Estimation of covariance matrix from geochemical data with observations below detection limits     

Chang-Jo F. Chung 《Mathematical Geology》1993,25(7):851-865

Multivariate statistical analyses have been extensively applied to geochemical measurements to analyze and aid interpretation of the data. Estimation of the covariance matrix of multivariate observations is the first task in multivariate analysis. However, geochemical data for the rare elements, especially Ag, Au, and platinum-group elements, usually contain observations the below detection limits. In particular, Instrumental Neutron Activation Analysis (INAA) for the rare elements produces multilevel and possibly extremely high detection limits depending on the sample weight. Traditionally, in applying multivariate analysis to such incomplete data, the observations below detection limits are first substituted, for example, each observation below the detection limit is replaced by a certain percentage of that limit, and then the standard statistical computer packages or techniques are used to obtain the analysis of the data. If a number of samples with observations below detection limits is small, or the detection limits are relatively near zero, the results may be reasonable and most geological interpretations or conclusions are probably valid. In this paper, a new method is proposed to estimate the covariance matrix from a dataset containing observations below multilevel detection limits by using the marginal maximum likelihood estimation (MMLE) method. For each pair of variables, sayY andZ whose observations containing below detection limits, the proposed method consists of three steps: (i) for each variable separately obtaining the marginal MLE for the means and the variances, , , , and forY andZ: (ii) defining new variables by and and lettingA=C+D andB=C–D, and obtaining MLE for variances, and forA andB; (iii) estimating the correlation coefficient _YZ by and the covariance _YZ by . The procedure is illustrated by using a precious metal geochemical data set from the Fox River Sill, Manitoba, Canada.  相似文献   

Topological properties of random crack networks     

N. H. Gray  J. B. Anderson  J. D. Devine  J. M. Kwasnik 《Mathematical Geology》1976,8(6):617-626

The junctions of cracks in mudcrack, patterned ground, and columnar joint patterns can be categorized into Y, T,and Xtypes. The mean number of sides, ,to the polygonal areas in such nets is = 2(2J_T + 3J_Y + 4J_X)/(J_T + J_Y + 2J_X)where J_T, J_Y,and J_X are the proportions of T, Y,and Xjunctions, respectively.  相似文献   

Manganese olivine I: Electrical conductivity     

Quan Bai  Z. -C. Wang  D. L. Kohlstedt 《Physics and Chemistry of Minerals》1995,22(8):489-503

To investigate the point defect chemistry and the kinetic properties of manganese olivine Mn₂SiO₄, electrical conductivity () of single crystals was measured along either the [100] or the [010] direction. The experiments were carried out at temperatures T=850–1200 °C and oxygen fugacities atm under both Mn oxide (MO) buffered and MnSiO₃ (MS) buffered conditions. Under the same thermodynamic conditions, charge transport along [100] is 2.5–3.0 times faster than along [010]. At high oxygen fugacities, the electrical conductivity of samples buffered against MS is 1.6 times larger than that of samples buffered against MO; while at low oxygen fugacities, the electrical conductivity is nearly identical for the two buffer cases. The dependencies of electrical conductivity on oxygen fugacity and temperature are essentially the same for conduction along the [100] and [010] directions, as well as for samples coexisting with a solid-state buffer of either MO or MS. Hence, it is proposed that the same conduction mechanisms operate for samples of either orientation in contact with either solid-state buffer.The electrical conductivity data lie on concave upward curves on a log-log plot of vs , giving rise to two regimes with different oxygen fugacity exponents. In the low- regime , the exponent, m, is 0, the MnSiO₃-activity exponent, q, is 0, and the activation energy, Q, is 45 kJ/mol. In the high regime 10^{ - 7} {\text{atm}}} \right)$$ " align="middle" border="0"> , m=1/6, q=1/4–1/3, and Q=45 and 200 kJ/mol for T<1100 °c=" and=">T>1100 °C, respectively.  相似文献   

