Implementation of a particle-in-cell method for the energy solver in 3D spherical geodynamic modeling

The thermal evolution of the Earth’s interior and its dynamic effects are the focus of Earth sciences.However,the commonly adopted grid-based temperature solver is usually prone to numerical oscillations,especially in the presence of sharp thermal gradients,such as when modeling subducting slabs and rising plumes.This phenomenon prohibits the correct representation of thermal evolution and may cause incorrect implications of geodynamic processes.After examining several approaches for removing these numerical oscillations,we show that the Lagrangian method provides an ideal way to solve this problem.In this study,we propose a particle-in-cell method as a strategy for improving the solution to the energy equation and demonstrate its effectiveness in both one-dimensional and three-dimensional thermal problems,as well as in a global spherical simulation with data assimilation.We have implemented this method in the open-source finite-element code CitcomS,which features a spherical coordinate system,distributed memory parallel computing,and data assimilation algorithms.

An Isotopic(Sr,Nd and Pb) Tracer Study on the Xiaoxinancha Gold-rich Copper Deposit in Yanbian,China:Implication for the Geodynamic Model of Diagenesis and Metallogenesis

An isotopic study was systemically carried out on the granitic complex,diorite-porphyrite, ores and ore minerals of the 103 Ma Xiaoxinancha gold-rich copper deposit in Jilin province to determine the geodynamic model of diagenesis and metallogenesis.Results show that the initial Nd and Sr isotopic compositions of the granitic complex are in the range of 0.70425-0.70505 for（87Sr/86Sr）i, 0.51243-0.51264 for INd,and -1.31 to ＋2.64 forεNd（t）;those of the diorite-porphyrite are in the range from 0.70438-0.70448 for（87Sr/86Sr）,,0.51259-0.51261 for INd,and ＋1.56 to ＋2.09 forεNd（t）.For ores and sulfides,the（87Sr/86Sr）i,7Nd,andεNd（t） values are in the range from 0.70440-0.70805,0.51259- 0.51279 and ＋1.72 to ＋5.56,respectively.The Pb isotopic ratios of the granitic complex range from 18.2992-18.6636 for 206Pb/204Pb,from 15.5343-15.5660 for 207Pb/204Pb,and from 38.1640-38.5657 for 208Pb/204Pb For diorite-porphyrite,the isotopic ratios of 206Pb/204Pb,207Pb/204Pb and 208Pb/204Pb are 18.3919,15.5794 and 38.3566,respectively,whereas those of the ores and ore sulfides vary from 18.2275-18.3770 for 206Pb/204Pb,from 15.5555-15.5934 for 207Pb/204Pb and from 38.1318-38.3131 for 208Pb/204Pb.The results indicate that the mineralization was correlated to the formation and evolution of the granitic complex and the diorite-porphyrite.Combining with the reported data in petrologic characteristics,elemental geochemistry and chronology,conclusions can be drawn that the geodynamic settings of diagenesis and metallogenesis of this deposit were consistent with the subduction of the Izanagi oceanic plate during the Early Cretaceous.The diorite-porphyrite was formed by the emplacement of the adakitic magma triggered by partial melting of the enriched mantle,which originated from the derivative continental lithospheric mantle metasomatized by dehydration fluids from the subducting oceanic crust.The granitic complex was produced by fractional crystallization of the mixture between the adakitic magma and the high-K calc-alkaline acidic magma,which were generated by the remelting of the lower crust in the course of intraplate upwelling of the adakitic magma.The ore-bearing fluid reservoir convened in a late stage of the evolution of the mixed magma chamber.

Besshi-type mineral systems in the Palaeoproterozoic Bryah Rift-Basin, Capricorn Orogen, Western Australia： Implications for tectonic setting and geodynamic evolution

