RV 
Geochemical Survey of MissouriMethods of Sampling, 

Laboratory Analysis, and 

Statistical Reduction of Data 

By A. T. MIESCH 

With sections on LABORATORY METHODS 

By P. R. BARNE1T, A. J. BARTEL, J. I. DINNIN, G. L. FEDER, T. F. HARMS, 

CLAUDE HUFFMAN, JR., V. J. JANZER, H. T. MILLARD, JR., HARRIET G. NEIMAN, 

M. W. SKOUGSTAD, and J. S. WAHLBERG 

GEOCHEMICAL SURVEY OF MISSOURI 

GEOLOGICAL SURVEY PROFESSIONAL PAPER 954- A 

Methods used in the collection, analysis, 

and interpretation of data in a 

regional geochemical survey 

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1976 
UNITED STATES DEPARTMENT OF THE INTERIOR 

THOMAS S. KLEPPE, Secretary 

GEOLOGICAL SURVEY 

V. E. McKelvey, Director 

Library of Congress Cataloging in Publication Data 

Miesch, Alfred T. 

Geochemical survey of Missouri-Methods of Sampling, Laboratory Analysis, and Statistical Reduction of Data 

(Geochemical survey of Missouri) (Geological Survey Professional Paper 954-A) 

Bibliography: p. 

Supt. of Docs. no.: I 19.16:954-A 

1. Geochemistry-Methodology. 2. Geochemistry-Missouri. 

I. Title. II. Series. III. Series: United States Geological Survey Professional Paper 954-A. 

QE515.M53 551.9 75-619351 

For sale by the Superintendent of Documents, U.S. Government Printing Office 

Washington, D.C. 20402 

Stock Number 024-001-02796-8 
CONTENTS 

Page 

Abstract .......................................................................................................................................... AI 

Introduction ......................................................................................... :......................................... 1 

Acknowledgments................................................................................................................... 2 

Some features of Missouri and its landscape................................................................................ 3 

Methods of sampling..................................................................................................................... 5 

General discussion.................................................................................................................. 5 

Sampling designs.................................................................................................................... 6 

Methods of laboratory analysis .................................. · .................................................................... 10 

Analysis of rocks and sbils by X-ray fluorescence, by J. S. Wahlberg ......................................... 11 

Fusion rnethod ......................................................................................................................... 11 

. Direct powder method ............................................................................................................ 12 

Preconcentration method ........................................................................................................ 12 

Analysis of rocks and soils by atomic absorption spectrometry and other methods, by Claude 

Huffman, Jr., and J. I. Dinnin ............................................................................................ 12 

Analysis of rocks, soils, and plant ashes by emission spectroscopy, by Harriet G. Neiman ...... 14 

Analysis of rocks and soils for iodine by radioisotope dilution-neutron activation, by A. J. 

Bartel and H. T. Millard, Jr ................................................................................................ 15 

Procedure ................................................................................................................................ 16 

Calculations ................. , .......................................................................................................... 16 

Results ..................................................................................................................................... 16 

Analysis of plants and plant ashes by methods other than emission spectroscopy, by T. F. 

Harms .................................................................................................................................. 17 

Analysis of water by chemical methods, by M. W. Skougstad and G. L. Feder .......................... 18 

Laboratory determinations ...................................................................................................... 18 

Field determinations ............................................................................................................... 21 

Analysis of water residue by emission spectroscopy, by P. R. Barnett ........................................ 22 

Procedure ........................................................................... , .... · ................................................ 22 

Analysis of water for radioactivity, by V. J. Janzer ...................................................................... 23 

Methods of data management and automatic data processing ..................................................... 25 

Frequency distributions and data transformations····································'·································· 26 

Detection ratios .............................................................................................................................. 27 

Estimates of means and total variance .......................................................................................... 28 

Measurement of correlation among compositional variables ....................................................... 29 

Estimation of variance components .............................................................................................. 29 

Estimation of sampling and analytical error variance ................................................................. 30 

Significance of differences among means ..................................................................................... 31 

Q-n1ode factor analysis .................................................................................................................. 32 

References cited ..... : ........................................................................................................................ 37 

ILLUSTRATIONS 

Page 

FIGURE I. Maps showing the principal subdivisions.of Missouri according to physiography, geology, soils, and vegetation .................... A4 

2. Graphs showing the approximate number of random samples required from each .mapped unit............................................... 9 

3. Diagram showing minor elements commonly determined in water by emission spectroscopy ..................................................... 22 

4. Generalized diagram of the RASS-STATPAC system of computer programs for the management and statistical reduction of geochemical data .............................................................................................................................................................................. 25 

5. Diagram showing distribution of sampling localities for the Q-mode experiment.. ..................................................................... 32 

6. Factor-variance diagram for the hypothetical data in table 8 ......................................................................................................... 35 

7. Diagrams showing distribution patterns for six constituents in 20 samples used in the Q-mode experiment.. ........................... 36 

8. Diagrams showing distribution patterns for the composition loadings from the Q-mode experiment ........................................ 37 

III 
IV CONTENTS 

TABLES 

Page 

TABLE 1. Definition of terms in the hierarchical statistical models used in sampling and analysis of variance for various phases 

of the geochemical survey of Missouri. ..................................................................................................................................... AS 

2. Lowe_r limits of determination for some of the methods used for the analysis of rocks and soils................................................. 14 

3. Approximate lower limits for the elements determined by emission spectroscopy........................................................................ 15 

4. Summary of methods used for analysis of plants and plant ashes, and lower limits of determination........................................ 18 

5. Analytical lines for emission spectrographic analysis of water residues ........................................................................ .'................ 23 

6. Precision of analysis of water residues from four standard reference water samples ..................................................................... 23 

7. Some u~1ivariate statistical estimates used in the geochemical survey of Missouri ........................................................................ 29 

8. Hypothetical data for 6 constituents-in 20 samples (as percentages) .............................................................................................. 32 

9. Hypothetical data for 6 constituents in 20 samples transformed to proportions of the ranges for each variable ......................... 33 

10. Hypothetical data for 6 constituents in 20 samples transformed and normalized .......................................................................... 33 

11. Matrix of coefficients of proportional similarity (cosine theta) for 20 hypothetical samples ........................................................ 34 

12. First six eigenvalues of the matrix of cosine theta, and cumulative proportions of N (CPN) .......... : ........................................... 34 

13. Composition scores for the three-factor Varimax model. ................................................................................................................ 34 

14. Composition loadings for the three-factor Varimax model ............................................................................................................ 34 

15. Original hypoth~tical data for sample I and a combination of the three sets of composition scores in the proportions indicated 

by the composition loadings ..........................................................•............ : ............................................................................. 35 
GEOCHEMICAL SURVEY OF MISSOURI 

GEOCHEMICAL SURVEY OF MISSOURI-METHODS OF SAMPLING, 

LABORATORY ANALYSIS, AND STATISTICAL REDUCTION OF DATA. 

By A. T. MIESCH 

ABSTRACT 

A reconnaissance geochemical survey of the State of Missouri was 

made primarily to develop and explore methods for conducting environmen tal geochemical surveys of large regions. Another important purpose 

was to provide 'information needed by epidemiologists in search of relationships between the geochemistry of the environment and health. The 

information will also prove useful in studies of environmental pollution and, perhaps, in the search for unknown mineral deposits. 

The geochemical survey included bedrock, unconsolidated surficial 

deposits, agriculture and currently uncultivated soils, selected native 

vegetation and farm crops, and ground and surface water. Approximately 7,000 samples of these materials were collected and each sample 

was analyzed for 3~40 chemical constituents. Nearly all of the sampling 

was according to hierarchical designs and involved complete randomization in the selection of sampling points. The samples from each phase 

of the survey were analyzed in completely randomized sequences, 

including duplicate samples unknown to the analysts, principally by 

methods of emission spectroscopy, X-ray fluorescence, and atomic ab-· 

sorption. Results indicate that the total experimental error in this d::na is, 

in general, more a function of sampling than of laboratory analysis. 

The laboratory and field data pertaining to the collected samples were· 

stored in the computer-based U.S. Geological Survey Rock Analysis 

Storage System (RASS) and were selectively retrieved onto magnetic tapes 

and disks for statistical reduction using programs of the U.S. Geological 

Survey Statistical Package (STATPAC). The principal statistical 

methods used were analysis of variance, Duncan's test for significance of 

differences among means, and Q-mode factor analysis. 

The ultimate objective of the statistical analysis was to identify geochemical variations over the State that are unlikely to have resulted from 

accidents of sampling or laboratory treatment. Most'of these variations 

arc described by means of geochemical maps. 

Q-mode factor maps serve to summarize the data and to provide bases 

for geochemical interpretations of the processes that created the 

variation. 

INTRODUCTION 

A reconnaissance geochemical survey of the State of 

Missouri was undertaken during the years 1969-73. The 

purpose of the survey was to describe the major geochemical variations over the State. Specifically, it has been 

directed at compositional variations in bedrock, unconsolidated surficial deposits, un.cultivated and agricultural 

soils, selected native vegetation and farm crops, and both 

ground water and surface water. Because of the large area 

of concern and the variety of materials examined, and because of the anticipated need for future investigations of 

this kind in other large areas of the United States, special 

concern has been given to the problem of efficiency. A concerted effort has been made to obtain the maximum information at the lowest possible cost. This effort required 

extensive use of formal experimental design procedures in 

·planning and executing sampling programs in order to 

reduce the fieldwork and the number of samples to be 

analyzed in the laboratories. Statistical methods· were 

employed to a more than ordinary extent in identifying 

variation that is unlikely to have resulted from errors in 

sampling or laboratory analysis. 

The geochemical survey· of Missouri has been a pilot 

study designed to explore and develop field and laboratory methods. for large-scale geochemical surveys. 

Missouri was selected for the pilot investigation partly 

. because of the immediate need for geochemical information by the Environmental Health Surveillance and 

·Research Center (EHSRC) of the University of Missouri at 

Columbia. Research at EHSRC has been aimed at the 

relation between health and the character of the environment. The geochemical character of the environment 

has been of special interest owing to a growing awareness 

among medical scientists of the importance of trace substances in human and animal health. (See, for .example, 

.Hemphill, 1.967, 1969, 1970, 1971, 1972, and 1973.) The 

beaTing of geochemistry on the problem and the interest of 

medical scien~ists in the geochemical environment have 

been described by Hopps (1971). 

The broad goals and general methods being used in the 

epidemiological research of the EHSRC were reviewed by 

Marienfeld (1972). One of the principai products of the 

research is a series of maps sho.wing variations in the rates 

Al 
A2 GEOCHEMICAL SURVEY OF MISSOURI 

of human and animal diseases over the entire State. The 

search for causes of disease consists, in part, of a search for 

correlation between disease rates and environmental 

factors. The principal objective of the geochemical survey 

of Missouri, therefore, has been to produce statewide maps 

of the geochemical variations. 

The subject matter scope of the survey-that is, the 

inclusion of rocks, soils, plants, and water-has been 

made broad because of the present elementary state of 

knowledge concerning relations between health and the 

geochemistry of the environment. Ground water and 

surface water, as well as farm crops and agricultural soils, 

have been included for obvious reasons. The bedrock and 

unconsolidated surficial deposits are included because 

these materials are the natural sources of chemical 

constituents in water, soil, and vegetation (Miesch, 1972). 

Selected species of native vegetation are included in order 

to search for indicators of not only the gross chemical character of the environment, but also the availability of the 

chemical elements to organisms. Uncultivated soils are 

included because they are the link between native vegetation and the underlying geology. 

Although the development of methods for conducting 

geochemical surveys and support of epidemiological 

research have been the primary purposes for the geochemical survey of Missouri, there are a number of other 

important purposes that this survey, and similar surveys of 

other large regions, may serve. It has become abundantly 

clear in recent investigations of environmental pollution 

that the identification of pollution and the delineation of 

its extent, presuppose a knowledge of the normal or 

natural state of the environment. The natural environment is very far from being geochemically uniform, 

and the presence of an element, or suite of elements, in 

sufficient abundance to be indicative of environmental 

pollution in one area may·be entirely norn1al for another. 

Thus, the same geochemical maps provided to support 

epidemiological research may be useful in defining the 

needed baselines in investigations of pollution. They have 

already proved useful in at least one instance (Ebens and 

others, 1973). 

The results of the survey may also find application in 

investigations and research unrelated, or only marginally 

related, to concern for the environment. For example, the 

baseline d~ta of the environmentalist are the background 

data of the· geochemical explorationist, and the survey 

results may prove useful in mineral exploration. The geochemical explorationist must presuppose a normal range 

of concentrations for various elements in the media he is 

sampling before he can identify the anomalies he is 

seeking. Aside from this, geochemists engaged in a wide 

range of research activities have continuing need for information on the occurrences and distribution of elements in 

natural materials. 

This report serves as an introduction to a series of 

specific reports on various phases of the survey. It describes the field and laboratory methods and the methods 

of statistical analysis and data reduction that are common 

to more than one of these phases. These methods have been 

held consistent wherever possible so that variations in the 

data, as summarized on geochemical maps and in statistical tables, will reflect actual variations in the environment rather than variations in the field and laboratory 

methods that were used. 

Preliminary results of the geochemical survey of Missouri have been released during the course of the work in a 

series of semiannual progress reports (U.S. Geological 

Survey, 1972a-f, 1973). The purpose and methods being 

used were summarized by Connor, Feder, Erdman, and 

Tidball (1972), and some preliminary findings were described by Tidball (1971), Connor, Erdman, Sims, and 

Ebens ( 1971 ), and Connor, Shacklette, and Erdman ( 1971 ). 

Feder ( 1972) described the sampling methods used in his 

study of ground and surface waters, and Feder, Ebens, and 

Connor' (1972) described some relations between the 

composition of ground water and the composition of the 

host rock. 

Tidball and Sauer (1972) have discussed some preliminary findings on the relations between soils and 

human health on a statewide basis. One small area in 

central Missouri has been studied intensively by Ebens and 

others ( 1973) and by Ebens, Erdman, and Feder ( 1972). The 

medical aspects of the investigations were discussed more 

fully by Case and others (1972, 1973). 

ACKNOWLEDGMENTS 

Although specific contributions to the geochemical 

survey of Missouri are acknowledged where appropriate in 

the reports on its various phases, it is appropriate here to 

acknowledge those who contributed to the overall design 

of the survey and to the establishment of workable 

operational procedures. Throughout the survey, but 

especially in its early stages when the specific objectives 

were being defined, the investigators benefited from 

frequent contact with scientists of the University of Missouri at Columbia. Useful suggestions and assistance were 

received, in particular, from Carl J. Marienfeld, Director 

of the Environmental Health Research and Surveillance 

Center, Lloyd A. Selby of the Department of Veterinary 

Microbiology, Walter Heidlage of the Environmental 

Health Extension, and Arthur A. Case of tlie School of 

Veterinary Medicine. 

Personnel of the Missouri Geological Survey and Water 

Resources at Rolla, Mo., provided particularly valuable 

information which was used in sampling the geologic 

units of the State. Special acknowledgement is made of the 

assistance of William C. Hayes, former State Geologist 

and Director, Wallace B. Howe, present State-Geologist 
METHODS OF SAMPLING, LABORATORY ANALYSIS, AND STATISTICAL REDUCTION OF DATA A3 

and Director, and Larry D. Fellows, Assistant State 

Geologist. 

The success of all phases of .the· geochemical survey 

depended heavily on the support and cooperation of U.S. 

Geological Survey analysts and those in charge of the 

major chemical laboratories. Special acknowledg,ment is 

made of the cooperation extended by Frank S. Grimal<;l,i, 

Irving May, Leonard B. Riley, Claude Huffman, Jr., 

Marvin W. Skougstad, and Frederick N. Ward. 

SOME FEATURES OF MISSOURI AND ITS 

LANDSCAPE 

Missouri has an area of 180,50Q_square kilometres and a 

population of 4.3 million. Nearly two-thirds of the 

population, however, is concentrated in two large 

metropolitan areas, St. Louis and Kansas City. The 

remainder of the population is in smaller cities, rural 

communities, and farms widely scattered throughout the 

State. 

Northern Missouri is part of the centrai interior low land 

of the United States, and most of southern Missouri occurs 

within the Ozark Pla~eaus region of the Interior High: 

lands (Fenneman, 1938). Six physiographic regions 

within the State are recognized by Vineyard (1967), and 

each of them has boundaries which coincide, to varying 

degrees, with those that have been drawn on the basis of 

geology, soils, and vegetation (fig. 1). The domal uplift 

centered around the St. Francois Mountains in the southeastern part of the State is the dominant control on the 

nature of the landscape. Precambrian igneous rocks, both 

inu·usive and extrusive, are exposed in the core of the 

uplift, and sediments of Paleozoic age dip gently away 

from the core in all directions. Much of the southern part 

of the State is underlain by westward- and northwestwarddipping beds of dolomite, limestone, and sandstone of 

Cambrian and Early Ordovician age, whereas nearly all of 

the. north half is underlain by northwestward-dipping 

beds of shale, limestone, and sandstone of Mississippian 

and Pennsylvanian age. Flood-plain deposits of alluvium 

occur along the Mississippi and Missouri Rivers and in the 

extreme southeastern part of the State where they compose 

part of the extensive Mississippi embayment deposits. 

Claystone, sandstone, and gravel of Cretaceous and Tertiary age are exposed locally within the southeastern 

flood-plain area. Deposits of glacial till cover most of the 

northern half of the State, severely restricting exposures of 

the sedimentary rocks of Mississippian and Pennsylvanian age. Deposits of windblown silt (loess) are 

prominent along the banks of the major rivers and they 

occur elsewhere throughout the State. In the southern part 

of the State, where glacial till is absent, a residuum of 

reddish clay and silt as much as several hundred feet thick 

has accumulated on the carbonate rocks. The glacial 

deposits in the northern part of the State and the reddish 

residuum in the southern part are the two most widespread and prominent types of geologic deposits, and are 

the major parent materials from which the soils have 

developed, 

The ~oils of Missouri are highly diverse in specific type; 

about 275 different soil units (Series) have been mapped. 

However, more than 90 percent of the State is covered by 

only three broad types (Orders)-Mollisols, Alfisols, and 

Ultisols. The Mollisols contain black friable organic 

material in their upper horizons and occur both along the 

flood plains of the Mississippi and Missouri Rivers and 

over the glacial till and loess deposits in the northwestern part of the State. The Alfisols occur in broad areas 

along the major rivers above the flood plains. The Ultisols 

are developed principally on the dolomites in the Ozark 

Plateaus region in the southern part of the State. There are 

only a few small areas in the State that are believed to never 

have been under cultivation, and it is likely that the 

chemical and physical character of all soils-those at 

present supporting agriculture and those currently uncultivated-have been modified by man to various degrees, 

depending on various agricultural techniques employed. 

The Missouri landscape as mapped by Kuchler (1964) 

according to the potential natural vegetation the land 

would support if reverted to nature falls into five 

categories. These categories-vegetation-type areas in this 

series of reports-are:· ( 1) a mixed bluestem prairie and 

Oak-Hickory Forest at the higher elevations in the north 

half of the State; (2) an Oak-Hickory Forest in most of the 

central part of the State and at lower elevations, along the 

rivers, in the northwestern part, and (3) an Oak-HickoryPine Forest in the southeast, (4) a Floodplain Forest along 

the Mississippi River in the extreme southeastern part of 

the State, and (5) Cedar Glades immediately north of the 

Arkansas border in the southwest (fig. I). The first 

category has been subdivided for the geochemical survey 

into two vegetation-type areas-(1) Glaciated Prairie 

north of the Missouri River arid (2) Ungladated Prairie 

south of the river. This subdivision was made because ofthe fundamentally different types of surficial geologic 

materials underlying the two parts of the region. Thus, six 

different vegetation-type areas have been studied and 

compared. Agriculture is greatly limited in two of these 

areas, the Cedar Glades and the Oak-Hickory-Pine Forest, 

but is extensive in parts of the other four. The principal 

crops are corn, soybeans, and wheat, with some production of cotton and rice in the southeastern flood-plain 

area. Livestock production, mostly cattle and swine, is 

widespread except in the southeastern flood-plain area. 

Cities and towns along the Mississippi and Missouri 

Rivers derive their water supplies mostly from these 

sources. Surface waters are also used by many 

communities jn the northern parts of the State that are 

covered with glacial deposits. Elsewhere in Missouri, 
A4 GEOCHEMICAL SURVEY OF MISSOURI 

Southern limit 

2 

A. Physiography B. Geology 

1. Dissected Till Plains 1. Quaternary-Tertiary rocks 

2. Osage Plains · 2. Cretaceous rocks 

3. Springfield Plateau 3. Pennsylvanian rocks 

4. Salem Plateau 4. Mississippian rocks 

5. St. Francois Mountains 5. Devonian-Silurian rocks 

6. Southeastern Lowlands 6. Ordovician rocks 

7. Cambrian rocks 

8. Precambrian rocks 

0 100 200 300 400 Kl LOMETRES 

5 

C. Soils (Order/Suborder) 

1. Mollisols/U dolls 

2. Mollisols/Aquolls 

3. Alfisols/Aqualfs 

4; Alfisols/U dalfs 

5. Ultisols/Udults 

6. lnceptisols/ Aquepts 

D. Vegetation-type 

1. Glaciated Prairie 

2. Unglaciated Prairie 

3. Oak-Hickory Forest 

4. Oak-Hickory-Pine Forest 

5. Cedar Glades 

6. Floodplain Forest 

FIGURE 1.-The principal subdivisions of Missouri according to physiography (from Vineyard, 1967), geology (from Missouri Geological Survey 

and Water Resources, 1969), soils (from Soil Conservation Service, 1970), and vegetation (from Kuchler, 1970). 

water supplies are derived largely from wells. The surface 

and ground waters of the State may be classlfied into six 

geohydrologic units, each unit consisting of a group of 

geologic strata in which the waters occur: ( 1) Quaternary 

alluvium, (2) Pleistocene glacial drift, (3) strata of Tertiary and Cretaceous age, (4) strata of Pennsylvanian age, 

(5) strata of Mississippian age, and (6) strata of Ordovician 

and Cambrian age. The ,Cambrian and Ordovician strata 

are further subdivided into a shallow geohydrologic unit 

which extends over much of southern Missouri, and a 

deeper geohydrologic unit covered by Mississippian strata 

in the southwestern part of the State. Thus, seven broad 
METHODS OF SAMPLING, LABORATORY ANALYSIS, AND STATISTICAL REDUCI'ION OF DATA AS 

geohydrologic units are recognized. 