High-temperature creep and kinetic decomposition of Ni2SiO4     

J. Wolfenstine  D. L. Kohlstedt 《Physics and Chemistry of Minerals》1994,21(4):234-243

To investigate high-temperature creep and kinetic decomposition of nickel orthosilicate (Ni₂SiO₄), aggregates containing 3 vol% amorphous SiO₂ have been deformed in uniaxial compression at a total pressure of one atomsphere. Twenty-three samples with grain sizes (d) from 9 to 30 m were deformed at temperatures (T) from 1573 to 1813 K, differential stresses () from 3 to 20 MPa, and oxygen fugacities (f o ₂) from 10^-1 to 10⁵ Pa. At temperatures up to 1773 K, the steady-state creep rate () can be described by the flow law

相似文献    12. Über p-Veatehit,eine neue Veatehit-Varietät aus dem Zechsteinsalz      Dr. Otto Braitsch 《Contributions to Mineralogy and Petrology》1959,6(5):352-356 Zusammenfassung Im Älteren Steinsalz von Reyershausen bei Göttingen wurde eine neue Veatchit-Varietät gefunden mita 0 = 6,721 Å,b 0 = 20,81 Å,c 0 = 6,647 Å, = 119° 4; Raumgruppe oderP21,Z = 4[(Sr, Ca) O · 3 B2O3 · 2 H2O]. (010) ist die Ebene der vollkommenen Spalt-barkeit. Die Polymorphie der Veatehit-Minerale wird geometrisch durch geringfügige Deformationen der rhombischen Raumgruppe (bzw.A21 a m) erklärt.Der neue Vertreter wirdp-Veatehit (mit einfach-primitivem Raumgitter) genannt im Unterschied zum Original-Veatehit, der in die Raumgruppe gehört und dessen Symametrieebene senkrecht auf der vollkommenen Spaltebene steht.  相似文献    13. Estimating relative bed-load contributions by lithology counts      Hugh H. Mills  Paul J. Tsai 《Mathematical Geology》1982,14(3):241-247 In gravel-bedded streams where bed material of a tributary differs distinctly in lithology from that of the main stream, rock-type percentages can be used to estimate bed-load contributions of the two streams. The rock type that shows the greatest difference in abundance between the two streams is selected as the indicator lithology. Percentages of this lithology are estimated in both the main stream and tributary stream above their junction, and also in the main stream at a distance sufficiently downstream from the junction to allow complete mixing. The fraction of bed load contributed by the main stream, p,is estimated by ,where is an estimate of the proportion of indicator rock fragments in the bed of the main stream above the junction, is an estimate of the proportion in the bed of the tributary above the junction, and is an estimate of the proportion in the bed of the main stream below the junction. The variance of is obtained as var ( )= [p1q1(pr – p2)2/n(p1 – p2)4] + [p2q2(pr – p1)2/n(p1 – p2)4] + [prqr/n(p1 – p2)2].Although no estimate of actual quantity of bed load is provided, the indicator rock technique supplies data that can serve as a check on data obtained by means of empirical formulas or actual transport measurements.  相似文献    14. Maximum entropy and shear strain of shear zone      H. Nagahama 《Mathematical Geology》1992,24(8):947-955 The principle of maximum entropy can be used to determine the shear strain in natural shear zones. When the margin of a shear zone is assumed, the principle leads to the truncated exponential distribution of the shear strain. Ifx is the distance remote from the shear zone center, which possesses the maximum shear strain, the shear strain (x) is given by   相似文献    15. Johillerit,Na(Mg,Zn)3 Cu(AsO4)3, ein neues Mineral aus Tsumeb,Namibia      