ArticlePDF Available

Aplicación de las pruebas estadísticas de discordancia y significancia en la comparación del vulcanismo dacítico de la parte central de Cinturón Volcánico Mexicano

Authors:

Abstract and Figures

Nuestro objetivo es presentar una metodología estadística, junto con dos nuevos programas (DODESSYS y UDASYS). Para esta tarea compilamos una base de datos de 249 muestras de rocas dacitas provenientes de cuatro regiones del cinturón volcánico mexicano (MVB): volcanes monogenéticos de la Sierra de Chichinautzin y el Valle de México, estratovolcán Nevado de Toluca, estratovolcán Iztaccíhuatl y estratovolcán Popocatépetl. Las pruebas estadísticas de discordancia y significancia (ANOVA –ANalysis Of Variance–, F de Fisher y t de Student) fueron aplicadas al 99% de nivel de confianza. Se calculó la estadística final para 98 parámetros, incluyendo óxidos mayores, elementos de tierras raras, elementos traza y parámetros adicionales, tales como parámetros de relaciones logarítmicas usados en nuevos diagramas de discriminación tectónica. Estos parámetros fueron tratados como muestras estadísticas univariadas y fueron clasificados en cuatro regiones del MVB. Las pruebas estadísticas de discordancia detectaron datos discordantes en 124 (aproximadamente en el 35%) muestras estadísticas univariadas. La prueba ANOVA mostró diferencias significativas entre todos los grupos en 32 parámetros. Las similitudes y diferencias entre los parámetros de relaciones logarítmicas pueden ser útiles en el futuro para proponer diagramas de discriminación tectónica a partir de una base de datos representativa.
Content may be subject to copyright.
Revista Electrónica Nova Scientia
Aplicación de las pruebas estadísticas de
discordancia y significancia en la comparación
del vulcanismo dacítico de la parte central de
Cinturón Volcánico Mexicano
Application of discordancy and significance
statistical tests for the comparison of dacitic
volcanism from the central part of the Mexican
Volcanic Belt
Lorena Díaz-González1 and René Cruz-Huicochea2
1Facultad de Ciencias, Universidad Autónoma de Estado de Morelos
2Posgrado en Ingeniería (Energía), Universidad Nacional Autónoma de México
México
Lorena Díaz-González. E-mail: ldg@uaem.mx
© Universidad De La Salle Bajío (México)
Díaz-González, L. y R. Cruz-Huicochea
Aplicación de las pruebas estadísticas de discordancia y significancia en la comparación del vulcanismo dacítico de la parte
central de Cinturón Volcánico Mexicano
Revista Electrónica Nova Scientia, Nº 11 Vol. 6 (1), 2013. ISSN 2007 - 0705. pp: 158 - 178
- 159 -
Resumen
Nuestro objetivo es presentar una metodología estadística, junto con dos nuevos programas
(DODESSYS y UDASYS). Para esta tarea compilamos una base de datos de 249 muestras de
rocas dacitas provenientes de cuatro regiones del cinturón volcánico mexicano (MVB): volcanes
monogenéticos de la Sierra de Chichinautzin y el Valle de México, estratovolcán Nevado de
Toluca, estratovolcán Iztaccíhuatl y estratovolcán Popocatépetl. Las pruebas estadísticas de
discordancia y significancia (ANOVA ANalysis Of Variance, F de Fisher y t de Student)
fueron aplicadas al 99% de nivel de confianza. Se calculó la estadística final para 98 parámetros,
incluyendo óxidos mayores, elementos de tierras raras, elementos traza y parámetros adicionales,
tales como parámetros de relaciones logarítmicas usados en nuevos diagramas de discriminación
tectónica. Estos parámetros fueron tratados como muestras estadísticas univariadas y fueron
clasificados en cuatro regiones del MVB. Las pruebas estadísticas de discordancia detectaron
datos discordantes en 124 (aproximadamente en el 35%) muestras estadísticas univariadas. La
prueba ANOVA mostró diferencias significativas entre todos los grupos en 32 parámetros. Las
similitudes y diferencias entre los parámetros de relaciones logarítmicas pueden ser útiles en el
futuro para proponer diagramas de discriminación tectónica a partir de una base de datos
representativa.
Palabras clave: ANOVA, F de Fisher, t de Student, datos discordantes, datos geoquímicos, ma-
nejo estadístico de datos composicionales
Recepción: 29-10-2012 Aceptación: 29-10-2013
Díaz-González, L. y R. Cruz-Huicochea
Revista Electrónica Nova Scientia, Nº 11 Vol. 6 (1), 2013. ISSN 2007 - 0705. pp: 158 178
- 160 -
Abstract
Our aim is to show a statistical procedure along with two new computer programs (DODESSYS
and UDASYS). For this task we compiled a database of 249 samples of dacite coming from four
closely located Mexican Volcanic Belt (MVB) areas: monogenetic volcanoes from the Sierra de
Chichinautzin and Valle de México, the Nevado de Toluca stratovolcano, the Iztaccíhuatl
stratovolcano and the Popocatépetl stratovolcano. The discordancy and significance (ANOVA
ANalysis Of Variance, Fishers´ F and Student´s t) statistical tests were applied at 99%
confidence level. The final statistical was calculated for 98 geochemical parameters, these
include major oxides, rare earth elements, trace elements and additional parameters, as well as
log-ratio parameters used in new tectonic discrimination diagrams. These geochemical
parameters were treated as univariate statistical samples and were classified according with the
four MVB regions. Discordancy statistical tests detected discordant outliers in 124 (amount to
about 35%) statistical samples. ANOVA tests showed significant differences among all groups in
32 parameters. The similarities and differences between the log-ratios parameters elements may
eventually be useful in future to propose tectonic discrimination diagrams from a representative
database.
Keywords: ANOVA, Fisher´s F, Student´s t, discordant outliers, geochemical data, statistical
handling of compositional data
Aplicación de las pruebas estadísticas de discordancia y significancia en la comparación del vulcanismo dacítico de la parte
central de Cinturón Volcánico Mexicano
Revista Electrónica Nova Scientia, Nº 11 Vol. 6 (1), 2013. ISSN 2007 - 0705. pp: 158 - 178
- 161 -
Introduction
Recently, a new computer programs has been developed, UDASYS (Univariate Data Analysis
SYStem) [1]. UDASYS is freely available from any of the authors to any scientist interested in
correctly processing experimental data. This program, written in Java [2], provides statistical
tools pertaining to both robust and outlierbased methods for univariate data. UDASYS also
incorporates an updated version of the DODESSYS software [3]. Whereas DODESSYS allowed
the application of discordancy tests ([3] for more details on these tests see Table S1 in online
Supplementary Material) for statistical sample sizes up to 1000, all discordancy tests can now be
applied to statistical sample sizes as large as 30000. Computer programs to enable the application
of discordancy tests were practically nonexistent as documented by Barnett and Lewis (1994).
Later about 12 years ago, a computer program (SIPVADE) was published by Verma et al.
(1998), but it is now outdated for several reasons. The most important among them are that
SIPVADE uses old, less precise and sometimes even inaccurate critical values then available in
the literature (Barnett and Lewis 1994; Verma 2005) and relies on linear interpolation of these
values when for a given statistical sample size n, the corresponding critical values were not
tabulated. Both of these aspects have been shown to cause errors in the final statistical inferences.
More importantly, unlike all available software to date (e.g., [4]), UDASYS allows a highly
efficient use of significance tests of Fisher's F, Student's t, and ANOVA.
This work illustrates the application of statistical discordancy and significance tests using
geochemical data. A geochemical database of major-elements in rocks from the Mexican
volcanic belt (MVB) was established long ago by Pal et al. [5]. These authors used their database
to objectively characterise for the first time the nature of volcanism in the MVB. This work was
later extended by including more analyses of MVB rocks in this database which permitted to
highlight the complexity of magmas in the MVB (e.g., [6]). Mean and standard deviation
estimates of compositional data were presented by these authors, but this was done without the
application of discordancy tests [7]. Similarly in local geochemical studies from this volcanic
province (MVB), these two statistical parameters for laboratory analytical data were specifically
reported by Verma [8-10] and Verma et al. [11]. Other researchers have used mean and standard
deviation estimates for geochemical interpretation [12].
In this work geochemical data are compiled for dacitic rocks from four nearby areas of the
MVB. The geochemical parameters are compared through the significance tests such as Fisher´s
Díaz-González, L. y R. Cruz-Huicochea
Revista Electrónica Nova Scientia, Nº 11 Vol. 6 (1), 2013. ISSN 2007 - 0705. pp: 158 178
- 162 -
F and Student´s t [13] without and with the application of discordancy tests [14-17]. The results
highlight the importance of these statistical tests in geosciences.
We searched the published geoscience literature for specific applications of discordancy
and significance tests and found that it is not a common practice to apply them in geoscientific
studies. Below we list some the reports found that made use of either one of these statistical
methodologies.
Rice and Church [18] presented a statistical study on the variability in grain size of
sediment from two confluent rivers in northeastern British Columbia (Canada). They stated that it
was not appropriate to apply ANOVA test because the statistical samples did not show a normal
distribution and their variances were unequal. However, the validity of the first condition can be
checked by discordancy tests, whereas the second condition (equal variances) is not a requisite
for ANOVA. They applied tests, such as Brown-Forsythe and chi-square, for comparing
statistical sample means when sample variances are unequal.