The principal metalliferous mining in Missouri has 

been for lead and zinc, and for small amounts of associated copper, cobalt, nickel, silver, and cadmium. The 

State has had a long history of lead and zinc production, 

dating back to the early 1700's. Although small deposits 

are known to be widespread in the southern part of the 

State, most of the production has been from three districts: 

(I) the Southeast district in the vicinity of the St. Francois 

Mountains, (2) the Southwest district, which includes the 

joplin area and the Missouri part of the famous Tri~State 

district, and (3) the less important Central district with a 

very limited amount of mining activity in recent years. In 

each of these districts the ores occur as replacement bodies 

in limestone and dolomite (Hayes and Guild, 1967). 

The ores occur from the surface to depths exceeding 

I ,000 feet. In the Southeast district the ores occur mainly in 

dolomites of Cambrian age and consist largely of lead 

sulfide (galena). The Southeast district includes the 

Viburnum Trend, an area mainly in northwestern 

Reynolds and Iron Counties where significant new lead 

deposits were discovered in l9SS (Weigel, l}96S). In the 

Southwest district the ores occur mainly in strata of Mississippian age and consist largely of zinc sulfide (sphalerite) 

with minor amounts of lead. The Central district contains 

many small deposits of barite, lead, and zinc, but most of 

the mining since 1910 has been for barite (Kiilsgaard, 1967, 

p. 62). 

The only other important metalliferous mining in Missouri has been for iron which occurs in several kinds of 

sedimentary and vein-type deposits throughout much of 

the Ozark Plateaus region. At present, two large vein-type 

deposits in igneous rocks of Precambrian age are being 

worked at Pea Ridge and Pilot Knob in the St. Francois 

Mountains region. 

METHODS OF SAMPLING 

GENERAL DISCUSSION 

A thorough discussion of sampling procedures should 

consist of two main aspects: (I) the sampling design, or 

plan, including the spacing of sampling sites and the 

selection of specific sampling points within sites, and (2) 

the techniques used to obtain the samples after these sites 

and points have been determined. Only the first aspect is 

described here; the second aspect is discussed in reports 

covering specific phases of the geochemical survey. The 

general features· of the sampling designs can be discussed 

here because they are basically similar, and follow the 

same general statistical model, from one phase of the 

survey to another. 

Before discussing the sampling designs employed in the 

geochemical survey of Missouri, · two separate and 

independent properties of geochemical maps-resolution and stability-are described as they have been 

viewed during the course of the program. A general plan 

for efficient sampling of large regions to achieve various 

degrees of detail in the final geochemical maps, as 

described previously (Connor and others, 1972), is also 

discussed briefly. Each of the sampling designs used in the 

Missouri program has been regarded as part of this general 

plan. 

A geochemical map is commonly constructed. by plotting geochemical val.ues and illustrating the variation 

among the values by means of contours, symbols, or other 

graphical devices. An individual value may represent (I) 

the analytical determination on an individual· sample of 

rock, soil, plant, or water, or (2) the mean for a number of 

determinations on samples that were collected from a 

sampling locality. The first situation may be regarded as a 

special case of the second, one where the sampling locality 

is small and the single analytical determination is the 

mean of one value. 

The resolution of a geochemical map is determined by 

the spacing between the centers of the sampling localities, 

a locality being defined as some part of the population 

being sampled that is larger than an individual specimen 

(Miesch, l967a, p. AS). Where the localities are closely 

spaced, small-scale geochemical variations may be 

detected and described, and so the resolution of the map is 

high. Where the spacing between localities is greater, 

small-scale geochemical variations will go undetected and 

so the resolution is poor. The variability among the 

sampling locality means and the confidence intervals, the 

degree to which the means are known, determines the geochemical map stability. If the variability among the 

locality means is large in relation to the confidence 

intervals about the means, then the stability of the geochemical map is relatively high. Where the variability 

among the locality means is small relative to the 

confidence intervals about the means, the map is more· 

likely to undergo substantial changes with the addition of 

new data, and so is less stable. 

It is rather common in field geochemical studies to use 

sampling designs of the hierarchical type, and designs of 

this type were used in the geochemical survey of Missouri. 

Where hierarchical designs are used, the sampling 

localities occur at several levels. For example, lS-minute 

quadrangles may serve as the sampling localities at the 

uppermost level of the design and, thereby, constitute the 

"master sampling units" in the terminology of Krumbein 

and Slack (l9S6, p. 744). Sampling locaiities at the next 

lower level of the design may consist of, say, 7~-minute 

quadrangles selected from the IS-minute quadrangles, 

and at the next lower level the sampling localities may 

consist of 30-second quadrangles selected from the 7~­

minute quadrangles. In such situations, the resolution of 

the geochemical map is determined by the spacing 

between the values plotted in construction of the geo-
A6 GEOCHEMICAL SURVEY OF MISSOURI 

chemical map and the proportion of the total map area 

that each value is intended to represent. Ordinarily, the 

plotted values will be averages of sampling units chosen in 

such a way that the plotted values will be as equally spaced 

as possible on the map. This will commonly preclude 

averaging over minor sampling localities at lower levels of 

the hierarchical design and, more often than not, will lead 

one to average over the master sampling units. In 

situations where approximately equal spacing can be 

achieved by averaging over sampling units at various 

levels of the design, a choice must be made. In general, if 

the smaller sampling units are averaged, the map will have 

higher resolution but poorer stability. If the larger 

sampling units are averaged, the resolution is lost in the 

interest of achieving stability. The latter choice is more 

often the better one because an unstable geochemical map 

is subject to possible misinterpretation by readers who are 

not acquainted with the nature of the difficulties faced in 

geochemical mapping. A generalized map that is reliable 

is more useful than a detailed map that is, in large part, not 

reproducible. 

Connor, Feder, Erdman, and Tidball (1972) have 

described a general sampling plan for geochemical surveys 

of large regions, a plan that has grown out of the geochemical survey of Missouri. The plan is designed to offer 

maximum efficiency in fieldwork and laboratory analysis; 

it is composed of two phases of sampling with two 

sampling stages within each phase. The first phase leads 

to geochemical maps of poor resolution, but a map of this 

type may be all that is required or all that available 

reso.urces allow in some investigations. The ~econd phase 

is aimed at the production of maps of higher resolution 

and is conducted only where maps from the first phase are 

determined to be inadequate for a given purpose. The first 

stage of sampling within each phase of the general design 

is for the purpose of estimating the extent of sampling and 

laboratory analysis required in order to produce geochemical maps and other statistical summaries with the· 

required degree of stability. The second stage is merely the 

execution of the sampling as determined to be required by 

the results of stage one. 

The first phase of sampling in the general plan is aimed 

at estimation of the differences among the average geochemical characters of various categories of materials 

being investigated. In most cases, the categories are 

mappable units of bedrock, soils, vegetation, and water. 

Thus, the first phase is aimed at a description of what are 

probably the major geochemical variations over any large 

region. Because the master sampling units in the first 

phase of the general plan are mapped, or mappable, subdivisions of the materials being investigated, the resolution 

of the geochemical maps resulting from this phase can be 

no better than that of the. geologic, soils, vegetation, or 

hydrologic map on which the sampling Is based. 

The second phase of sampling in the general plan is 

conducted on any one or on any number of the mapped 

rock, soil, vegetation, or hydrologic units, but each of 

these would require a separate and perhaps unique 

sampling design depending on the type of geochemical 

variability in the unit. If much of the variability is on local 

scales, a high resolution sampling design involving 

closely spaced sampling localities will be required if any 

large proportion of the total variability is to be described 

in the final geochemical map. If much of the variability is 

on regional scales, widely spaced sampling localities 

providing poor resolution in the final map may be 

adequate .to describe a large proportion of the total 

variability. 

The general plan has been summarized as follows 

(Connor and others, 1972): 

Phase 1: Sampling to describe differences among categories. 

Stage 1 a:. Preliminary sampling designed to determine 

the extent to which the categories are indeed geochemically distinct, and to provide the basis for planning stage 1 b. 

Stage 1 b: Final sampling to provide reliable esumates 

of differences among categories, and the amounts of 

compositional variability within each category. 

Phase 2: Sampling to describe patterns of variation within categories. 

Stage 2a: Preliminary sampling within each category 

to determine the sampling locality spacing that 

would be most efficient for describing the geochemical variation patterns within each category, and the 

number of samples required from each locality. 

Stage 2b: Final sampling to describe the geochemical 

patterns within each category. 

SAMPLING DESIGNS 

Most of the sampling designs used in the geochemical 

survey of Missouri were of the phase 1 type, and were for 

the purpose of describing differences in geochemical 

character among mapped rock, soil, vegetation, and 

hydrologic units. Most of the final geochemical maps, 

therefore, are of poor resolution and are intended only to 

show the major geochemical variations across the State. 

Until it has been determined by medical researchers, or by 

others, that maps of higher resolution are required, and 

where they are required, it seems unnecessary to proceed to 

phase 2 of the general plan. Phase 1 provides a means for 

showing the gross geochemical variations over a large area 

at relatively low cost, whereas phase 2 should be 

entered into only where the need for the more detailed 

information can justify the much greater cost per unit area 

that is involve_d. 

Various statistical populations are recognized within 

the rocks, soils, vegetation, and waters of the State, and 
METHODS OF SAMPLING, LABORATORY ANALYSIS, AND STATISTICAL REDUcriON OF DATA A7 

these populations constitute the first breakdown of these 

materials. Examples of these populations are ( 1) carbonate 

rocks of Cambrian and Early Ordovician age, (2) sandstones of Pennsylvanian age, (3) glacial loess, (4) clay 

residuum developed on carbonate rocks, (5) currently cultivated (agricultural) soils, (6) soils of the prairie in the 

northern parts of the State, (7) sumac of the State, (8) 

pasture grasses of the State, (9) ground water of the State, 

and ( 1 0) surface water of the State. However, the sampling 

in the geochemical survey was not aimed directly at these 

populations. Rather, it was aimed at units of area because 

the purpose of the survey has been to describe variations 

among areas. Consequently, the individuals in the 

populations of interest have been units of area in all cases, 

and the rocks, soils, vegetation, and waters have been 

regarded as attributes of the areas. Accordingly, in the 

randomization procedures that were used, each unit area 

wherein the attribute of interest occurred was given an 

equal chance of being selected. This is quite different from 

sampling in such a way that each individual in the 

population is given an equal chance of being selected, and, 

as stated above, was done because the purpose of the 

investigation was to produce maps showing chemical 

variations in the rocks, soils, vegetation, and water across 

the State. 

The populations and groups of populations that were 

the attributes of interest within the areas sampled are listed 

in table 1. The table also shows the master sampling units 

for each sampling design; for most designs the master 

sampling units are mapped units within the corresponding population. In addition, the table shows how 

each of the mas~er sampling units was subdivided areally 

for sampling within it. The hierarchical-type subdivision 

was used in the stage la sampling in order to search for an 

efficient design for stage 1 b. This is discussed further later 

in this s<::ction. 

The general statistical model followed in the sampling 

within each population was: 

X··k =j.t+a.+f3i1·+ Yi1

·k+8i1'km + .. · (1) lJ m... ' 

where x is a measure of the amount of a given constituent 

in an individual sample, #lis the mean for all areas of the 

State where the population occurs, ai represents a mapped 

unit, and {:J, 'Y, and 8 represent subdivisions of decreasing 

size within the mapped unit. In sampling of the bedrock 

units of the State, the term "a" was not included in the 

formal design because the mapped units are vastly different with respect to most chemical constituents and there 

seemed to be little point in testing for statistically significant differences. The term "a" was also omitted from the 

sampling models used for the loess deposits of the State 

and for agricultural soils, because useful mapped units 

were not recognized in either of these materials. 

The definition of p. in equation 1 as the means for all 

areas of the State where the population occurs is important 

because it provides a more precise definition of the 

population of individuals that were sampled within each 

phase of the survey. For example, the individuals within 

the sampled population of carbonate rocks of Cambrian 

and Early Ordovician age do not include all of the 

potential carbonate samples that exist throughout this 

sequence of strata; they include only those within areas 

where the strata have been mapped, and exclude those in 

the subsurface. The individuals within the sampled population of sumac are not all sumac of the State, but rather all 

of the equal-size areas (for example, 7~-minute quadrangles) where sumac occurs. These rather subtle, but 

important, distinctions are in keeping with the objective 

of the survey which is to describe geochemical variation 

among areas. 

The intent behind the phase 1 sampling in each of the 

sampling programs, except those programs directed at the 

loess and agricultural soils, was to produce estimates of the 

average compositions of the mapped units as designated 

on table 1, and the symbol "a/' is used throughout this 

series of reports, except where noted, to designate a 

mapped unit of rock, soil, vegetation, or water. Thus, in 

the model used as a basis for vegetation sampling, a 1 

represents the mean concentration of a chemical 

constituent in a plant species among all areas within the 

glaciated prairie vegetation-type area; a 2 represents the 

same for the unglaciated prairie, and so forth. The 

principal objective of the survey is to identify significant 

differences among the a i· ai is in units of deviation from 

the grand mean, }-t ;· the absolute mean for any given 

mapped unit isj.t+ai. 

The ability to identify significant differences among the 

mapped units, with a given number of samples collected 

and analyzed, depends on the variation among thea/sand 

on the homogeneity within each mapped unit. This 

homogeneity determines the variation among the 

individual values of /3ij and among similar terms on the 

right side of equation 1. In the sampling of bedrock and 

surficial deposits, {3 i/represents the mean concentration of 

a chemical constituent in a geologic province or some 

major area of occurrence of the bedrock unit within the 

population. In sampling vegetation and associated soils~ 

/3ij represents the mean for a 7~-minute quadrangle. Like 

ai, /3ij is in units of deviation; the absolute mean for any 

subarea within a mapped unit is expressed as p.+ai+f3ij. In 

a similar way, subsequent terms on the right side of 

equation 1 represent subdivisions of the units represented 

by the preceding terms. Each of them is in terms of 

deviation from a mean. A final term, e, has been added in 

most phases of the survey to represent errors in laboratory 

analysis. Where this term is absent, the laboratory errors 

·contribute to variation in the last term actually used. The 
AS GEOCHEMICAL SURVEY OF MISSOURI 

TABLE I.-Definition of terms in the hierarchical statis.tical models used in sampling for various phases (populations) of the geochemical 

survey of Missouri 

Population or . group of populations Mapped units Subdivisions of mapped units Analytical error 

y 8 

Bedrock1 ••••••••••••••••••••••••••••• 

Surficial geologic 

deposits. 

Geologic systems or sequences.2 Glacial loess and 

Major areas of occurrence. s Stratigraphic sections within major areas. Portions of strati- graphic sections. Samples within portions of sections. Duplicate analyses of samples. . .-.. do ........................ . . ... do ........................ . Samples within stratijP<lphic sections. Do. 

Oassified soils ................... . carbonate residuum.t 

~il suborders.5 ••••••••••••••• Soil subgroups ............... . Soil series ....................... . Localiues ....................... . Samples within localities. Do. 

Do. 

Do. 

Selected native vegetation and associated soils. 

None .............................. . Parent material ,types.5 

Counties.! ...................... . 7lS-minute quadrangles. 

7lS-minute quadrangles within areas. 

Samples within counties. Composite sample~; of soil profiles within quadrangles. 

Vegetation-type 

areas.5 

Samples within quadrangles. 

Do. 

Selected farm crops and associated soils. .... do ........................ . . ... do ........................ . .... do ........................ . Do. 

Ground water .................... . Geohydrologic units5 ••••• Townships within units. Wells within townships. 

Samples from wells. 

Surface water ..................... . . ... do ........................ . Samples within units. 

1Sampling designs varied somewhat for each lithologic type and for each geologic system or sequence. 2The variance of a was not estimated. 5Master sampling units in the sampling design. 

general model has been discussed further in a previous 

report (Miesch, 1967a). 

In all of the sampling based on the model in equation 1, 

the concentration of a chemical constituent in a sample is 

regarded as a function of the mean concentration for all 

·areas of the State plus deviations determined by the particular part of the State from which the sample was taken 

and by random errors arising in laboratory treatment. 

According! y, the variance among the determined concentrations is a function of the variance among mapped units, 

the variance within units, and the variance arising from 

analytical procedures. This follows from equation 1 when 

we subtract p. from both sides and square. Then, summing 

across i, j, k; m, ... , the sums of the resulting cross-product 

terms on the right side tend toward zero if the selection 

of units represented by f3 ,Y, and8 has been unbiased. 

Finally,' djviding each sid~ by N, where N represents the 

number of samples, we obtain: 

a2 = u2 + u2 + a.2 + a2 + 

x a 13 y 8 · (2) 

where a,i is the variance among all areas of the State, aJ is 

the variance among mapped units, and subsequent terms 

represent variance among areas within mapped units. The 

final term may represent variance arising from analytical 

imprecision, or combined effects of analysis and of 

variation within the smallest areal unit used in the design. 

Estimates of the variance of x, and of the variance 

components on the right side of equation 2, are denoted 

by: 

s2 =s2 +~~ +s2 +s2 + x a "1:J y 0 · · ·, (3) 

and are derived by means of the analysis of variance 

procedures outlined by Anderson and Bancroft (1952, p. 

325-330). These procedures are applicable to data from 

both balanced and unbalanced designs; unbalanced 

designs result when, for some reason, the number of areas 

sampled varies from one master sampling unit to another, 

the number of subareas sampled varies from one area to 

another, or where a similar circumstance occurs at any 

level of the design. 

The estimates of the variance components in equation 3 

provide a useful description of the type of areal variation 

in composition that the sampled population possesses. 

Where s~ is large and the remaining components are 

small, the mapped units about which thesampling plan 

has been designed are compositionally homogeneous and 

distinct from one another. Where sA: is small and the other 

compone·nts are large, the mapped units are not compositionally distinct. Where sB is large compared with subsequent terms in equation 3, the variation within the 

mapped units tends to be on a large scale; where the 

opposite is true, the variation tends to be dominantly 

local. If the final term represents variance arising from 

analytical imprecision, its magnitude compared with 

preceding terms can indicate the adequacy or inadequacy 

of the laboratory method for the particular problem at 

hand. 

Extensive use has been made of a quantity termed the 

variance ratio, v, in examination of the efficiencies of 

various executed and potential sampling designs. The 

variance ratio is given as: 

Nv s& 

v= Dv = 1} +s~+sa +. 

(4) 

The numerator of v, NV' is the estimated variance among 

mapped units, and the denominator, Dv, is the estimated 

total variance within mapped units. Thus, the variance 

ratio is a relative measure of the compositional heterogeneity among, and the compositional homogeneity 

within, mapped units of the population being studied~ It 
METHODS OF SAMPLING, LABORATORY ANALYSIS, AND STATISTICAL REDUCTION OF DATA A9 

is also a relative inverse measure of the degree of the 

sampling problem. Where the variance ratio is large, 

relatively little sampling is required to describe the 

compositional differences among mapped units. Where 

the ratio is small, in ore sampling and laboratory work will 

be required. The variance ratio is related to the conventional and familiar F-statistic as follows: 

F=I +n1v (5) 

where n1 is the effective number of samples collected at 

random, using a simple random sampling design, from 

within each mapped unit. The number of such samples 

required in order to distinguish compositional differences 

between any two mapped units, at a given level of 

confidence, is the value of n1 in equation 5 that will 

produce a value ofF that exceeds the critical value for I and 

2n1 -2 degrees of freedom. Curves giving the required n1·for 

various values of v, at the 80- and 95-percent confidence 

levels., are shown in figure 2A. 

Once n 1 has been determined from the curves in figure 

2A, or from iterative calculation, the maximum acceptable 

error variance of the means for mapped units is given by: 

S 2 +s2 +s2 + 

E -'f1 y 8 ... r- (6) 

"r 

Where the sampling is according to a hierarchical design 

such as given in equation I, the variance of the mean for a 

mapped unit is (Baird and others, I967, p. I6) 

s2 s~ s8 

Es=J}_+-+ +· (7) 

"!3 "f3 "r "f3 "r"8 

where "B· ny, and n8 are, respectively, the number of 

randomly selected areas _sampled within each mapped 

unit, the number of randomly selected subareas within 

each area, and so forth. Where, after an initial sampling 

program (stage Ia) has been conducted, the computed Es 

from the expression in equation 7 exceeds the computed Er 

from expression 6, additional sampling (stage I b) is 

required in order to achieve sufficient power to describe 

the gross compositional differences among mapped units. 

