Orbit uncertainty propagation and sensitivity analysis with separated representations

Most approximations for stochastic differential equations with high-dimensional, non-Gaussian inputs suffer from a rapid (e.g., exponential) increase of computational cost, an issue known as the curse of dimensionality. In astrodynamics, this results in reduced accuracy when propagating an orbit-state probability density function. This paper considers the application of separated representations for orbit uncertainty propagation, where future states are expanded into a sum of products of univariate functions of initial states and other uncertain parameters. An accurate generation of separated representation requires a number of state samples that is linear in the dimension of input uncertainties. The computation cost of a separated representation scales linearly with respect to the sample count, thereby improving tractability when compared to methods that suffer from the curse of dimensionality. In addition to detailed discussions on their construction and use in sensitivity analysis, this paper presents results for three test cases of an Earth orbiting satellite. The first two cases demonstrate that approximation via separated representations produces a tractable solution for propagating the Cartesian orbit-state uncertainty with up to 20 uncertain inputs. The third case, which instead uses Equinoctial elements, reexamines a scenario presented in the literature and employs the proposed method for sensitivity analysis to more thoroughly characterize the relative effects of uncertain inputs on the propagated state.     

The Gol-e-Zard Zn-Pb Deposit,Lorestan Province,Iran: a Metamorphosed SEDEX Deposit简

The Gol-e-Zard Zn-Pb deposit is one of several sediment-hosted Zn-Pb deposits found in the central part of the Sanadaj-Sirjan Zone, known as the Isfahan-Malayer belt, western Iran. Mineralization occurs in Upper Triassic to Jurassic phyllites and meta-sandstones. Sphalerite and galena are the most abundant metallic ores, with minor chalcopyrite. Calcite and quartz are the main gangue minerals. Fissure filling, replacement textures and especially mineralized faults, suggest an epigenetic stage in the Gol-e-Zard deposit formation. Geochemical studies of mineralized rocks show high concentrations of Zn, Pb and Cu,（Zn and Pb 〉 10000 ppm and Cu average 3000 ppm）. LREE enrichment（LREE〉HREE, La/Lu average 1.44） and positive Eu anomalies（Eu/Eu＊〉1 average 1.67） indicate reducing conditions during the deposition of deposit. However, some samples do not display negative Ce anomalies, which indicate that localized oxidizing conditions are also present. This study indicates that the Gol-e-Zard deposit formed due to circulating hydrothermal fluids in a marine environment. A SEDEX-type genesis, which is defined by circulating hydrothermal fluids through sediments in a marine environment, and syngenetic precipitation of Zn and Pb sulphides, is suggested for the Gol-e-Zard deposit. Emplacement of some granitoid intrusions such as the Aligudarz granitoid intrusion remobilized mineralizing fluids and metamorphosed the Gol-e-Zard deposit.     

Ascribing soil erosion types for sediment yield using composite fingerprinting technique

Abstract

Soil erosion and eroded sediment are serious threats to sound land management. However, less attention has been given to quantifying the importance of different soil erosion features based on appropriate control measures that could be designated. Accordingly, this research was planned to quantify the contribution of potential sediment sources, i.e. sheet, rill and gully erosion, in Idelo watershed in Zanjan Province, Iran, using composite fingerprinting. Toward this aim, 16 geochemical and organic tracers were detected in sediment sources and sediment deposited at the outlet. The results of applying the composite fingerprinting technique, with a relative error of 16%, showed that sheet, rill and gully sources contributed 56%, 44% and 0%, respectively, to sediment yield. It was also apparent from the results that the composite fingerprinting approach could be successfully utilized to assess the provenance of sediment deposited at the main outlet of the study watershed by soil erosion type.

