Single Endmember Research Articles

Multi-stage evolution of the Lost City hydrothermal vent fluids

Serpentinization-influenced hydrothermal systems, such as the Lost City Hydrothermal Field (LCHF), are considered as potential sites for the origin of life. Despite an abundance of reducing power in this system (H2 and CH4), microbial habitability may be limited by high pH, elevated temperatures, and/or low concentrations of bioavailable carbon. At the LCHF, the relative contribution of biotic and abiotic processes to the vent fluid composition, especially in the lower temperature vents, remain poorly constrained. We present fluid chemistry and isotope data that suggest that all LCHF fluids are derived from a single endmember produced in the hotter, deeper subsurface essentially in the absence of microbial activity. The strontium isotope composition (87Sr/86Sr) of this fluid records the influence of underlying mantle and/or gabbroic rocks, whereas sulfur isotope composition indicates closed-system thermochemical sulfate reduction. Conductive cooling and transport is accompanied by continued sulfate reduction, likely microbial, and mixing with unaltered seawater, which produce second-order vents characterized by higher δ34Ssulfide and lower δ34Ssulfate values. Third-order vent fluids are produced by varying degrees of subsurface mixing between the first- and second-order fluids and a seawater-dominated fluid. Additional biotic and abiotic processes along different flow paths are needed to explain the spatial variability among the vents. Relationships between sulfur geochemistry and hydrogen concentrations dominantly reflect variations in temperature and/or distance from the primary outflow path. Methane concentrations are constant across the field which point to an origin independent of flow path and venting temperature. At Lost City, not all vent fluids appear to have zero Mg concentrations. Thus, we propose an extrapolation to a Sr isotope-endmember composition as an alternative method to estimate endmember fluid compositions at least in similar systems where a two-component mixing with respect to Sr isotopes between seawater and endmember fluids can be established.

An improved method combining Fisher transformation and multiple endmember spectral mixture analysis for lunar mineral abundance quantification using spectral data

Mineral abundance quantification of lunar surface materials using remotely acquired spectra can be achieved with spectral unmixing methods, but this has remained a challenging problem. The existing unmixing methods neglect the existence of widespread glass material and the spectral similarity of different minerals. To solve this problem, this study proposes a method to calculate the main mineral abundances in lunar regolith based on reflectance spectra by utilizing Fisher transformation combined with multiple endmember spectral mixture analysis (MESMA). A set of spectra of lunar main constituents, including plagioclase, pyroxene, ilmenite, olivine and glass material, were selected from the RELAB spectral database and used as endmembers. The endmember spectra were utilized to compute the projection vectors, with which the spectral characteristics can be transformed into low-dimensional Fisher space in which intraclass spectral variability can be minimized while the interclass variability of different mineral spectra can be maximized. The endmember spectra and the lunar soil spectra in the Lunar Soil Characterization Consortium (LSCC) dataset were both transformed into Fisher space, in which MESMA was executed to acquire the fraction of each endmember. MESMA allows for comprehensive endmember expressions by representing a type of mineral using multiple spectra rather than a single endmember. Compared with laboratory mineral measurements, this approach estimated the mineral abundances with determination coefficient R2 values equal to 0.88 and 0.65 in the lunar mare and highland regions, respectively. After validation with laboratory data, the method was further applied at the regional scale where Apollo 12 and Apollo 16 landed by using M3 images, and the estimated accuracy of different minerals was similar to that of the laboratory spectra.

Evolutionary Multiobjective Optimization with Endmember Priori Strategy for Large-Scale Hyperspectral Sparse Unmixing

Mixed pixels inevitably appear in the hyperspectral image due to the low resolution of the sensor and the mixing of ground objects. Sparse unmixing, as an emerging method to solve the problem of mixed pixels, has received extensive attention in recent years due to its robustness and high efficiency. In theory, sparse unmixing is essentially a multiobjective optimization problem. The sparse endmember term and the reconstruction error term can be regarded as two objectives to optimize simultaneously, and a series of nondominated solutions can be obtained as the final solution. However, the large-scale spectral library poses a challenge due to the high-dimensional number of spectra, it is difficult to accurately extract a few active endmembers and estimate their corresponding abundance from hundreds of spectral features. In order to solve this problem, we propose an evolutionary multiobjective hyperspectral sparse unmixing algorithm with endmember priori strategy (EMSU-EP) to solve the large-scale sparse unmixing problem. The single endmember in the spectral library is used to reconstruct the hyperspectral image, respectively, and the corresponding score of each endmember can be obtained. Then the endmember scores are used as a prior knowledge to guide the generation of the initial population and the new offspring. Finally, a series of nondominated solutions are obtained by the nondominated sorting and the crowding distances calculation. Experiments on two benchmark large-scale simulated data to demonstrate the effectiveness of the proposed algorithm.