Adjustment of the subscripted n's in expression 7 to 

reduce the variance of the means for mapped units 

sufficiently affords an opportunity to consider not only 

the number of additional samples it may be necessary to 

collect, but also the most efficient spacing of the sampling 

points. In general, the fieldwork will be less costly fo:r: an 

increase in "8 than for an increase in ny, and an increase 

in ny will be .less costly than an increase in "f3. The reason, 

of course, is that intensive sampling in a· relatively few 

small areas does not call for the time and travel required 

for the collection of an equal number of samples from 

widely separated points within a large region. However, in 

situations where s~ is large compared with stand s8 , 

increasing "f3 ma'Y be the only way possible to reduce Es 

sufficiently. 

... ~ 

u) 

w 

..J 

D.. 

::2 

<( 

(/) 

::2 

0 

Q 

z 

<( 

a: 

u. 

0 

a: 

w 

co 

::2. 

:J 

z 

..J 

<(1-

ZI 

2CJ 

1-:J 

a:o 

0(J) 

D..w 

Ou 

a:z 

D..w 

::21! 

:JW 

::2u. _u. 

z-

..... o ::2 

0.1 0.2 0.3 0.4 0.5 0.6 0. 7 0.8 0.9 1.0 

VARIANCE RATIO, v =Nv/Dv 

5 ~ 95 percent 80 percent~ I \ 

3 

1~~~~~~~~~~~WW~~~LW~LU~ 

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 

LOG VARIANCE WITHIN UNITS, Dv 

B 

· FIGURE 2.-Graphs showing the approximate number of random 

samples, n1 , required from each mapped unit. A, number required 

in order to describe the gross differences among a number of units. 

V m• variance mean ratio (see text). B, number reQuired in order 

to search for a minimum proportional difference between two units. 

Computer simulation experiments, by R. R. Tidball 

(unpub.), employing a Monte Carlo technique, have 

shown ·that the degree to which the general configuration 

of a map pattern can be recovered through sampling is 

proportional to the ratio of the variance among sampling 

sites to the variance within them. At the' very least, the 

variance among sites must equal the variance within sites 

in order for the true map pattern to be approximated by 

( 
AlO GEOCHEMICAL SURVEY OF MISSOURI 

means of sampling. Accordingly, it is useful to define a 

variance mean ratio, Vm, as: 

Nv vm = ____, 

Dm 

(?a) 

where Nv is as defined for equation 4 and Dm is the errm 

variance of the means for mapped units and is equal to 

either Er or Es in equations 6 and 7, respectively, 

depending on the type of sampling used. In planning 

stage 1 b sampling, then, it is possible to increase then's in 

equations 6 and 7 until Vm is 1.0 or greater, as an alternative to using the F-test criterion already discussed. This 

procedure is approximately equivalent to using the F-test 

at the SO-percent confidence level, however, as may be seen 

by comparison of the c·urve for vm=l.O with the SO-percent 

curve in figure 2A. Whether or not it is to be used in 

planning stage 1 b sampling, vm is a valid and useful 

relative measure of the stability of a geochemical map. 

A different F-test approach has been previously 

recommended by Garrett (1969; see also Michie, 1973, and 

Garrett, 1973), and the vm ratio approach appears to have 

been used, in effect, by Baird and others (1967). 

These procedures are appropriate where the objective of 

the sampling is to describe gross compositional variations among a number of mapped units or sampling 

localities. The collection and analysis of the numbers of 

samples indicated by the F-tests or the vm ratio will lead to 

the production of a geochemical map that at least has a 

good chance of reflecting the actual geochemical variations in the materials being sampled. However in some 

instances the objectives may be somewhat more ambitious, 

and the sampling requirements will be correspondingly 

greater. For example, the objective may be to identify 

mapped units or sampling localities tha.t differ with 

respect to the concentration of some element by a factor of 

2 or more. Further, one may wish to make these identifications in such a way that there is small likelihood of 

erroneously identifying a difference that does not actually 

exist, or of not recognizing a difference of this magnitude 

that does exist. These two kinds of errors are identified in 

statistical terminology as Type I and Type II errors, 

respectively. Where the objective is of this kind, a method 

described by Davies (1954, p. 36) is more appropriate than 

the methods previously discussed. Where the variances are 

of logarithms, and where the minimum difference being 

sought is relative rather than absolute, the tables given by 

Davies can be summarized into diagrams such as given in 

figure 2B. Figure 2B is based on Davies' tables for the case 

where the probabilities of Type I and Type II errors are 

both 0.05. Thus, knowing the log variance within mapped 

units, D-u, and the minimum proportional difference 

sought, one can use the diagram in figure 28 to determine 

the minimum number of independent samples required 

from each unit. 

METHODS OF LABORATORY ANALYSIS 

The experimental designs used in the geochemical 

survey of Missouri included evaluation of the precision of 

each method of laboratory analysis that was used, as well 

as a determination of the adequacy or inadequacy of that 

precision for the problem at hand. In general, the 

laboratory methods were of the rapid low-cost variety, and 

the precisions were poorer than might have been realized 

with more costly methods. In a few instances laboratory 

methods had to be abandoned because of inadequate 

precision, but in most cases the precision ranged from 

satisfactory to excellent. In fact, the results of the survey 

provide clear evidence that, in general, more costly 

laboratory procedures resulting in better precision would 

have been a waste of money. The reasoning that leads to 

this conclusion is that total error, not simply error 

resulting from laboratory analysis, is the important factor. 

Where the material being sampled is highly variable in 

composition on a local scale, the errors resulting from 

sampling tend to be large, and where sampling errors are 

large there is little point in expending resources to reduce 

error in the laboratory. The resources are better spent 

reducing the error in sampling. That is, where the 

sampling error is large, the total experimental error is 

more effectively reduced by rapid laboratory treatment of a 

large number of samples than by costly treatment of only a 

few. In fact, where sampling error composes the dominant 

part of the total experimental error, even a perfect 

analytical technique would not be helpful in achieving 

the required experimental precision. 

Throughout the survey all samples from each phase 

were analyzed for a given constituent by the same method, 

in the same laboratory employing the same instruments, 

and, wi_th some unavoidable exceptions, by the same 

analyst. Consistency in laboratory method also extended 

across various phases of the survey wherever this was 

possible. For example, all rock, soil, and plant ash samples 

were analyzed by the same spectrographic method in the 

same laboratory. Residues from water samples were 

analyzed by a nearly identical method, although in a 

different laboratory. Rock and soil samples were treated by 

identical laboratory methods for each constituent. 

Laboratory. methods for treatment of plant samples and 

water samples necessarily differed. Methods of preparation of samples for laboratory analysis also differed 

for rocks, soils, plants, and water. 

Within each phase of the survey (except in the studies of 

ground and surface water) all samples were collected 

before any o( them were submitted to the laboratories. In 

general, 10:....30 percent of the specimens were then split 

into two apparently homogeneous parts. All samples, 

including the duplicate splits, were placed in a 

randomized sequence-achieved by use of a table of 

permuted random numbers. The laboratories received and 
METHODS OF SAMPLING, LABORATORY ANALYSIS, AND STATISTICAL REDUCTION OF DATA All 

analyzed the samples in this sequence, without identification of the duplicates. This procedure assured fair and 

realistic estimates of laboratory precision, estimates not 

possibly affected by the conscious or unconscious bias of 

the analyst. This fact, and the fact that laboratory preci_sion as used here includes the effects of sample preparation, should be borne in mind when comparing 

estimates of laboratory precision in the Missouri survey 

with the analytical precision claimed in many other 

studies. The laboratory treatment of samples in a formally 

and completely randomized sequence is of utmost 

importance. The procedure insures that drifts in the 

analytical method, or different biases among individual 

analysts, will not generate false patterns on geochemical 

maps. Such drifts and biases are effectively con¥erted to 

random errors, the effects of which can be overcome 

through statistical treatment of the data. 

In the study of ground and surface water, it was not 

possible to hold samples for randomization until all were 

collected because chemical changes in the water might · 

have occurred. Consequently, ground-water samples were 

collected in a randomized sequence and each sample was 

submitted to the laboratories immediately after collection. 

In the study of surface waters, such randomization in 

collection was not feasible, and the results of the 

laboratory work must be interpreted with the possibility of 

analytical drift in mind. 

When a randomized sequence of rock samples was 

received in the laboratory, each sample was crushed in a 

jaw crusher and a ~-litre portion was split out for reserve 

storage. The remainder was ground in a vertical Braun 

pulverizer with ceramic plates set to pass 80 mesh. The 

ground sample was then mixed and split into seven parts 

for distribution to various laboratories. 

The soil samples were thoroughly dried at 28°-30°C in 

an air-circulating oven, some taking 3 days to dry. The 

caked soil aggregates were then gently broken up in a 

ceramic mortar and passed over a 2-mm (millimetre) 

stainless steel screen. A Nasco-Asplin soil grinder, 

equipped with a ceramic mortar, ceramic screw type 

grinding head, and stainless steel screen, was used for this 

purpose. The material greater than 2 mm, mostly gravel, 

was discarded. The finer material was ground in a vertical 

Braun pulverizer using ceramic plates set to pass 80 mesh. 

As for the rock samples, the ground soil samples were then 

mixed and split into seven parts for distribution to various 

laboratories. 

Plant samples were dried at 38°-40°C and ground in a 

Wiley mill to pass through a 1.3-mm screen. Mercury, 

selenium, arsenic, fluorine, and iodine were determined 

on this dried pulverized material. Other constituents were 

determined on the plant ashes obtained by dry ignition of 

the specimen in a furnace which is slowly heated from 

room temperature to 500°C. 

Each ground-water sample consisted of about 6 litres 

collected in seven polyethylene containers ranging in 

volume from 120 ml (millilitres) to 2 litres. The seven 

containers were submitted to ·various laboratories for 

differ~nt chemical and spectrographic determinations. 

Similarly, each surface water sample consisted of about 6 

litres collected in six polyethylene containers that were 

distributed to various laboratories. One set of surface water 

samples was filtered at the time of collection and _another 

was not filtered. Certain containers of both ground water 

and surface water were acidified at the time of collection as 

was appropriate for the determinations to be made. 

Details of the collection and preparation procedures are 

given in the following discussions of analytical methods 

and in the individual reports of this series on various parts 

of the geochemical survey. 

ANALYSIS OF ROCKS AND SOILS BY X-RAY 

FLUORESCENCE 

By j. S. WAHLBERG 

The suites of samples of rocks and soils, collected for the 

geochemical survey of Missouri, were analyzed by X-ray 

fluorescence spectrometry methods for Si02, Al20 3, total 

Fe as F~0 , CaO, K20, P 20 5, and Se. 

The basis of analysis by X-ray spectrometry is that when 

an X-ray of sufficient energy is absorbed by an atom, that 

atom re-emits an X-ray with a wavelength characteristic of 

the element. Using a crystal of known lattice spacing to 

diffract these emitted X-rays, their wavelengths can be 

identified from their angle of diffraction. The analogy to 

optical emission spectrometry is nearly perfect, with a 

crystal in place of a diffraction grating. The intensity of 

the specific emitted X-ray is measured by a device such as a 

scintillation counter rather than a photographic plate. 

Useful texts on this method are those by Jenkins and 

deVries (1967) and by Bertin (1970). 

As in most forms of spectrometry, the concentration of 

an element may be obtained by comparing the intensity of 

the emitted rays from the sample with those from known 

standards. However, as in other spectrometric methods, 

the amount that the unknowns may differ in composition 

from the standards is subject to many limitations. The 

various methods of fluorescence analysis are largely 

concerned with removing or suppressing interferences so 

that the concentrations of interest in the unknowns can be 

obtained by comparison with a limited number of 

standards. Three different methods were used for the 

samples of rocks and soils collected for the geochemical 

survey of Missouri. 

FUSION METHOD 

A fusion method was used for determining five "major" 

elements-silicon, aluminum, total iron, calcium, and 

potassium. These elements were generally present in 
Al2 GEOCHEMICAL SURVEY OF MISSOURI 

major amounts, and by custom and for convenience were 

expressed as percent oxides (SiOz, Ah03, Fe203, CaO, and 

K20). The fusion method is relatively fast, it overcomes 

most interferences by dilution, and it homogenizes the 

sample since the fusion is essentially a fluid solution. 

In this procedure, 0.3000 g (gram) of ground sample is 

weighed onto 10.300 g of flux and mixed. This flux 

consists of 10.000 g Na2B40 7 (anhydrous) and 0.300 g 

NaN03• The mixture, in a 30-ml platinum crucible, is 

placed in a muffle furnace and heated at 1050°C for 

approximately 20 minutes. A 2%-cm i.d. (inside diameter) 

brass ring is placed on a gold disk that is on a hotplate 

.heated to about 400°C. The fusion is poured into the brass 

ring and allowed to cool slowly. 

The samples are counted in a vacuum X-ray 

spectrometer. The percent concentrations are obtained by 

comparing the net counting rate of the sample with the 

counting rate from standards of known concentration 

similarly prepared. National Bureau of Standards samples 

were used for this study, such as NBS No. lA (limestone), 

No. 98 (plastic clay) and No. 102 (silica brick). The 

following table summarizes the X-ray parameters used: 

X-ray parameter 

Element Target Detector Crystal Path 28 (in degrees) 

Si ................... Cr ................... Flow .............. PET1 .............. Vacuum......... 109.06 AI ................... Cr ...................... do ................ PET .................. do................ 144.67 K .................... Cr: ..................... do ................ PET .................. do................ 50.64 Ca .................. Cr ...................... do ................ PET .................. do................ 45.15 Fe ................... W ...................... do ................ LiF(200) ......... Air................. 57.52 

1Pentaerythritol 

DIRECT POWDER METHOD 

A direct powder method was used to determine 

phosphorus in the Missouri samples. It is a simple method 

and not of high accuracy-it may even be considered 

"semiquantitative." 

The direct powder procedure for phosphorus involvea 

half filling a 2%-cm o.d. (outside diameter) Caplug with a 

sample previously ground between ceramic plates set to 

pass 80 mesh. The Caplug was then covered with a poly~ 

propylene film held in place by two 2%-cm i.d. iron curtain 

rings. The sample was placed in a vacuum X-ray spectrometer and a 1-minute peak and offpeak count was made. 

The conditions used for the count were: Cr target X-ray 

tube, flow proportional detector, germanium analyzing 

crystal, vacuum path, and 28 of 141.38° peak and 143.00° 

off-peak. The phosphorus was reported as percent P20 5• 

PRECONCENTRATION METHOD 

In the determination of trace elements, dilution is 

obviously undesirable, whereas a preconcentration 

method may both remove interferences and concentrate 

the element or elements sought to amounts more 

amenable to detection and estimation. In some cases a suitable matrix may also be obtained. Such a method was used 

to determine selenium in the Missouri samples. 

The determination of the traces of selenium included a 

preconcentration. Two grams of sample was fused with 15 

g Na 2C03 and 6 g Na20 2. The cake from the fusion was 

dissolved in water, about 20 g of NH4Cl was added, and the 

mixture filtered. To the filtrate were added 0.1 mg of 

Na 2Te04, 5 g KI, 0.2 g N2H 4·H2S04(hydrazinesulfate) and 

0.1 g Na2S03· to precipitate the selenium. This precipitate was_ collected on a micropore membrane filter, 

dried, and placed on a l-inch Cap lug for co-unting. A peak 

and offpeak count was made and the amount of selenium 

was determined by comparing the net count with that 

obtained from a known amount of selenium similarly 

processed and counted. The X-ray parameters· were: Mo 

target X-ray tube, scintillation detector LiF(200) crystal, 

airpath, and 28 of 31.89° peak and 33.00° offpeak. The 

method has a lower limit of determination of 0.2 ppm 

selenium. 

ANALYSIS OF ROCKS AND SOILS BY ATOMIC 

ABSORPTION SPECTROMETRY AND OTHER 

METHODS 

By CLAUDE HUFFMAN, jR., and j. I. DINNIN 

This section describes the analytical procedures other 

than X-ray fluorescence, emission spectroscopy, and 

neutron activation that were used for the analysis of rocks 

and soils throughout the duration of the project. The 

selection of analytical methods was based on such criteria 

as speed, general applicability to the kinds of materials to 

be sampled, and the required precision. Analytical 

procedures for the determinations of Na, Mg, Li, Zn, Cd, C 

(three types), F, As, and Hg are described briefly. 

Na and Mg t;tnalyses of rocks and soils were made by V. 

M. Merritt and J. M. Gardner; Li andZn analyses by J. A. 

Thomas; Cd by J.P. Cahill; and the three types of carbon 

determinations were by I. C. Frost and T. L. Yager; F 

analyses for the rocks and soils were made by R. Moore, J. 

W. Budinsky, B. A. McCall, H. Kirschenbaum, S. D. 

Kevan, and M. J. Joyce; As analyses by F. W. Brown, L. 

Mei, B. A. McCall, C. L. Burton, H. Kirschenbaum, and 

M. J. Joyce. Analyses for Hg were made by R. L. Turner. 

Atomic absorption spectrophotometric methods were 

used to determine Na, Mg, Li, Zn, and Cd. The theory and 

concepts of atomic absorption spectroscopy have been 

explained in detail by Slavin (1968). The atoms of every 

element can absorb light radiation at narrow-wavelength 

emission lines which are different for each element. In 

order to be in a condition to absorb, the atoms must be 

chemically unbound and in their minimum energy state 

(ground state); this condition may be achieved by 

·vaporizing the sample solution in a flame. A common 

source of radiation is the hollow-cathode lamp, whose 

ca.thode is made of the element to be determined, and 

which emits the wavelength lines of that element. The 
METHODS OF SAMPLING, LABORATORY ANALYSIS, AND STATISTICAL REDUCTION OF DATA A13 

light from the lamp is passed through the flame 

containing the sample vapor. The ground-state atoms of 

the element to be determined absorb an amount of light 

proportional to the concentration of that element present 

in the sample. The light passes through a grating monochromator which isolates the desired wavelength for the 

element to be determined from all other energy in the light 

beam and is subsequently measured by a photomultiplier 

tube in combination with a precise photometer. Na, Mg, 

Li, and Zn were determined by use of a single sample 

solution. The method consists of decomposing 1 g of rock 

or soil sample with nitric, hydrofluoric, and perchloric 

acids, fuming to dryness, and finally taking the salts into 

solution in 100 ml of 5-percent volume/volume hydrochloric acid. Portions of this sample solution were 

aspirated into the air-acetylene flame of an atomic 

absorption spectrophotometer to determine Na, Mg, Li, 

and Zn. Appropriate hollow cathode lamps were used for 

each element. The aliquot taken for the determination of 

Mg was diluted with a lanthanum chloride solution so 

that the final volume of solution contained 5 percent HCl 

and 1 percent lanthanum. Lanthanum acts as a releasing 

agent in the Mg determination. Standard solutions 

containing known concentrations of each of the elements 

to be determined were used for calibration. 

Cd was determined by an atomic absorption spectrophotometric method slightly modified from that described 

by Nakagawa and Harms (1968). In this procedure a 1-g 

portion of sample is digested with nitric acid in a culture 

tube and allowed to cool. The volume of the solution is 

adjusted to 20 ml with demineralized water, mixed 

thoroughly, and centrifuged. A portion of this solution is 

then aspirated into the air-hydrogen flame of the atomic 

absorption spectrophotometer. 

The Na, Mg, Li, Zn, and Cd values were obtained with a 

Perkin-Elmer model 303 atomic absorption spectrophotometer using the following instrument parameters 

recommended by the manufacturer: 

Wave· Element Grating length Slit (nm) 

Na ......... Vis........ 587.0 

Mg ........ U........... 285.2 

Li .......... Vis........ 670.8 Zn ......... U........... 215.8 Cd ......... u........... 228.8 

1

Hollow cathode lamp. 

Instrument parameter 

Lamp Source• current 

(rnA) 

Na 

Mg 15 

Li 15 Zn 15 Cd 8 

Burner 

5- and 

10-cm 

premix. 

10-cm 

premix. 

... do ...... ... do ...... ... do ...... 

Flame 

airacety· 

len e. ... do ...... 

... do ...... ... do ...... 

airhydrogen. 

Flame 

condition 

Oxidizing 

Reducing 

Oxidizing 

... do ...... ... do ...... 

Filter 

Out 

Out 

In 

Out 

Out 

Three types of carbon determinations were made: for 

carbonate carbon (that is, the carbon present in carbonate 

minerals), total carbon, and organic carbon. The gasometric method described by Rader and Grimaldi (1961) 

was used to determine carbonate carbon. In this method, 

carbon dioxide is liberated by the action of 1 + 1 hydrochloric acid on the sample. The sample size is varied from 

0.5 to 2.0 g. The volume of the liberated carbon dioxide 

plus the air present in the reaction flask is measured at a 

known temperature and known atmospheric pressure. 

The combined gases are then scrubbed free of carbon 

dioxide by passage through a potassium hydroxide 

solution. The volume of the residual gases is then 

measured at the same temperature and pressure. The 

difference in the observed volumes., due to the carbon 

dioxide absorbed, is calculated to standard conditions of 

temperature and pressure, using the ideal gas relationships. The percentage of carbon dioxide is then calculated 

from its volume, and reported as C. 

