Joint probability density function of the stochastic responses of nonlinear structures

The joint probability density fimction （PDF） of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution method, which is successfully developed to capture the instantaneous PDF of an arbitrary single response of interest, is extended to evaluate the joint PDF of any two responses. A two-dimensional partial differential equation in terms of the joint PDF is established. The strategy of selecting representative points via the number theoretical method and sieved by a hyper-ellipsoid is outlined. A two-dimensional difference scheme is developed. The free vibration of an SDOF system is examined to verify the proposed method, and a flame structure exhibiting hysteresis subjected to stochastic ground motion is investigated. It is pointed out that the correlation of different responses results from the fact that randomness of different responses comes from the same set of basic random parameters involved. In other words, the essence of the probabilistic correlation is a physical correlation.     

∼3,850 Ma tonalites in the Nuuk region,Greenland: geochemistry and their reworking within an Eoarchaean gneiss complex

The Eoarchaean (>3,600 Ma) Itsaq Gneiss Complex of southern West Greenland is dominated by polyphase orthogneisses with a complex Archaean tectonothermal history. Some of the orthogneisses have c. 3,850 Ma zircons, and they vary from rare single phase metatonalites to more common complexly banded migmatites. This is due to heterogeneous strain, in situ anatexis and granitic veining superimposed during younger tectonothermal events. In the single-phase tonalites with c. 3,850 Ma zircon, oscillatory-zoned prismatic zircon is all 3,850 Ma old, but shows patchy ancient loss of radiogenic Pb. SHRIMP spot analyses and laser ablation ICP-MS depth profiling show that thin (usually < 10 μm) younger (3,660–3,590 Ma and Neoarchaean) shells of lower Th/U metamorphic zircon are present on these 3,850 Ma zircons. Several samples with this simple zircon population occur on islands near Akilia. In contrast, migmatites usually contain more complex zircon populations, with often more than one generation of igneous zircon present. Additional zircon dating of banded gneisses across the Complex shows that samples with c. 3,850 Ma igneous zircon are not just a phenomenon restricted to Akilia and adjacent islands. For example, migmatites from Itilleq (c. 65 km from Akilia) contain variable amounts of oscillatory-zoned 3,850 Ma and 3,650 Ma zircon, interpreted, respectively, as the rock age and the time of crustal melting under Eoarchaean metamorphism. With only 110–140 ppm Zr in the tonalites and likely magmatic temperatures of >850°C, zircon solubility–melt composition relationships show that they were only one-third saturated in zircon. Any zircon entrained in the precursor magmas would thus have been highly soluble. Combined with the cathodoluminesence imaging, this demonstrates that the c. 3,850 Ma oscillatory zoned zircon crystallised out of the melt and hence gives a magmatic age. Thus the rare well-preserved tonalites and palaeosome in migmatites testify that c. 3,850 Ma quartzo–feldspathic rocks are a widespread (but probably minor) component in the Itsaq Gneiss Complex. C. 3,850 Ma zircon with negative Eu anomalies (showing growth in felsic systems) also occurs as detrital grains in rare c. 3,800 Ma metaquartzites and as inherited grains in some 3,660 Ma granites (sensu stricto). These demonstrate that still more c. 3,850 Ma rocks were present, but were recycled into Eoarchaean sediments and crustally derived granites. The major and trace element characteristics (e.g. LREE enrichment, HREE depletion, low MgO) of the best-preserved c. 3,850 Ma rocks are typical of Archaean TTG suites, and thus argue for crust formation processes involving important contributions from melting of hydrated mafic crust to the earliest Archaean. Five c. 3,850 Ma tonalites were selected as the best preserved on the basis of field criteria and zircon petrology. Four of these samples have overlapping initial ɛ_Nd (3,850 Ma) values from +2.9 to +3.6± 0.5, with the fourth having a slightly lower value of +0.6. These data provide additional evidence for a markedly LREE-depleted early terrestrial mantle reservoir. The role of c. 3,850 Ma crust should be considered in interpreting isotope signatures of the younger (3,800–3,600 Ma) rocks of the Itsaq Gneiss Complex. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Equatorial electrojet in the south Atlantic anomaly region

Features of the equatorial electrojet are studied at Sao Luiz (2.6°S, 44.2°W, inclination −0.25°) in eastern Brazil and Sikasso (11.3°N, 5.7°W, inclination 0.1°) in the western African sector. The stations are situated on either side of the lowest magnetic field intensity in the region of rapid changes in the declination. The daily variations of ΔX at the two stations are almost similar with the peak around noon with maximum values during equinoxes and minimum values during J-solstices. Daily variations of ΔY differ with the maximum deviation of about −35 nT around noon at Sao Luiz and much smaller value of about −10 nT around 14 h LT for Sikasso. The direction of the H vector varies from 15°W of north at 08 h to more than 30°W of north at 17 h for Sao Luiz and from 14°E of north to 25°W of north at 18 h for Sikasso. The plot of the deviations in ΔX and ΔY at different hours for the two stations shows the points along narrow ellipses with major axis aligned along 22°W of north for Sao Luiz and along 3°W of north for Sikasso as compared to declination of 20°W for Sao Luiz and 6°W for Sikasso. The deviations in ΔX at the two stations are fairly well correlated.     