Spectral Unmixing for Mapping a Hydrothermal Field in a Volcanic Environment Applied on ASTER, Landsat-8/OLI, and Sentinel-2 MSI Satellite Multispectral Data: The Nisyros (Greece) Case Study

The aim of this study was to propose a methodology that provides a detailed description of the argillic zone of a hydrothermal field, based on satellite multispectral data. More specifically, we developed a method based on spectral unmixing where hydroxyl-bearing alteration is represented by a single endmember (representing clays) and the three (nearly) non-altered primary volcanic lithologies, namely, two types of lava flows (basic and acidic compositions) and the loose materials (alluvial/beach deposits, scree, pyroclastic deposits, etc.), are represented by three endmembers. We also used one endmember representing elemental sulfur that is present in fumarolic vents hosted by active hydrothermal craters. The methodology was applied in the south part of Lakki plain inside the Nisyros volcano caldera (Greece), using Sentinel-2, Landsat-8/OLI, and ASTER satellite multispectral datasets. Specifically, it was applied separately to each one of the three datasets. The spectral unmixing results, combined with the relative geological map, provide quantitative estimations of the primary volcanic and loose material areas affected by alteration. In addition, pixels with high abundance values of hydroxyl-bearing alteration corresponded to mapped areas with strong hydrothermal alteration. The developed methodology is superior to conventional approaches (e.g., alteration spectral index) in terms of its ability to describe the overall pattern of the hydrothermal field. The most accurate results were taken when applied to ASTER or Sentinel-2 MSI data.

Tracing the migration of mantle CO2 in gas fields and mineral water springs in south-east Australia using noble gas and stable isotopes

Abstract Geochemical monitoring of CO2 storage requires understanding of both innate and introduced fluids in the crust as well as the subsurface processes that can change the geochemical fingerprint of CO2 during injection, storage and any subsequent migration. Here, we analyse a natural analogue of CO2 storage, migration and leakage to the atmosphere, using noble gas and stable isotopes to constrain the effect of these processes on the geochemical fingerprint of the CO2. We present the most comprehensive evidence to date for mantle-sourced CO2 in south-east Australia, including well gas and CO2-rich mineral spring samples from the Otway Basin and Central Victorian Highlands (CVH). 3He/4He ratios in well gases and CO2 springs range from 1.21 to 3.07 RA and 1.23–3.65 RC/RA, respectively. We present chemical fractionation models to explain the observed range of 3He/4He ratios, He, Ne, Ar, Kr, Xe concentrations and δ13C(CO2) values in the springs and the well gases. The variability of 3He/4He in the well gases is controlled by the gas residence time in the reservoir and associated radiogenic 4He accumulation. 3He/4He in CO2 springs decrease away from the main mantle fluid supply conduit. We identify one main pathway for CO2 supply to the surface in the CVH, located near a major fault zone. Solubility fractionation during phase separation is proposed to explain the range in noble gas concentrations and δ13C(CO2) values measured in the mineral spring samples. This process is also responsible for low 3He concentrations and associated high CO2/3He, which are commonly interpreted as evidence for mixing with crustal CO2. The elevated CO2/3He can be explained solely by solubility fractionation without the need to invoke other CO2 sources. The noble gases in the springs and well gases can be traced back to a single end-member which has suffered varying degrees of radiogenic helium accumulation and late stage degassing. This work shows that combined stable and noble gas isotopes in natural gases provide a robust tool for identifying the migration of injected CO2 to the shallow subsurface.