Total carbon was determined by the Leco inductionfurnace gasometric method, a method which has been used 

in the steel indistry for many years. I. C. Frost (written 

commun., 1968) has shown how the method may be 

applied to the analysis of rocks, soils, and other geologic 

materials. A sample of known weight (0.25-0AO g) is 

placed in a Leco ceramic crucible to which are added one 

or more combustion accelerators (tin metal, iron chips, 

and tin-coated copper). The crucible containing the 

sample is then placed in a high-frequency induction 

furnace within an enclosed combustion tube through 

which pure oxygen is passed. The sample is heated to over 

1300°C where it oxidizes or burns readily. Evolved gases, 

including carbon dioxide, oxides of sulfur, and possibly 

carbon monoxide, are passed through a trap containing 

specially prepared manganese dioxide to remove the 

sulfur oxides, then through a heated catalyst tube where 

any CO formed is converted to C02• The carbon dioxide 

gas volume is measured with the Leco semiautomatic 

gasometric determinator. Carbon dioxide is measured and 

the percentage carbon is calculated in the same manner as 

used in the determination of carbonate carbon. 

Organic carbon is a computed value based on the 

difference between the separate determinations of total 

carbon and carbonate carbon. 

Fluorine was determined by the procedure described by 

Ingram (1970). In this procedure, fluorine is determined 

potentiometrically using a fluoride specific-ion electrode. 

A 100-mg sample is fused with a mixture of sodium 

carbonate and zinc oxide and the melt leached with water. 

The leachate is filtered, acidified with hydrochloric acid, 

and dputed to a specific volume. An aliquot is taken, 

sodium citrate and potassium. nitrate added, and the 

potential of the solution is compared to the potential of 

solutions containing known concentrations of fluoride. 

Arsenic was determined by an arsine evolution-spectrophotometric-isotope dil.ution method (F. W. Brown, L. P. 

Greenland, and F. 0. Simon, written commun., 1973 ). 

One-half gram of sample plus added 76As tracer is fused 
A14 GEOCHEMICAL SURVEY OF MISSOURI 

with a mixture of sodium hydroxide and sodium peroxide, 

leached with water, and acidified with hydrochloric acid. 

Zinc shot is added and the evolved arsine is absorbed in an 

iodine-potassium iodide-sodium bicarbonate solution. 

the 76As activity of the solution is counted with a singlechannel analyzer to determine the percentage removed of 

the arsenic originally present. The arsenic in solution is 

then determined by a molybdenum blue spectrophotometric procedure and corrected for loss. 

Mercury was determined by the mercury vapor detector 

described by Vaughn (1967). In this flameless atomic 

absorption technique, mercury is vaporized from 100 mg 

of powdered sample in an induction furnace. The mercury 

vapor is collected by amalgamation onto silver to 

eliminate interferences. The silver amalgamator is subsequently heated by an induction furnace and the released 

mercury vapor is swept through an absorption chamber 

where its concentration is measured. 

The mercury vapor detector is calibrated with mercurysaturated air, which is obtained by placing a few grams of 

mercury in a 60-ml serum bottle having a sleeve-type 

rubber-membrane stopper. The air is withdrawn from the 

bottle with a hypodermic syringe by puncturing the 

membrane to insert the needle. The membrane seals itself 

as the needle is removed. The temperature-saturation 

curve for mercury vapor in air is shown by Vaughn (1967, 

fig. 6). 

The lower limits of determination for the elements 

analyzed by the preceding methods are listed in table 2. 

The lower limits are based on the sample weights 

normally used for the determination. 

TABLE 2.-Lower limits of determination for some of the methods used 

for the analysis of rocks and soils 

Element 

Na20 ................. . 

MgO ................. . Li ...................... . Zn ..................... . Cd ..................... . 

C (total) ............ . 

C (in C03) ••••••••• 

C (organic) ....... . 

F ....................... . 

As ...................... . 

Hg .................... . 

Method 

Atomic absorption ................... . . ... do .................................. . . ... do .................................. . . ... do .................................. . . ... do .................................. . Induction furnace-gasometric .. 

Acid liberation-gasometric ...... . By difference ............................ . 

Sample 

weight 

(g) 

1.0 

1.0 

1.0 

1.0 

1.0 

.25-.40 

.5-2.0 

F specific-ion electrode............. .1 

Arsine evolution-spectrophotometricIsotope dtluuon. .5 

Flame less atomic absorption.... .1 

Lower 

limit 

(ppm) 

100 

300 

5 

10 

1 

500 

100 

1,000 

40 

1 

.01 

ANALYSIS OF ROCKS, SOILS, AND PLANT ASHES 

BY EMISSION SPECTROSCOPY 

By HARRIET G. NEIMAN 

The optical emission spectroscopic analyses of rock and 

soil samples were performed by methods similar· to those 

described by Myers, Havens, and Dunton ( 1961 ). However, 

the results were reported in six geometric brackets per 

order of magnitude, rather than three, as explained below. 

The rock and soil samples were received in the spectrographic laboratory after having been ground with 

alumina-ceramic plates set to pass 80 mesh and 

thoroughly mixed. A 10-mg sample was mixed with 20 mg 

of a sodium carbonate-graphite mixture (1 percent Na) 

and then packed into a shallow crater electrode and burned 

for 2 minutes in a direct-current arc. The sodium 

carbonate-graphite mixture serves as a spectrographic 

buffer and ensures even burning of the sample. The 

resulting spectra were recorded on a photographic plate 

which was developed under suitable conditions and 

visually compared to reference standards. 

The reference standards were prepared as follows: 

rni:xtures of the elements to be determined, generally as 

oxides, were added to a powdered matrix of pegmatite-like 

composition consisting of 60 parts quartz, 40 parts 

perthite, and 1 part Fe20 3• The element mixture was 

diluted, stepwise, with matrix ma~erial so that the element 

concentration decreased geometrically by a factor equal to 

the reciprocal of the cube root of 10 (about 0.464), usually 

from 10 percent to 0.0001 percent (1 ppm). The decreasing 

series of concentrations of elements in these standards, 

therefore, is: 10., 4.6, 2.15, 1., 0.46, ... , 0.001, 0.00046, 

0.000215, 0.0001 percent. 

The mixtures of the elements and matrix material were 

mixed with graphite powder in the amounts of 10 mg of 

standard mixture to 20 mg of graphite powder and packed 

into a shallow-crater electrode. Using the same procedure 

as for samples, spectra of the various standards were 

recorded on photographic plates. These "standard plates" 

are made for each batch (about 90 dozen plates) with the 

same emulsion number. 

The amounts of the various elements in each sample 

were determined by visually comparing the sample's 

spectrum to the spectra on the standard plates. The analyst 

determines whether the density (blackness) of a specific 

element line in the sample matches that of the same line of 

known concentration in the standard, or whether the 

density appears to be about midway between those of two 

adjacent spectra of the standards. If the density of the 

element line for the sample is determined to 

approximately match that of the line for one of the 

standards, the concentration of the element is reported as 

one of the values in the series 10, 5, 2, 1, 0.5, ... , 0.001, 

0.0005, 0.0002, 0.0001 percent (values of the standard 

samples rounded to one significant figure). If the density 

of the element line for the sample is determined to be about 

midway between those for the standards, the concentration is reported as one of the values in the series 7, 3, 1.5, 

0. 7, ... , 0.0015, 0.0007, 0.0003, 0.00015 percent (values 

which are approximate geometric midpoints between the 

corresponding values of the standards). The procedure 

just described is analogous to one that has been used 
METHODS OF SAMPLING, LABORATORY ANALYSIS, AND STATISTICAL REDUCTION OF DATA A15 

previously in the same laboratory which consisted of 

preparing standards in the following series of concentrations: 12, 8.3, 5.6, 3.8, 2.6, 1.8, 1.2, 0.83, 0.56, ... , 0.0012, 

0.00083, 0.00056, 0.00038, 0.00026, 0.00018, 0.00012, 

0.000083 percent. This series was generated by using a 

factor equal to the reciprocal of the sixth, rather than cube, 

root of 10 (about 0.681 ). Element concentrations were 

determined to occur between two of the values in the series 

(no matching was done) and reported as one of the values 

in theseriesofgeometricmidpoints; 10,.7,5,3,2, 1.5, 1,0.7, 

... , 0.0010, 0.0007, 0.0005, 0.0003, 0.0002, 0.00015, 0.0001 

per~ent. This is the same series of values reported with the 

method presently used, but the smaller number of 

standards now used greatly reduces the time required for 

analysis, and extensive testing has shown that little 

precision is sacrificed. 

The lowest concentration that can be measured (the 

limit of determination) varies for each element, and this 

limit can also vary for a given element depending on the 

other eiements present in the material being analyzed. 

Table 3 gives the elements looked for in all rock, soil, and 

plant ash samples and the approximate lower limits of 

determination. Where the element is not discussed or 

referred to in subsequent reports of this series, the concentrations were found to be generally less than these 

approximate lower determination limits. 

The reported concentration values are reproducible 

within a factor of 1.5 about 68 percent of the time, and 

within a factor of 2 .about 95 percent of the time. However, 

these percentages vary somewhat from one element to 

another and for various types of materials being analyzed. 

More appropriate estimates of reproducibility are given in 

the individual reports of this series. 

TABLE 3.-Approximate lower limits for the elements determined by 

emission spectroscopy 

Lower limits of determination, in percent 

Si .................. . 0.002 Mg................. 0.002 K ............. . 0.7 

AI ................. .. 1.01 c:a.................. .002 P .............. . Fe .................. . .001 Na ................. .05 Ti ........... .. 

Lower limits of determination, in parts per million 

Ag.................. 0.5 

As ................... 1,000 

Au.................. 20 

B.................... 20 

Ba .................. 2 

Be................... 1.5 

Bi................... 10 

Cd.................. 50 

Ce .................. 200 

Co.................. 5 

Cr................... 1 

Cu.................. 1 

Dy.................. 50 

Er................... 50 

Eu .................. 100 

Ga.................. 5 

Gd.................. 50 

Ge.................. 10 

Ho................. 20 

H£. ................. 100 Sb............. 200 

In .................. 10 Sc ................. 5 

lr ................... 50 Sm............ 100 

La .................. 50 Sn............. 10 

Li .................. 100 Sr................. 5 

Lu ................. 30 Ta ............ 500 

Mn ................ 1 Tb ............ 300 

Mo ................. 3 Te ............. 2,000 

Nb ................. 10 Th ............ 200 

Nd ................. 70 Tl............. 50 

Ni .................. 5 Tm ........... 20 

Os .................. 50 u .............. 500 

Pb .................. 10 v .............. 7 

Pd .................. 2 w ············· 100 Pr .................. 100 y .............. 10 

Pt .................. 50 Yb............ 1 

Re .................. 50 Zn ............. 300 

Rh ................. 2 Zr............... 10 

Ru ................. 10 

.2 

.0002 

1

Co';1centrations of AI below 0.1 percent may result from grinding with high-alumina ceramics plates. 

Plant samples are received in the spectrographic 

laboratory after having been ashed and thoroguhly mixed, 

in accordance with procedures used in the plant laboratory 

of the U.S. Geological Survey. (The ashing procedure is 

described in the section on analysis of plants and plant 

ashes by T. F. Harms.) 

In general, the technical procedure for the spectrographic analysis of plant ash is similar to that used for the 

analysis of rock and soil samples but there are some 

important differences. 

As previously described, the mixtures of elements used 

in the preparation of the standards are contained in a 

matrix that approximates that of silicate rocks. In order for 

the plant ash samples to be in a similar milieu, one part 

plant ash is diluted with 1.15 parts of a mixture of 90-

percent pure quartz and 10-percent sodium carbonate. 

TJ:len, 10 mg of this diluted plant ash is mixed with 20 mg 

of graphite powder and the procedure is continued exactly 

as described for the analysis of rocks and soils. 

Reporting the plant-ash results differs from that of rocks 

and soils in that the dilution factor must be considered. 

Therefore, the observed reading from the photographic 

plate is increased by one-third order of magnitude (two 

"steps" in the series used for reporting results); for 

example, a reading of 0. 7 percent is reported as 1.5 percent, 

and 5 percent as 10 percent. Because the diluting mixture 

contains sodium and silica, these elements cannot be determined by this procedure. 

Owing to the dilution of the plant-ash samples, the 

limits of determination of the various elements are 

generally one-third order of magnitude higher than those 

for rock and soil samples. 

ANALYSIS OF ROCKS AND SOILS FOR IODINE BY 

RADIOISOTOPE DILUTION-NEUTRON 

ACTIVATION 

By A. J. BARTEL and H. T. MILLARD, JR. 

The reliable determination of iodine in most geologic 

materials has been a problem to the analyst. This problem 

results from the low concentrations encountered (for 

example, O.OX to O.X ppm in igneous rocks and O.X to X. 

ppm in sedimentary rocks and soils), the volatility of the 

elemental form, and interferences from other, more 

abundant halogens (especially bromine). Most chemical 

methods lack sufficient sensitivity to determine iodine in 

rocks and soils. 

. Neutron activation analysis (NAA) has been used by a 

number of researchers to determine iodine at the parts-perbillion concentration level in meteorites and lunar 

samples (Coles and Anders, 1962; Reed and Allen, 1966; 

Goles and others, 1967; Clad< and others, 1967; and Reed 

and Jovanovic, 1970), and at the parts-per-million concentration levels in deep-sea sediments (Bennett and Manuel, 

1968) and in soils (Lag and Steinnes, 1971). The 25-min 
A16 GEOCHEMICAL SURVEY OF MISSOURI 

(minute) 1281 produced can be measured by either beta or 

gamma counting. Although beta counting is more 

sensitive, the lack of discrimination from the interferences of fission-produced iodine isotopes decreases this 

advantage to some extent. 

The radioisotope dilution-neutron activation analysis 

(RD-NAA) technique (A. J. Bartel and H. T. Millard, Jr., 

unpub. data, 1975) used in the present study employs preconcentration of the iodine followed by determination by 

neutron activation and gamma counting. This approach 

utilizes the high sensitivity of neutron activation analysis 

but avoids the necessity of rapid radiochemical separation 

following activation. However, because chemical 

separations are performed prior to irradiation, the reagent 

blank must be evaluated and its magnitude determines the 

lower limit of detection. 

PROCEDURE 

The preconcentration steps involve fusion of 1 gofrock 

powder or soil with sodium peroxide, dissolution of the 

fusion cake with water, and acidification with sulfuric 

acid. The resulting iodate is then reduced to iodide with 

stannous sulfate, oxidized to iodine with sodium nitrite, 

and the iodine extracted into MIBK (methyl isobutyl 

ketone). The chemical yield for the preconcentration steps 

is determined by adding 50.0JL 1 (microlitre) of a carrierfree 1251 tracer solution ~0.02 mCi(millicurie)/ml) prior 

to fusion of the sample and then comparing the 1251 

activity in the preconcentrate to a reference standard. 

The iodine-MIBK solutions are poured into 2-dram 

polyethylene snap-cap vials, which are then heat-sealed 

and irradiated. Monitoring presents special difficulties. 

Monitors prepared by dispersing 50.0 JL 1 of a standard 

iodide solution in l\1IBK and heat-sealing in polyethylene 

vials experience loss of iodine during irradiation to the 

extent of about 4 percent. In addition, the heat-seal 

occasionally fails and the top blows off. The first problem 

is treated by adding 1251 tracer prior to irradiation and performing a chemical yield determination after irradiation. 

The second problem is solved by using short lengths of 

aluminum wire loaded with cobalt as secondary monitors 

and counting the 10.5-min 60ITICo which is produced. 

These wires are attached to all samples and iodine 

monitors and are calibrated against iodine monitors (now 

the primary monitors) in a series of irradiations. 

Two samples at a time are irradiated for 30 mininthe 

rotating specimen rack of the U.S. Geological Survey 

TRIGA Reactor at a nominal thermal neutron Uux of 

2xl012 neutrons cm-2S-1. Immediately following irradiation, the Al-Co flux monitors are rinsed with water, placed 

on Al planchets, and the 59-keV (kiloelectronvolt) gamma 

peak of 10.5-min 60mCo is counted for 6.7 min on a 30-cm3 

coaxial Ge(Li) detector. During these counts, the polyethylene vials containing the iodine-MIBK solutions are 

opened, the solutions transferred to new polyethylene 

vials, and nitrogen .gas bubbled through the solutions to 

remove 41 Ar, which results from irradiation of trapped air. 

The polyethylene vials are heat-sealed and the 443-keV 

gamma peak of 25-min 128I is counted on the 30-cm3 Ge(Li) 

detector for 16.7 min. All solutions are allowed to decay 

for 16 hrs after counting 1281. Then the 35-ke V gamma peak 

of 60-day 1251 in the samples, iodine monitors, and 1251 

reference standards are counted on a high-resolution 

planar GE(Li) detector (LEPS). 

CALCULATIONS 

The blank is assumed to have two parts. One part of the 

blank is due to contamination from any iodine in the I25J 

tracer solution, the sodium peroxide, the zirconium 

crucible, and the sulfuric acid. The fraction of iodine in 

this blank which reaches the preconcentrate is evaluated 

from the chemical yield. Another part of the blank is due to 

any iodine in the MIBK, the stannous sulfate, and the 

sodium nitrite. This part is assumed to reach the preconcentrate as a constant amount and is not corrected for 

chemical yield. One set of reagents contained 0.007±0.003 

p.g(microgram)I and 0.008±0.001 p.g I respectively for 

these two portions and another set contained 0.022±0.009 

p.g I and 0.011±0.004 p.g I respectively for the same two 

portions. 

The net total areas, A, in counts per minute (CPM), 

under the 35-keV gamma-peak of 1251, the 443-keV gammapeak of 1281, and the 59-keV gamma-peak of 60mCo are 

found by integrating under the peak and substracting the 

background below the baseline. The concentrations of iodine in the sample, Isample in parts per million, are then 

computed using the equation: 

__ I_ [ A~?:mple Wwire I J 

I sample = W. R A . - blank 

sample wire wue 

where Wsample is the weight of sample in grams, Wwire is 

the weight of the Al-Co flux monitor wires in micrograms, A~!:Uple is the activity of 1281 in the sample in CPM 

(corrected f~r chemical yield and radioactive decay), Awire 

is the activity of Gomco in the wire in CPM (corrected for 

decay), and I blank represents the amount of iodine in the 

blank in micrograms. Rwire is the calibration ratio for the 

Al-Co wires, 

CPM128.!_/CPM 60m Co 

p.g I 7 - p.g wire . 

RESULTS 

The accuracy of the RD-NAA technique was evaluated 

by means of multiple determinations of iodine, over a 6-

month period, in a soil sample in which iodine had been 

determined by conventional neutron activation analysis 

(NAA). Two values of iodine were determined in each of 
METHODS OF SAMPLING, LABORATORY ANALYSIS, AND STATISTICAL REDUCTION OF DATA Al7 

three N AA runs. The mea~s and standard errors of the 

means are 3.11±0.081 ppm I (chemical yield found using 125I tracer) and 3.31±0.046 ppm I (chemical yield found by 

re-irradiation). The mean and standard error of the mean 

of 23 RD-NAA runs are 3.03±0.044 ppm I. Thus the 

maximum bias indicated for the RD-NAA technique 

relative to the NAA technique is -8.5 percent. 

The precision of the RD-NAA technique was estimated 

from the data for the 23 runs on the soil sample. The 

coefficient of variation is 6.9 percent. The three-sigma 

detection limit for the technique, as computed from the 

standard deviation of the blank, is 0.02 p.g iodine. 

ANALYSIS OF PLANTS AND PLANT ASHES BY 

METHODS OTHER THAN EMISSION 

SPECTROSCOPY 

By T. F. HARMS 

Prior to any analyses, the plant samples are dried at a 

low temperature (38°'-40°C) and ground in a Wiley mill to 

form a homogeneous sample. After grinding, the particle 

size of the vegetation is such that it will pass through a 

screen with apertures of 1.3 mm. 

Analyses for mercury, selenium, arsenic, fluorine, and 

iodine are made on the dried vegetation. Cadmium, cobalt, 

zinc, sodium, lithium, calcium, potassium, and 

phosphorus are determined on the ash obtained by dry 

ignition of the vegetation in a furnace which is slowly 

heated from room temperature to 500°C. 

Selenium is determined fluorometrically; fluorine is 

measured by a selective ion electrode; and iodine, arsenic, 

and phosphorus are determined by colorimetric 

procedures. All the other elements determined in the dried 

vegetation and plant ash are measured by atomic 

absorption spectrometry. · 

A brief description of the chemical methods which were 

used follows. 

Mercury.-Dried ground vegetation is digested with 

nitric, sulfuric, and perchloric acids under reflux to 

prevent loss of mercury during the early stages of 

digestion. A small amount of sodium molybdate solution 

is added to serve as a catalyst for the digestion (Munns and 

Holland, 1971). After sample dissolution, the digestate is 

heated to fumes of sulfur trioxide, cooled, and diluted with 

metal-free water. Stannous chloride solution is added to 

reduce the mercury to its elemental state. 

The mercury is then swept from solution by a stream of 

air into an absorption cell attached to an atomic 

absorption spectrophotometer. The absorbance is 

measured and compared to the absorbances of known 

concentrations of mercury that have been treated 

similarly. . 