Takano et al. [19] made a statistical comparison of inter-laboratory analytical data of fluid
samples from crater lake of Maly Semiachik volcano, located in the central part of the Eastern
Volcanic Belt of Kamchatka (Japan), obtained from eight different institutions. They used
different analytical techniques (atomic absorption spectrometry, atomic emission spectrometry,
mass spectrometry, ion chromatography, high performance liquid chromatography, colorimetry,
and titrimetry) to compare the measured isotopic data coming from elements such as hydrogen,
sulfur, and oxygen. Their comparison consisted of simply calculating the central tendency (mean)
and dispersion (coefficient of variation) parameters for each one of these techniques. Experience
shows that it would have been worthwhile to apply the discordancy and significance tests for
such inter-laboratory evaluations as suggested earlier by several authors [20-21].
Wani and Mondal [22] carried out a geochemical study of shale samples from the
Mesoproterozoic-Neoproterozoic Chhattisgarh and Indrāvati basins. They compared chemical
compositions of the calcareous and non-calcareous shales of the Chhattisgarh and Indrāvati
basins applying only the Student’s t at 95% confidence level. They should have applied Fisher’s
F test prior to the application of the t test since this significance test is sensitive to the presence of
discordant outliers. We emphasize once again that discordancy tests should be applied to detect
Aplicación de las pruebas estadísticas de discordancia y significancia en la comparación del vulcanismo dacítico de la parte
central de Cinturón Volcánico Mexicano
Revista Electrónica Nova Scientia, Nº 11 Vol. 6 (1), 2013. ISSN 2007 - 0705. pp: 158 - 178
- 163 -
anomalous data in individual statistical samples previous to the comparison and use of
significance tests.
The correct statistic application, such as the work we are reporting, tries to promote the
evolution of geochemistry towards geochemometrics, where statistics is an essential part of
experimental data treatment. In general, in the area of geochemistry is not customary to apply a
correct statistics methodology in the processing of databases. For example, Takano et al. [19]
assessed the statistic differences in their experimental databases, but failed to apply the
methodology based on significance tests and discordancy. However, recently some authors
applied successfully this complete methodology in processing geochemical data [17, 23].
Particularly, the discordance tests have been applied in a diversity of scientific and engineering
fields, including some branches of earth sciences such as determination of Nernst distribution
coefficients [24]; quality control through reference materials [14-16, 23]; geothermal research
[25-27]; geochemistry [12, 15, 17]; volcanoes studies [28, 29]; pollution studies [30]; petroleum
research [31]; soil research [32]; proteomics research [33]. Also, sensitivity and uncertainty
analysis is another important statistical application [34-38].
Method
Database and procedures
Geochemical data for 249 Neogene dacitic rock samples from four closely located areas
of the MVB were compiled. The literature sources were as follows: [9, 21, 39-60]. Data are
identifiqued as group numbers Gr1 to Gr4 (see locations of these regions on a map presented in
Figure 1): Region 1 (Gr1)diverse locations of the Sierra de Chichinautzin and the southern of
the Valle de México (monogenetic volcanoes); Region 2 (Gr2)the Nevado de Toluca
stratovolcano; Region 3 (Gr3)the Iztaccíhuatl stratovolcano, and Region 4 (Gr4)the
Popocatépetl stratovolcano.
Díaz-González, L. y R. Cruz-Huicochea
Revista Electrónica Nova Scientia, Nº 11 Vol. 6 (1), 2013. ISSN 2007 - 0705. pp: 158 178
- 164 -
98°102°106°
19
20°
21
a
Mexican Volcanic Belt
N
W
Tac
MexicoMexico
Guatemala
Popoc atépetl
Nevado de Tol uca
Iztaccíhua tl
Vall e de México
Sierra de Chi chinautzin
Figure 1. Schematic location of the site under study: Sierra de Chichinautzin, south of Valle de México, Nevado de
Toluca, Iztaccíhuatl and Popocatepetl (Mexico).
TAS (Total Alkalis vs Silica) diagram was generated by IgRocs sofware [61]; see Figure 2.
Geochemical data are concentrated in classification area for dacite rocks.
(SiO2)adj (%m/m)
(Na2O + K2O)adj (%m/m)
55 60 65 70 75
2
4
6
8
Popocatépetl
Nevado de Tol uca
Iztaccíhua tl
Vall e de México
Sierra Chic hinautzin
D
TD
TA
R
A
Figure 2. This figure shows a diagram of discrimination TAS. Geochemical data are concentrated in classification
area for dacite rocks.
The statistical central tendency (mean) and dispersion (standard deviation) parameters were
calculated for several conventional variables, which were 11 major oxides (adjusted values) from
(SiO2)Adj to (P2O5)Adj, selected normative minerals, Mg-number (or Mg-value), and 6 other
indices detailed by [61], followed by 14 rare earth elements from La to Lu, and 22 trace elements
from Ba to Zr. In addition to these conventional chemical data, 30 additional parameters were
computed and evaluated. These include two ratio parameters defined by Verma [62] called Nb-
anomaly with respect to Ba and La and Ta-anomaly with respect to Ba and La, as well as 28 log-
Aplicación de las pruebas estadísticas de discordancia y significancia en la comparación del vulcanismo dacítico de la parte
central de Cinturón Volcánico Mexicano
Revista Electrónica Nova Scientia, Nº 11 Vol. 6 (1), 2013. ISSN 2007 - 0705. pp: 158 - 178
- 165 -
ratio parameters of elements used in new multi-dimensional tectonic discrimination diagrams
[63-65].
Figure 3 shows the flow diagram of statistical methodology applied in this work.
Conventionally, significant test are applied without prior application of discordancy tests.
However, because these tests should be applied to normally distributed statistical samples, data
for each variable from all individual groups (Gr1-Gr4) were first processed for discordant outliers
by single-outlier type discordancy tests (see Table S1 in [1]) at 99% confidence level, and the
discordant outlier-free groups were evaluated from the two-sided ANOVA-test and t-test at 99%
confidence level (see Geological implications in [1] for more details on application of two-sided
version of significant tests). The statistical parameters of mean and standard deviation were
simply calculated from the discordant outlier-free individual groups.
Figure 3. Schematic flow diagram of statistical methodology applied in this work.
We note that, ANOVA test can only be applied to three or more groups or statistical samples [7],
therefore this significant test was applied to the data from each group (Gr1-Gr4). The application
of ANOVA would result in any of the following: (i) no statistically significant differences among
the four regions (Gr1-Gr4); (ii) one e.g., Gr1 of the four regions showing a statistically
significant difference as compared to the other three regions e.g., Gr2- Gr4; and (iii)
Díaz-González, L. y R. Cruz-Huicochea
Revista Electrónica Nova Scientia, Nº 11 Vol. 6 (1), 2013. ISSN 2007 - 0705. pp: 158 178
- 166 -
statistically significant differences among the four regions (Gr1- Gr4), which will have to be
resolved by Fisher´s F and Student´s t significance tests. When ANOVA detects significant
differences among the four regions, the data should be processed thorough the combination of
Fisher´s F and Student´s t tests, which are applicable to only two groups at a time [63, 64]. The
Fisher´s F test compares the two variances and could result in either the two variances are equal
or the two are different. Depending on the result of the F test, the appropriate version of the t test
should be applied. The Fisher’s F and Student’s t tests were applied to each one of the
combinations Gr1-Gr2, Gr1-Gr3, Gr1-Gr4, Gr2-Gr3, Gr2-Gr4 and Gr3-Gr4.
It has been suggested that the data from different groups or regions should only be
combined after ascertaining that no statistically significant differences exist among them [1].
Thus, for a given chemical parameter or variable, the groups that showed no significant
differences were combined and statistical information was obtained for the combined data.
Finally, these combined data were once again processed for discordant outliers, and the
discordant outlier-free data were used to obtain final statistical (mean and standard deviation).
Resultados
Identification and separation of discordant outliers
Geochemical data for a total of 96 variables o parameters from each group (Gr1-Gr4) were
processed in this work. Single-outlier type discordancy tests at a very strict 99% confidence level
were then applied to individual groups, outlying observations were separated, and statistical
parameters were calculated from discordant outlier-free data. These statistical parameters are
reported in Table 1; the first column gives the name of the chemical or ratio parameter, the next
columns gives statistical parameters such as statistical sample size (n), mean and standard
deviation from all individual groups (Gr1-Gr4); i.e. columns 2-4 show stastistical parameters
from Sierra de Chichinautzin and Valle de Mexico monogenetic volcanoes. The second column
gives the final statistical sample size (n) after discordant outlier detection and separation, the third
column reports the mean, and the fourth one provided the standard deviation. The number of
discordant outliers is represented by a symbol as superscript: α one–; β two–; γ three–; δ
four ; £ five–; ζ –seven–; η –eight–; λ –ten. For the total of 350 statiscal samples processed in
this work, 124 (35%) samples showed discordant outliers.