A LiDAR signature library simulated from 3-dimensional Discrete Anisotropic Radiative Transfer (DART) model to classify fuel types using spectral matching algorithms

Fuel types are one of the key variables that drive wildfire ignition and propagation. A new method is proposed to automatically classify and map fuel types from LiDAR data. The 3-dimensional Discrete Anisotropic Radiative Transfer (DART) model generated a fuel type LiDAR signature library. These simulations provided reference endmembers and additional data to demonstrate the feasibility to classify fuel types using spectral matching algorithms, like multiple endmember spectral mixture analysis (MESMA) and spectral angle mapper (SAM). When choosing a single endmember per fuel type, MESMA outperformed SAM with 63.3% and 48.9% agreement, respectively. Multiple endmembers per fuel type improved the classification results to 85.3% in SAM and 86.5% in MESMA. Endmembers need to identify different scan angles that account for the variability in height and number of trees for better results. Contrary to empirical models, a fuel type LiDAR signature library provides a comprehensive suite of solutions to classify fuel types from LiDAR data that is less study site dependent and applicable to multiple sensors.

A Modified Multi-Source Parallel Model for Estimating Urban Surface Evapotranspiration Based on ASTER Thermal Infrared Data

To date, little attention has been given to remote sensing-based algorithms for inferring urban surface evapotranspiration. A multi-source parallel model based on ASTER data was one of the first examples, but its accuracy can be improved. We therefore present a modified multi-source parallel model in this study, which has made improvements in parameterization and model accuracy. The new features of our modified model are: (1) a characterization of spectrally heterogeneous urban impervious surfaces using two endmembers (high- and low-albedo urban impervious surface), instead of a single endmember, in linear spectral mixture analysis; (2) inclusion of an algorithm for deriving roughness length for each land surface component in order to better approximate to the actual land surface characteristic; and (3) a novel algorithm for calculating the component net radiant flux with a full consideration of the fraction and the characteristics of each land surface component. HJ-1 and ASTER data from the Chinese city of Hefei were used to test our model’s result with the China–ASEAN ET product. The sensitivity of the model to vegetation and soil fractions was analyzed and the applicability of the model was tested in another built-up area in the central Chinese city of Wuhan. We conclude that our modified model outperforms the initial multi-source parallel model in accuracy. It can obtain the highest accuracy when applied to vegetation-dominated (vegetation proportion > 50%) areas. Sensitivity analysis shows that vegetation and soil fractions are two important parameters that can affect the ET estimation. Our model is applicable to estimate evapotranspiration in other urban areas.

Extraction of Endmembers From Hyperspectral Images Using A Weighted Fuzzy Purified-Means Clustering Model

Hyperspectral endmembers are the spectra of pure materials that are responsible for generating the mixed pixels in hyperspectral images (HSIs). Hyperspectral endmember extraction (HEE) is essentially an inverse problem, where the unknown endmembers are inferred from the spectral measurements. Efficient extraction of endmembers in HSI relies on a well-defined generative model that captures key factors in HSI generation process, such as the clustering effect in the spatial domain and the noise heterogeneity effect in the spectral domain. This paper presents a weighted fuzzy purified-means (WFP-means) clustering model for HEE, where the endmembers are modeled as mean vectors of individual classes, and the fractional contributions of individual endmembers, called abundances, are treated as soft class membership. Accordingly, an endmember is estimated as the weighted mean of purified pixels in HSI, while the abundances are estimated as the nonnegative regression coefficients. In contrast to a mixed pixel that consists of multiple endmembers, a “purified pixel” is due to a single endmember. The introduction of the concept of “purified pixels” into the fuzzy clustering model leads to an elegant optimization scheme. Moreover, the proposed model accounts for the noise variance heterogeneity issue, which is essential for achieving unbiased abundance estimation. The proposed method is tested on both simulated and real HSI, in comparison with several other HEE methods. The results demonstrate that the proposed method compares favorably with respect to the referenced methods in terms of both endmember and abundance estimation.