Remote effects of mixed layer development on ocean acidification in the subsurface layers of the North Pacific

Using the outputs of projections under the highest emission scenario of the representative concentration pathways performed by Earth system models (ESMs), we evaluate the ocean acidification rates of subsurface layers of the western North Pacific, where the strongest sink of atmospheric CO₂ is found in the mid-latitudes. The low potential vorticity water mass called the North Pacific Subtropical Mode Water (STMW) shows large dissolved inorganic carbon (DIC) concentration increase, and is advected southwestward, so that, in the sea to the south of Japan, DIC concentration increases and ocean acidification occurs faster than in adjacent regions. In the STMW of the Izu-Ogasawara region, the ocean acidification occurs with a pH decrease of ~0.004 year^?1 , a much higher rate than the previously estimated global average (0.0023 year^?1), so that the pH decreases by 0.3–0.4 during the twenty-first century and the saturation state of calcite (Ω_Ca) decreases from ~4.8 down to ~2.4. We find that the ESMs with a deeper mixed layer in the Kuroshio Extension region show a larger increase in DIC concentration within the Izu-Ogasawara region and within the Ryukyu Islands region. Comparing model results with the mixed layer depth obtained from the Argo dataset, we estimate that DIC concentration at a depth of ~200 m increases by 1.4–1.6 μmol kg^?1 year^?1 in the Izu-Ogasawara region and by 1.1–1.4 μmol kg^?1 year^?1 in the Ryukyu Islands region toward the end of this century.     

Soil moisture dynamics under different land uses on karst hillslope in northwest Guangxi,China

Temporal and spatial dynamics of soil moisture are little known on karst hillslope with shallow soil in subtropical region. The objectives of this paper were (1) to investigate the temporal dynamics of soil moisture at depth of 0–10 cm under different land uses; and (2) to understand the relationship between mean and coefficient of variation (CV) of moisture contents on karst hillslope in northwest Guangxi, China. Soil moisture contents had a moderate variation (CV 17.5–30.3%) over an 8-month period and they had a significant difference among different land uses at the 0.01 level with a decreasing order: native scrubland > abandoned cropland and sloping cropland > economic forestland. There were higher mean and lower CV of moisture contents in rainy season than those in drought season. Mean and CV of moisture contents had a significant negative linear relationship except in abandoned cropland with higher soil and vegetation heterogeneity. This suggested that spatial variability of soil moisture within sampling sites would decrease when soils were wet and increase when soils were arid. Compared with rainy season, more soil samples may be needed and the interval for sampling should be shortened in drought season. Such information provided some insights to better understand the dynamics and variability of soil moisture at a larger scale in karst region of southwest China.     

Identifying influence areas with connectivity analysis – application to the local perturbation of heterogeneity distribution for history matching

Numerical representations of a target reservoir can help to assess the potential of different development plans. To be as predictive as possible, these representations or models must reproduce the data (static, dynamic) collected on the field. However, constraining reservoir models to dynamic data – the history-matching process – can be very time consuming. Many uncertain parameters need to be taken into account, such as the spatial distribution of petrophysical properties. This distribution is mostly unknown and usually represented by millions of values populating the reservoir grid. Dedicated parameterization techniques make it possible to investigate many spatial distributions from a small number of parameters. The efficiency of the matching process can be improved from the perturbation of specific regions of the reservoir. Distinct approaches can be considered to define such regions. For instance, one can refer to streamlines. The leading idea is to identify areas that influence the production behavior where the data are poorly reproduced. Here, we propose alternative methods based on connectivity analysis to easily provide approximate influence areas for any fluid-flow simulation. The reservoir is viewed as a set of nodes connected by weighted links that characterize the distance between two nodes. The path between nodes (or grid blocks) with the lowest cumulative weight yields an approximate flow path used to define influence areas. The potential of the approach is demonstrated on the basis of 2D synthetic cases for the joint integration of production and 4D saturation data, considering several formulations for the weights attributed to the links.     