Aplicación de las pruebas estadísticas de discordancia y significancia en la comparación del vulcanismo dacítico de la parte
central de Cinturón Volcánico Mexicano
Revista Electrónica Nova Scientia, Nº 11 Vol. 6 (1), 2013. ISSN 2007 - 0705. pp: 158 - 178
- 167 -
Application of ANOVA, t and F tests after elimination of outliers
ANOVA test determined that 32 variables did not show statistically significant
differences among all groups, hence they were combined; e.g., (Na2O)Adj, (K2O)Adj, orNorm,
abNorm, anNorm , La, Pr, Nd, Sm, Eu, ln((Na2O)Adj/Si), ln((K2O)Adj/Si), ln((P2O5)Adj/Si), ln(Nb/Yb),
ln(Th/Yb), ln(Y/Yb) and ln(Zr/Yb). ANOVA also identified a discordant group (Gr2, Gr3 and
Gr4 in 3, 17 and 12 variables, respectively) in 32 variables; e.g., the Gr2 group was identified as
discordant group in (P2O5)Adj variable, therefore, Gr2 group was separated and Gr1, Gr2 and Gr4
groups were combined. Finally, ANOVA determined statistically significant differences among
the four regions in 32 elements, e.g., all groups from (TiO2)Adj major element were identified as
discordant groups and were not combined. Fisher´s F and Student´s t tests were applied to these
32 variables.
Application of discordancy tests after combining data (significance tests)
Single-outlier type discordancy tests were applied to the combined groups, outlying observations
were separated, and statistical parameters were calculated from discordant outlier-free data (see
Table 2 in appendix). These discordant outliers were rejected (or separated) and final statistical
were calculated and shown in Table 2. Discordant outliers were represented by a symbol as
superscript: α one–; β –two–; γ –three–; δ –four ; £ five–; ζ –seven–; η –eight–; λ –ten.
Conclusions
In this work, we have shown a statistical procedure to decipher mean compositions and
uncertainty estimates including various regions. For this, geochemical data are compiled for 249
Neogene dacitic rock samples from the four MVB regions.
All single-outlier type discordancy tests and significance (ANOVA ANalysis Of Variance,
Fishers´ F and Student´s t) statistical tests were applied at the very strict 99% confidence level.
These statistical tests were applied to each one of the 98 geochemical parameters, which were
major oxides, selected normative minerals, rare earth, trace elements, two ratio parameters called
Nb-anomaly and Ta-anomaly, as well as 28 log-ratio parameters of elements used in new multi-
dimensional tectonic discrimination diagrams.
Díaz-González, L. y R. Cruz-Huicochea
Revista Electrónica Nova Scientia, Nº 11 Vol. 6 (1), 2013. ISSN 2007 - 0705. pp: 158 178
- 168 -
All geochemical parameters were treated as univariate statistical samples. Final statistical
parameters were calculated from discordant outlier-free data. We suggest that the final mean
compositions could be used to compare statistically the geochemical data for the same type of
igneous rocks, i.e., dacite type, sampled around the world.
Furthermore, significance statistical tests determined significant differences and similarities
among various geochemical parameters from the four MVB regions. Particularly, the similarities
and differences among the log-ratios parameters could be useful to propose new diagrams to
discriminate tectonic settings, with a more representative database.
Acknowledgements
L.D-G. acknowledges PROMEP support to the project “Estadística Computacional para el
tratamiento de datos experimentales” (PROMEP/103-5/10/7332). R.C-H. acknowledges
CONACyT-Mexico for a scholarship to carry out his master studies.
Referencias
[1] Verma S P, Cruz-Huicochea and Díaz-González L, Univariate data analysis system:
deciphering mean compositions of island and continental arc magmas and effects of
underlying crust, International Geology Review, in press.
[2] Deitel P J and Deitel H M, Java: How to Program, 7 Ed., Prentice Hall, Java: How to
Program, 2006.
[3] Verma S P and Díaz-González L, Application of the discordant outlier detection and
separation system in the geosciences, International Geology Review, Vol. 54, No. 5,
2012, pp. 593-614
[4] StatSoft I. STATISTICA (data analysis software system), statsoft.com, 2004.
[5] Pal S, et al., Magma characterization of the Mexican volcanic belt (Mexico), Bulletin of
Volcanology, Vol. 41, No. 4, 1978, pp. 379-389
[6] Verma S P, Aguilar-Y-Vargas, V.H., Bulk chemical composition of magmas in the
Mexican Volcanic Belt (Mexico) and inapplicability of generalized arc-models, Chemie
der Erde, Vol. 48, 1988, pp. 203-221
[7] Barnett V and Lewis T, Outliers in statistical data, J. Wiley, 1994.
Aplicación de las pruebas estadísticas de discordancia y significancia en la comparación del vulcanismo dacítico de la parte
central de Cinturón Volcánico Mexicano
Revista Electrónica Nova Scientia, Nº 11 Vol. 6 (1), 2013. ISSN 2007 - 0705. pp: 158 - 178
- 169 -
[8] Verma S P, Alkali and alkaline earth element geochemistry of Los Humeros Caldera,
Puebla, Mexico, Journal of Volcanology and Geothermal Research, Vol. 20, No. 1-2,
1984, pp. 21-40
[9] Verma S P, Geochemistry of evolved magmas and their relationship to subduction-
unrelated mafic volcanism at the volcanic front of the central Mexican Volcanic Belt,
Journal of Volcanology and Geothermal Research, Vol. 93, No. 1-2, 1999, pp. 151-171
[10] Verma S P, Geochemical evidence for a lithospheric source for magmas from Los
Humeros caldera, Puebla, Mexico, Chemical Geology, Vol. 164, No. 1-2, 2000, pp. 35-
60
[11] Verma S P, Carrasco-N'uñez G, and Milán M, Geology and geochemistry of Amealco
Caldera, Qro., Mexico, Journal of Volcanology and Geothermal Research, Vol. 47, No.
1-2, 1991, pp. 105-127
[12] Madhavaraju J L, Y. I., Geochemistry of the Dalmiapuram Formation of the Uttatur
Group (Early Cretaceous), Cauvery basin, southeastern India: Implications on
provenance and paleo-redox conditions, Revista Mexicana de Ciencias Geológicas, Vol.
26, No. 2, 2009, pp. 380-394
[13] Miller J N and Miller J C, Statistics and chemometrics for analytical chemistry, Fifth
Ed., Pearson Prentice Hall, 2005.
[14] Marroquín-Guerra S G, Velasco-Tapia F, and Díaz-González L, Evaluación estadística
de Materiales de Referencia Geoquímica del Centre de Recherches Pétrographiques et
Géochimiques (Francia) aplicando un esquema de detección y eliminación de valores
desviados, Revista mexicana de ciencias geológicas, Vol. 26, 2009, pp. 530-542
[15] Pandarinath K, Evaluation of geochemical sedimentary reference materials of the
Geological Survey of Japan (GSJ) by an objective outlier rejection statistical method,
Revista Mexicana de Ciencias Geológicas, Vol. 26, No. 3, 2009b, pp. 638-646
[16] González-Ramírez R, Díaz-González, L., Verma, S.P., Eficiencia relativa de 15 pruebas
de discordancia con 33 variantes aplicadas al procesamiento de datos geoquímicos,
Revista Mexicana de Ciencias Geológicas, Vol. 26, No. 2, 2009, pp. 501-515
[17] Armstrong-Altrin J S, Provenance of sands from Cazones, Acapulco, and Bahía Kino
beaches, México, Revista Mexicana de Ciencias Geológicas, Vol. 26, No. 3, 2009, pp.