Spectral Unmixing Evaluation for Oil Spill Characterization

Hyperspectral remote sensing exploits the optical properties of materials and provides detailed information about them. From a theoretical point of view, in case of oil spills, it cannot only detect and delineate them, but also provide information about the oil type and oil thickness, significantly contributing at the remediation stage of clean-up. In practice, many factors, either associated with the inherent characteristics of oil spills (oil type, quantity, weathering stage, etc.), or with environmental factors (sea bottom cover and depth, waves, etc.) affect the spectral signature of the oil, set constraints on the effectiveness of hyperspectral methods. In this study, the key factors that enable an airborne hyperspectral campaign to implement effective surveys for oil spill detection and characterization are investigated. Additionally, the study focuses on the assessment of environmental and slick parameters for which spectral unmixing-based methods successfully address the problem of oil spill detection and oil type and thickness estimation. For this purpose, study of the spectral behavior of the oil through laboratory measurements and measurements in the complex marine environment was a prerequisite and has initially been carried out. The results showed that almost all the measured spectral signatures as well as their variations can be extracted as endmembers from synthetic images using the unmixing theory. Consequently, laboratory spectral libraries could enable the labeling procedure during the spectral unmixing application on hyperspectral imagery. Unfortunately, oil spectral measurements implemented in marine environment were significantly different because they were affected either by sea bottom contributions (case of light oil and petroleum products) or by sea state conditions which cause high dispersion of oil and spatial variation in oil spill thickness (case of heavy oil and petroleum products). When airborne hyperspectral imagery is processed, it has been found that transparent clouds significantly affect the efficiency of unmixing methods for thin oil spill detection. Their removal, as well as atmospheric correction is strongly recommended. Applying spectral unmixing-based methods on hyperspectral imagery, oil spill detection is effective even in the marginal case of sheens. The results showed that all types and thicknesses of oils can be detected independently of seawater depth through the differences that their spectral signatures present in the wavelengths between 720 μm and 1000 μm. For oil sheens, a single endmember is usually extracted, which leads to relative thickness estimation. For thicker oil spills, many endmembers are extracted each one corresponding to a different thickness and/or emulsion. Further research based on an extended spectral library of measurements in marine environment should be performed in order to enable spectral unmixing-based methods to accurately estimate the oil type, the oil to water ratio of an emulsion as well the oil thickness.

Spectral Unmixing Model Based on Least Squares Support Vector Machine With Unmixing Residue Constraints

Spectral unmixing has been an important technique for hyperspectral imagery processing. In traditional spectral unmixing methods that are based on the linear spectral mixture model (LSMM), unmixing accuracy is limited by the inherent deficiency of the model. It was shown that the support vector machine (SVM) can be extended for spectral unmixing, based on the advantage that the SVM model can accommodate the variations within a relative pure class by using multiple pure samples instead of a single endmember for one class. In the SVM model, class label errors are considered in constraints. However, the errors concerned in spectral unmixing are the unmixing residue instead of the class label ones. This letter presents a method of imposing unmixing residue constraints on the least squares SVM unmixing model. The related problems, including deducing the closed-form solution and substituting the single endmember for multiple ones, were studied together. Experiments showed that the new SVM model was superior to the original SVM as well as the traditional LSMM in terms of unmixing residue, fractional abundance, and confused matrix criterions.

Assimilation of endmember variability in spectral mixture analysis for urban land cover extraction

Variable Endmember Constrained Least Square (VECLS) technique is proposed to account endmember variability in the linear mixture model by incorporating the variance for each class, the signals of which varies from pixel to pixel due to change in urban land cover (LC) structures. VECLS is first tested with a computer simulated three class endmember considering four bands having small, medium and large variability with three different spatial resolutions. The technique is next validated with real datasets of IKONOS, Landsat ETM+ and MODIS. The results show that correlation between actual and estimated proportion is higher by an average of 0.25 for the artificial datasets compared to a situation where variability is not considered. With IKONOS, Landsat ETM+ and MODIS data, the average correlation increased by 0.15 for 2 and 3 classes and by 0.19 for 4 classes, when compared to single endmember per class.

Improving Discrimination of Savanna Tree Species Through a Multiple-Endmember Spectral Angle Mapper Approach: Canopy-Level Analysis