Selenium.-Air-dried ground vegetation is partially 

digested by heating with nitric acid. The soh~tion is. cooled 

slightly and small amou~ts of hydrogen pero~ide are 

added to help destroy the remaining organic material. The 

digestion is completed by adding perchloric acid to the 

sample solution and boiling off the nitric acid. The 

perchloric acid digestate is warmed with dil'-:lte hydrochloric acid to reduce the selenate in the solution of 

selenite ion. The pH is adjusted to 2.0 with ammonium 

hydroxide and the selenium is reacted with 2,3-diaminonaphthalene to form a fluorescent complex whi.ch is 

extracted into hexane. Known concentrations of selenium 

are reacted with 2,3-diaminonaphthalene and the 

fluorescence is plotted against concentration to form a 

calibration curve. The fluorescence of the sa~ple is 

measured and the selenium content is established by 

reference to the calibration curve. 

Arsenic.-Air-dried ground vegetation is mixed with a 

slurry of magnesium oxide and magnesium nitrate, dried 

in an oven, and ashed in a porcelain dish at 500°~ for 3 

hours. The ash is acidified with hydrochloric acid, filtered 

to remove insoluble material, and treated with stannous 

chloride to reduce the arsenic to the trivalent arsenious 

ion. Zinc shot is added, and the evolved hydrogen and 

arsine are passed into an absorbing tube containing silver 

diethyldithiocarbamate dissolved in pyridine. The arsine 

reacts with silver diethyldithiocarbamate to form a soluble 

red complex which has a maximum absorbance at 540 nm 

(nanometres). The absorbance is measured spectraphotometrically and is compared with the absorhances 

measured from known concentrations of arsenic to determine the arsenic content of the sample. 

Fluorine.-Air-dried ground vegetation is mixed with 

50-percent sodium hydroxide solution, dried in an oven, 

and completely ashed at 500°C in an open nickefcrucible. 

The ash is leached several times with hot distilled water 

and the leachate is placed in a plastic petri dish which 

serves as a diffusion cell. Perchloric acid is added to acidify 

the solution and the sample is diffused overnight using a 

small container of dilute 's.odium hydroxide to trap the 

hydrogen fluoride. A smail amount of dilute pe~chloric 

acid is saturated with he;xamethyldisiloxane and is added 

to the solution in the petri dish to aid in th,e diffusion of 

the fluoride ion (Taves, 1968). The sodium hydroxide 

solution is mixed with TISAB (total ionic strength 

adjustment buffer) and the fluoride ion is measured using 

a fluoride selective ion electrode. Known concentrations of 

fluoride which have been diffused and diluted with TISAB 

before measurement are used for preparing calib~ation 

curves. 

Iodine.:_ The ~odine content w·as determined l..lsing the 

method of Cuthbert and. Ward (1964). On~ hundred milligrams qf finely divided plant material is burned in ari 

oxygen combustion flask, anc the combu~tion produqs 

are collected in .. dilu.te sodium nydroxide. The a~l<ali i~ 

acidified with sulfuric acid and the iodide ion is determined indi~ectly by its c~taly.tic. ~ffect on .the reduction of . 
A18. GEOCHEMICAL SURVEY OF MISSOURI 

eerie ion by arsenious ion in a dilute acid solution. For a 

given time and at a given temperature, the extent of the 

reduction of eerie ion is directly proportional to the 

amount of iodide present. The time allowed for the 

reaction is controlled by the addition of silver ion, and the 

extent of the reduction of eerie ion is measured spectrophotometrically. A standard curve is prepared by placing 

iodide solution on ashless (ilter paper, burning the paper 

in an oxygen flask, and carrying the combustion products 

through the procedure. Concentration is plotted against 

the extent of reduction of eerie ion as determined spectrophotometrically to establish a calibration curve. 

Percent ash.-Four grams of dried, ground vegetation is. 

weighed and placed in a crucible. The crucibles are placed 

in a cold muffle furnace and the temperature of the furnace 

is slowly raised over a period of approximately 10 hours to 

480°-500°C. The furnace is maintained at this temperature 

for 12 hours and then is allowed to cool. The ash is 

weighed to three significant figures and the percent ash is 

calculated. 

After the percent ash for each sample has been determined, sufficient quantities of vegetation are ashed to 

obtain the amount of ash required for those elements 

which are determined in the ash and for spectrographic 

analysis. A small plastic ball is .added to each container of 

ash and the contents are shaken thoroughly to pulverize 

and mix the ash. 

Cadmium and cobalt.-Air-dried ground vegetation is 

ashed at 500°C. The ash is heated with nitric and dilute 

hydrochloric acids. The samples are filtered to remove the 

insoluble materials, and the pH of the filtrate is adjusted to 

2.2 with ammonium hydroxide. The solubilized cadmium 

and cobalt are reacted with diethylammonium diethyldithiocarbamate to form complex species which are then 

extracted into methyl isobutyl ketone. The ketone is 

atomized into an air-acetylene flame of an atomic 

absorption spectrophotometer, and the absorption due to 

cadmium or cobalt is measured. Known concentrations of 

cadmium and cobalt are extracted into ketone and 

atomized as for the samples, and a calibration curve is 

established by plotting concentration of the element 

against absorbance. 

Zinc, lithium, sodium, calcium, and 

potassium.-These elements are determined by ato~ic 

absorption spectrometry. Air-dried ground vegetation is 

ashed at 500°C. For the determination of zinc, lithium, and 

sodium the ash is leached with hot 4 N nitric acid. The 

samples are centrifuged and the supernatant solution is 

atomized directly into an acetylene-air flame. For calcium 

and potassium, the ash is leached with 6 N HCI on a steam 

bath. The sample solutions are diluted and 10-percent 

lanthanum solution is added to the aliquot for calcium so 

that the final solution contains !-percent lanthanum ion 

to mask interferences caused by aluminum, phosphate, 

and sulfate ions. The solution is atomized directly into an 

air-acetylene flame. Standard solutions containing known 

concentrations of the element to be determined are used for 

calibration. 

Phosphorus.-Air-dried ground vegetation is ashed at 

500°C, and the ash is heated with 4 N HN03 • The samples 

are diluted and centrifuged, and an aliquot of the supernatant liquid is reacted with ammonium molybdateammonium metavanadate reagent to form a yellow phosphorus complex. The yellow color is compared 

visually with the color of standard solutions prepared in a 

similar manner to determine the phosphorus concentration. 

The lower limits of determination for the elements 

analyzed by the preceding methods are listed in table 4. 

The lower limits are based on the sample weight normally 

used for the determination and may vary because of limitations on the sample size. 

TABLE 4.-Summary of methods used for analysis of plants and plant 

ashes, and lower limits of determination 

Element Method 

Dry weight of sample 

Lower limit (ppm) 

Hg .. . ... . . . . ... Flame less AA.. ... . . ... .. ... .. ... . ... . ... .. .. . ... 2 0.025 

Se ............... 2, 3-diaminonaphthalene ................. 2 .OI 

As............... Silver diethyldithiocarbamate .......... 2 .25 

F................ Selective-ion electrode....................... 2 .5 

I................. Catalytic............................................ .I I 

Ash of sample 

Cd ............. . Atomic absorption ........................... . Co ............. . .... do .......................................... . Zn ............. . .... do .......................................... . Na ............. . .... do .......................................... . Li .............. . . ... do .......................................... . Ca ........... : .. .... do .......................................... . K ............... . ... do .......................................... . P ............... . Colorimetric .................................... . 

0.5 

.5 

.05 

.05 

.05 

.05 

.05 

.05 

0.2 

I 

20 

25 

4 

IOO 

IOO 

IOO 

ANALYSIS OF WATER BY CHEMICAL METHODS 

By M. W. SKOUGSTAD and G. L. FEDER 

LABORATORY DETERMINATIONS 

Instrumentation in the water-analysis laboratory 

permits rapid, accurate determination of a wide variety of 

constituents occurring as dissolved material in natural 

waters. Many of these constituents commonly occur at very 

low concentrations, but their determination is nevertheless important from the standpoint of uses of the water for 

various purposes as well as investigations of water as a 

geologic agent in weathering and decomposition of rocks, 

minerals, and soils. Thus, the present-day laboratory is 

ordinarily well equipped to determine not only the 

common, major constituents in water, but also a number 

of minor metallic and other constituents. For the most 

part, methods for the determination of the various 

substances are fairly well standardized and widely used by 
METHODS OF SAMPLING, LABORATORY ANALYSIS, AND STATISTICAL REDUCTION OF DATA Al9 

analysts engaged in this sort of work. The methods used by 

the U.S. Geological Survey to analyze water samples 

collected as a part of the geochemical survey of Missouri, 

reported here, have been described by Brown, Skougstad, 

and Fishman ( 1970). The reader is referred to this publication for procedural details. However, a brief description of 

the method used for the determination of each constituent 

is given here. 

All samples, with the exception of those collected for the 

determination of nitrogen and phosphorus species, were 

analyzed in the U.S. Geological Survey laboratories in 

Denver, by M. J. Fishman and 0. ]. Feist, Jr., or in Salt 

Lake City, under the direction of R. L. McAvoy and A. H. 

Handy. Determinations of nitrogen and phosphorus 

species were made in the U.S. Geological Survey laboratory in Little Rock, Ark., under the general supervision of 

R. T. Sniegocki and C. T. Bryant, by]. W. Gibbs, R. L. 

James, B. F. Lambert, R. D. McKibban, Marie K. Moore, 

and E. E. Morris. 

Alkalinity.-The alkalinity determination involves an 

electrometric titration with standard sulfuric acid 

solution, and reflects the overall concentration of substances reacting with hydrogen ions under the conditions 

of the titration. The titration will show two endpoints if 

the sample pH exceeds 8.3, indicating the presence of 

C03 -2 or C03- 2 and OH-1 ions. In such cases the titration 

is carried to PH=8.3, and then continued to pH 4.5, 

enabling the calculation of OH-1, C03-2, and HC03 - 1 

concentrations, when all are present. Total alkalinity is 

reported in terms of equivalent concentration of CaCOs. 

While water alkalinity is commonly due to bicarbonate 

or carbonate ions, or both, the presence of other titratable 

substances should not be precluded. Several acid radicals 

such as borate, phosphate, and silica, if present, contribute to the measured alkalinity. 

Ammonia-nitrogen.-To determine ammonia (or 

ammonium ion) the sample is buffered to a pH of 9.5 to 

prevent hydrolysis of organic nitrogen compounds and yet 

ensure the subsequent complete recovery of ammonia 

upon distillation. An aliquot of the collected distillate is 

nesslerized or reacted with a reagent consisting of mercuric 

iodide in a potassium iodide solution. The reaction yields 

an intensely red compound, mercuric amidoiodide 

(Hg(NH2)I), whose color intensity is directly proportional to the ammonia concentration of the sample. 

Arsenic.-Arsenic is determined spectrophotometrically by reduction to arsine (AsH3) gas by zinc metal 

in acid solution, distillation of the arsine through a lead 

acetate scrubber to remove sulfides, and collection of the 

arsine in a solution of silver diethyldithiocarbamate, 

which reacts to form a deep-red compound. The intensity 

of the resultant red color is proportional to the arsenic 

content of the sample. The method is exceptionally free of 

interferences if carefully performed; only antimony interferes seriously, and its occurrence ·in water is generally 

quite rare. 

Bromide ion.-Trace concentrations of bromide ion, as 

most commonly occur in fresh waters, are determined by a 

spectrophotometric method based on the catalytic effect of 

bromide ion on the oxidation of iodine to iodate by 

permanganate in acid solution. Two reactions occur consecutively: (1) iodide oxidizes rapidly to iodine, and (2) the 

resulting iodine oxidizes slowly to iodate. It is the latter 

reaction that is catalyzed by traces of bromide ion, and at 

any given temperature the oxidation rate is directly proportional to the amount of bromide present. In the determination, the reaction is stopped after a suitable time by 

extracting the unreacted iodine with carbon tetrachloride 

and measuring the absorbance of the extract. The ratio of 

the absorbance of an unknown sample to that of a 

reference sample containing no bromide is inversely 

proportional to the bromide ion concentration. 

Calcium and magnesium.-Both calcium and 

magnesium are determined directly by AAS (atomic 

absorption spectrophotometry). Alkaline samples 

(pH>7.0) must first be acidified, and all samples must be 

treated with a lanthanum chloride solution in order to 

minimize interferences due to phosphate~ sulfate, and 

aluminum. An air-acetylene flame is used in the spectrophotometer. 

Cadmium. -Cadmium is determined by AAS by either 

of two methods: (1) directly without pretreatment of the 

sample if its cadmium concentration exceeds about 

20 p.g/1, or (2) after chelation of the cadmium with 

ammonium pyrrolidine dithiocarbamate (APDC), 

extraction of the cadmium complex into methyl isobutyl 

ketone (MIBK), and aspiration of the extract into the airacetylene flame of the atomic absorption 

spectrophotometer. The second method is very sensitive 

and is preferred when concentrations of less than 10 p.g/1 

are to be determined. 

Chloride.-Chloride is a common constituent and its 

determination is either by the well-known Mohr titration 

method, or, preferably, especially for samples containing 

less than 10 mg/1, by a mercurimetric titration method, 

using a solution of mercuric nitrate as the titrant and 

diphenyl carbazone as the indicator. Bromide and iodide 

titrate along with the chloride, but their concentrations 

are usually insignificant by comparison. 

Iodide ion.-The very low concentrations of iodide ion 

commonly found in fresh waters are best determined 

spectrophotometrically by a method based on the catalytic 

effect of iodide on the oxidation of arsenic (III) to arsenic 

(IV) by cerium (IV) in acid solution. At a given temperature, the oxidation rate is directly proportional to the 

amount of iodide present. The reaction may be stopped at 

any suitable time by adding silver nitrate solution. The 

absorbance of the solution at 450 nm, when compared 

with the absorbance of a sample containing no iodide, 
A20 GEOCHEMICAL SURVEY OF MISSOURI 

provides a ratio whose value varies inversely with the 

iodide concentration of the sample. 

Iron.-Two forms of iron may be present in water 

samples: Fe(II) and Fe(III). Both may be determined and 

reported separately, or the total dissolved iron in both 

forms may be determined without distinguishing the 

relative amounts of each. Fe(II) is determined spectrophotometrically on the basis of its reaction with 2, 2'-

bipyridine to yield a red complex. Total dissolved iron 

may be determined by the same reaction after first reducing 

all Fe(III) to Fe(II) with hydroxylamine hydrochloride; 

Fe(III) is then determined by differenc~. Alternatively, the 

total dissolved iron concentration is determined by AAS, 

the sample being aspirated directly into the air-acetylene 

flame of the spectrophotometer without pretreatment 

other than dilution or filtration as may be required. 

Samples containing iron in concentrations of at least 0.10 

mg/1 may be analyzed by this latter method; those 

containing less than 0.10 mg/1 iron must be analyzed by 

the spectrophotometric-bipyridine method. 

Magnesium.-See "Calcium and Magnesium." , 

Manganese.-Manganese is determined by AAS, either 

by direct aspiration of the sample without pretreatment 

(for concentrations of at least 10 p.g/1), or after chelation 

with APDC and extraction of the complex into MIBK (for 

concentrations of 1-10 ,u.g/1). 

Mercury.-A flameless AAS (cold-vapor AAS) method 

permits determination of as little as 0.5 ,ug/1 mercury with 

a precision approaching 0.1 ,u.g/1. The method is based on 

the preliminary digestion and reduction of all mercury 

compounds, including organic-mercury compounds, to 

metallic mercury, flushing the mercury vapor from 

solution by aeration, and then measuring the absorbance 

of the vapor at 253.7 nm in the conventional atomic 

absorption spectrophotometer. The percent absorption is 

plotted on a recorder arid mercury is determined by 

reference to an analytical curve prepared from standards. 

Some samples may contain volatile organic compounds 

which absorb radiation at 253.7 nm and which may be 

swept from the solution along with the mercury vapor. 

These constitute a positive interference and the possibility 

of their presence must not be overlooked. 

Nitrite- and nitrate-nitrogen.-Nitrite-nitrogen is 

determined spectrophotometrically by direct diazotization 

with sulfanilamide and subsequent coupling of the 

resulting diazo compound with 1-naphthylethylenediamine to form an intensely colored red dye. Nitratenitrogen is determined by measuring spectrophotometrically the intensity of the yellow color that is 

produced by the reaction between the alkaloid, brucine, 

and nitrate ion in an acid medium. 

Organic-nitrogen.-A high-temperature digestion 

(Kjeldahl) of a water sample decomposes organicnitrogen-containing compounds including amino acids, 

polypeptides, and proteins. The digestion is carried out in 

concentrated sulfuric acid solution in the presence of 

copper sulfate which catalyzes the decomposition and 

leads to the ultimate formation of ammonium ion. The 

digested mixture is subsequently made alkaline with 

sodium hydroxide, and the free amonia is distilled off and 

is nesslerized. When high concentrations of organicnitrogen are present, the ammonia may be distilled into 

boric acid (H3B03) and titrated with standard sulfuric acid 

solution. 

Phosphorus, dissolved orthophosphate.-Orthophosphate is the most common ionized form of phosphorus in 

water. The method of analysis is highly specific for orthophosphate, but does not distinguish between the three 

ionization products of phosphoric acid, H 2P04- 1, 

HP04- 2, and P04- 3• The relative concentrations of these 

ionic forms in any given sample are a function of pH. 

Orthophosphoric acid reacts with molybdate ion in acid 

solution to form the yellow phosphomolybdate ion which 

can be reduced to form an intensely colored (blue) 

complex. Ascorbic acid, in the presence of antimony ion as 

a catalyst, is used as the reducing agent. 

Phosphorus, total dissolved.-1£ a sample is digested 

with a mixture of sulfuric acid and potassium persulfate, 

complex polyphosphates are hydrolyzed to orthophosphate, and complex organic phosphorus-containing compounds are decomposed and ultimately form the orthophosphate ion. The resulting orthophosphate may then 

be determined by the spectrophotometric method outlined 

in the preceding paragraph. This method permits determination of total dissolved phosphorus: Organic 

phosphorus content can be computed by difference 

between total phosphorus and orthophosphate, although 

it must be understood that such a value for organic phosphorus includes any hydrolyzable polyphosphates that 

rna y be present. 

Potassium.-See "Sodium and potassium." 

Selenium.-The spectrophotometric-diaminobenzidine method is used to determine selenium. Selenium is 

quantitatively separated from most other elements by distillation of the volatile tetra bromide from an acid sol uti on 

containing bromine, the bromine being generated in situ 

by a hydrogen peroxide-bromide reaction. Selenium tetra 

bromide is volatilized and absorbed in water, the excess 

bromine precipitated as tribromophenol, and the selenium then determined by reacting the resulting selenous 

acid with 3, 3' -diaminobenzidine to form a piazselenol 

of intense yellow color. The yellow color of the solution 

is compared with that of standards prepared in a similar 

manner. 

Silica.-Silica may occur both as dissolved silicate or 

silicic acid, and as colloidal or so-called unreactive silica, 

Si02• Dissolved silicate or silicic acid reacts with 

molybdate ion in a strongly acid medium to form a yellow 
METHODS OF SAMPLING, LABORATORY ANALYSIS, AND STATISTICAL REDUCTION OF DATA A21 

silicomolybdate compound. This substance reacts further 

with sulfite ion to form a reduced compound of intense 

blue color whose intensity is proportional to the silica 

content of the sample. The silicomolybdate complex exists 

in two different polymorphic forms, a and {3, of which the 

latter has the deeper color. Formation of the {3-polymorph 

is favored if the solution is kept strongly acid. Silica may 

also be determined directly by AAS provided a hightemperature burner, such as the ntirous oxide-acetylene 

burner, is used. 

Sodium and potassium.-The alkali metals sodium and 

potassium, found in all natural waters, are determined 

directly by AAS. 

Solids, dissolved.-Evaporation of a known volume of a 

filtered sample followed by heating for an hour at 180°C 

provides a dry residue whose weight represents the 

dissolved-solids content of the sample. A platinum dish is 

commonly used for the evaporation. A final drying 

temperature of 180°C is a compromise between a temperature high enough to ensure complete removal of all water 

of hydration from the hydrated salts and one low enough 

to avoid either volatilization or thermal decomposition of 

salts and organic and labile materials. 

Sulfate ion.-Sulfate-ion concentrations are determined titrimetrically with standard barium chloride 

solution using thorin as the indicator. Thorin and barium 

react to form a deep-red complex. The color intensity is 

greater in organic solvents, so the titration is carried out in 

a mixture of about 66 percent dioxane by volume and the 

mixture adjusted to a pH of between 2.2 and 5.0. Several 

multivalent cations besides barium form intensely colored 

complexes with thorin. To eliminate interference from 

such cations, the sample aliquot is treated with a cationexchange rf:!sin prior to titration. 

Zinc.-Zinc, like most other minor, transition elements, 

is best determined by AAS. Because of the good sensitivity 

of the AAS method for this element, it may be determined 

by direct aspiration of an untreated sample into the airacetylene flame of the spectrophotometer. Concentrations as low as 10 p.g/1 may readily be determined. 

FIELD DETERMINATIONS 

Soon after a water sample is collected, its physical and 

chemical properties may change. Among the changes are: 

(a) temperature, (b) loss of gases, (c) reactions with suspended sediment in the sample, (d) hydrolysis, (e) 

oxidation, and (f) precipitation of compounds, especially 

calcium carbonate. In order to minimize the possible 

inaccuracies to chemical and physical determinations 

caused by these factors, certain determinations are made in 

the field. These determinations were: alkalinity, specific 

conductance, dissolved oxygen, pH, and temperature. 

Other changes in chemical properties of samples may be 

greatly minimized by pretreatment of samples before 

shipping. The methods used were described by Brown, 

Skougstad, and Fishman ( 1970) and Barnett and Mallory 

(1971). 