Prof. Dr. P. Keller  Prof. Dr. H. Hess  P. J. Dunn 《Mineralogy and Petrology》1982,29(3):169-175 Zusammenfassung Die chemische Analyse des neuen Minerals Johillerit mit der Elektronenmikrosonde ergab: Na2O 5,4, MgO 18,3, ZnO 5,4, CuO 15,8 und As2O5 55,8, Summe 100.7%. Aus diesem Ergebnis wurde die idealisierte Formel Na(Mg, Zn)3 Cu(AsO4)3 abgeleitet. Johillerit ist monoklin mit der RaumgruppeC2/c. Die Gitterkonstanten sind:a=11,870 (3),b=12,755 (3),c=6,770 (2) , =113,42 (2)°,Z=4. Die stärksten Linien des Pulverdiagramms sind: 4,06 (5) (22 ), 3,50 (4) (310), 3,25 (8) (11 ), 2,75 (10) (330, 240), 2,64 (5) (311, 13 , 40 ), 1,952 (4) (13 , 35 ), 1,682 (4) (20 , 460), 1,660 (5) (40 , 71 , 550, 64 ), 1,522 (4) (442, 153, 13 ). Es bestehen enge strukturelle Beziehungen zwischen Johillerit und O'Danielit, Na(Zn, Mg)3H2(AsO4)3, sowie einigen synthetischen. Verbindungen.Johillerit ist violett durchscheinend. Die Spaltbarkeit nach {010} ist ausgezeichnet und nach {100} und {001} gut.H (Mohs)3.D=4,15 undD X =4,21 g·cm–3. Das Mineral ist optisch zweiachsig positiv, 2V80 (5)°. Die Werte der Lichtbrechung sindn =1,715 (4),n =1,743 (4) undn =1,783 (4). Die Auslöschung istn b und auf (010)n c16°. Johillerit ist stark pleochroitisch mit den AchsenfarbenX=violett-rot,Y = blauviolett undZ = grünblau. Das neue Mineral kommt in radialstrahligen Massen gemeinsam mit kupferhaltigem Adamin und Konichalcit in zersetzem Kupfererz von Tsumeb, Namibia, vor. Die Benennung erfolgte nach Prof. Dr.J.-E. Hiller (1911–1972). Johillerite, Na(Mg, Zn) 3 Cu(AsO 4 ) 3 , a new mineral from Tsumeb, Namibia Summary Electron microprobe analysis of the new mineral johillerite gave Na2O 5.4, MgO 18.3, ZnO 5.4, CuO 15.8, and As2O5 55.8, total 100.7%. From this result, the ideal formula is given as Na(Mg, Zn)3 Cu(AsO4)3. Johillerite crystallizes monoclinic,C2/c. The unit cell dimensions are:a=11.870(3),b=12.755 (3),c=6.770 (2) , =113.42 (2)°,Z=4. The strongest lines on the X-ray powder diffraction pattern are: 4,06 (5) (22 ), 3,50 (4) (310), 3,25 (8) (11 ), 2,75 (10) (330, 240), 2,64 (5) (311, 13 , 40 ), 1,952 (4) (13 , 35 ), 1,682 (4) (20 , 460), 1,660 (5) (40 , 71 , 550, 64 ), 1,522 (4) (442, 153, 13 ). There is a close relationship between johillerite, o'danielite, Na(Zn, Mg)3H2(AsO4)3, and some synthetic compounds. Johillerite is violet in colour, transparent. Cleavage is {010} perfect, {100} and {001} good.H (Mohs)3.D=4.15 andD X =4.21 g·cm–3. The mineral is optically biaxial positive, 2V80 (5)°. The refractive indices are:n =1.715 (4),n =1.743 (4),n =1.783 (4). The extinction isn b and on (010)n c16°. Strongly pleochroic with axial coloursX=violet-red,Y=bluish violet andZ=greenish blue. The new mineral was found in radiated masses together with cuprian adamite and conichalcite in an oxidized copper ore from Tsumeb, Namibia. It is named in honour of Prof. Dr.J.-E. Hiller (1911–1972). Mit 1 Abbildung  相似文献    16. The dependence of the Fe2+-Mg cation-partitioning between olivine and basaltic liquid on pressure,temperature and composition      Peter Ulmer 《Contributions to Mineralogy and Petrology》1989,101(3):261-273 The equilibrium partitioning of Fe2+ and Mg between olivine and liquid along a liquid line of descent has been determined for a calc-alkaline system, ranging in composition from picritic to andesitic. Experiments were conducted between 1000–1450° C and 1 bar to 30 kbar. Within the compositional range