764-782
[18] Rice S and Church M, Grain size along two gravel-bed rivers: statistical variation,
spatial pattern and sedimentary links, Earth Surface Processes and Landforms, Vol. 23,
No. 4, 1998, pp. 345-363
[19] Takano B, Fazlullin S M, and Delmelle P, Analytical laboratory comparison of major
and minor constituents in an active crater lake, Journal of Volcanology and Geothermal
Research, Vol. 97, No. 1-4, 2000, pp. 497-508
Díaz-González, L. y R. Cruz-Huicochea
Revista Electrónica Nova Scientia, Nº 11 Vol. 6 (1), 2013. ISSN 2007 - 0705. pp: 158 178
- 170 -
[20] Guevara M, Verma, S.P., Velasco-Tapia, F., Evaluation of GSJ intrusive rocks JG1,
JG2, JG3, JG1a, and Jgb1 by an objective outlier rejection statistical procedure, Revista
Mexicana de Ciencias Geológicas, Vol. 18, No. 1, 2001, pp. 74-88
[21] Velasco-Tapia F, Verma, S.P., Magmatic Processes at the volcanic front of Central
Mexican Volcanic Belt: Sierra de Chichinautzin volcanic field (Mexico), Turkish
Journal of Earth Sciences, No. in press, 2011,
[22] Wani H and Mondal M E A, Evaluation of provenance, tectonic setting, and paleoredox
conditions of the Mesoproterozoic-Neoproterozoic basins of the Bastar craton, Central
Indian Shield: Using petrography of sandstones and geochemistry of shales,
Lithosphere, Vol. 3, No. 2, 2011, pp. 143-154
[23] Pandarinath K, Clay minerals in SW Indian continental shelf sediment cores as
indicators of provenance and palaeomonsoonal conditions: a statistical approach,
International Geology Review, Vol. 51, No. 2, 2009, pp. 145-165
[24] Torres-Alvarado I S, et al., DC_BASE: a database system to manage Nernst distribution
coefficients and its application to partial melting modeling, Computers &
Geosciences, Vol. 29, No. 9, 2003, pp. 1191-1198
[25] Díaz-González L, Santoyo E, and Reyes-Reyes J, Tres nuevos geotermómetros
mejorados de Na/K usando herramientas computacionales y geoquimiométricas:
aplicación a la predicción de temperaturas de sistemas geotérmicos, Revista Mexicana
de Ciencias Geológicas, Vol. 25, No. 3, 2008, pp. 465-482
[26] Gómez-Arias E, et al., Determinación de la viscosidad y su incertidumbre en fluidos de
perforación usados en la construcción de pozos geotérmicos: aplicación en el campo de
Los Humeros, Puebla, México, Revista mexicana de ciencias geológicas, Vol. 26, 2009,
pp. 516-529
[27] Pandarinath K, Applicability of solute geothermometry for springs and wells of the Los
Azufres and Las Tres Vírgenes geothermal fields, Mexico, International Geology
Review, No. in press, 2011,
[28] Sanci R, Panarello, H.O., and Ostera, H.A., Flujo de dióxido de carbono en el flanco
oriental del Volcán Peteroa Andes del Sur, Revista Mexicana de Ciencias Geológicas,
Vol. 27, No. 2, 2010, pp. 225-237
[29] Torres-Alvarado I S, Smith A D, and Castillo-Román J, Sr, Nd and Pb isotopic and
geochemical constraints for the origin of magmas in Popocatépetl volcano (central
Mexico) and their relationship with the adjacent volcanic fields, International Geology
Review, Vol. 53, No. 1, 2011, pp. 84-115
[30] Heath E, et al., Second interlaboratory exercise on non-steroidal anti-inflammatory drug
analysis in environmental aqueous samples, Talanta, Vol. 81, No. 4-5, 2010, pp. 1189-
1196
Aplicación de las pruebas estadísticas de discordancia y significancia en la comparación del vulcanismo dacítico de la parte
central de Cinturón Volcánico Mexicano
Revista Electrónica Nova Scientia, Nº 11 Vol. 6 (1), 2013. ISSN 2007 - 0705. pp: 158 - 178
- 171 -
[31] Salleh H S, Rosales, E., and Flores-de la Mota, I., Influence of different probability
based models on oil prospect exploration decision making: a case from southern Mexico,
Revista Mexicana de Ciencias Geológicas, Vol. 24, No. 3, 2007, pp. 306-317
[32] González-Márquez L C and Hansen A M, Adsorción y mineralización de atrazina y
relación con parámetros de suelos del DR 063 Guasave, Sinaloa, Revista mexicana de
ciencias geológicas, Vol. 26, 2009, pp. 587-599
[33] Viner R I, et al., Quantification of post-translationally modified peptides of bovine ?-
crystallin using tandem mass tags and electron transfer dissociation, Journal of
Proteomics, Vol. 72, No. 5, 2009, pp. 874-885
[34] Santoyo E, et al., Rheological property measurement of drilling fluids used in
geothermal wells, Applied Thermal Engineering, Vol. 21, No. 3, 2001, pp. 283-302
[35] Santoyo E, et al., Convective heat-transfer coefficients of non-Newtonian
geothermaldrilling fluids, Journal of Geochemical Exploration, Vol. 78-79, No. 0, 2003,
pp. 249-255
[36] Santoyo E, Guevara M, and Verma S P, Determination of lanthanides in international
geochemical reference materials by reversed-phase high-performance liquid
chromatography using error propagation theory to estimate total analysis uncertainties,
Journal of Chromatography A, Vol. 1118, No. 1, 2006, pp. 73-81
[37] Santoyo E, et al., Separation and quantification of lanthanides in synthetic standards by
capillary electrophoresis: A new experimental evidence of the systematic "odd-even"
pattern observed in sensitivities and detection limits, Journal of Chromatography A, Vol.
1149, No. 1, 2007, pp. 12-19
[38] Espinosa-Paredes G, et al., Mass flow rate sensitivity and uncertainty analysis in natural
circulation boiling water reactor core from Monte Carlo simulations, Nuclear
Engineering and Design, Vol. 240, No. 5, 2010, pp. 1050-1062
[39] Gunn B M, Mooser, F., Geochemistry of the volcanics of central Mexico, Bulletin
Volcanologique, Vol. 34, No. 2, 1971, pp. 577-613
[40] Negendank J F W, Volcanics of the Valley of Mexico. Description of some Mexican
volcanic rocks with special consideration of the opaques. Part I: petrography of the
volcanics, Neues Jahrbuch für Mineralogie-Abhandlungen, Vol. 116, No. 3, 1972, pp.
308-320
[41] Bloomfield K, A late-Quaternary monogenetic volcano field in central Mexico,
Geologische Rundschau, Vol. 64, No. 1, 1975, pp. 476-497
[42] Pérez R. J, Pal, S., Terrell, D.J., Urrutia F., J., López M., M., Preliminary report on the
analysis of some "in-house" geochemical reference samples from Mexico, Geofísica
Internacional, 18, Vol. 2, 1979, pp. 197-209
Díaz-González, L. y R. Cruz-Huicochea
Revista Electrónica Nova Scientia, Nº 11 Vol. 6 (1), 2013. ISSN 2007 - 0705. pp: 158 178
- 172 -
[43] Robin C, Le Volcan Popocatepetl (Mexique): structure, evolution pétrologique et
risques, Bulletin of Volcanology, Vol. 47, No. 1, 1984, pp. 1-23
[44] Boudal. Pétrologie d'un grand volcan andésitique mexicain: le Popocatépetl, Univ.
Clermont-Ferrand II., 1985, pp. 140.
[45] Nixon G T, Petrology of the Younger Andesites and Dacites of Iztaccíhuatl Volcano,
Mexico: I. Disequilibrium Phenocryst Assemblages as Indicators of Magma Chamber
Processes, Journal of Petrology, Vol. 29, No. 2, 1988, pp. 213-264
[46] Martin del Pozzo A L. Geoquímica y paleomagnetismo de la Sierra Chichinautzin,
U.N.A.M., 1989.
[47] Swinamer R T. The geomorphology, petrography, geochemistry and petrogenesis of the
volcanic rocks in the Sierra del Chichinautzin, Mexico, Queen's University., 1989.
[48] Nixon G T, The geology of Iztaccíhualtl volcano and adjacent areas of the Sierra Nevada
and Valley of Mexico, Geological Society of America, Vol. Special paper, 1993, pp.
219, 1-58
[49] Larocque A C L, Stimac J A, and Siebe C, Metal-residence sites in lavas and tuffs from
Volcán Popocatépetl, Mexico: implications for metal mobility in the environment,
Environmental Geology, Vol. 33, No. 2, 1998, pp. 197-208
[50] Siebe C, Schaaf P, and Urrutia-Fucugauchi J, Mammoth bones embedded in a late
Pleistocene lahar from Popocatépetl volcano, near Tocuila, central México, Geological
Society of America Bulletin, Vol. 111, No. 10, 1999, pp. 1550-1562
[51] Wallace P J and Carmichael I S E, Quaternary volcanism near the Valley of Mexico:
implications for subduction zone magmatism and the effects of crustal thickness
variations on primitive magma compositions, Contributions to Mineralogy and
Petrology, Vol. 135, No. 4, 1999, pp. 291-314
[52] García-Palomo A, Macías, J.L., Arce, J.L., Capra, L., Garduño, V.H., Espíndola, J.M..
Geology of Nevado de Toluca volcano and surrounding areas, Central Mexico,
Geological Society of America, 2002, pp. 26
[53] Arce J L, Macías J L, and Vázquez-Selem L, The 10.5 ka Plinian eruption of Nevado de
Toluca volcano, Mexico: Stratigraphy and hazard implications, Geological Society of
America Bulletin, Vol. 115, No. 2, 2003, pp. 230-248
[54] Martínez-Serrano R G, et al., Sr, Nd and Pb isotope and geochemical data from the
Quaternary Nevado de Toluca volcano, a source of recent adakitic magmatism, and the
Tenango Volcanic Field, Mexico, Journal of Volcanology and Geothermal Research,
Vol. 138, No. 1-2, 2004, pp. 77-110
Aplicación de las pruebas estadísticas de discordancia y significancia en la comparación del vulcanismo dacítico de la parte
central de Cinturón Volcánico Mexicano
Revista Electrónica Nova Scientia, Nº 11 Vol. 6 (1), 2013. ISSN 2007 - 0705. pp: 158 - 178
- 173 -
[55] Siebe C, et al., Geochemistry, Sr-Nd isotope composition, and tectonic setting of
Holocene Pelado, Guespalapa and Chichinautzin scoria cones, south of Mexico City,
Journal of Volcanology and Geothermal Research, Vol. 130, No. 3-4, 2004, pp. 197-226
[56] Schaaf P, et al., Geochemical Evidence for Mantle Origin and Crustal Processes in
Volcanic Rocks from Popocatépetl and Surrounding Monogenetic Volcanoes, Central
Mexico, Journal of Petrology, Vol. 46, No. 6, 2005, pp. 1243-1282
[57] Meriggi L, Macías, J.L., Tommasini, S., Capra, L., Conticelli, S., Heterogeneous
magmas of the Quaternary Sierra Chichinautzin volcanic field (central Mexico): the role
of an amphibole-bearing mantle and magmatic evolution processes, Revista Mexicana
de Ciencias Geológicas, Vol. 25, 2008, pp. 197-216
[58] Straub S M and Martin-Del Pozzo A L, The significance of phenocryst diversity in
tephra from recent eruptions at Popocatepetl volcano (central Mexico), Contributions to
Mineralogy and Petrology, Vol. 140, No. 4, 2001, pp. 487-510
[59] Straub S M, et al., Evidence from high-Ni olivines for a hybridized peridotite/pyroxenite
source for orogenic andesites from the central Mexican Volcanic Belt, Geochem.