Differences in within-species phenology and structure are controlled by genetic variation, as well as topography, edaphic properties, and climatic variables across the landscape, and present important challenges to species differentiation with remote sensing. The objectives of this paper are as follows: 1) to evaluate the classification performance of a multiple-endmember spectral angle mapper (SAM) classification approach in discriminating ten common African savanna tree species and 2) to compare the results with the traditional SAM classifier based on a single endmember per species. The canopy spectral reflectance of the tree species ( Acacia nigrescens, Combretum apiculatum , Combretum imberbe, Dichrostachys cinerea, Euclea natalensis, Gymnosporia buxifolia, Lonchocarpus capassa, Pterocarpus rotundifolius, Sclerocarya birrea, and Terminalia sericea) was extracted from airborne hyperspectral imagery that was acquired using the Carnegie Airborne Observatory system over Kruger National Park, South Africa, in May 2008. This study highlights three important phenomena: 1) Intraspecies spectral variability affected the discrimination of savanna tree species with the SAM classifier; 2) the effect of intraspecies spectral variability was minimized by adopting the multiple-endmember approach, e.g., the multiple-endmember approach produced a higher overall accuracy (mean of 54.5% for 20 bootstrapped replicates) when compared to the traditional SAM (mean overall accuracy = 20.5%); and 3) targeted band selection improved the classification of savanna tree species (the mean overall percent accuracy is 57% for 20 bootstrapped replicates). Higher overall classification accuracies were observed for evergreen trees than for deciduous trees.

Normalized spectral mixture analysis for monitoring urban composition using ETM+ imagery

With rapid urban growth in recent years, understanding urban biophysical composition and dynamics becomes an important research topic. Remote sensing technologies introduce a potentially scientific basis for examining urban composition and monitoring its changes over time. The vegetation–impervious surface–soil (V–I–S) model, in particular, provides a foundation for describing urban/suburban environments and a basis for further urban analyses including urban growth modeling, environmental impact analysis, and socioeconomic factor estimation. This paper develops a normalized spectral mixture analysis (NSMA) method to examine urban composition in Columbus Ohio using Landsat ETM+ data. In particular, a brightness normalization method is applied to reduce brightness variation. Through this normalization, brightness variability within each V–I–S component is reduced or eliminated, thus allowing a single endmember representing each component. Further, with the normalized image, three endmembers, vegetation, impervious surface, and soil, are chosen to model heterogeneous urban composition using a constrained spectral mixture analysis (SMA) model. The accuracy of impervious surface estimation is assessed and compared with two other existing models. Results indicate that the proposed model is a better alternative to existing models, with a root mean square error (RMSE) of 10.1% for impervious surface estimation in the study area.

Interannual controls on Weddell Sea surface water fCO 2 during the autumn–winter transition phase

The fugacity of carbon dioxide ( fCO 2) of the surface waters of the Weddell Sea along the prime meridian has been described for the austral autumn in 1996 and 1998. For individual years, fCO 2 has a strong linear relationship with sea surface temperature, although the relationships cannot be reconciled to provide an interannually consistent algorithm for remotely sensed assessment of fCO 2. However, from the assumption that Weddell Sea surface water has a single end member (upwelled Warm Deep Water) we have determined the relative contributions of heating, ice-melt, and biological activity on fCO 2. A breakdown of the controls shows that the measured annual fCO 2 distributions can be recreated for both transects by adjusting solely for thermodynamic forcing, and model adjustments for salinity are small except in regions of significant upwelling during 1998. The incorporation of nitrate utilisation into the model results in a general and significant underestimation of fCO 2. This runs contrary to the earlier findings of Sabine and Key (Mar. Chem. 60 (1998) 95) in the Southern Ocean although it is consistent with models in the area (Louanchi et al., Deep-Sea Res. I 48 (2001) 1581). A major caveat to these findings is the significant departure of the thermodynamic model and a tightening of the nitrate-adjusted model in 1998 in areas with deeper mixing in the southern Weddell Sea. We propose that there are two reasons for the discrepancies in our model: the source waters are not as homogenous as the model assumes; and there are geographical and seasonal variations of CO 2 exchange with the atmosphere and the input of inorganic carbon and nitrate from below the mixed layer resulting in imbalances in the mixed layer concentration ratios.

Endmember bundles: a new approach to incorporating endmember variability into spectral mixture analysis

Accuracy of vegetation cover fractions, computed with spectral mixture analysis, may be compromised by variation in canopy structure and biochemistry when a single endmember represents top-of-canopy reflectance. In this article, endmember variability is incorporated into mixture analysis by representing each endmember by a set or bundle of spectra, each of which could reasonably be the reflectance of an instance of the endmember. Endmember bundles are constructed from the data itself by an extension to a previously described method of manually deriving endmembers from remotely sensed data. Applied to remotely sensed images, bundle unmixing produces maximum and minimum fraction images bounding the correct cover fractions and specifying error due to endmember variability. In this article, endmember bundles and bounding fraction images were created for an airborne visible/infrared imaging spectrometer (AVIRIS) subscene simulated with a canopy radiative transfer/geometric-optical model. Variation in endmember reflectance was achieved using ranges of parameter values including leaf area index (LAI) and tissue optical properties observed In a North Texas savanna. The subscene's spatial pattern was based on a 1992 Landsat Thematic Mapper image of the study region. Bounding fraction images bracketed the cover fractions of the simulated data for 98% of the pixels for soil, 97% for senescent grass and 93% for trees. Averages of bounding images estimated fractional coverage used in the simulation with an average error of /spl les/0.05, a significant improvement over previous methods with important implications for regional-scale research on vegetation extent and dynamics.