investigated and , the compositional dependence of the Fe2+ and Mg partitioning is a function of the Mg-content of the liquid. The Mg-content of the liquid correlates strongly with temperature. The variation of the Fe2+ and Mg partitioning were therefore evaluated individualy as functions of composition and temperature alone. The composition dependence of the cation-partitioning coefficients (Kd) is given by the following two equations:   相似文献    17. Long-term earthquake prediction in the North Pacific seismic zone based on the time and magnitude predictable model      Eleftheria E. Papadimitriou 《Natural Hazards》1994,9(3):303-321 Earthquake recurrence intervals for large and great shallow mainshocks in 12 seismogenic sources along the North Pacific seismic zone (Alaska-Aleutians-Kamchatka-Kuril Islands) have been estimated and used for the determination of the following relations:   相似文献    18. Synthesis and stability of bastnaesites in a part of the system (Ce,La)-F-H-C-O      Dr. L. C. Hsu 《Mineralogy and Petrology》1992,47(1):87-101 Summary Bastnaesites of Ce and La and their OH-analogs were synthesized and their stability relations were determined atPf = 1 kbar andT = 400 to 900°C in a part of the system (Ce,La)-F-H-C-0. The initial fluid compositions were such that and HF/(HF + H2O) ratios were 0 to 0.172. XRD and IR studies indicate that bastnaesites equilibrated in initial fluids low in HF are all F-enriched. The hydroxylbastnaesite-(La) is stable up to 810°C and the fluorbastnaesite-(La) is stable up to 860°C. Their condensed breakdown products are La2O2CO3 and LaOF, respectively. The stability of Ce bastnaesites is slightly dependent. The hydroxylbastnaesite-(Ce) is stable up to 660°C at the defined by the IQF buffer and up to 640°C by the MH buffer. The fluorbastnaesite-(Ce) is stable up to 800°C at the defined by the IQF and up to 760°C by the MH buffer. The condensed breakdown product for the hydroxyl end-member is simply CeO2 but for the fluorine one is a combination of CeO2, CeF3, and CeOF. Factors, such as OH vs F, , and bulk composition, that affect the stability of individual species are discussed. Petrogenic implications resulting from the present study include that bastnaesites can be stable from hydrothermal to magmatic conditions, that F-enriched species can form in an environment relatively low in F content, and that OH-species are rare and occur only in low-temperature environments essentially devoid of F. Synthese und Stabilität von Bastndsil in einem Teil des Systems (Ce,La)-F-H-C-O Zusammenfassung Ce- und La-Bastnäsite, sowie deren OH-Analoga wurden synthetisiert und ihre Stabilitätsbeziehunger beiP f = 1 kbar undT = 400 bis 900°C wurden im System (Ce,La)F-H-C-O bestimmt. Die anfänglichen Flüssigkeitszusammensetzungen waren so, daß und die HF/(HF + H2O)-Verhältnisse 0–0.172 waren. Röntgenpulver- und Ultrarot-Untersuchungen zeigten, daß Bastnäsite, die mit anfänglich HF-armen Flüssigkeiten equilibriert wurden, alle an F angereichert sind. Hydroxilbastndsit-(La) ist bis 810°C und Fluorbastnäsit-(La) bis 860°C stabil. Ihre festen Zersetzungsprodukte sind La2O2O3, bzw. LaOF. Die Stabilität der Ce-Bastnäsite hängt etwas von ab. Hydroxilbastnäsit-(Ce) ist bei des Eisen-Quarz-Fayalit-Puffers bis 660°C stabil und mit Magnetit-Hämatit-Puffer bis 640°C. Das feste Zerfallsprodukt ist für das Hydroxil-Glied nur CeO2, für das Fluor-Glied eine Mischung aus