Geophys. Geosyst., Vol. 9, No. 3, 2008
[60] Velasco-Tapia F, Guevara, M., Verma, S.P., Evaluation of concentration data in
geochemical reference materials, Chemie der Erde, Vol. 61, No. 1, 2001, pp. 69-91
[61] Verma, S.P., Rivera-Gómez, M.A., Computer programs for the classification and
nomenclature of igneous rocks: Episodes, 2013 (in press).
[62] Verma, S.P., 2009, Continental rift setting for the central part of the Mexican Volcanic
Belt: a statistical approach: Open Geology Journal, v. 3, p. 8-29.
[63] Verma, S.P., Pandarinath, K., Verma, S.K., and Agrawal, S., 2013, Fifteen new
discriminant-function-based multi-dimensional robust diagrams for acid rocks and their
application to Precambrian rocks: Lithos, v. 168-169, p. 113-123.
[64] Verma, S.P., and Verma, S.K., 2013, First fifteen probability-based multi-dimensional
discrimination diagrams for intermediate magmas and their robustness against post-
emplacement compositional changes and petrogenetic processes: Turkish Journal of
Earth Sciences, in press.
[65] Verma, S.P., 2013. Application of 50 multi-dimensional discrimination diagrams and
significance tests: deciphering compositional similarities and differences between
Hawaiian and Icelandic volcanism International Geology Review, 2013. Vol. 00, No. 00,
120. http://dx.doi.org/10.1080/00206814.2013.788239
Díaz-González, L. y R. Cruz-Huicochea
Revista Electrónica Nova Scientia, Nº 11 Vol. 6 (1), 2013. ISSN 2007 - 0705. pp: 158 178
- 174 -
Table 1. Final statistical of samples of dacitic rocks from four nearby regions of the Mexican volcanic belt.
Element
Gr1 (Sierra de Chichi-
nautzin- Valle de México
monogenetic volcanoes)
Gr2 (Nevado de Toluca
stratovolcano)
Gr3 (Iztaccíhuatl strato-
volcano)
Gr4 (Popocatépetl stra-
tovolcano)
n
mean
standard
deviation
n
mean
standard
deviation
n
mean
standard
deviation
n
mean
standard
deviation
(SiO2)Adj
84λ
64.50
1.05
34
65.44
0.88
54α
64.65
1.09
22
63.93
0.82
(TiO2)Adj
94β
0.661
0.122
34
0.6420
0.0313
53
0.710
0.067
22
0.742
0.050
(Al2O3)Adj
93α
16.64
0.79
34
16.75
0.47
55
16.34
0.50
21α
16.352
0.321
(Fe2O3)Adj
94
1.214
0.168
34
1.157
0.081
54α
1.240
0.109
21α
1.3693
0.0414
(FeO)Adj
94
3.034
0.420
34
2.893
0.203
54α
3.100
0.274
21α
3.423
0.104
(MnO)Adj
90δ
0.0848
0.0146
34
0.0645
0.0100
55
0.0783
0.0095
22
0.0780
0.0136
(MgO)Adj
94
2.53
0.80
26η
1.785
0.090
55
2.87
0.66
22
2.94
0.53
(CaO)Adj
90δ
4.61
0.51
32β
4.348
0.159
54α
4.551
0.359
22
4.816
0.250
(Na2O)Adj
93α
4.286
0.348
34
4.411
0.131
55
4.246
0.220
22
4.270
0.282
(K2O)Adj
91γ
1.968
0.286
32β
1.991
0.109
55
1.988
0.167
22
1.867
0.173
(P2O5)Adj
94
0.168
0.052
33α
0.1817
0.0164
55
0.1946
0.0297
22
0.1730
0.0223
qNorm
91γ
17.81
2.59
34
18.75
1.69
55
17.81
2.43
21α
16.19
2.38
orNorm
91γ
11.63
1.69
32β
11.76
0.64
55
11.75
0.99
22
11.03
1.02
abNorm
93α
36.27
2.94
34
37.32
1.11
55
35.93
1.87
22
36.13
2.39
anNorm
91γ
19.30
2.31
34
19.45
1.01
55
19.15
1.69
21
19.57
1.40
enNorm
93
1.13
1.04
33
0.53
0.59
55
1.15
0.95
22
1.66
1.23
fsNorm
92
0.52
0.47
34
0.311
0.319
55
0.475
0.359
22
0.76
0.51
diNorm
92β
1.62
1.45
33α
0.82
0.87
55
1.63
1.30
22
2.42
1.73
hymNorm
94
5.77
1.78
30δ
4.44
0.47
55
6.62
1.34
22
6.55
1.02
hyfNorm
93α
3.321
0.402
34
3.250
0.277
54α
3.376
0.283
22
3.631
0.254
hyNorm
94
9.10
1.99
32β
7.80
0.84
55
9.97
1.57
22
10.18
1.06
mtNorm
94
1.760
0.244
34
1.678
0.118
54α
1.798
0.159
21α
1.985
0.060
ilNorm
94
1.256
0.233
34
1.219
0.059
53β
1.348
0.127
22
1.410
0.094
apNorm
94
0.388
0.121
33α
0.4210
0.0381
55
0.451
0.069
22
0.401
0.052
Mg#
94
58.4
7.8
26η
52.85
0.98
54α
62.19
3.54
22
60.18
4.40
FeOt/Mg
86η
1.650
0.394
34
2.007
0.316
54α
1.487
0.229
21α
1.579
0.238
Salic
94
85.35
2.98
31γ
88.12
1.06
54α
84.49
2.34
22
83.49
2.11
Femic
94
13.87
3.19
27ζ
10.94
0.51
55
14.73
2.76
22
15.97
2.20
C.I.
94
25.72
3.84
29£
23.37
0.82
55
26.28
3.07
22
27.95
1.93
D.I.
92β
65.97
3.54
34
68.11
2.29
54α
65.24
2.75
20β
63.31
0.85
S.I.
94
19.0
4.8
27ζ
14.67
0.75
55
21.19
3.54
22
21.09
2.76
A.R.
93α
1.849
0.100
33α
1.875
0.054
54α
1.850
0.063
22
1.816
0.076
La
32
18.15
3.58
22
16.31
2.75
---
---
---
32δ
16.06
1.23
Ce
32
40.6
7.9
21α
32.52
3.69
---
---
---
33α
35.1
4.6
Pr
11α
3.93
0.62
16α
4.18
0.52
---
---
---
14
3.66
0.45
Nd
17
18.11
3.61
22
17.40
2.56
---
---
---
13α
16.41
1.51
Sm
14
3.76
0.48
22
3.72
0.52
---
---
---
32β
3.630
0.365
Eu
12β
1.098
0.046
22
1.142
0.125
---
---
---
33α
1.166
0.101
Gd
13
3.418
0.415
17
3.181
0.283
---
---
---
14
3.540
0.348
Tb
14
0.560
0.061
21α
0.4643
0.0394
---
---
---
32β
0.523
0.073
Dy
10α
3.034
0.182
17
2.552
0.164
---
---
---
14
3.112
0.378
Ho
12
0.588
0.078
17
0.4900
0.0260
---
---
---
14
0.599
0.090
Er
12
1.657
0.221
17
1.326
0.097
---
---
---
14
1.750
0.290
Tm
10
0.2180
0.0399
17
0.1971
0.0172
---
---
---
14
0.251
0.053
Yb
14
1.576
0.213
22
1.343
0.223
---
---
---
34
1.560
0.252
Lu
13α
0.2233
0.0400
22
0.2055
0.0332
---
---
---
14
0.2671
0.0278
Ba
56
506
74
22
483
48
45
522
55
43
446
56
Be
7
1.51
0.49
3α
1
0
---
---
---
13
1.31
0.48
Co
27
12.01
2.68
22
11.02
4.48
---
---
---
36γ
13.31
2.03
Cr
45
69.0
36.6
22
57.0
45
42γ
58.5
21.1
40α
87.4
30.6
Cs
9
2.85
1.26
5
1.70
0.71
---
---
---
34
2.88
0.63
Aplicación de las pruebas estadísticas de discordancia y significancia en la comparación del vulcanismo dacítico de la parte
central de Cinturón Volcánico Mexicano
Revista Electrónica Nova Scientia, Nº 11 Vol. 6 (1), 2013. ISSN 2007 - 0705. pp: 158 - 178
- 175 -
Table 1 (continuation). Final statistical of samples of dacitic rocks from four nearby regions of the Mexican volcanic belt.