Breadth and depth in research on health disparities: commentary on the work of Nancy Krieger

Geocoding and spatial analysis of data describing populations and health events are important methods in health social science now carried out using GIS technology. This commentary considers Nancy Krieger’s work on health disparities in light of the various ways individuals and organizations use geocoded population and health data: analyzing spatial patterns of health and disease including health disparities, aggregating data spatially, assessing health status of individuals based on characteristics of aggregates, modeling neighborhood contextual factors affecting health, designing observation and intervention studies, and delivering health interventions and services. The extent to which her work addresses each of these purposes is considered. The strengths and limitations of the research including choice of spatial analytic units and techniques as reported in the published work are discussed. Krieger’s work, with her colleagues, has used standard methods of spatial analysis to raise the profile of GIS and spatial analysis in the public health community.     

An approximate analytical solution for measuring air permeability of asphalt samples partially saturated with water

In coastal areas, abnormally high pressure may be caused by the tide-induced water table variation under extensive pavements, particularly during rainfall. To simulate the rainfall infiltration effects on the air permeability of asphalt pavements in coastal area, column-shaped asphalt sample was fixed in the upper part of a steel cylinder with its upper surface saturated with ponding water (depth < 5 mm) and open to the atmosphere. The cylinder’s lower part formed an air chamber. The chamber was pressurized and then the air therein was released naturally through the sample. The pressure variation with time in the chamber was recorded for analysis. Based on the Green–Ampt piston model for the surface water infiltration, an approximate analytical solution was derived to describe the pressure–time relationship in the chamber. A new parameter called the escape pressure was introduced to describe the air pressure needed for the chamber air to break through the capillary pressure induced by the ponding water. The analytical solution gave good estimations of both the escape pressures and the harmonic averages of the permeabilities of the wet and dry parts of 14 samples in the sense that excellent fittings were obtained between the observed and predicted air pressures in the air chamber. The estimated escape pressure ranges from 0.0 to 1.74 kPa. The harmonic average of the permeabilities of the wet and dry parts is 5–94% of the dry sample’s permeability.     

The characteristics of the seismic signals induced by landslides using a coupling of discrete element and finite difference methods

Landslide seismic signals support researchers to estimate magnitudes and locations of landslides. They can serve as a crucial data for landslide warning systems. However, the randomness of landslide locations makes the acquisition of landslide-induced seismic signals difficult and limits the number of available field data. The objectives of this study are to establish a numerical modeling approach to examine the characteristics of seismic signals induced by landslides and perform parametrical study. The two-dimensional particle flow code (PFC) and Fast Lagrangian Analysis of Continua (FLAC) are coupled to simulate the landslide process. The force and velocity data at the coupled interfaces of FLAC and PFC are transferred back and forth via a Socket I/O connection. Four locations were monitored for the induced vertical seismic signals, including velocity, acceleration, and stress histories. The signals were analyzed by Hilbert-Huang transform to obtain the time-frequency spectrograms for examining the characteristics of the signals. The particle size, wall friction, particle friction, and parallel bond of PFC input parameters were parametrically investigated. The Xiaolin landslide in 2009 was successfully simulated, and the characteristics of the seismic signals were studied and compared with the data from a broadband seismic station. These results demonstrate that terrain and transition in the movement type of a complex landslide do influence the seismic signals. A landslide with larger rock particles generates lower-frequency content seismic signals. Also, there can be approximately 40 s to escape before a large-scale landslide hits if seismic instrumentation is installed. The method proposed can be further applied for studies on many other large-scale rock avalanches to verify recorded signals and further correlate the signals with the landslide characteristics.     

Lithological and geochemical record of anthropogenic changes in recent sediments of a small and shallow lake (Lake Pusty Staw,northern Poland)

The article presents the results of lithological and geochemical investigations of recent sediments of Lake Pusty Staw. The analysed sediments document about 300 years of the history of this lake. Historical materials indicate that significant changes in the catchment of the lake took place from the beginning of the 18th century (deforestation and afforestation) followed by 19th century tourist development, and 20th century industrialisation. The sediments were dated using the ²¹⁰Pb and ¹³⁷Cs method and core lithology. These made it possible to establish a reliable chronology to the year 1730. The calculated sedimentation rates ranged between 0.17 and 0.83 cm year^–1. There was a period of intensified erosion caused by land clearance between 1734 and 1810, which resulted in an acceleration in sedimentation rate (0.36 cm year^–1) and a change of lithological type of sediment from detritus gyttja to clayey gyttja. On the basis of Cu, Zn, Cd and Pb content in the sediments, it was determined that the beginning of pollution of the lake dates back to the 19th century and was caused probably by the existence of a health resort. A systematic increase in pollution occurred in the 20th century as a result of industrial plants. Normalised with respect to Al, the content of heavy metals in polluted sediments was from several to twenty times higher than in sediments of the preindustrial period, and a comparison of historical materials with changes of sediments in most cases made it possible to identify the direct causes of the increase in pollution.