying Danzhou Groups, respectively. The detrital zircon UPb age relative probability plot of the Jiangnan Orogen matches well with those of the Yangtze and Cathaysia blocks since ca. 865 Ma. Integrating geological, geochemical and geochronological results, we suggest that the Paleo–South China Ocean began to subduct under the Yangtze block at ca. 1000 Ma, and was partly closed at ca. 865 Ma. Afterwards, the Yangtze and Cathaysia blocks initially collide at 865 Ma, forming the Jiangnan Orogen. This collision resulted in not only the folding of the Sibao Group, but also sediment deposition in a syn-collisional setting, which makes the upper part of the Sibao Group. The youngest S-type granite dated at ca. 820 Ma that intruded in the Sibao Group marks the late stage of the Jiangnan Orogeny.