Geostatistical Simulation with a Trend Using Gaussian Mixture Models     

Jianan Qu  Clayton V. Deutsch 《Natural Resources Research》2018,27(3):347-363

Geostatistics applies statistics to quantitatively describe geological sites and assess the uncertainty due to incomplete sampling. Strong assumptions are required regarding the location independence of statistical parameters to construct numerical models with geostatistical tools. Most geological data exhibit large-scale deterministic trends together with short-scale variations. Such location dependence violates the common geostatistical assumption of stationarity. The trend-like deterministic features should be modeled prior to conventional geostatistical prediction and accounted for in subsequent geostatistical calculations. The challenge of using a trend in geostatistical simulation algorithms for the continuous variable is the subject of this paper. A stepwise conditional transformation with a Gaussian mixture model is considered to provide a stable and artifact-free numerical model. The complex features of the regionalized variable in the presence of a trend are removed in the forward transformation and restored in the back transformation. The Gaussian mixture model provides a seamless bin-free approach to transformation. Data from a copper deposit were used as an example. These data show an apparent trend unsuitable for conventional geostatistical algorithms. The result shows that the proposed algorithm leads to improved geostatistical models.  相似文献   

Experiments on melt–rock reaction in the shallow mantle wedge     

Alexandra?L.?MitchellEmail author  Timothy?L.?Grove 《Contributions to Mineralogy and Petrology》2016,171(12):107

This experimental study simulates the interaction of hotter, deeper hydrous mantle melts with shallower, cooler depleted mantle, a process that is expected to occur in the upper part of the mantle wedge. Hydrous reaction experiments (~6 wt% H₂O in the melt) were conducted on three different ratios of a 1.6 GPa mantle melt and an overlying 1.2 GPa harzburgite from 1060 to 1260 °C. Reaction coefficients were calculated for each experiment to determine the effect of temperature and starting bulk composition on final melt compositions and crystallizing assemblages. The experiments used to construct the melt–wall rock model closely approached equilibrium and experienced <5% Fe loss or gain. Experiments that experienced higher extents of Fe loss were used to critically evaluate the practice of “correcting” for Fe loss by adding iron. At low ratios of melt/mantle (20:80 and 5:95), the crystallizing assemblages are dunites, harzburgites, and lherzolites (as a function of temperature). When the ratio of deeper melt to overlying mantle is 70:30, the crystallizing assemblage is a wehrlite. This shows that wehrlites, which are observed in ophiolites and mantle xenoliths, can be formed by large amounts of deeper melt fluxing though the mantle wedge during ascent. In all cases, orthopyroxene dissolves in the melt, and olivine crystallizes along with pyroxenes and spinel. The amount of reaction between deeper melts and overlying mantle, simulated here by the three starting compositions, imposes a strong influence on final melt compositions, particularly in terms of depletion. At the lowest melt/mantle ratios, the resulting melt is an extremely depleted Al-poor, high-Si andesite. As the fraction of melt to mantle increases, final melts resemble primitive basaltic andesites found in arcs globally. An important element ratio in mantle lherzolite composition, the Ca/Al ratio, can be significantly elevated through shallow mantle melt–wall rock reaction. Wall rock temperature is a key variable; over a span of <80 °C, reaction with deeper melt creates the entire range of mantle lithologies from a depleted dunite to a harzburgite to a refertilized lherzolite. Together, the experimental phase equilibria, melt compositions, and reaction coefficients provide a framework for understanding how melt–wall rock reaction occurs in the natural system during melt ascent in the mantle wedge.  相似文献   

The beginnings of hydrous mantle wedge melting   总被引：5，自引：3，他引：2  

Christy?B.?TillEmail author  Timothy?L.?Grove  Anthony?C.?Withers 《Contributions to Mineralogy and Petrology》2012,163(4):669-688

This study presents new phase equilibrium data on primitive mantle peridotite (0.33 wt% Na₂O, 0.03 wt% K₂O) in the presence of excess H₂O (14.5 wt% H₂O) from 740 to 1,200°C at 3.2–6 GPa. Based on textural and chemical evidence, we find that the H₂O-saturated peridotite solidus remains isothermal between 800 and 820°C at 3–6 GPa. We identify both quenched solute from the H₂O-rich fluid phase and quenched silicate melt in supersolidus experiments. Chlorite is stable on and above the H₂O-saturated solidus from 2 to 3.6 GPa, and chlorite peridotite melting experiments (containing ~6 wt% chlorite) show that melting occurs at the chlorite-out boundary over this pressure range, which is within 20°C of the H₂O-saturated melting curve. Chlorite can therefore provide sufficient H₂O upon breakdown to trigger dehydration melting in the mantle wedge or perpetuate ongoing H₂O-saturated melting. Constraints from recent geodynamic models of hot subduction zones like Cascadia suggest that significantly more H₂O is fluxed from the subducting slab near 100 km depth than can be bound in a layer of chloritized peridotite ~ 1 km thick at the base of the mantle wedge. Therefore, the dehydration of serpentinized mantle in the subducted lithosphere supplies free H₂O to trigger melting at the H₂O-saturated solidus in the lowermost mantle wedge. Alternatively, in cool subduction zones like the Northern Marianas, a layer of chloritized peridotite up to 1.5 km thick could contain all the H₂O fluxed from the slab every million years near 100 km depth, which suggests that the dominant form of melting below arcs in cool subduction zones is chlorite dehydration melting. Slab P–T paths from recent geodynamic models also allow for melts of subducted sediment, oceanic crust, and/or sediment diapirs to interact with hydrous mantle melts within the mantle wedge at intermediate to hot subduction zones.  相似文献   