Editor Z.W. Kundzewicz     

Developing an agricultural flood loss estimation function (case study: rice)

In recent years, flood control has been replaced by flood management concept in terms of living with flood, making benefit of it, and minimizing its losses. Succeeding in flood management in any region depends on the evaluation of different types of flood losses. Because of providing water resources and suitable arable lands, especially in arid and semiarid countries, floodplains are very important for agricultural activities. These lands are naturally vulnerable to flood; henceforth, determining the degree of protection and acceptable risk in flood damage-reduction projects without agricultural flood loss evaluation could be unrealistic. In this research, effective hydraulic parameters for flood loss estimation were determined and a set of laboratory tests were performed to evaluate the loss of rice, as the main crop in the study region, under different hydraulic conditions. In this regard, flow parameters like depth, velocity, multiplication of depth and velocity, shear stress, the Froude number, and the Reynolds number were employed for different rice growth stages including after transplanting, shooting, clustering, and harvesting. Analyzing the results showed that the Reynolds number, as a dimensionless parameter, is the best one for simulation of flood physical factor-loss function. Statistical analysis revealed that the logarithmic function is the best regression equation fitted to the Reynolds number-loss function. The amount of loss depends on growth stage; therefore, the time of flood occurrence is of vital importance for agricultural loss estimation. In this research, it was realized that the amount of loss is increased in the following order: after transplanting, shooting, harvesting, and clustering.     

Enhancing PIV image and fractal descriptor for velocity and shear stresses propagation around a circular pier

In this study,the fractal dimensions of velocity fluctuations and the Reynolds shear stresses propagation for flow around a circular bridge pier are presented.In the study reported herein,the fractal dimension of velocity fluctuations(u′,v′,w′) and the Reynolds shear stresses(u′v′ and u′w′) of flow around a bridge pier were computed using a Fractal Interpolation Function(FIF) algorithm.The velocity fluctuations of flow along a horizontal plane above the bed were measured using Acoustic Doppler Velocity meter(ADV)and Particle Image Velocimetry(P1V).The PIV is a powerful technique which enables us to attain high resolution spatial and temporal information of turbulent flow using instantaneous time snapshots.In this study,PIV was used for detection of high resolution fractal scaling around a bridge pier.The results showed that the fractal dimension of flow fluctuated significantly in the longitudinal and transverse directions in the vicinity of the pier.It was also found that the fractal dimension of velocity fluctuations and shear stresses increased rapidly at vicinity of pier at downstream whereas it remained approximately unchanged far downstream of the pier.The higher value of fractal dimension was found at a distance equal to one times of the pier diameter in the back of the pier.Furthermore,the average fractal dimension for the streamwise and transverse velocity fluctuations decreased from the centreline to the side wall of the flume.Finally,the results from ADV measurement were consistent with the result from PIV,therefore,the ADV enables to detect turbulent characteristics of flow around a circular bridge pier.     

Pressuremeter test parameters of a compacted illitic soil under thermal cycling

The incorporation of heat exchangers in geostructures changes the temperature of the adjacent soil, raising important issues concerning the effect of temperature variations on hydro-mechanical soil behaviour. The objective of this paper is to improve the understanding and quantification of the impact of temperature variation on the bearing capacity of thermo-active piles. Currently, the design of deep foundations is based on the results of in situ penetrometer or pressuremeter tests. However, there are no published data on the effect of temperature on in situ soil parameters, preventing the specific assessment of the behaviour of thermo-active piles. In this study, an experimental device is developed to perform mini-pressuremeter tests under controlled laboratory conditions. Mini-pressuremeter tests are performed on an illitic soil in a thermo-regulated metre-scale container subjected to temperatures from 1 to 40 °C. The results reveal a slight decrease in the pressuremeter modulus (E _p) and a significant decrease in the creep pressure (p _f) and limit pressure (p _l) with increasing temperature. The results also reveal the reversibility of this effect during a heating–cooling cycle throughout the investigated temperature range, whereas the effect of a cooling–heating cycle was only partially reversible. In the case of several thermal cycles, the effect of the first cycle on the soil parameters is decisive.     

System dynamics approach for simulating water resources of an urban water system with emphasis on sustainability of groundwater

Water resources management is an important driver in social and economic development. Water shortage is one of the most critical issues threatening human welfare, public health, and ecosystems. This issue has turned into a major challenge in many river basins all around the world due to the imbalance in water supply and demand. Use of simulation models can be effective tools in providing water managers with scientifically supported decisions in dealing with complex and uncertain water resource systems. System dynamics approach serves as a management tool and may play an important role in understanding the cause–effect in water resources systems. In the present study, system dynamics approach was applied to simulate management strategies dealing with Tehran metropolitan water resources systems. In the developed model, the trend of water storage in the next 30-year period and the effectiveness of water supply strategies were simulated. The results showed that, despite the growing shortage of the water resources, optimal use of existing resources under appropriate strategies could reduce water deficit within the next 30 years.     