In this contribution we use VMS mineral systems in the Bryah rift-basin to constrain the tectonic setting of the widespread mafic and ultramafic magmatism that characterises the rift-basin in question.Two distinct,but temporally closely associated,lithostratigraphic sequences,Narracoota and Karalundi Formations,are discussed.The Karalundi Formation is the main host of VMS mineral systems in the region.The Karalundi Formation consists of turbiditic and immature clastic sediments,which are locally intercalated with basaltic hyaloclastites,dolerites and banded jaspilites.We propose that the basaltic hyaloclastites,dolerites and elastics and jaspilites rocks,form a distinct unit of the Karalundi Formation,named Noonyereena Member.The VMS mineral systems occur near the north-east trendingJenkin Fault and comprise the giant and world-class DeCrussa and the Red Bore deposits.The nature of these deposits and their intimate association with terrigenous clastic rocks and dominantly marine mafic volcanic and subvolcanic rocks,as well as the common development of peperitic margins,are considered indicative of a Besshi-type environment,similar to that of present-day Gulf of California.Our Re-Os age data from a primary pyrite yielded a mean model age of 2012 ± 48 Ma,which coincides（within error） with recent published Re-Os data（Hawke et al.,2015） and confirms the timing of the proposed geodynamic evolution.We propose a geodynamic model that attempts to explain the presence of the Narracoota and Karalundi Formations as the result of mantle plume activity,which began with early uplift of continental crust with intraplate volcanism,followed by early stages of rifting with the deposition of the Karalundi Formation（and Noonyereena Member）,which led to the formation of Besshi-type VMS deposits.With on-going mantle plume activity and early stages of continental separation,an oceanic plateau was formed and is now represented by mafic-ultramafic rocks of the Narracoota Formation.

GEODYNAMICAL MODELING OF CRUSTAL DEFORMATION OF THE NORTH CHINA BLOCK

The North China block,the western portion of the Sino- Korean Craton,is rounded byYanshanian in the north and Qinling- Dabie orogenic belts in the south.The widespread de-velopment of extensional basins in thisblock indicates horizontal extension or continued thin-ning of a previousely thickened,unstable lithosphere throughout the Mesozoic.In this pa-per,we attempt to simulate numerically the geodynamical process of the basin formation byusing the mountain- basin evolution system.We assume thatthe formation of numeroussedi-mentary basins in the North China block is the resultofthe crustal extension,which destruc-ts rapidly the previously thickened crust.The gravitational collapse of the thickened crust ispossibly triggered by the re- orientation of the far- field stress regime,or the relaxation of theboundary resistantstress.

Lithospheric structure and geodynamics at the northern margin of Tibetan plateau

A recent integrated geophysical survey has been completed along a transect from Baicheng, Xinjiang to Da Qaidam, Qinghai, China. In this study, wide-angle seismic reflection/refraction exploration with 10 shot points has been carried out to acquire the velocity structure of the crust and uppermost mantle. The earthquake focal mechanism solutions and terrestrial heat flow along the transect have also been obtained and analyzed. Based on the velocity structure of the crust and uppermost mantle along the transect, and combined with the focal mechanism solutions and terrestrial heat flow we develop a geodynamic model for the northern margin of the Tibetan plateau. This model reveals the detailed structure of the crust and uppermost mantle, determines the relationship of basin and range coupling, explores the deep dynamic setting for superposed basins, and establishes the northern boundary condition for Tibetan plateau research.

Modeling of normal faulting in the subducting plates of the Tonga,Japan,Izu-Bonin and Mariana Trenches:implications for near-trench plate weakening

The plate flexure and normal faulting characteristics along the Tonga, Japan, Izu-Bonin and Mariana Trenches are investigated by combining observations and modeling of elastoplastic deformation of the subducting plate. The observed average trench relief is found to be the smallest at the Japan Trench(3 km) and the largest at the Mariana Trench(4.9 km), and the average fault throw is the smallest at the Japan Trench(113 m) and the largest at the Tonga Trench(284 m). A subducting plate is modeled to bend and generate normal faults subjected to three types of tectonic loading at the trench axis: vertical loading, bending moment, and horizontal tensional force. It is inverted for the solutions of tectonic loading that best fit the observed plate flexure and normal faulting characteristics of the four trenches. The results reveal that a horizontal tensional force(HTF) for the Japan Trench is 33%, 50% and 60% smaller than those of the Mariana, Tonga and Izu-Bonin Trenches, respectively. The normal faults are modeled to penetrate to a maximum depth of 29, 23, 32 and 32 km below the sea floor for the Tonga,Japan, Izu-Bonin and Mariana Trenches, respectively, which is consistent with the depths of relocated normal faulting earthquakes in the Japan and Izu-Bonin Trenches. Moreover, it is argued that the calculated horizontal tensional force is generally positively correlated with the observed mean fault throw, while the integrated area of the reduction in the effective elastic thickness is correlated with the trench relief. These results imply that the HTF plays a key role in controlling the normal faulting pattern and that plate weakening can lead to significant increase in the trench relief.