Reply to ‘Comment on “The beginnings of hydrous mantle wedge melting” by Till et al.’ by Stalder     

Christy B. Till  Timothy L. Grove  Anthony C. Withers 《Contributions to Mineralogy and Petrology》2012,164(6):1073-1076

The comment of Stalder raises three main concerns regarding the interpretation of the experiments presented by Till et al. (2012): (1) our inability to uniquely distinguish between high-pressure hydrous silicate melt and solute-rich aqueous fluid leads to the incorrect interpretation of phase relations, (2) the temperature interval over which hydrous melting takes places is inordinately large and contrary to expectations, and/or (3) the possibility that the system may be above the second critical end point (SCEP) in this H₂O-rich silicate system has been insufficiently discussed. In this reply, we provide clarification on these concerns and argue that with the extent of knowledge available today, the chemical characteristics of our experimental products at 3.2 and 4?GPa evince the presence of a silicate melt at temperatures <1,000?°C and we are below the SCEP in the peridotite–H₂O system at the P–T conditions of our experiments. If in fact the quench observed in our experiments does represent that of a supercritical (SC) fluid, then our data suggest Mg and Fe are highly soluble in SC fluids at the P–T conditions of the base of the mantle wedge below arc volcanoes. Therefore, our results would require a significant change in thinking about the chemical compositional characteristics of SC fluids.  相似文献   

Projection Pursuit Multivariate Transform   总被引：5，自引：2，他引：3  

Ryan M. Barnett  John G. Manchuk  Clayton V. Deutsch 《Mathematical Geosciences》2014,46(3):337-359

Transforming complex multivariate geological data to a Gaussian distribution is an important and challenging problem in geostatistics. A variety of transforms are available for this goal, but struggle with high dimensional data sets. Projection pursuit density estimation (PPDE) is a well-established nonparametric method for estimating the joint density of multivariate data. A central component of the PPDE algorithm transforms the original data toward a multivariate Gaussian distribution. The PPDE approach is modified to map complex data to a multivariate Gaussian distribution within a geostatistical modeling context. Traditional modeling may then take place on the transformed Gaussian data, with a back-transform used to return simulated variables to their original units. This approach is referred to as the projection pursuit multivariate transform (PPMT). The PPMT shows the potential to be an effective means for modeling high dimensional and complex geologic data. The PPMT algorithm is developed before discussing considerations and limitations. A case study compares modeling results against more common techniques to demonstrate the value and place of the PPMT within geostatistics.  相似文献   

FRENCH TROPICAL GEOGRAPHIES: EDITORS' INTRODUCTION     

Gavin Bowd  Daniel Clayton 《Singapore journal of tropical geography》2005,26(3):271-288

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Experimental and petrological constraints on lunar differentiation from the Apollo 15 green picritic glasses     

Linda T. Elkins‐Tanton  Nilanjan Chatterjee  Timothy L. Grove 《Meteoritics & planetary science》2003,38(4):515-527

Abstract— Phase equilibrium experiments on the most magnesian Apollo 15C green picritic glass composition indicate a multiple saturation point with olivine and orthopyroxene at 1520°C and 1.3 GPa (about 260 km depth in the moon). This composition has the highest Mg# of any lunar picritic glass and the shallowest multiple saturation point. Experiments on an Apollo 15A composition indicate a multiple saturation point with olivine and orthopyroxene at 1520°C and 2.2 GPa (about 440 km depth in the moon). The importance of the distinctive compositional trends of the Apollo 15 groups A, B, and C picritic glasses merits the reanalysis of NASA slide 15426,72 with modern electron microprobe techniques. We confirm the compositional trends reported by Delano (1979, 1986) in the major element oxides SiO₂, TiO₂, Al₂O₃, Cr₂O₃, FeO, MnO, MgO, and CaO, and we also obtained data for the trace elements P₂O₅, K₂O, Na₂O, NiO, S, Cu, Cl, Zn, and F. Petrogenetic modeling demonstrates that the Apollo 15 A‐B‐C glass trends could not have been formed by fractional crystallization or any continuous assimilation/fractional crystallization (AFC) process. The B and C glass compositional trends could not have been formed by batch or incremental melting of an olivine + orthopyroxene source or any other homogeneous source, though the A glasses may have been formed by congruent melting over a small pressure range at depth. The B compositional trend is well modeled by starting with an intermediate A composition and assimilating a shallower, melted cumulate, and the C compositional trend is well modeled by a second assimilation event. The assimilation process envisioned is one in which heat and mass transfer were separated in space and time. In an initial intrusive event, a picritic magma crystallized and provided heat to melt magma ocean cumulates. In a later replenishment event, the picritic magma incrementally mixed with the melted cumulate (creating the compositional trends in the green glass data set), ascended to the lunar surface, and erupted as a fire fountain. A barometer created from multiple saturation points provides a depth estimate of other glasses in the A‐B‐C trend and of the depths of assimilation. This barometer demonstrates that the Apollo 15 A‐B‐C trend originated over a depth range of ?460 km to ?260 km within the moon.  相似文献   