A lkalinity.-A field determination of alkalinity is made 

of each sample at the time it is collected. The determination is made by electrometric titration with standard 

sulfuric acid solution. A Beckman Electromate solid-state 

portable pH meter is used to measure the pH during 

titration. If the sample pH exceeds 8.3, the titration is 

carried out to two end points. The first titration to pH 8.3 

indicates the presence of C032 or C032 and OH- 1 ions. 

The second titration which is continued to pH 4.5 

indicates the presence of HC031• 

The main interferences in this determination are caused 

by salts of weak organic and inorganic acids, such as 

silicates, borates, and phosphates, which if present, contribute to the measured alkalinity. A more detailed discussion of field procedures for determining alkalinity is 

given in Barnes (1964). 

Conductance, specijic.-Specific conductance is 

measured in the field using a Beckman model RB-3 

portable specific conductance meter, with manual temperature compensator. After measuring the temperature of 

the water sample and adjusting the manual temperature 

compensator, the conductivity is read by inserting a diptype conductivity cell into a 1 ,000-ml beaker filled with the 

sample. 

Oxygen, dissolved.-Dissolved oxygen is measured at 

each surface water sampling site during low flow. The 

sample is collected in a 300-ml BOD (biochemical oxygen 

demand) bottle, with a minimum of aeration. The 

dissolved oxygen content of the sample is determined 

using a modification of the Winkler process (Brown and 

others, 1970, p. 126-129). The method depends on the 

formation of a precipitate of manganous hydroxide. The 

oxygen dissolved in the water is rapidly absorbed by 

manganous hydroxide, forming a higher oxide. Upon 

acidification in the presence of iodide, iodine is released in 

a quantity equivalent to the dissolved oxygen present. The 

liberated iodine is then titrated with standard sodium thiosulfate solution using starch indicator. The method is susceptible to interferences from heavily polluted waters, free 

chlorine, more than 200 mg/1 ferric iron, and readily 

oxidizable or reducible organic substances. 

pH.-The pH is measured at the sampling site using a 

Beckman Electromate solid-state portable pH meter. The 

instrument is first standardized with pH 4.00 and 7.00 

standard buffer solutions. The buffer solutions are kept at 

the same temperature as the sample. Most potable waters 

have few interferences that may affect the accuracy of the 

pH determination. When not being used, the glass 

electrode is kept immersed in distilled water. 

Temperature.-Temperature is measured at the time of 

sampling using a mercury thermometer. The temperature 

is read to the nearest 0.2° Celsius. 
A22 GEOCHEMICAL SURVEY OF MISSOURI 

H He 

Li Be 0 F Ne 

Na Mg s Cl Ar 

K Ca Sc Ti v Cr Mn Fe Co Ni Cu Zn Se Br Kr 

~ y Tc Ru Rh Pd Te Xe 

a La Hf Ta w Re Os Ir Pt Au Hg Po At Rn 

Fr Ra Ac 

Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er TmG Lu 

Th Pa u Np Pu Am Cm Bk Cf Es Fm Md No Lw 

FIGURE 3.-Minor elements (outlined) commonly determined in water by emission spectroscopy. 

ANALYSIS OF WATER RESIDUE BY EMMISSION 

SPECTROSCOPY 

By P.R. BARNETT 

The emission spectrogr~ph provides a means of reasonably rapid analysis of water samples for many elements 

simultaneously. The elements determined or specifically 

sought in the water samples of the Missouri survey are 

endosed with solid lines in the periodic table of figure 3. 

Some of these elements are ubiquitous in natural waters, 

and each of them has been found in various waters. 

The spectrographic detection limits vary for different 

elements. The detection limits for arsenic, cadmium, and 

zinc, for example, are relatively poor; whereas, the limits 

for silver and copper are very good. As a result of poor 

spectral sensitivity and (or) low concentrations, a few of 

the elements are frequently not. detected and must be 

reported as less than some computed value. Where the 

combination of these two factors made the lack of success 

of finding a given element a reasonable certainty, it was 

not sought. Notable among the elements of probable 

environmental significance that fall into this category are 

arsenic and selenium. 

The detection limit for each of the elements, in terms of 

the concentration in the water sample, varies inversely 

with the quantity of total solids in the sample, whenever 

the dried residue is used for analysis. This is true because 

the minimum detectable concentration of an element in 

the residue is a relatively high concentration with respect 

to water containi~g ab~ndant solids and a lower concentration with respect to water low in solids. In spite of this 

limitation, the residue technique used, involving greater 

preconcentration, has considerably better limits of detection .than so-called direct methods such as the rotating 

disk, porous cup, vacuum cup, and plasma jet. 

PROCEDURE 

Before any aliquot of a sample was taken, the sample 

was homogenized by placing the polyethylene bottle in an 

ultrasonic bath for 30 minutes or in an especially modified 

paint shaker for 3 minutes. 

Because the elements were determined as a percentage of 

the analyzed solids but reported in terms of micrograms 

per litre of water, it was necessary to determine the total 

solids per litre. A carefully measured 50-ml aliquot was 

evaporated to dryness in a weighed 2- to 2~-inch clean glass 

bulb prepared from a Christmas ornament. A heat lamp 

placed above the bulb served as the heat source. When the 

water was completely evaporated, the bulb was dried at 

l80°C for I hour, cooled to room temperature in a 

desiccator, and weighed. From the increase in weight, the 

total solids per litre was calculated. This determination 

was repeated on a different day and the average of the two 

values used if the duplicates differed by not more than 3 

percent from the average. Otherwise, the determination 

was repeated. 

The residue used for analysis was prepared by 

evaporating to dryness, in a dish lined with plastic film, 

sufficient water to yield about 100 to 150 mgof solids. The 

residue was transferred as nearly quantitatively as possible 

from the plastic film to an agate mortar for homogenizing 

with an agate pestle. The residue was then transferred to a 

glass vial, dried in an oven at l80°C for I hour and stored in 

a desiccator. 

The arcing mixture was prepared by weighing 3 parts 

high-purity graphite, I part sample residue, and 2 parts 

buffer-matrix1 into a small polystyrene vial, in which a 

plastic ball had been placed, and mixing for 3 minutes in a 

small, high-speed,_ impact shaker. Duplicate charges of 24 

mg of this mixture were weighed into high-purity 

graphite electrodes having a cup of inner diameter of 3.66 

mm, a wall thickness of 0.38 mm, and a depth of 6.10 mm. 

The sample end of the electrode was preheated to red heat 

in a flame to drive off any remaining water or gases that 

might c~use expulsion of the sample during arcing. 

1The matrix material has an element composition approximating the average major-element 

composition o£ North American waters (Clarke, 1924) and is made by thoroughly mixing the 

following high-purity compounds in the proportions indicated: CaC05, 46.6 percent; MgSO., 

23.2 percent; NaCI, 18.11 percent; KCI, 11.6 percent; and Si02, 8.11 percent. The addition o£ 2 parts 

matrix to I part sample helps to minimize diHerences among samples and between the sample and 

the standards used £or quantitative comparison, and minimizes the variation in the intensity o£ 

minor-element lines due to diHering matrices. Occasionally, a particular element may be diluted 

below its detection limit but is sacrificed in the interest o£ increased accuracy £or the others. 
METHODS OF SAMPLING, LABORATORY ANALYSIS, AND STATISTICAL REDUCilON OF DATA A23 

TABLE 5.-Analyticallines for emission spectrographic analysis of water 

residues 

[The two·step method of emulsion calibration described in Method E 116-67 (American 

Society for Testing and Materials, 1968) was used] 

Element 

Aluminum(Al) ..................................... . 

Barium (Ba) .......................................... . Beryllium (Be) ...................................... . Bismuth (Bi) ......................................... . Boron (B) .............................................. . 

Cadmium (Cd) ..................................... . Chromium (Cr) .................................... . Cobalt (Co) ........................................... . Copper (Cu) ......................................... . 

Gallium (Ga) ....................................... . Germanium (Ge) .................................. . 

Iron (Fe) ............................................... . 

Lead (Ph) .............................................. . Manganese (Mn) .................................. . 

Molybdenum (Mo) ............................... . 

Nickel (Ni) ........................................... . 

Silver (Ag) ............................................ . Strontium (Sr) ...................................... . Tin (Sn) ................................................ . Titanium (Ti) ...................................... . 

Vanadium (V) ...................................... . Zinc (Zn) ............................................... . 

Zirconium (Zr) ...................................... . 

Wavelength 

(nm) 

308.216 

266.039 

265.249 

455.404 

313.042 

306.772 

249.773 

249.678 

326.106 

302.156 

345.350 

324.754 

327.396 

294.364 

303.906 

271.902 

272.358 

283.307 

257.610 

294.920 

293.306 

257.276 

317.035 

320.883 

341.476 

305.082 

328.068 

460.733 

317.502 

323.452 

324.199 

318.341 

334.502 

334.557 

327.926 

327.305 

Lower limit 

of determination 

(percentage of 

arcing mixture) 

0.0003 

.005 

.01 

.0001 

.0002 

.0005 

.0005 

.001 

.002 

.0005 

.0005 

.0001 

.0002 

.0002 

.0005 

.0005 

.002 

.0005 

.0005 

.001 

.002 

.02 

.0001 

.001 

.0005 

.001 

.00005 

.0001 

.001 

.0005 

.002 

.0005 

.02 

.1 

.001 

.002 

A series of comparison standards were prepared by 

incorporating the elements to be determined in the buffermatrix. The concentration factor between each successive 

standard was 0.464 giving three standards per order of 

magnitude. The lower end of the series was at the detection limit of the most sensitive analytical line. 

Internal standards were not used. Instead, the complete 

series of external standards were recorded on each plate, 

along with the spectra of the duplicated samples. This 

technique was found to be more precise than internal 

standardization with standards and samples on separate 

plates. 

The excitation and exposure conditions were as follows: 

Voltage ......................................... 220 (open circuit) volts 

Amperage ..................................... Gradual increase from 0 to 8 A 

during first 7 sec, then increase to 

12 A 

Spectral region ............................. 220-350 nm 

Slit' width ..................................... 25 p.m 

Slit length .................................... 1.4 mm 

Neutral filter ................................ 24 percent transmission 

Length of burn ............................. To completion 

The percentage transmittances of the analytical lines 

were measured with a microphotometer and a background reading made near each line. The lines most frequently used, together with the lower limit of determination for each line, are given in table 5. With the linewidth measuring device described by Barnett ( 1967), the 

upper limit of the concentration range for any line is that 

of the standard. 

A computer program was used to calculate the concentrations of the elements in the residue and the concentrations in the water from the densitometric data. 

On each -plate of samples and primary standards were 

also recorded the duplicate spectra of one of four so-called 

Standard Reference Water Samples (SRWS). These are 

water samples prepared in one of the laboratories of the 

U.S. Geological Survey and analyzed by a number of 

laboratories of the U.S. Geological Survey and analyzed by 

a number of laboratories throughout the Nation. The 

determinations on these secondary standards were used as 

a check on the quality of the results on a particular plate. 

The long-term precision of analysis is given for each 

SR WS in table 6. A more detailed account of the method of 

analysis is given by Barnett and Mallory (1971). 

TABLE 6.-Precision1 of analysis of water residues from jour standard 

reference water samples 

[GM, geometric mean concentration as micrograms per litre in the water sample; GD 

geometric deviation, or antilog of standard deviation of the logarithms of the concen· 

trations; number of determinations on which estimates are based is approximately 50 

for SRWS•25, 25 for SRW5-28 and SRWS-!2, and 17 for SRWS-38] 

SRW5-25 SRW5-28 SRWS~32 SRWS-!8 

Element GM GD GM GD GM GD GM GD 

AI ............. 554 1.070 620 1.077 211 1.097 401 1.081 3a ............ !16.8 1.110 578 1.100 51 1.103 28 1.067 B .............. 5.4 1.156 15.5 1.1!2 9.9 1.163 Cr ............. 15.3 1.104 21.8 1.092 9.9 1.119 52.8 1.092 Cu ............ 76.6 1.131 274 1.135 620 1.115 125 1.1!2 Fe ............. !90 1.075 140 1.084 902 1.046 1200 1.078 Pb ............ 14.6 1.140 77.9 1.088 26.6 1.106 15.9 1.110 Mn ........... 312 1.100 75.0 1.121 126 1.152 !9.5 1.214 Mo ........... !.2 1.117 18.1 1.072 9.3 1.112 Ni ............ 14.0 1.261 4.8 1.170 29.6 1.15! 4.2 U72 Ag ............ 4.2 U22 14.9 1.269 Sr ............. 252 1.149 56.0 1.095 251 1.116 158 J:-i28 v .............. 4.8 1.126 .:092 4.6 1.155 7.6 1.118 Zn ............ 580 60S 1.085 187 1.076 

'Precision is expressed as a geometric deviation, GD. For example, about 68 percent of the aluminum determinations on sample SRS-25 are in the range from 518 (554/1.070) to 59! (554xi.070) and about 95 percent are in the range from 483 (554/(1.070)1) to 634 (554x(l.070)1). 

ANALYSIS OF WATER FOR RADIOACTIVITY 

By v. J. jANZER 

As water passes through the ·hydrologic cycle, it 

gradually dissolves traces of the rocks, soils, and other 

materials with which it comes in .contact. All of these 

materials contain trace or greater amounts of radioactivity if due only to the presence of potassium. Lightcolored sedimentary rocks such as salt beds, gypsum, limestone, and dolomite, with the exception of potash 

deposits, usually contain the lowest concentrations of the 

radioelements normally found in rocks. Thorium occurs 
A24 GEOCHEMICAL SURVEY OF MISSOURI 

primarily in deposits of monazite sands and in some 

relatively rare minerals. Black marine shales and some 

phosphate rocks contain the highest concentrations of 

uranium. For example, at one time the black marine 

Gassaway Member of the Chattanooga Shale of Devonian 

age, with a uranium content locally greater than 50 ppm, 

was considered to be a potential source of uranium 

(Pollaro and others, 1958). 

Uranium ore deposits consisting of uraninite and pitchblende occur in igneous and metamorphic rocks, whereas 

secondary deposits such as carnotite and coffinite occur in 

sedimentary rocks. Generally, the effect of these deposits 

on water quality is very localized and relatively minimal, 

aithough uranium concentrations in water near ore bodies 

may exceed several milligrams per litre. 

Either natural or manmade radioactivity, or both, are 

found in varying concentrations in all precipitation, 

surface, and ground waters. The natural radioactivity 

which is present in these waters is due to traces of ( 1) the 

long-lived parent members of the three natural radioactive decay series (uranium-238,. uranium-235, and 

thorium-232) and their daughters, (2) single long-lived 

radioactive elements, with potassium-40 being the most 

abundant, and (3) relatively short lived cosmic-rayproduced radionuclides such as tritium and carbon-14. 

Tritium and carbon-14 are also produced by nuclear 

devices. 

Several hundred manmade radionuclides are present 

worldwide as a result of the use of nuclear reactors and the 

detonation bf many fission and fusion devices. The 

relatively long lived radionuclides such as cesium-137, 

strontium-90, and iodine-131 can be detected in many 

environmental samples, and under some conditions they 

may constitute serious health hazards. 

Radioactive decay of all these nuclides results in the 

emission of alpha, beta, or gamma radiation either singly 

or in combination. These emissions can be counted using 

the appropriate detectors and electronic instruments. 

Determination of the gross alpha and gross beta-gamma 

radioactivity of a water sample is a relatively simple and 

rapid analysis which is· useful as an indication of total 

sample radioactivity or as a screening technique. If radioactivity is detected that is above the normal range for the 

type of sample analyzed, more definitive· analyses for 

specific elements may be required. However, identification and measurement of the specific alpha and beta 

emitters in a sample is often extremely difficult and time 

consuming. In most cases, such detailed knowledge is 

unnecessary and a gross alpha and beta value is adequate. 

A gross value merely indicates that the radioactivity of 

unknown origin in a sample is equivalent to a known 

amount of a specified calibration isotope. 

The counting rates of a series of calibration planchets, 

each containing a known amount of alpha or beta radioactivity, and a range of solid weights obtained by evaporation of simulated natural waters, are used to prepare a 

graph of counting efficiency versus weight of residue for 

each radiation counting system that is used. The counting 

efficiency factors from these curves are used to calculate 

and express the radioactivity of each sample in terms of 

equivalent fractional curies per litre of the respective calibration isotopes. 

A curie (Ci) is that amount of radioactivity which yields 

3.7xl010 disintegrations per second. A picocurie (pCi) or 

lxl0-12 curie yields 2.22 disintegrations per minute (dpm) 

and is one of the more common terms used to express the 

low level of radioactivity usually associated with environmental· samples. 

Natural uranium is commonly used as an alphacalibration isotope. One microgram (p.g) of natural 

uranium contains 1

/ 3 picocurie of uranium-238, an equilibrium amount of uranium-234, or an additional /~ pCi, 

and a trace of uranium-235. The total acti-vity associated 

with 1 p.g of natural uranium is thus approximately 0.68 

pCi. 

Two of the most common beta calibration isotopes are 

cesium-137 and strontium-90. Cesium-137, with half-life 

(T ~)of approximately 30 years, decays by beta emission to 

the 3-minute half-life metastable barium-137 which in 

turn decays to barium-137 by emission of a 0.662 MeV 

gamma ray. One beta and one gamma event are thus 

associated with each cesium-137 atom which decays. 

The proportional counter used for counting alpha and 

beta particles can also detect gamma rays but with a greatly 

reduced· efficiency. 

Strontium-90 (T~ = 28 days) decays by beta emission to 

yttrium-90 (T ~ = 3 ~ays) which decays in turn by another 

beta emission to stable zirconium-90. Two beta events are 

thus associated with each strontium-90 atom which 

decays. 

Gross beta values for a sample will differ slightly 

depending upon which of the calibration isotopes is used 

as a reference. 

If the detection system used "saw" 100 percent of the 

beta emissions for every calibration isotope, it would 

register two counts for each atom of strontium-90 which 

decayed. (This assumes that sufficient time has elapsed for 

a complete ingrowth of the yttrium-90 daughter.) The 

system would register only one count for each atom of 

cesium-137 decaying by beta emission. Because of the 

lower detection efficiency of the counting system for 

gamma rays associated with the cesium atom (metastable 

barium-137) decay, it might only "see" one-tenth of the 

gamma events. The total counts registered for each cesium 

atom decay would thus average about 1.1 cpm. 

Consequently, each count registered and considered as a 

strontium beta represents less activity than one count 

considered as a cesium beta. Thus, the gross beta radio-
METHODS OF SAMPLING, LABORATORY ANALYSIS, AND STATISTICAL REDUCTION OF DATA A25 

activity of a sample expressed as strontium-90 will be 

approximately 20 percent lower than if the same amount 

of radioactivity is expressed as cesium-137. No direct 

conversion can be made from one value to the other, 

however. Similar problems exist in attempting to convert 

(or compare) gross values expressed in terms of other 

calibration isotopes. 

Analysis of a water sample for gross alpha and gross 

beta-gamma radioactivity generally requires no more than 

1 litre or a sample aliquot selected to yield, on evaporation, a residue weighing approximately 5Q-150 mg. This 

residue is transferred to a stainless steel counting planchet 

in the form of a thin deposit of uniform size and thickness. 

The planchet is then counted for alpha and beta radioactivity using a low background proportional counter 

calibrated for counting efficiency (Barker and Robinson, 

1963). The sample count rates, corrected fbr background, 

are then used to calculate the gross alpha and beta radioactivity for each sample in terms of micrograms or 

picocuries, respectively, for the calibration isotope used, 

per litre of water. 

All gross alpha and gross beta radioactivity analyses of 

water samples collected for the geochemical survey of 

Missouri were made by Robert S. Dewar and P. K. Roscio. 

METHODS OF DATA MANAGEMENT AND AUTOMATIC DATA PROCESSING 

Extensive use was made of the U.S. Geological Survey 

RASS-ST ATPAC system of computer . programs 

developed specifically for data from studies in field geochemistry. The programs are in FORTRAN IV and have 

been used on an IBM 360/65 in Washington, D.C., 

accessed from Denver, Colo. through a 360/20 terminal. 

The Rock Analysis Storage System (RASS) programs 

are used for storage and selective retrieval of laboratory 

data on rock, soil, plant, or water samples. Coded 

descriptions of the samples, and identification of the 

localities from which the samples were collected, were· 

provided by the investigator at the time the samples were 

submitted to the laboratories. The coded descriptions and 

the laboratory results were received by a permanent data 

processing group which entered both into the RASS file. 

The RASS file is maintained on a magnetic disk; each 

record consists of an alphanumeric portion containing 

identification of the sample and where it was collected, the 

collector, the coded sample description, and some 

administrative data, followea by a numeric portion containing the laboratory determinations. Each record also 

contains free format comments about the sample as 

provided by the investigator. These comments are the only 

part of the record that cannot be queried on retrieval. 

Selected records can be retrieved from the RASS file 

according to sample laboratory number, or by specifying 

such criteria as name of collector, locality of collection, 

type of material, date of submittal to the laboratory, or by 

any combination of these. They may also be retrieved by 

specifying ranges or upper and lower limits for any of the 

analytical determinations. Thus, it is possible to retrieve, 

say, all records on granites collected by R. J. Ebens from St. 