CeO2, CeF3 und CeOF. Faktoren, welche die Stabilität der einzelnen Spezies beeinflussen, werden diskutiert, wie das Verhältnis OH zu F, und die Gesamtzusammensetzung. Petrogenetische Folgerungen aus der vorliegenden Studie schließen ein, daß Bastnäsite von hydrothermalen bis zu magmatischen Bedingungen stabil sein können, daß sich an F angereicherte Glieder in relativ F-armer Umgebung bilden können, und daß OH-Glieder selten sind und nur unter Bildungsbedingungen niedriger Temperatur und weitgehender Abwesenheit von F auftreten. With 8 Figures  相似文献    19. Thermodynamic modelling of non-convergent ordering in orthopyroxenes: a comparison of classical and Landau approaches      Herbert Kroll  Hartmut Schlenz  Michael W. Phillips 《Physics and Chemistry of Minerals》1994,21(8):555-560 The excess Gibbs free energy due to non-convergent ordering is described by a Landau expansion in which configurational and non-configurational entropy contributions are separated:   相似文献    20. The crystal structure of a triclinic roscherite      Prof. L. Fanfani  Prof. P. F. Zanazzi  Dr. Anna Rosa Zanzari 《Mineralogy and Petrology》1977,24(3):169-178 Summary The crystallography of roscherite is more complicated than previously thought. Single crystal X-ray work on material from Foote Mine (California) gave triclinic symmetry. The unit cell corresponding to the one adopted for monoclinic roscherite hasa=15.921,b=11.965,c=6.741 Å, =91°04, =94°21, =89°59 1/2, space group . The least-squares refinement of the structure using 2380 non zero reflections with anisotropic temperature factors resulted in a conventional reliability factorR=0.060.The X-ray study indicates the formula while that proposed for monoclinic roscherite is The atomic arrangements of both varieties of roscherite are very similar. The lowering of symmetry is caused by the segregation of the trivalent cations into only half of the sites of a monoclinic point position. Crystallochemical considerations suggest that the symmetry of roscherite does not depend on the kind of trivalent cations occupying the 6-coordinated position, but rather by the ratio between trivalent and divalent metal ions. Die Kristallstruktur eines triklinen Roscherites Zusammenfassung Die Kristallographie des Roscherites ist komplizierter als man bisher annahm. Einkristall-Röntgenuntersuchungen an Material von Foote Mine (Kalifornien) ergaben trikline Symmetrie. Die Elementarzelle, welche der für monoklinen Roscherit angenommenen entspricht, hata=15,921,b=11,965,c=6,741 Å, =91°04, =94°21, =89°59 1/2, Raumgruppe . Die Verfeinerung der Struktur mit der Methode der kleinsten Quadrate ergab unter Verwendung anisotroper Temperaturfaktoren für 2380 beobachtete Reflexe einen konventionellen ZuverlässigkeitsindexR=0,060.Die Röntgenuntersuchung weist auf die Formel , während für monoklinen Roscherit vorgeschlagen wurde. Die Atomanordnungen beider Abarten des Roscherites sind sehr ähnlich. die Symmetrieerniedrigung wird dadurch hervorgerufen, daß die dreiwertigen Kationen nur die Hälfte der Positionen einer monoklinen Punktlage besetzen. Kristallchemische Überlegungen weisen darauf hin, daß die Symmetrie nicht von der Art der dreiwertigen Kationen, welche eine 6-koordinierte Punktlage besetzen, abhängt, sondern vielmehr von dem Mengenverhältnis zwischen 3-wertigen und 2-wertigen Metallionen. With 1 Figure  相似文献    设为首页 | 免责声明 | 关于勤云 | 加入收藏 Copyright©北京勤云科技发展有限公司  京ICP备09084417号