Analytical and numerical simulations of uplift processes at the Tibet-Sichuan boundary

Previous studies have shown that the uplift of Tibetan plateau started in response to the collision of Indian plate and Eurasian plate. During this process, the crust of Tibetan plateau has been greatly thickened which leads to significant elevations. The elevation gradient is extremely large at the east boundary of Tibetan plateau where Longmenshan fault exists, dropping from 4500 to 500 m within a distance of 100 km, while it is more gentle at the south and north sides of Sichuan basin. Such a difference of elevation gradient has been explained with a crustal channel flow model. However, pre- vious crustal flow models consider the thickness of the lower crust as a constant which is highly simplified. Therefore, it is essential to build a more realistic crustal flow model, in which the thickness of the lower crust is variable and dependent on the inflow velocity of crustal materials. Here we build up both analytical and numerical models to study the mechanism and process of the uplift of Tibetan plateau at the eastern boundary. The results of the analytical model show that if the thickness of the lower crust can vary during the uplift process, the lower crustal viscosity of the Sichuan basin needs to be 1022 Pas to fit the observed elevation gradient. Such a viscosity is one-order magnitude larger than the previous results. Numerical model results further show that the state of stresses at the plateau boundary changes during uplift processes. Such a stress state change may cause the formation of different fault types in the Longmenshan fault area during its uplift history.

Early Cretaceous Post-Collisional Collapse of the Yidun Terrane: Geochronological and Geochemical Constraints from Calc-alkaline to Alkaline Basalts in Xiqiu Area, Southwest China

Several Cretaceous Carlin-like or hydrothermal gold deposits along the Garze-Litang suture zone and Early Cretaceous hydrothermal copper mineralization along the southeastern margin of the Songpan-Garze fold belt were presumed to have a magmatic heat source. However, no actual coeval mag- matic events nearby were discovered. Here, we report zircon SIMS U-Pb age, whole-rock geochemical and Sr-Nd isotopic data of the Xiqiu basalts in the southern end of the Yidun terrane, eastern Tibetan Plateau. New zircon U-Pb ages yield weighted mean ^206pb/^238U age of 117.7±1.6 Ma. The basalts are classified as calc-alkaline to alkaline and have relatively high MgO （4.77 wt.%-10.84 wt.%） and Mg number values （Mg^#=（100×Mg/（Mg＋Fe^2＋））; 45.35-67.28） and positive εNd（t） （t=118 Ma） values （＋1.86 to ＋3.2）, suggesting a OIB-like mantle source that is consistent with the normalized patterns of trace elements and rare earth elements （REEs）. Geochemical data suggest that the primary basaltic magma was generated by low degree partial melting of a heterogeneous source of peridotite-dominated with a minor component of garnet- eclogite or pyroxenite and experienced olivine＋clinopyroxene dominated fractional crystallization. The primary melt compositions calculated from the high MgO samples, in turn, suggest that the Xiqiu basalts were generated at 1.6-2.9 GPa with abnormally hot mantle potential temperatures from 1 465 to 1 540℃. The melting temperatures are similar to the abnormally hot mantle underneath the Colorado Plateau and hotter than the mid-ocean range basalt （MORB） mantle and normal intra-continental mantle. Combined with previous studies, the Cretaceous Xiqiu basalts allow us to reconstruct a tectonic and geodynamic evolution- ary model responsible for the Late Jurassic to Late Cretaceous geological records （magmatism, ore deposits and enhanced exhumation） in the Yidun terrane and southern Songpan-Garze fold belt.

SEPRAN: A Versatile Finite-Element Package for a Wide Variety of Problems in Geosciences

Numerical modelling of geological processes, such as mantle convection, flow in porous media, and geothermal heat transfer, has become quite common with the increase in computing and the availability of usable software. Today modelling these dynamical processes entails the solving of the governing equations involving the mass, momentum, energy and chemical transport. These equations represent partial differential equations and must be solved on powerful enough computers because they require sufficient spatial and temporal resolution to be useful. We describe here the salient and outstanding features of the SEPRAN software package, developed in the Netherlands, as a case study for a robust and user-friendly soft- ware, which the geological community can utilize in handling many thermal-mechanical-chemical problems found in geology, which will include geothermal situations, where many types of partial differential equations must be solved at the same time with thermodynamical input parameters.