R Coronae Borealis Stars, Dust, and Evolution     

Geoffrey C. Clayton 《Astrophysics and Space Science》1997,255(1-2):479-480

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Northwest Africa 032: Product of lunar volcanism     

T. J. Fagan  G. J. Taylor  K. Keil  T. E. Bunch  J. H. Wittke  R. L. Korotev  B. L. Jolliff  J. J. Gillis  L. A. Haskin  E. Jarosewich  R. N. Clayton  T. K. Mayeda  V. A. Fernandes  R. Burgess  G. Turner  O. Eugster  S. Lorenzetti 《Meteoritics & planetary science》2002,37(3):371-394

Abstract— Mineralogy, major element compositions of minerals, and elemental and oxygen isotopic compositions of the whole rock attest to a lunar origin of the meteorite Northwest Africa (NWA) 032, an unbrecciated basalt found in October 1999. The rock consists predominantly of olivine, pyroxene and chromite phenocrysts, set in a crystalline groundmass of feldspar, pyroxene, ilmenite, troilite and trace metal. Whole‐rock shock veins comprise a minor, but ubiquitous portion of the rock. Undulatory to mosaic extinction in olivine and pyroxene phenocrysts and micro‐faults in groundmass and phenocrysts also are attributed to shock. Several geochemical signatures taken together indicate unambiguously that NWA 032 originated from the Moon. The most diagnostic criteria include whole‐rock oxygen isotopic composition and ratios of Fe/Mn in the whole rock, olivine, and pyroxene. A lunar origin is documented further by the presence of Fe‐metal, troilite, and ilmenite; zoning to extremely Fe‐rich compositions in pyroxene; the ferrous oxidation state of all Fe in pyroxene; and the rare earth element (REE) pattern with a well‐defined negative europium anomaly. This rock is similar in major element chemistry to basalts from Apollo 12 and 15, but is enriched in light REE and has an unusually high Th/Sm ratio. Some Apollo 14 basalts yield a closer match to NWA 032 in REE patterns, but have higher concentrations of Al₂O₃. Ar‐Ar step release results are complex, but yield a whole‐rock age of ?2.8 Ga, suggesting that NWA 032 was extruded at 2.8 Ga or earlier. This rock may be the youngest sample of mare basalt collected to date. Noble gas concentrations combined with previously collected radionuclide data indicate that the meteorite exposure history is distinct from currently recognized lunar meteorites. In short, the geochemical and petrographic features of NWA 032 are not matched by Apollo or Luna samples, nor by previously identified lunar meteorites, indicating that it originates from a previously unsampled mare deposit. Detailed assessment of petrographic features, olivine zoning, and thermodynamic modelling indicate a relatively simple cooling and crystallization history for NWA 032. Chromite‐spinel, olivine, and pyroxene crystallized as phenocrysts while the magma cooled no faster than 2 °C/h based on the polyhedral morphology of olivine. Comparison of olivine size with crystal growth rates and preserved Fe‐Mg diffusion profiles in olivine phenocrysts suggest that olivine was immersed in the melt for no more than 40 days. Plumose textures in groundmass pyroxene, feldspar, and ilmenite, and Fe‐rich rims on the phenocrysts formed during rapid crystallization (cooling rates ?20 to 60 °C/h) after eruption.  相似文献   

Yamato 792947, 793408 and 82038: The most primitive H chondrites,with abundant refractory inclusions     

M. Kimura  H. Hiyagon  H. Palme  B. Spettel  D. Wolf  R. N. Clayton  T. K. Mayeda  T. Sato  A. Suzuki  H. Kojima 《Meteoritics & planetary science》2002,37(10):1417-1434

Abstract— In this paper we report petrological and chemical data of the unusual chondritic meteorites Yamato (Y)‐792947, Y‐93408 and Y‐82038. The three meteorites are very similar in texture and chemical composition, suggesting that they are pieces of a single fall. The whole‐rock oxygen isotopes and the chemical compositions are indicative of H chondrites. In addition, the mineralogy, and the abundances of chondrule types, opaque minerals and matrices suggest that these meteorites are H3 chondrites. They were hardly affected by thermal and shock metamorphism. The degree of weathering is very low. We conclude that these are the most primitive H chondrites, H3.2–3.4 (S1), known to date. On the other hand, these chondrites contain extraordinarily high amounts of refractory inclusions, intermediate between those of ordinary and carbonaceous chondrites. The distribution of the inclusions may have been highly heterogeneous in the primitive solar nebula. The mineralogy, chemistry and oxygen isotopic compositions of inclusions studied here are similar to those in CO and E chondrites.  相似文献