HIGHER MINERAL ARSENIDES OF COBALT, NICKEL, AND IRON

X-ray, microscopic, microchemical, contact-print, and mineral synthesis techniques have been applied to the problem of the relationships of the higher natural arsenides of cobalt, nickel, and iron. The data obtained have been correlated with a review of existing analyses. Both the isometric and “orthorhombic” groups exhibit limited isomorphism in regard to the three metals, and the two groups appear to be essentially complementary. The isometric members form a single group of triarsenides with the skutterudite structure. The long-held assumption that published analyses indicate the existence of an isometric diarsenide series is not substantiated by a critical review of the analyses. Extensive arsenic deficiency shown by published analyses of isometric arsenides is due largely to mechanical inhomogeneity involving “orthorhombic” diarsenides, niccolite, and other minerals. Isomorphous substitution of metal for arsenic may contribute to the arsenic deficiency, but evidence for this was not obtained. The lattice constants of the isometric arsenides are related to the ratio between the three metals, varying directly with increasing nickel, iron, or nickel and iron content. Variations in arsenic ratio do not appear to influence the lattice constants appreciably. The lattice constants range from 8.187 A to 8.311 A, an increase over that previously recorded (8.18A to 8.27 A). Isometric arsenide crystals are almost invariably zoned and inhomogeneous, containing both isometric and nonisometric constituents. Fine granular aggregates of “orthorhombic” diarsenides frequently occur in these complex cubic crystals and have probably often been overlooked since the anisotropism is weak. The inhomogeneous character of these zonal crystals could account for many of the reported compositional peculiarities of the isometric arsenides such as extensive arsenic deficiency and extreme variation in the cobalt-nickel-iron ratio. Since there is no valid basis for an isometric diarsenide series, it is urged that the names smaltite, chloanthite, chathamite, and arsenoferrite, long associated with an alleged series of isometric diarsenides, be dropped. The single term skutterudite should be applied to all isometric arsenides of cobalt, nickel, and iron and in a restricted sense to those in which cobalt is dominant; the appropriate modifiers, nickelian and ferrian, would indicate dominance of nickel and iron respectively. Such a terminology is believed adequate since the isomorphism between cobalt, nickel, and iron in the isometric group is clearly limited, and only a single end member (cobalt) appears to exist. The “orthorhombic” diarsenides exhibit both discontinuous and limited isomorphism between cobalt, nickel, and iron; those high in nickel are completely separated from the iron-bearing members by a broad wedge of isometric arsenides. The term rammelsbergite is retained for the common high-nickel member, and pararammelsbergite for the rarer nickel—rich form. The term loellingite is applied to all iron-rich orthorhomic diarsenides and in a restricted sense to those with an iron ratio greater than 85. The group of iron-rich orthorhombic diarsenides with an iron ratio of less than 85 and with cobalt dominant over nickel may be termed cobaltian loellingite. The corresponding group with nickel dominant over cobalt is designated nickelian loellingite. Safflorite has been rather generally accepted for the cobalt end member of an allegedly unlimited isomorphous series of orthorhombic diarsenides, the other end members being loellingite and rammelsbergite. There is no evidence for the existence of such a cobalt end member of the “orthorhombic” series, either from the available data on natural material or from the experiments in synthesis. The plotting of the published analyses indicates a clustering of “orthorhombic” analyses in the mid-portion of the cobalt-iron edge of the diagram. The symmetry of these iron-cobalt arsenides is monoclinic according to (Peacock, 1944), justifying the retention of the name safflorite as a species distinct from loellingite. However it should be redefined as a monoclinic diarsenide of cobalt and iron in which the proportions of the two metals are approximately equal