Element
Gr1 (Sierra de Chichi-
nautzin- Valle de México
monogenetic volcanoes)
Gr2 (Nevado de Toluca
stratovolcano)
Gr3 (Iztaccíhuatl strato-
volcano)
Gr4 (Popocatépetl stra-
tovolcano)
n
mean
standard
deviation
n
mean
standard
deviation
n
mean
standard
deviation
n
mean
standard
deviation
Cu
50
12.6
4.9
22
13.3
7.1
---
---
---
20
17.0
6.8
Ga
33
20.30
1.24
---
---
---
---
---
---
14
20.93
1.21
Hf
11
4.214
0.433
22
3.58
0.52
---
---
---
32β
4.307
0.371
Nb
49
6.22
1.57
17
4.447
0.405
45
8.91
2.12
12β
5.24
0.56
Ni
60α
36.5
21.7
18α
21.3
18.0
4δ
25.3
8.7
45
45.9
17.1
Pb
48γ
9.44
1.93
3
6.33
1.53
---
---
---
16β
11.45
2.30
Rb
63
45.1
11.7
22
38.2
5.0
45
58.6
7.2
44
52.5
7.9
Sb
---
---
---
---
---
---
---
---
---
19α
0.167
0.046
Sc
9
11.73
0.82
5
10.42
3.07
---
---
---
35
11.21
1.14
Sr
59£
476
62
21α
555
65
37η
420.9
24.1
39α
467
51
Ta
11α
0.405
0.070
19
0.382
0.053
---
---
---
33α
0.472
0.097
Th
35
4.94
1.56
22
3.865
0.442
---
---
---
37
4.84
0.82
U
12
1.74
0.74
20β
1.496
0.109
---
---
---
32β
1.740
0.234
V
25
83.4
13.1
22
70
10.9
44α
91.7
10.7
15
92.5
8.4
Y
51
18.18
2.57
20β
14.61
0.78
43β
21
2.85
14
17.21
1.71
Zn
52α
64.9
8.5
22
71.3
8.8
---
---
---
19α
69.8
7.8
Zr
51
171.8
28.3
22
146.8
11.9
45
161.6
17.8
37
167.0
24.2
Nb/Nb*2
30
0.1778
0.0312
17
0.1339
0.0114
---
---
---
13α
0.1785
0.0109
Ta/Ta*2
8
0.239
0.063
19
0.2013
0.0243
---
---
---
32β
0.2545
0.0315
ln((TiO2)Adj /SiO2)
94
-0.4605
0.217
34
-0.4625
0.057
54α
-0.4510
0.116
22
-0.4458
0.069
ln((Al2O3)Adj /SiO2)
93α
-0.1362
0.055
34
-0.13633
0.0322
55
-0.13774
0.0359
21α
-0.13636
0.0220
ln((Fe2O3)/SiO2)
94
-0.3989
0.169
34
-0.4037
0.080
54α
-0.3957
0.104
21α
-0.38427
0.0370
ln((FeO)Adj /SiO2)
94
-0.3073
0.169
34
-0.3121
0.080
54α
-0.3041
0.104
21α
-0.29264
0.0370
ln((MnO)Adj /SiO2)
93α
-0.6636
0.205
34
-0.6934
0.157
55
-0.6726
0.142
22
-0.6725
0.209
ln((MgO)Adj /SiO2)
93α
-0.3291
0.377
27ζ
-0.3600
0.063
53β
-0.3111
0.211
22
-0.3098
0.207
ln((CaO)Adj /SiO2)
89£
-0.2643
0.122
32β
-0.27140
0.0452
54α
-0.2657
0.096
22
-0.2587
0.060
ln((Na2O)Adj /SiO2)
89£
-0.2708
0.075
34
-0.26973
0.0249
55
-0.2726
0.048
22
-0.2708
0.076
ln((K2O)Adj /SiO2)
94
-0.3492
0.149
32β
-0.3494
0.054
55
-0.3487
0.084
22
-0.3537
0.095
ln((P2O5)Adj /SiO2)
86η
-0.5919
0.248
34
-0.5881
0.111
55
-0.5819
0.160
22
-0.5920
0.133
ln(La/Th)
12
1.247
0.252
22
1.433
0.154
---
---
---
34
1.222
0.104
ln(Sm/Th)
12
-0.132
0.311
22
-0.040
0.123
---
---
---
33α
-0.276
0.124
ln(Yb/Th
12
-0.1026
0.342
22
-0.1063
0.166
---
---
---
34
-0.1137
0.221
ln(Nb/Th
21
0.067
0.230
17
0.138
0.091
---
---
---
13α
0.112
0.111
ln(Nb/(TiO2)Adj)
49
-0.7056
0.254
17
-0.7288
0.107
45
-0.6690
0.230
13α
-0.7234
0.121
ln(V/(TiO2)Adj)
24α
-0.4450
0.103
22
-0.4505
0.136
45
-0.4352
0.090
15
-0.4392
0.093
ln(Y/(TiO2)Adj)
48α
-0.5957
0.107
22
-0.6067
0.095
42γ
-0.5808
0.066
14
-0.6071
0.107
ln(Zr/(TiO2)Adj)
50α
-0.3736
0.132
22
-0.3786
0.097
44α
-0.3781
0.108
18
-0.3850
0.144
ln(MgO/(TiO2)Adj)
94
1.298
0.316
26η
1.021
0.046
55
1.380
0.204
22
1.360
0.209
ln(P2O5/(TiO2)Adj)
89£
-0.1365
0.230
34
-0.1255
0.103
55
-0.1295
0.156
22
-0.1462
0.127
ln(Ni/(TiO2)Adj)
61
-0.544
0.69
19
-0.590
0.86
45
-0.5579
0.447
22
-0.5141
0.392
ln(La/Yb)
11
2.355
0.246
22
2.496
0.210
---
---
---
34
2.359
0.164
ln(Ce/Yb)
11
3.111
0.217
22
3.211
0.215
---
---
---
34
3.129
0.192
ln(Sm/Yb)
14
0.869
0.174
22
1.023
0.171
---
---
---
34
0.879
0.160
ln(Nb/Yb)
11
1.183
0.193
17
1.224
0.144
---
---
---
14
1.246
0.181
ln(Th/Yb)
12
1.026
0.342
22
1.063
0.166
---
---
---
34
1.137
0.221
Díaz-González, L. y R. Cruz-Huicochea
Revista Electrónica Nova Scientia, Nº 11 Vol. 6 (1), 2013. ISSN 2007 - 0705. pp: 158 178
- 176 -
ln(Y/Yb)
13
2.390
0.113
22
2.422
0.088
---
---
---
14
2.363
0.085
ln(Zr/Yb)
13
4.601
0.136
22
4.703
0.181
---
---
---
34
4.666
0.204
Number of discordant outliers detected: α one; β two; γ three; δ four ; £ five; ζ seven; η eight; λ ten.
Table 2. Final statistical of the combined regions and separated, resulting of application of significance test.
Element
Combined regions
Gr1 (Sierra de Chichi-
nautzin- Valle de México
monogenetic volcanoes)
Gr2 (Nevado de Toluca
stratovolcano)
Gr3 (Iztaccíhuatl stratovol-
cano)
Gr4 (Popocatépetl strato-
volcano)
N
mean
standard
deviation
n
mean
standard
deviation
n
mean
standard
deviation
n
mean
standard
deviation
n
mean
standard
deviation
(SiO2)adj
160
64.47
1.06
---
---
---
34
65.44
0.88
---
---
---
---
---
---
(TiO2)adj
125
0.65
0.098
---
---
---
---
---
---
53
0.71
0.067
22
0.742
0.05
75
0.719
0.064
94
0.661
0.122
34
0.642
0.0313
---
---
---
---
---
---
(Al2O3)adj
157
16.37
0.49
---
---
---
34
16.75
0.47
---
---
---
---
---
---
(Fe2O3)adj
180α
1.212
0.136
---
---
---
---
---
---
---
---
---
21
1.3693
0.0414
(FeO)adj
180α
3.029
0.339
---
---
---
---
---
---
---
---
---
21
3.423
0.104
(MnO)adj
162α
0.0809
0.0113
---
---
---
34
0.0645
0.01
---
---
---
---
---
---
(MgO)adj
170α
2.71
0.73
---
---
---
26
1.785
0.09
---
---
---
---
---
---
(CaO)adj
175α
4.554
0.414
---
---
---
---
---
---
---
---
---
22
4.816
0.25
(Na2O)adj
196£
4.306
0.242
---
---
---
---
---
---
---
---
---
---
---
---
(K2O)adj
198
1.957
0.207
---
---
---
---
---
---
---
---
---
---
---
---
(P2O5)adj
138η
0.1765
0.0303
---
---
---
---
---
---
55
0.1946
0.0297
---
---
---
qNorm
180
17.99
2.41
---
---
---
---
---
---
---
---
---
21
16.19
2.38
orNorm
198
11.56
1.22
---
---
---
---
---
---
---
---
---
---
---
---
abNorm
196£
36.44
2.05
---
---
---
---
---
---
---
---
---
---
---
---
anNorm
193γ
19.27
1.53
---
---
---
---
---
---
---
---
---
---
---
---
cNorm
---
---
---
---
---
---
---
---
---
---
---
---
---
---
---
dimNorm
168
1.17
0.99
---
---
---
33
0.53
0.59
---
---
---
---
---
---
difNorm
179
0.451
0.394
---
---
---
---
---
---
---
---
---
22
0.76
0.51
diNorm
165
1.63
1.34
---
---
---
33
0.82
0.87
---
---
---
---
---
---
hymNorm
77
6.6
1.25
94
5.77
1.78
30
4.44
0.47
---
---
---
---
---
---
hyfNorm
180α
3.33
0.342
---
---
---
---
---
---
---
---
---
22
3.631
0.254
hyNorm
76α
10.1
1.33
94
9.1
1.99
32
7.8
0.84
---
---
---
---
---
---
mtNorm
180α
1.756
0.197
---
---
---
---
---
---
---
---
---
21
1.985
0.06
ilNorm
125
1.234
0.186
---
---
---
---
---
---
53
1.348
0.127
22
1.41
0.094
75
1.366
0.121
94
1.256
0.233
34
1.219
0.059
---
---
---
---
---
---
apNorm
138η
0.409
0.07
---
---
---
---
---
---
55
0.451
0.069
---
---
---
Mg#
113β
59
6.4
---
---
---
26
52.85
0.98
54
62.19
3.54
---
---
---
75α
61.79
3.57
94
58.4
7.8
26
52.85
0.98
---
---
---
---
---
---
FeOt/Mg
153
1.542
0.28
---
---
---
34
2.007
0.316
---
---
---
---
---
---
Salic
170
84.84
2.75
---
---
---
31
88.12
1.06
---
---
---
---
---
---
Femic
170
14.38
2.98
---
---
---
27
10.94
0.51
---
---
---
---
---
---
C.I.