Francois County that contain more than 80 percent SI02 

and 10-15 percent Al 20 3• The alphanumeric and numeric 

portions of each record are printed in either one of two 

formats, and the numeric portion may also be punched on 

cards or written on a magnetic tape or disk for further 

computer processing. The formats of the cards and the 

magnetic devices are direct! y acceptable to the ST A TP AC 

programs for automatic plotting and statistical data 

reduction. 

A generalized diagram of the RASS-ST A TP AC system 

is given in figure 4. It shows that numeric data retrieved 

from the RASS file may be entered onto a magnetic device 

in tbe ST ATP AC format and, from there, passed into three 

other types of computer programs. Output from the 

programs for data preparation are generally printed, but 

are also written on another magnetic device for further 

processing. Data preparation commonly consists of data 

transformations, such as conversion to logarithms, or 

changes in units, such as conversion from weight percent 

of the oxide as may have been reported by the analyst, to 

parts per million of the element as may be required for 

some·further computation. It consists also of computation 

of a correlation or some similar matrix for further 

examination by methods of factor analysis, or may consist 

simply of selection of some part of the total data from the 

ST ATP AC device. 

The statistical programs in the ST A TP AC system 

include most of the univariate, bivariate, and multivariate techniques that have proved to be useful in geochemical studies. 

RASS file 

FIGURE 4.-Generalized diagram of the RASS-STATPAC system of 

computer programs for the management and statistical reduction 

of geochemical data. 
A26 GEOCHEMICAL SURVEY OF MISSOURI 

The programs for the preparation of plotter tapes allow 

preparation of the data for plotting on symbol maps, 

contour-type maps, triangular diagrams, or simple x-y 

graphs. 

Because the RASS-ST A TP AC system has been designed 

specifically for geochemical data, each numeric quantity 

entered into the system may be qualified, as are many of 

the geochemical values produced by the laboratories. Five 

types of qualifying codes are used: N (not detected), L (less 

than), T (trace,) G (greater than), and H (analytical interference). (The code "H" is used here rather than "I" 

because of possible confusion of the latter with the number 

"1.") In addition, a sixth code of B is used to indicate a 

blank, or the fact that no value is available for some 

unspecified reason. No unqualified values of zero are 

entered into the RASS data files because zero is regarded as 

an unrealistic geochemical value. An analyst's report of 

0.00 percent, for example, would be recorded in RASS as 

less than 0.01 percent, or actually as L 0.01. Some further 

examples of the manner in which data values are stored in 

RASS, and their meanings, are as follows: 

N 0.002 Constituent was not detected using an analytical method having a lower limit of determination of 0.002 percent. 

L 0.01 Constituent may be present, but in a concentration of less than 0.01 percent. 

T 0.0001 Constituent appears to be present, but in very 

minor concentrations too low to be measured by the analytical method used. The 

method has a lower limit of determination 

of 0.0001 percent. 

G 10.0 Constituent is present in a concentration too 

H 0.0005 

B 0.0 

0.03 

L N 0.0 0.0} 

T 0.0 

G 0.0 

H 0.0 

high to be measured by the analytical 

method employed-greater than 10.0 

percent. 

Determination of the constituent is interferred 

with by the presence of another constituent. 

Maximum concentration is 0.0005 percent. 

No data available. 

Unqualified estimate of the concentration 

present. Most constituents are recorded in 

units of either percent or parts per million. 

Same as above, but lower or upper limits of 

concentration are not specified. 

Most of the univariate statistical computer programs in 

the ST A TP AC system, and the plotter tape preparation 

programs, accept these qualified analytical values directly 

and treat them as is appropriate for the calculation being 

performed. Some of the programs for bivariate statistical 

analysis also accept the qualified analytical values. The 

programs for analysis of variance and for multivariate 

statistical analysis, however, require data matrices consisting entirely of unqualified values. Accordingly, one of 

the data preparation programs allows the user to replace a 

qualified geochemical value with any unqualified value 

he feels is appropriate before proceeding with analysis of 

variance or multivariate methods. These replacement 

values may be means representing similar kinds of 

specimens, or they may be more or less arbitrary values 

immediately outside the range of determination for the 

analytical method used. In general, qualified values are 

replaced with unqualified values only where they 

compose fewer than 20 percent of the values for that constituent in the data set being examined. In most instances, 

values qualified with N or L were replaced with a value 

equal to seven-tenths of the lower limit of determination 

of the analytical methods used. For example, where 80 

percent of the values form a continuo1..1s frequency distribution censored at the lower limit of analytical determination, say 0.01 percent, it seems more reasonable to 

assume that the remaining values cluster near 0.01 than 

near zero (an infinitely low value on a logarithmic scale). 

For purposes of computation the remaining values would 

be treated as 0.007. However, if the final geochemical interpretations depend on whether they are treated as, say, 

0.007, 0.005, or 0.001, there is no. justification for the 

procedure at all. The only possible justification for the 

replacement of qualified analytical values with values that 

are unqualified is that the final geochemical inter"' 

pretation is largely insensitive to the choice of unqualified 

values used; that is, any reasonable assumed value would 

lead to about the same final geochemical interpretation. 

FREQUENCY DISTRIBUTIONS AND 

DATA TRANSFORMATIONS 

More than one-half of the data accumulated in the geochemical survey of Missouri consist of semiquantitative 

spectrographic analyses (Myers, and others, 1961) which 

are reported in a series of six geometric classes for each 

order of magnitude. That is, the data as received are 

grouped in statistical terminology, and, therefore, can be 

analyzed using grouped data methods. The theoretical 

boundaries of the groups, to two figures, are as follows: 

0.000083, 0.00012, 0.00018, 0.00026, 0.00038, 0.00056, 

0.00083, 0.0012, ... , 5.6, 8.3, and 12 percent, and the 

corresponding geometric midpoints are 0.0001, 0.00015, 

0.0002, 0.0003, 0.0005, 0.0007, 0.0010, ... , 7, and 10 percent. 

A geometric series is used because the line density on the 

spectrographic plate is approximately proportional to the 

log of the concentration of the element, and the expected 

error in reading line densities is, consequently, also 

logarithmically related to concentration. The semiquantitative spectrographic method, thus, is like most 

other methods used for the determination of minor 

constituents in natural materials; the error variance on an 
METHODS OF SAMPLING, LABORATORY ANALYSIS, AND STATISTICAL REDUCTION OF DAT~ A27 

arithmetic scale is generally proportional, in at least an 

approximate way, to· the amount of the constituent 

present. For this reason alone, a logarithmic transformation of all minor element data was appropriate. Log 

transformation of the spectrographic reporting classes 

listed above yields a series of values equally spaced on an 

arithmetic scale, and thus provides a convenient and 

.appropriate means for expressing the data in a form suitable for conventional statistical procedures. 

The proportional nature of laboratory error is 

paralleled in sampling. Even when a highly precise 

laboratory method is used, it is found that the geochemical variation in a rock or soil is at least approximately proportional to the average amount of the constituent present. On log transformation of the data, the 

variance either is homogeneous across all parts of the rock 

or soil unit, or it varies independently of the average. Thus 

logarithmic transformation of the data tends to homogenize both the variance arising from laboratory treat-. 

ment and that actually present in the material ~eing 

sampled. Homogeneous variance is assumed in attempts 

to extract variance components in the analysis of variance 

and in most statistical tests for significant variation 

between two or more populations or strata within populations. 

There are a number of helpful consequences of the log 

transformation other than the tendency to equalize the 

variances. One of these for minor element data is that the 

frequency distributions of the logarithms are almost 

always closer to the normal (gaussian) form than are the 

original data. Consequently, the requirements of the data 

for probability tests are nearly always more closely satisfied. Statistical estimates in general are more stable (that is, 

with smaller error variances) where the data are 

symmetrically distributed about their means. More<?ver, 

statistical methods for treating censored normal 

distributions, such as the one described by Cohen (1959, 

1961 ), are valid and applicable. 

Another helpful consequence of the log transformation 

in treating geochemical data is that the variance estimates 

are independent of the manner in which the original data 

are expressed. The log variance for titanium, for example, 

is the same whether the original data are as percent Ti02, 

parts per million Ti02, percent Ti, or parts per million Ti. 

Finally, the appropriateness of the log transformation 

of geochemical data prior to statistical analysis might be 

obvious from the widespread practices of experienced geochemists who intuitively judge the significance of geochemical differences on a proportional basis. Thus, a geochemical anomaly is spoken of as so many times above 

background, rather than as being of so many parts per 

million. Examination of logarithmic variation by means 

of analysis of variance is a perfectly analogous procedure; 

proportional rather than absolute variation is being 

examined and appraised. 

Most analytical data were transformed to logarithms 

whether reported by the analysts in geometric classes or 

not. There were, however, a few exceptions. Silica in 

highly siliceous materials (granites, sandstones, and some 

soils, for example) nearly always displays a frequency 

distribution with large negative skewness, and log transformation appeared to be wholly inappropriate because it 

magnifies this skewness. Similarly, a few other major 

constituents in some rocks and soils, measured largely by 

the relatively precise X-ray fluorescence method, were 

almost symmetrically distributed and also did not appear 

to warrant log transformation. Log transformation here 

would have imposed a negative skewness on the data. 

Log transformations were not used in preparation of the 

data for Q-mode factor analysis because this method, as 

used in the Missouri study, requires that all determinations for a given specimen sum to a constant, 

generally 100 percent or 106 ppm. As the determinations 

included all major and mo~t commonly determined minor 

constituents, each elemental determination was converted 

to percent or parts per million as the common oxide 

(except for ionic constituents in water and a few other 

constituents that tend to occur in elemental form in 

various materials), and the analysis was adjusted to sum to 

100 or 106• The values for each constituent were then scaled 

to range from zero to unity, in the manner suggested by 

Manson and Imbrie (1964) for giving each variable 

approximately equal weight in the factor analysis 

outcome. The factor analysis method as used in these 

studies does not presuppose any given form for the parent 

frequency distributions. 

DETECTION RATIOS 

Every analytical method is applicable over a limited 

range of concentrations. The semiquantitative spectrographic method used for the analysis of rocks, soils, and 

plant ashes from Missouri, for example, is used to measure 

silver concentrations in the range 0.0001 to 10 percent; the 

X-ray fluorescence method is used to measure most major 

oxides in the range 0.01 to 100 percent. Concentrationsdetermined to occur outside these ranges are reported as 

qualified values using N (not detected), L (less than), or G 

(greater than). Therefore, in statistical analysis of the 

resulting data the situation is commonly encountered 

where some of the data for a particular constituent in a 

particular suite of samples are straightforward estima~es of 

concentration, and some are qualified-that is, maximum 

or minimum possible concentrations. The frequency 

distribution of the data is censored, generally at either the 

lower or upper end. Doubly censored distributions have 

not been encountered in the Missouri survey. 

The estimation of means and variances from censored 

data can be accomplished by use of rigorous and efficient 

formal procedures, and approximate estimates of variance 
A28 GEOCHEMICAL SURVEY OF MISSOURI 

_components, bivariate statistical properties, and multivariate models can be made, under certain conditions, by 

assuming some reasonable approximate values for the 

missing data. In addition, it is commonly useful to 

estimate statistical properties for the unqualified values 

only, but the final estimates must be clearly labeled as 

applicable to only part of the total range of the population. Regardless of the course chosen to treat the censored 

data, it is imperative that reports of the final statistical 

estimates be accompanied by some indication of the degree 

to which the raw data were censored. For this purpose, we 

have used the detection ratio. The detection ratio is given 

in· the form, for example, of 295:300, where the numerator 

gives the number of data values that are unqualified and 

the denominator gives the total number of samples that 

were analyzed. Detection ratios are given for each 

constituent included in the geochemical survey of 

Missouri-generally in tables of estimated mean concentrations, but the ratios are also applicable to the data' as 

used subsequently in bivariate and multivariate statistical 

analyses. 

ESTIMATES OF MEANS AND TOTAL VARIANCE 

As previously discussed in the section on sampling 

designs, the purpose of the geochemical survey of Missouri 

has been to estimate and identify geochemical variation 

over the State, and not to estimate mean compositions of 

the various natural materials. Therefore, the sampling 

schemes were designed for this purpose and in a strict sense 

are not valid for the latter. Nevertheless, estimates of mean 

concentration are of common interest to geochemists and 

so are included in the final survey results even though they 

are admittedly biased to varying degrees. Because the 

sampling schemes have given equal weight to all areas of 

the State where the population of interest occurs, the bias 

will be maximum where the population is highly concentrated, and of unusual composition, in restricted areas. 

The bias will be minimum where large-scale geographic 

variation in the composition of the population is small or 

absent. 

Because most of the f:r~equency distributions are, by far, 

more nearly symmetrical on a logarithmic scale than on an 

arithmetic scale, most averages are estimated as geometric 

means. The geometric mean is the antilogarithm of the 

arithmetic mean of the logs: 

x=log10y, (8) 

where y 1s the analytical value in percent or parts per 

million, 

- I X x=-- n ' (9) 

where n is the number of values of x, and xis the arithmetic 

mean of the logarithms, and _ 

GM=10x, (10) 

where GM is the geometric mean of y. If the detection ratio 

is less than one (that is, some qualified valu~s are present), 

the mean logarithm is first estimated for the unqualified 

values only: ' 

x'= ~~ (11) 

where n' is the numerator of the detection ratio. The 

estimate of the mean logarithm for the entire population is 

then given by a relation from Cohen (1959): 

x=x'-.\(x'-x0 ), (12) 

where x 0 is the logarithm of the point at which the 

frequency distribution is censored (that is, the upper or 

lower limit of the range for the analytical method), and A. 

is from graphs by Cohen (1959, p. 231; reproduced in 

Miesch, l967b, p. B7). The geometric mean, as before, is 

the antilogarithm of x. 

Where a log transformation of the data has not been 

made, averages are estimated as the conventional 

arithmetic mean: 

(13) 

where AM is the arithmetic mean. 

In cases where the data warrant logarithmic 

·transformation, and estimates of the arithmetic mean are 

desired, they are derived by the method of Sichel (1952, 

1966; see also Miesch, 1967b): 

AM=TGM, (14) 

where T is from values tabulated by SiChel (1952, 1966) or 

from graphs by Miesch (1967b, p. B8). 

Even though the geometric mean is a more appropriate 

measure of central tendency than the arithmetic mean 

where the frequency distribution of the data is nearly symmetrical on a log scale, arithmetic means are desirable in 

some instances as estimates of geochemical abundance 

(Miesch, 1967b), or for direct comparison with arithmetic 

means from the literature. 

Where the data, y, are logarithmically transformed, the 

variance of the logarithms is estimated by: 

s~--1; (x-x)2 . ( 15) 

n-I 

If the detection ratio is less than one (that is, some 

qualified values are present), the variance of the. 

logarithms is first estimated for the unqualified values 

only: 

s'2 _l;(x-x)2' 

x n'-I (16) 

where n', as before, is the numerator of the detection ratio. 

The estimate of the logarithmic variance for the entire 

population is then· derived from another equation of 

Cohen (1959): 

s~=s'~+A.(x'-x )2, (17) 

where 'A, as in equation 12, is from graphs by Cohen (1959) 

reproduced in Miesch (1967b). For convenience in interpretation, the variance of the logarithms is converted to 

the geometric deviation, CD, where: 

GD=lQ-5x. (18) 
METHODS OF SAMPLING, LABORATORY ANALYSIS, AND STATISTICAL REDUCTION OF DATA A29 

Where the data are derived from a lognormally distributed 

population, then 68 percent of the population values are 

estimated to occur in the range GM!GD to GMxGD, and 

95 percent of the population is estimated to occur in the 

range from GM/GD2 to GMxGD2. The range in which 95 

percent of the population is estimated to occur is referred 

to as the expected range (Ebens and others, 1973) in subsequent reports of the Missouri study. 

Where the analytical data were not logarithmically 

transformed, the conventional estimate of the standard 

deviation, rather than the geometric deviation, is used: ~ 

SD= • 1 ( 19) 

and the expected range is estimated to be from AM-2SD to 

AM+2SD. 

Because stratified sampling designs were used, and the 

various strata commonly vary greatly in size,· it is 

commonly useful to estimate a weighted mean. The 

weighted mean logarithm is estimated by: 

x ~Wi.Xi (20) w- ~Wi 

where W; and x; are, respectively, the relative size and the 

mean logarithm for the ith strata. 

The weighted geometric mean, GMw, is the antilogarithm 

of xw. Where the data have not been transformed 

logarithmically, the weighted arithmetic mean, AMw, is 

estimated in the conventional manner. 

Some of the statistical estimates discussed in this section 

are evaluated for two typical groups of data in table 7. 

TABLE 7.-Some univariate statistical estimates used in the geochemical 

suroey of Missouri 

Data ........................... . 

Yj(ppm) 

!0 

!0 

50 

100 

!0 

70 

10 

50 

!0 

!0 

70 

!0 

Barium• 

x;=log1oYi 

1.4771 

1.4771 

1.6990 

2.0000 

1.4771 

1.8451 

1.0000 

1.6990 

1.4771 

1.4771 

1.8451 

1.4771 

Detection ratio ........... 12:12 Mean logarithm......... i=l.5792 (equation 9) 

Geometric mean ........ . Log variance ............. . 

Lole::::i~~~d 

Geometric 

deviation. 

GM=!8 ppm (~uation 10) st=0.0677 (equauon 15) 

s=0.260! 

GD=I.82 (equation 18) 

Ex~cted range........... 11-126 ppm (see text) Anthmetic mean........ AM=45 ppm (equation 14)' 

8:12 

Yi(ppm) 

< 0.8! 

< .8! 

1.5 

! 

I 

< .8! 

< .8! 

5 

I 

2 

2 

3 

Cobalt• 

0.1761 

.4771 

.0000 

.6990 

.0000 

.3010 

.3010 

.4771 

i'=0.3039 (equation II) x=0.0961 (equation 12)2 GM=I.25 ppm (equation 10) s't=0.0596 (equation 16) s2=0.1396 (equation 17)2 

s=0.3736 

GD=2.36 (equation 18) 

0.2-7 ppm (see text) AM=l.8 ppm (equation 14)4 

•Data pertain to the sandstone in the Ordovician Roubidoux Formation of Missouri (from R. J. Ebens and J. J. Connor, wriuen commun., 1973). t'"fhe value of x0 , the logarithm of the lower limit of analytical determination, for 

equations 12 and 17 is -0.0809. The value of A for equations 12 and 17 is 0.54 and was determined from a graph of Cohen (1959, p. 231) which gives A as a function of h, computed from the detection ratio (h=(l2-8)/12=0.33), and the quantity s'f/(i'=x0 )2• 

'The value ofT for equation 14 is 1.19. (See table A of Sichel, 1966.) 4The value of Tfor equation 14 is 1.41. (See table A of Sichel, 1966.) 

MEASUREMENT OF CORRELATION AMONG 

COMPOSITIONAL VARIABLES 

Estimates of correlation among chemical constituents 

are helpful in understanding the geochemical behavior of 

·the constituents, and have been used in interpretation of 

some of the Missouri data. The simple correlation 

coe££icient is computed as the covariance divided by the 

geometric mean of the corresponding variances. Simple 

correlations among logarithms measure the degree to 

which the log data fit a straight line on a'common x-y plot. 

Correlations of+ 1.0 indicate that the data, or the log data, 

exactly fit a straight line of positive slope; correlations of 

-1.0 indicate that the slope is negative. Correlations of zero 

indicate the total absence of a linear relation between the 

variables. 

Where either of the two frequency distributions is 

censored (that is, where the detection ratios for either of the 

variables is less than one), the method of estimation of the 

correlation depends on the way in which it is to be used. I£ 

the correlations are to be analyzed by means of R-mode 

factor analysis methods, the censored (qualified) 

analytical values are replaced by some reasonable, 

although arbitrary, estimates of the actual concentration. 

This assures that the correlation matrix possesses the 

Gramian properties required for factor analysis. If the 

correlation matrix is not to be further analyzed by factor 

analysis methods, the qualified analytical values are 

ignored, and the correlation is estimated for the 

uncensored part of the bivariate distribution only. In this 

case, the correlation coefficient is regarded as an index of 

geochemical association only, and because its frequency 

distribution is complex and unknown, no attempt is made 

to judge its statistical significance. 

Chayes ( 1960) showed that correlations among 

compositional variables do not necessarily reflect petrologic~ or geochemical, relationships because these 

variables must sum to a constant for each specimen. His 

mathematical argument is directed at untransformed 

compositional data, but would appear to hold in 

principle, if not in mathematical detail, for logarithmic 

data as well. As suggested by Miesch, Chao, and Cuttitta 

(1966), however, the problem is probably not important 

where both compositional variables are present in minor 

concentration. If either variable is present in major 

concentration the covariance, and consequently the 

correlation coe££icient, does not necessarily reflect a 

genetic, or geochemical, relation. The test of the 

correlation recommended by Chayes and Kruskal (1966) 

was not used, because of arguments presented elsewhere 

(Miesch, 1969). 