Long-term coupled behaviour of cemented paste backfill in load cell experiments

A pressure cell apparatus has been developed in this research work to study the long-term hydro-mechanical behaviour of cemented paste backfill (CPB) cured under applied stress. The samples are cured for 7, 28, 90 and 150 days and the evolution of their mechanical, hydraulic, physical and microstructural properties is studied. Also, the suction, temperature and electrical conductivity are monitored for a period of 150 days of curing. The testing and monitoring programmes are conducted in undrained conditions, with and without pressure application. The obtained results show that the curing stress affects the hydro-mechanical behaviour of CPB for up to 28 days. Within this curing period, the CPB exhibits enhanced hydro-mechanical performance. However, application of sustained excessive curing stress onto the CPB samples induces the propagation of microcracks in the backfill structure, thus causing lower mechanical strength and higher fluid permeability at the more advanced ages. Furthermore, the mineralogical and chemical compositions of the tailings (e.g., sulfidic tailings) can significantly alter the mechanical strength properties (uniaxial compressive strength and elastic modulus) and the permeability of the CPB. The evolution of coupled factors and characteristics of the CPB at an early age control and influence its long-term behaviour and performance.     

Hydrothermal Alteration, Fluid Inclusion and Stable Isotope Studies of the North Roby Zone, Lac des Iles PGE Mine, Ontario, Canada

The Archean mafic–ultramafic complex of Lac des Iles, Ontario, Canada, hosts economic platinum group elements (PGE)-Au-Cu-Ni mineralization in the Roby Zone. All lithologies in the North Roby Zone have been affected by hydrothermal alteration. The alteration products include talc (the most dominant mineral), anthophyllite, serpentine, actinolite, tremolite, chlorite, hornblende, zoisite, clinozoisite, epidote and sericite. In the altered rocks, light rare earth elements (La, Ce, Nd, Sm), Pb, Rb, Ba, Cs, S and possibly Y have been added by hydrothermal solution whereas Eu and heavy rare earth elements (Yb, Gd, Dy, Er) remained immobile. There are five types of fluid inclusions in the pegmatitic plagioclase with homogenization temperature and salinity ranging from 240°C to 445°C and 15.37 to 48.52 wt% equivalent NaCl, respectively. The δ¹⁸O and δD of talc range form 6.2‰ to 6.9‰ and −28‰ to −48‰, respectively. δ¹⁸O and δD water in equilibrium with talc during the hydrothermal alteration suggest a modified source for the hydrothermal solution. Microthermometry and stable isotope studies suggest that high temperature–high salinity fluid was diluted by, and mixed with, low temperature–low salinity meteoric solution. This mechanism precipitated the hydrothermal assemblage and redistributed trace elements during and after pegmatite formation in the North Ruby Zone.     

Deep reflection seismic imaging of iron-oxide deposits in the Ludvika mining area of central Sweden

Reflection seismic data were acquired within two field campaigns in the Blötberget, Ludvika mining area of central Sweden, for deep imaging of iron-oxide mineralization that were known to extend down to 800–850 m depth. The two surveys conducted in years 2015 and 2016, one employing a seismic landstreamer and geophones connected to wireless recorders, and another one using cabled geophones and wireless recorders, aimed to delineate the geometry and depth extent of the iron-oxide mineralization for when mining commences in the area. Even with minimal and conventional processing approaches, the merged datasets provide encouraging information about the depth continuation of the mineralized horizons and the geological setting of the study area. Multiple sets of strong reflections represent a possible continuation of the known deposits that extend approximately 300 m further down-dip than the known 850 m depth obtained from historical drilling. They show excellent correlation in shape and strength with those of the Blötberget deposits. Furthermore, several reflections in the footwall of the known mineralization can potentially be additional resources underlying the known ones. The results from these seismic surveys are encouraging for mineral exploration purposes given the good quality of the final section and fast seismic surveys employing a simple cost-effective and easily available impact-type seismic source.