167γ
26.35
3.09
---
---
---
29
23.37
0.82
---
---
---
---
---
---
D.I.
141α
65.53
2.91
---
---
---
34
68.11
2.29
---
---
---
20
63.31
0.85
S.I.
170
19.94
4.3
---
---
---
27
14.67
0.75
---
---
---
---
---
---
A.R.
200α
1.85
0.079
---
---
---
---
---
---
---
---
---
---
---
---
La
84
16.73
2.65
---
---
---
---
---
---
---
---
---
---
---
---
Ce
54
34.11
4.41
32
40.6
7.9
---
---
---
---
---
---
---
---
---
Aplicación de las pruebas estadísticas de discordancia y significancia en la comparación del vulcanismo dacítico de la parte
central de Cinturón Volcánico Mexicano
Revista Electrónica Nova Scientia, Nº 11 Vol. 6 (1), 2013. ISSN 2007 - 0705. pp: 158 - 178
- 177 -
Pr
41
3.93
0.56
---
---
---
---
---
---
---
---
---
---
---
---
Nd
50
17.04
2.23
---
---
---
---
---
---
---
---
---
---
---
---
Sm
67
3.662
0.401
---
---
---
---
---
---
---
---
---
---
---
---
Eu
67
1.146
0.104
---
---
---
---
---
---
---
---
---
---
---
---
Gd
44
3.365
0.372
---
---
---
---
---
---
---
---
---
---
---
---
Tb
46
0.534
0.071
---
---
---
21
0.4643
0.0394
---
---
---
---
---
---
Dy
24
3.08
0.309
---
---
---
17
2.552
0.164
---
---
---
---
---
---
Ho
26
0.594
0.083
---
---
---
17
0.49
0.026
---
---
---
---
---
---
Er
26
1.707
0.26
---
---
---
17
1.326
0.097
---
---
---
---
---
---
Table 2 (continuation). Final statistical of the combined regions and separated, resulting of application of significance test.
Element
Combined regions
Gr1 (Sierra de Chichi-
nautzin- Valle de México
monogenetic volcanoes)
Gr2 (Nevado de Toluca strato-
volcano)
Gr3 (Iztaccíhuatl strato-
volcano)
Gr4 (Popocatépetl strato-
volcano)
n
mean
standard
deviation
n
mean
standard
deviation
n
mean
standard
deviation
n
mean
standard
deviation
n
mean
standard
deviation
Tm
27
0.2048
0.029
---
---
---
---
---
---
---
---
---
14
0.251
0.053
24
0.237
0.05
---
---
---
17
0.1971
0.0172
---
---
---
---
---
---
Yb
48
1.565
0.239
---
---
---
22
1.343
0.223
---
---
---
---
---
---
Lu
35
0.2121
0.0364
---
---
---
---
---
---
---
---
---
14
0.2671
0.0278
Ba
120α
506
60
---
---
---
---
---
---
---
---
---
43
446
56
Be
23
1.33
0.47
---
---
---
---
---
---
---
---
---
---
---
---
Co
85
12.31
3.14
---
---
---
---
---
---
---
---
---
---
---
---
Cr
105
59.2
29.1
---
---
---
---
---
---
---
---
---
40
87.4
30.6
Cs
48
2.75
0.85
---
---
---
---
---
---
---
---
---
---
---
---
Cu
90
13.3
5.5
---
---
---
---
---
---
---
---
---
---
---
---
Ga
47
20.49
1.25
---
---
---
---
---
---
---
---
---
---
---
---
Hf
43
4.283
0.385
---
---
---
22
3.58
0.52
---
---
---
---
---
---
Nb
---
---
---
49
6.22
1.57
17
4.447
0.405
45
8.91
2.12
12
5.24
0.56
Ni
105
40.5
20.3
---
---
---
18
21.3
18
41
25.3
8.7
---
---
---
58
23.3
10.8
60
36.5
21.7
---
---
---
---
---
---
45
45.9
17.1
Pb
---
---
---
48
9.44
1.93
3
6.33
1.53
---
---
---
16
11.45
2.3
Rb
---
---
---
63
45.1
11.7
22
38.2
5
45
58.6
7.2
44
52.5
7.9
Sb
20
0.164
0.047
---
---
---
---
---
---
---
---
---
---
---
---
Sc
49
11.23
1.39
---
---
---
---
---
---
---
---
---
---
---
---
Sr
97
469
54
---
---
---
21
555
65
36
420.8
24.4
---
---
---
Ta
30
0.39
0.06
---
---
---
---
---
---
---
---
---
33
0.472
0.097
44
0.455
0.095
---
---
---
19
0.382
0.053
---
---
---
---
---
---
Th
72
4.89
1.23
---
---
---
22
3.865
0.442
---
---
---
---
---
---
U
62
1.617
0.257
---
---
---
---
---
---
---
---
---
---
---
---
V
82β
90.4
9.9
---
---
---
22
70
10.9
---
---
---
---
---
---
Y
65
17.97
2.43
---
---
---
20
14.61
0.78
43
21
2.85
---
---
---
Zn
93
67.4
8.8
---
---
---
---
---
---
---
---
---
---
---
---
Zr
130
165.4
22.1
---
---
---
22
146.8
11.9
---
---
---
---
---
---
Nb/Nb*2
43
0.178
0.0266
---
---
---
17
0.1339
0.0114
---
---
---
---
---
---
Ta/Ta*2
26
0.2064
0.0289
---
---
---
---
---
---
---
---
---
32
0.2545
0.0315
40
0.2514
0.0392
---
---
---
19
0.2013
0.0243
---
---
---
---
---
---
ln(Ti/SiO2)
125α
-0.4612
0.175
---
---
---
---
---
---
54
-0.451
0.116
22
-0.4458
0.069
76
-0.4495
0.107
94
-0.4605
0.217
34
-0.4625
0.057
---
---
---
---
---
---
Díaz-González, L. y R. Cruz-Huicochea
Revista Electrónica Nova Scientia, Nº 11 Vol. 6 (1), 2013. ISSN 2007 - 0705. pp: 158 178
- 178 -
ln(Al/SiO2)
200α
-0.13671
0.0423
---
---
---
---
---
---
---
---
---
---
---
---
ln(Fe/SiO2)
180α
-0.3987
0.134
---
---
---
---
---
---
---
---
---
21
-
0.38427
0.037
ln(FeO/SiO2)
180α
-0.3071
0.134
---
---
---
---
---
---
---
---
---
21
-
0.29264
0.037
ln(Mn/SiO2)
166β
-0.6677
0.168
---
---
---
34
-0.6934
0.157
---
---
---
---
---
---
ln(Mg/SiO2)
75
-0.3107
0.209
93
-0.3291
0.377
27
-0.36
0.063
---
---
---
---
---
---
ln(Ca/SiO2)
165
-0.264
0.109
---
---
---
32
-0.2714
0.0452
---
---
---
---
---
---
ln(Na/SiO2)
195£
-0.2706
0.054
---
---
---
---
---
---
---
---
---
---
---
---
ln(K/SiO2)
198β
-0.3498
0.101
---
---
---
---
---
---
---
---
---
---
---
---
ln(P/SiO2)
194γ
-0.5873
0.175
---
---
---
---
---
---
---
---
---
---
---
---
ln(La/Th)
34
1.367
0.21
---
---
---
---
---
---
---
---
---
34
1.222
0.104
45
1.215
0.128
---
---
---
22
1.433
0.154
---
---
---
---
---
---
ln(Sm/Th)
32β
-0.037
0.155
---
---
---
---
---
---
---
---
---
33
-0.276
0.124
44
-0.253
0.169
---
---
---
22
-0.04
0.123
---
---
---
---
---
---
ln(Yb/Th)
68
-0.1094
0.233
---
---
---
---
---
---
---
---
---
---
---
---
Table 2 (continuation). Final statistical of the combined regions and separated, resulting of application of significance test.
Element
Combined regions
Gr1 (Sierra de Chichi-
nautzin- Valle de México
monogenetic volcanoes)
Gr2 (Nevado de Toluca
stratovolcano)
Gr3 (Iztaccíhuatl strato-
volcano)
Gr4 (Popocatépetl stratovol-
cano)
n
mean
standard
deviation
n
mean
standard
deviation
n
mean
standard
deviation
n
mean
standard
deviation
n
mean
standard
deviation
ln(Nb/Th)
51
0.102
0.167
---
---
---
---
---
---
---
---
---
---
---
---
ln(Nb/TiO2)
30
-0.7265
0.114
49
-
0.7056
0.254
---
---
---
45
-0.669
0.23
---
---
---
ln(V/TiO2)
61
-0.4456
0.12
---
---
---
---
---
---
45
-
0.4352
0.09
---
---
---
ln(Y/TiO2)
36
-0.6069
0.098
48
-
0.5957
0.107
---
---
---
42
-
0.5808
0.066
---
---
---
ln(Zr/TiO2)
130β
-0.3775
0.117
---
---
---
---
---
---
---
---
---
---
---
---
ln(MgO/TiO2)
170α
1.338
0.263
---
---
---
26
1.021
0.046
---
---
---
---
---
---
ln(P2O5/TiO2)
172γ
-0.132
0.162
---
---
---
---
---
---
---
---
---
22
-0.1462
0.127
ln(Ni/TiO2)
125β
-0.542
0.54
---
---
---
19
-0.59
0.86
---
---
---
---
---
---
ln(La/Yb)
67
2.403
0.202
---
---
---
---
---
---
---
---
---
---
---
---
ln(Ce/Yb)
67
3.153
0.205
---
---
---
---
---
---
---
---
---
---
---
---
ln(Sm/Yb)
36
0.963
0.186
---
---
---
---
---
---
---
---
---
34
0.879
0.16
48
0.876
0.162
---
---
---
22
1.023
0.171
---
---
---
---
---
---
ln(Nb/Yb)
42
1.221
0.168
---
---
---
---
---
---
---
---
---
---
---
---
ln(Th/Yb)
68
1.094
0.233
---
---
---
---
---
---
---
---
---
---
---
---
ln(Y/Yb)
49
2.396
0.095
---
---
---
---
---
---
---
---
---
---
---
---
ln(Zr/Yb)
69
4.665
0.187
---
---
---
---
---
---
---
---
---
---
---
---
Number of discordant outliers detected: α one; β two; γ three; δ four ; £ five; ζ seven; η eight; λ ten.
Chapter
In this chapter, we present statistical tests called discordancy tests (Barnett and Lewis in Outliers in statistical data. Wiley, Chichester, 1994), which are of great importance in appropriate handling of experimental data. The pre-1950 population-based outdated procedure commonly encountered in most books has been shown to be invalid and probably statistically incorrect for handling of finite-sized experimental data. The statistical correct post-1950 discordancy tests consist of single-outlier, multiple-outlier, recursive, and robust tests, of which the best combination was found to be three conventional and two new recursive tests with prior application of the corresponding single-outlier tests. The recommended procedure represents the best combination of highest test performance or power of test and lowest swamping and masking effects. The critical values play an essential role in the functioning of these tests. Precise and accurate values were simulated and incorporated in new computer programs. From the discussion of Type I and type II errors, it is argued that the statistical tests be applied at the strict 99% confidence level, and not at the 95% as is common according to most books and research publications. Similarly, to reduce these errors, the sample sizes should be increased as much as possible. The proposed methodology is illustrated from the compositional data of the geochemical reference material (GRM) BHVO1. The mean and standard deviation and related statistical parameters should only be calculated after the application of appropriate discordancy tests. Finally, the parameter z is briefly explained.
Article
Full-text available
Drilling the hard–rock found in and around geothermal systems for the completion of wells is widely recognized as a difficult and costly task. Drilling fluids of high viscosity (also called muds) are required for the well drilling operations. These fluids must be analyzed for the evaluation of their rheological properties, which are crucial for transporting geological formation cuttings to the surface, among other important applications. The goal of the present work was to develop a new rheological–statistical methodology to calculate dynamic viscosities of drilling fluids using 813 rheological data sets (i.e., shear stress and shear rate measurements). The methodology involved the selection and computer programming of nine rheological–regression models (Bingham Plastic, Power Law, Robertson–Stiff, Casson, Herschel–Bulkley, Sisko, Quadratic, Modified Robertson–Stiff, and Modified Sisko) for finding out the "best fit" line or curve through the experimental data. "Studentized" residuals were calculated and later used for the data fitting evaluation through the application of thirteen univariate discordant tests of single–outlier types. The rheological–statistical analysis of the data sets showed that the most efficient discordant tests were the N14 (skewness), N15 (kurtosis), and N1 (Grubbs). It was also found that the Herschel–Bulkley equation provided the best regression model which enabled to estimate dynamic viscosities of drilling fluids at shear rates ranging from 100 to 1100 s–1. Drilling fluid viscosities and their uncertainties were estimated using "normalized" rheological data sets. These viscosities together with some physical properties of rocks were finally used for calculating the critical velocities of drilling fluids required to transport the formation cuttings in some wells (of different lithologies) drilled in Los Humeros geothermal field. Details of all the application results obtained in this survey are outlined.
Article
Full-text available
The present study describes the different approaches to process Geochemical Reference Material (GRM) databases and the application of an scheme involving fourteen statistical tests to establish concentration data in five GRMs from the U.S. Geological Survey (basalt BHVO-1, andesite AGV-1, rhyolite RGM-1, and diabases W-1 and W-2). These tests include deviation/spread, Grubbs-type, Dixon-type, and high-order moment statistics. For about 50% of the cases, final mean values are more reliable (characterized by smaller standard deviations) than those obtained earlier using the inadequate "two standard deviation" method. Although about 53% of present mean data are identical (within 1%) to those reported previously, a disagreement > 1 to 5% is observed in 32% of the cases. The remaining mean values show larger differences (20-50%) compared to the literature data. The present procedure of outlier detection and elimination is therefore recommended in the study of GRMs, instead of the probably erroneous "two standard deviation" method. Use of geochemical criteria indicates that the new mean values in basalt BHVO-1 might be closer to the "true" concentrations.
Article
Full-text available
We review the most important computer programs for the classification of igneous rocks and point out those that follow the recommendations of the International Union of Geological Sciences (IUGS). A new program "Igneous Rock Classification System" (IgRoCS), written in Visual Basic, is then described in detail. IgRoCS allows the user to follow strictly the IUGS classification and nomenclature scheme for igneous rocks. The special rocks are first classified, then plutonic rocks are named after the IUGS mineralogical classification, next high-Mg and picritic volcanic rocks are identified from the IUGS criteria, and finally other volcanic rocks are classified according to the TAS diagram and CIPW norm. The chemical classification of volcanic rocks can also be achieved directly without going through the classification of other rock types. The IgRoCS program incorporates the revised standard igneous norm. Thus, the use of this new software is encouraged for a strict application of the IUGS recommendations for igneous rock classification and nomenclature.
Article
Full-text available
The Sierra de Chichinautzin (SCN) volcanic field is considered one of the key areas to understand the complex petrogenetic processes at the volcanic front of the Mexican Volcanic Belt (MVB). New as well as published major- and trace-element and Sr and Nd isotopic data are used to constrain the magma generation and evolution processes in the SCN. From inverse and direct modelling, combined Sr-87/Sr-86 and Nd-143/Nd-144 data, and use of multi-dimensional log-ratio discriminant function based diagrams and other geological and geophysical considerations, we infer that mafic magmas from the SCN were generated by partial melting of continental lithospheric mantle in an extensional setting. Inverse modelling of primary magmas from the SCN further indicates that the source region is not depleted in high-field strength elements (HFSE) compared to large ion lithophile elements (LILE) and rare-earth elements (REE). The petrogenesis of evolved magmas from the SCN is consistent with the partial melting of the continental crust facilitated by influx of mantle-derived magmas. Generally, an extensional setting is indicated for the SCN despite continuing subduction at the Middle America Trench.
Article
Petrographic, major, trace, and rare-earth element geochemistry of sands from three beaches of México (Cazones, Acapulco, and Bahía Kino) were studied to determine their provenance. The textural study reveals that the proportion of quartz is higher in Bahía Kino (~48-83 %) than in Cazones (~22-48 %) and Acapuclo (~20-48 %) sands. Most of the sand samples are classified as felsic sands using SiO2 content. The variations in SiO2, Fe2O3, MgO, TiO2 contents and Al2O3/TiO2, K2O/Na2O, SiO2/Al2O3 ratios among the three study areas reflect differences in source rock characteristics. The low Chemical Index of Alteration values (CIA: ~38-58) suggest the prevalence of week weathering conditions in the source regions. A steady weathering trend identified in the A-CN-K diagram for Acapulco and Cazones sands is indicative of uplift along the source region and indicates that sands were derived from diverse sources. A major variation in ΣREE content is observed in Acapulco sands (~22-390 ppm) than in Cazones (~49-83 ppm) and Bahía Kino sands (~50-89 ppm), and is likely due to differences in fractionation of minerals. However, all the sand samples show similar REE patterns with enriched LREE, depleted HREE and a negative Eu anomaly. The comparison of REE data of sands with those of source rocks located relatively close to the study areas suggest that Cazones and Acapulco sands were derived from felsic and intermediate rocks, whereas Bahía Kino sands were derived from felsic rocks.
Article
The effect of soil properties on the natural attenuation of the herbicide atrazine was investigated in soil samples from the irrigation district 063. Adsorption and mineralization of atrazine in soils were evaluated using guidelines recommended by the Organization for Economic Cooperation and Development and radiolabeled (14C) atrazine. Confidence limits of 99% for mean of adsorption coefficients were 0.297-0.587 L kg-1 and for the half life 2.0-5.8 yr. Atrazine adsorption isotherms were linear and adsorption coefficients of the herbicide were in the range reported in the literature for agricultural soils. The mineralization of atrazine in the soil samples was slow, an indicator that soil microorganisms are not adapted to the herbicide. This may be due to a reduction in the application rate of atrazine. Soil samples were characterized for sand, silt, clay contents, as well as organic matter, nitrates, ammonium, pH, and electrical conductivity. The correlation analysis between the natural attenuation of atrazine and soil properties shows a negative relationship between adsorption and soil depth as well as between atrazine mineralization and organic matter, ammonium and electrical conductivity. This means that atrazine is more mobile due to its lower adsorption in deeper soils and more persistent due to the increase in concentrations of such components. The results obtained in this work will be useful in the formulation of better scenarios of atrazine lixiviation in agricultural soils.