ESTIMATION OF VARIANCE COMPONENTS 

Estimation of the mean squares at various levels of the 

hierarchical sampling designs, and, therefore, the variance 
A30 GEOCHEMICAL SURVEY OF MISSOURI 

components represented in equation 3, was by the method 

described by Anderson and Bancroft ( 1952, p. 325-'-330), as 

mentioned previously. Where the sampling designs were 

complete (that is, equal numbers of items across all categories at each level of the design), the method of Anderson 

and Bancroft is perfectly equivalent to that described in 

detail by Krumbein and Slack (1956) and by numerous 

authors in various statistical texts. The primary advantage 

of the method of Anderson and Bancroft is that sampling 

designs are commonly intentionally or inadvertently 

incomplete. They aie intentionally incomplete when 

there is a wish to redistribute the degrees of freedom from 

that ordinarily encountered in a complete hierarchical 

design. For example, if only a portion of the specimens are 

analyzed in duplicate for estimation of the error variance 

term at the lowest level, then the degrees of freedom can be 

increased at some higher levels with no increase in the 

number of specimens to be analyzed. Inadvertently incomplete designs occur when, for example, certain samples 

were not available in the field, or could not be obtained. 

In order to facilitate comparison of estimated variance 

components for different variables, each component can 

be expressed as a percentage of the total variance for that 

variable. Thus, if the estimated variance components for a 

particular variable are, say, sa,=0.3, 11=0.0, and s~=0.2, then 

the estimated total variance is 0.5, and the percentage components are, respectively, 60, 0, and 40. That is, 60 percent 

of the total variance is estimated to be at the upper level, 0 

percent at the intermediate level, and 40 percent at the 

lowest level of the sampling hierarchy. 

ESTIMATION OF SAMPLING AND ANALYTICAL 

ERROR VARIANCE 

·As pointed out previously in this report, and elsewhere· 

(Miesch, 1967a), errors in sampling and laboratory 

analysis are of two fundamental types-bias and 

imprecision. Bias in sampling can occur when the areas, 

subareas, or points where samples are to be taken are not 

selected by some appropriate randomization procedure, 

and bias in laboratory analysis can occur where the 

analytical method is inherently incorrect. Attempts have 

been made to avoid serious bias in sampling by employing 

formal randomization procedures throughout, with only a 

few exceptions. Bias was avoided in the laboratory by 

careful selection ana design of the analytical procedures 

and by repeated analysis of standard reference samples 

throughout the course of the analytical work. 

2The variance of the laboratory analysis, as used here, refers to variance resulting from treatment of the samples from the time they are submitted to the laboratory to the time the laboratory 

results are received. Thus, analytical variance includes the effects of errors arising from sample 

preparation (crushing and grinding of rock and soil samples, ashing of plant samples, and so 

forth). This usage follows from a previous discussion of the subject of errors (Miesch, 1967a, p. 

All). Because this notion of analytical variance is all inclusive, some writers prefer to use 

proced_u'ral variance. 

The variances of the errors due to sampling and 

laboratory analysis2 were estimated in the analysis of 

variance, either separately or combined. In some cases, 

randomly selected samples were split into duplicates and 

the ·duplicates were. randomly interspersed with the 

remaining samples before submitting them to the 

laboratory. The analytical variance, then, wasestimatedas 

the lowest mean square, or variance component, in the 

analysis ofvariance. Where this was not done, the lowest 

mean square, or variance component, is properly interpreted as the analytical variance plus sampling error 

variance at the lowest level of the sampling design. 

An estimated analytical varl.ance of, say, 0.09 indicates 

an analytical standard error of 0.3 (square root of 0.09). If 

the variance had been estimated for the log data, the value 

of 0.3 is the log standard error, and the geometric error, 

GE, is 2.0 (antilog of 0.3). Therefore, the analytical 

method is reproducible within a factor of 2.0 at the 68-

percent confidence level and within a factor of 4 (2.0 

squared) at the 95-percent level. The in~erpretation of the 

geometric error, GE, therefore, is similar to that of the geometric deviation, GD, described previously. The geometric error of the mean for, say, two independent analyses 

of the same sample would he the antilog of the square root 

of the estimated e:rror variance divided by 2, and in the 

example used previously: 

GE=IO(sJ12)l-2 = I0(0.0912)l-2:::J.6. (21) 

Duplicate independent analyses of each sample, therefore, 

would reduce the geometric error from 2.0 to 1.6, and 

assuming that the laboratory method is unbiased, the 

mean of the two analyses would be within a factor of 1.6 of 

the correct value at the 68-percent confidence level, or 

within a factor of 2.56 ( 1.6 squared) at the 95-percent level. 

Estimates of the variance arising from the imprecision 

of sampling also follow from the analysis of variance. If 

the sampling was done according to a hierarchical design, 

by sampling, say, points within subareas, subareas within 

areasr and areas within mapped units, sampling 

imprecision may occur at each of these three levels. Let sJ 

represent the estimated variance among areas within 

mapped units, s~ the variance among subareas within 

areas, and sA the variance among points within subareas. 

Assume that the last term, sA, does not include the 

analytical error variance. Tlien the variance of . the 

sampling error due to the selection of points within 

subareas is given by: 

_!L_ 

n ' 8 

(22) 

where na is the number of points sampled within each 

subarea. The variance.of the sampling error due to both 

the selection of points within subareas and the selection of 

subareas within areas is: 

s~ sA (23) -+---· ny nyn8 
METHODS OF SAMPLING, LABORATORY ANALYSIS, AND STATISTICAL REDUGnON OF DATA A31 

where ny is the number of subareas sampled within each 

area. The total sampling erro~ variance for~ mapped unit 

is estimated by: 

~ s2 sA 

.j:L +....:::L_+..,.----X---- n/3 n/3 ny n/3 ny na (24) 

where n13· is the number of areas sampled within each 

mapped unit. The total error variance for the estimated 

mean of a mapped unit, due to both sampling and 

laboratory analysis, is: 

sft. s~ sg s~ (25) ~+----+ - + , n/3 ,n/3 ny n/3 ny na -n/3 ny na ne 

where ne is the number of independent analyses made of 

each sample. 

Expression 25 is equivalent to the right side of equation 

7, and to equation 10.27 of Cochran (1963, p. 286) for the 

case where all sampling fractions approach zero. 

Thus, the four terms in expression 25 represent, 

respectively, the error variances due to (I) sampling areas 

within the mapped unit, (2) sampling subareas within 

areas, (3) sampling points within subareas, and (4) 

analytical procedures. The numerators of these terms, the 

estimated variance components, indicate the importance 

of each source of error; their effects can always be reduced 

by increasing the appropriate values of n. 

SIGNIFICANCE OF DIFFERENCES AMONG MEANS 

Because of the general approach used in most phases of 

the geochemical survey of Missouri, the estimation of 

mean compositional properties of mapped units, the 

comparison of means is a crucial part of the statistical 

analysis of the data. Without statistical testing, we have no 

way to judge whether observed differences among means 

COl:Jld have, or are unlikely to have, resulted from random 

errors in sampling or laboratory analysis. The· 

conventional statistic for the comparison of two means 

that were selected before actually being computed is: 

t- XI-X2 

sx(.L +~ )~ , n. n2 

(25a) 

where xi and x2 are estimates of the two means from 

populations with equal variance, estimated by s~, and are 

based on ni and n2 independent measurements of xi and x 2, 

respectively. For a test at the 95-percent confidence level 

(a=0.05), the computed t is compared with Student's t 

(1-~, v), where vis the degrees of freedom on which the 

estimate of sx is based (equal to n·Itn2-2). 

If ni,=n2=n, and the critical value of t(l-~, v) is used for 

t, equation 25a becomes: 

XI-x2=R2='\fi. tJ=I.41 t SM • (25b) 

R2 is the shortest significant range for the two means, and 

sM .is the standard error common to xi and x2. The 

quantity l.41t is referred to as the significant studentized 

range by Duncan (1955, p: 3). For a=0.05, and, say, v=12, 

the significant studentized range· is 3.08. Thus, differences 

of at least 3.08 times the standard error of the means are 

required in order to declare the means as significantly 

different. If R 2 is in terms of logarithms, its antilog is the 

factor by which the means must differ in order for them to 

differ significantly at the 95-percent level of conficence. 

Duncan ( 1955) has extended this method for the 

comparison of more than two means. The means are first 

ordered by magnitude. Then, if two adjacent means are 

being compared, p=2; if the two means being compared are 

separated by one other mean, p=3, and so forth. The significant studentized range increases some, but not much, 

with an increase in p. Where p= 100, for example, again 

with v= 12, the value is 3.48 as compared with 3.08 where 

.p=2 ( a=0.05 ). 

Therefore, tests of means by Duncan's method (the 

Multiple Range Test) involve a, v, p, and sM . The 

selections of a and p are straightforward, and sM is 

estimated as VF.s in equation 7. The only uncertain value 

in the M~ssouri studies has been v. The uncertainty stems 

from the estimation of sM from data collected accoiding to 

the hierarchical designs previously described. 

For example, consider 60 samples collected according 

to a simple two-level design as follows: 

Number of mapped units .................................................................... 6 

Number of samples from each uni~ (collected and analyzed independently) .......................................................................... : .............. 10 

Total number of samples .......................................................... 60 

Degrees of freedom for estimating variance among units .................. 5 

Degrees of freedom for estimating error variance ............................... 54 

Total degrees of freedom .......................................................... 59 

The error variance is clearly estimated with 54 degrees 

of freedom because 10 independent measurements were 

obtained from each of 6 units. However, where more than 

two, say three, levels are involved, the situation may be 

as follows: 

Number of mapped units·.................................................................... 6 

Number of areas sampled within each unit (selected at random) ...... 5 

Number of samples from each area (collected and analyzed independently)......................................................................................... 2 

Total number of samples .......................................................... 60 

Degrees of freedom for estimating variance among units.................. 5 

Degrees of freedom for estimating variance among areas within 

units .................................................................................................. 24 

Degrees of freedom for estimating variance among samples within 

areas .................................................................................................. 30 

Total degrees of freedom .......................................................... 59 

Thus, the error variance estimated by equation 7 is based 

on at least 24 degrees of freedom, but fewer than 54. There 

are only 5 completely independent values from each unit 

now, instead of 10, but each of thes.e 5 is based on 2 

independent observations. The number of actual degrees 

of freedom depends on the relative magnitudes of the 

variances among areas and among samples from within 

areas. 
A32 GEOCHEMICAL SURVEY OF MISSOURI 

The uncertainty of v, however, is of little consequence. 

The significant studentized range for two means is 2.92 

where v=24 and 2.84 where v=54. For v equal to infinity, the 

significant studentized range is reduced only to 2. 77. For 

the comparison across seven means, the significant 

studentized range varies only from 3. 47 for v= 10 to 3.19 for 

v _equal to infinity. Whether or not two or more means can 

be declared significantly different depends almost entirely 

on the differences among them and on their standard error. 

Q-MODE FACTOR ANALYSIS 

Each of the rock, soil, plant, and water samples collected 

in the geochemical survey of Missouri was analyzed for 

about 30 to 40 chemical constituents: Obviously, not all of 

these constituents are independent of each of the others. 

For example, most of the calcium and inorganic carbon, as 

well as much of the magnesium; occur together in rocks 

and soils in the carbonate minerals. The alkali metals 

occur together with aluminum and silicon in feldspar 

minerals and clay, and mercury is known to occur largely 

with carbon in organic matter. The result of this geochemical coherence is that variation in these 30 to 40 

chemical constituents may be effectively described in terms 

of fewer than 30 to 40 factors. In fact, most of the variation 

in rocks, soils, and water can be described in terms of three 

or four factors. FaCtor analysis, therefore, offers a means 

for summarizing and reducing the problem of describing 

geochemical variation. To be sure, geochemical maps 

showing. the geographic variation of each of the 30 to 40 

chemical constituents over the State are required, but 

factor maps of three or four theoretical variables (factors) 

can serve to summarize the data and to show variation in 

general geochemical character. 

The method of Q-mode factor analysis was introduced 

into the geological sciences by Imbrie and Purdy (1962) 

and Imbrie ( 1963 ), and its application to large data sets was 

.made practical by the work of Klovan and Imbrie ( 1971 ). 

Klovan and Imbrie also showed a means for derivation of 

the normalized form of the factor scores. Extensions of the 

method of Q-mode analysis that may be ·applied to 

compositional data were given by Miesch (1975, -1976), 

and a computer program for the extended method was 

given by Klovan and Miesch ( 1975). The extended method 

requires that the variables in the matrix of data sum to a 

constant for each sample, but compositional data 

generally have, or can be adjusted to have, this property. In 

most situations the variables sum to 100 percent or 106 

ppm. 

The extended method will be illustrated here by 

applying it to a hypothetical problem. Consider that 20 

samples of rock, soil, vegetation, or water have been 

collected according to the scheme represented in figure 5 

and that the analyses of the samples for 6 constituents yield 

results as shown in table 8. The data in table 8 are 

x3 

x1 x2 x4 

xs 

x7 xG 

x11 

x12 

x13 

x14 

x9 

x17 x18 

x15 

x16 x19 x20 

FIGURE 5.-Distribution of sampling localities for the Q-mode experiments. (See hypothetical data in table 8.) 

TABLE B.-Hypothetical data for 6 constituents in 20 samples 

(as percentages) 

Sample Constituent 

No. A B c D E F Sum 

! ............... 82 8 6 ~ 1 .0 100. 

2 ............... 77 II 6 4 I 1 100 

~--············· 85 15 0 I 0 I 100 4 ............... 72 10 9 6 2 1 100 5 .... ~ .......... 80 16 0 2 1 1 100 

6 ............... .78 7 9 5 1 0 100 7 ............... 67 1~ 9 7 2 2 100 8 .... : .......... 74 6 12 6 1 1 100 9 ............... 81 12 ~ 2 1 1 100 10 ............... 86 9 ~ 2 0 0 100 

11 ....••....•.... 62 20 6 7 ~ 2 100 12 ............... 67 21 ~ 5 2 2 100 15 ............... 57 ~ 6 8· ~ ~ 100 14 .... : .......... 61 24 ~ 6 ~ ~ 100 15 ............... 41 56 ~ 10 5 5 100 

16 ............... 46 ~~ ~ 9 4 5 100 17 ............... 5~ 1 27 14 ~ 2 100 18 ............... 57 6 21 II ~ 2. 100 19 ............... 5~ 5 24 1~ ~ 2 100 20 ............... 58 2 24 12 2 2 100 

_constructed to have an underlying structure that is not 

readily apparent on inspection, just as most- real data 

possess an underlying structure imposed by natural 

. geochemical processes. 

The first step in the factor analysis procedure is to 

transform each column of the data matrix (table 8) to range 

from zero to one so that each value in the column is 

expressed as a proportion of the coluinn range. The 

purpose of the transformation is to put each constituent 

on an equal basis, with the result that each constituent is 

given approximately equal weight in determining the 

factor analysis outcome. The transformed data matrix is 

given in table 9. The transformed data matrix is then 

normalized by dividing each row through by the square 

root of the row sum of squares. The normalized data 

matrix is given in table 10. 

The transformed data matrix in table 10 is then postmultiplied by its transpose to form a 20 by 20 matri~ of 
METHODS OF SAMPLING, LABORATORY ANALYSIS, AND STATISTICAL REDUCTION OF DATA A33 

TABLE 9.-Hypothetical data for 6 constituents in 20 samples transformed to proportions of the ranges for each variable 

Sample Constituent No. 

A 8 c D E F 

) .................................. 0.911 0.200 0.222 0.154 0.200 0 2 .................................. .800 .286 .222 .2!11 .200 0.200 !! .................................. .978 .!14!1 0 0 0 .200 4 .................................. .689 .257 .!1!1!1 .!185 .400 .200 5 .................................. .867 .4!19 0 .077 .200 .200 

6 .................................. .822 .171 .!1!1!1 .!108 .200 0 7 .................................. .578 .!14!1 .!1!1!1 .462 .400 .400 8 .................................. .7!1!1 .14!1 .444 .!185 .200 .200 9 .................................. .889 .!114 .Ill .077 .200 .200 10 .................................. 1.000 .229 .Ill .077 0 0 

)) .................................. .467 .54!1 .222 .462 .600 .400 12 .................................. .578 .571 .Ill .!108 .400 .400 !!! .................................. .!156 .629 .222 .5!18 .600 .600 

14 .................................. .444 .657 .Ill .!185 .600 .600 

15 .................................. 0 1.000 .Ill .692 1.000 1.000 

16 .................................. .Ill .914 .Ill .615 .800 1.000 17 .................................. .267 0 1.000 1.000 .600 .400 18 .................................. .!156 .14!1 .778 ·.769 .600 .400 19 .................................. .267 .114 .889 .92!1 .600 .400 20 .................................. .!178 .029 .889 .846 .400 .400 

TABLE 10.-Hypothetical data for 6 constituents in 20 samples transformed and normalized 

Sample Constituent 

No. 

A 8 c D E F 

1 .................................. 0.919 0.202 0.224 0.155 0.202 0 2 .................................. .841 .!100 .2!14 .24!1 .210 0.210 !! .................................. .926 .!125 0 0 0 .190 4 .................................. .689 .257 .!1!1!1 .!185 .400 .200 5 .................................. .858 .424 0 .076 .198 .198 

6 .................................. .84!1 .176 .!142 .!115 .205 0 7 .................................. .552 .!128 .!118 .441 .!182 .!182 8 .................................. .7!19 .144 .448 .!188 .202 .202 9 .................................. .895 .!116 .Ill .077 .201 .201 10 ......................... : ........ .967 .221 .107 .074 0 0 

)) .................................. .410 .477 .195 .406 .527 .!152 12 .................................. .554 .548 .107 .295 .!184 .!184 1!1 .................................. .28!1 .500 .177 .428 .477 .477 14 .................................. .!161 .5!15 .090 .!II !I .488 .488 15 .................................. 0 .5!15 .059 .!170 .5!15 .5!15 

16 .................................. .065 .5!19 .065 .!16!1 .471 .589 17 .................................. .166 0 .621 .621 .!17!1 .248 18 .................................. .260 .105 .570 .56!1 .440 .29!1 19 .................................. .178 .076 .59!1 .616 .400 .267 20 .................................. .269 .020 .6!1!1 .60!1 .285 .285 

coefficients of proportional similarity among the 

samples:3 The coefficients range from zero to plus one and 

measure the compositional ·sim.ilarity for each sample 

pair. Two samples that are similar in composition have a 

coefficient near one; two samples almost totally dissimilar 

have a coefficient near zero. The coefficient of proportional similarity was designed by Imbrie and Purdy 

(1962), and the matrix of these coefficients (referred to as a 

cosine theta matrix) is the basis for the factor analysis. The 

cosine theta matrix is given in table II; it shows, for 

example, that samples I and 2 are very similar (cosine· 

theta=0.97) and samples 10 and 15 are almost totally dissimilar (cosine theta=O.l5). The first 6 of the 20 eigenvalues of the cosine theta matrix are given in table 12; the· 

fact that the fourth value is considerably smaller than the 

third indicates that the normalized data matrix in table 10 

'Where the number of samples is large, it is desirable to avoid actual computation of the cosine 

theta matrix by use of the method of Klovan and Imbrie (1971). 

may be resolved into three factors. That is, most of the 

variability in the normalized data may be described in 

terms of three factors rather than six variables. The value 

of CPN associated with the third eigenvalue indicates that 

99.5 percent of the variability (expressed as sum of squares) 

in the normalized data can be accounted for by a threefact0r model. In practical terms, this implies that only 

about 0.5 percent of the variability in the normalized data 

will be lost by reduction of the six variables to only three. 

The degree to which each sample will conform to the 

factor model is indicated by the derived sample 

communality. The original communality of each sample 

is one, as is shown by the fact that the sum of squares of 

each row in the normalized data matrix (table 10) is unity. 

When the factor model is used to reproduce the normalized 

data matrix the row sums of squares are found to be 

something less than unity. That is, the derived 

communalities are less than unity and where greatly less 

than unity they indicate that the corresponding sample 

does not conform well with the factor model. Where most 

of the derived communalities are near one, but a few of 

them are small, the smalJ values may indicate that the corresponding samples are anomalous with respect to the 

others. The value of CPN associated with the third eigenvalue in table 12 indicates that the average derived 

communality for the 20 samples in our hypothetical data, 

using a three-factor model, will be 0.995. 

The degree- to which Q-mode models containing up to 

six factors will account for the variance in each constituent represented in the original data (table 8), rather than 

the normalized data (table 10), is given by the factorvariance diagram of figure 6. The diagram was 

constructed by computing the coefficients of determination, rj , between the original data and the data 

reproduced for each variable, j, by models containing two 

to six factors (Miesch, 1975, 1976). All values of r~ are 

zero for the trivial (:ase where the model contains only one 

factor, inasmuch as one-factor models lead to reproduced 

data with no intracolumn, variance. The factor-variance 

diagram shows that the data of table 8, like that of table 10, 

may be reproduced in large part by Q-mode models 

containing three factors. 

Each of the three factors (new theoretical variables) is a 

combination of the original six variables, and is 

represented by a set of fact~r composition scores. There is 

an unlimited number of sets of factors and associated 

scores from which to choose, but for the purpose of merely 

·summarizing the data it is appropriate to use the Varimax 

axes. The scores for the Varimax axes have the property of 

being totally dissimilar by the measure of cosine theta 

referred to previously. The Varimax composition scores 

are given in table 13 and the composition loadings of the 

20 samples on these scores are given in table 14. When the 

scores are combined in the proportions indicated by the 
A34 GEOCHEMICAL SURVEY OF MISSOURI 

TABLE 11.-Matrix of coefficients of proportional similarity (cosine theta) for 20 hypothetical samples 

[The complete matrix is symmetrical with unities in the diagonal; only the upper triangle is shown] 

Sample No. 

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 

0.90 0.93 0.98 0.79 0.91 0.96 0.97 0.69 0.77 0.56 0.61 0.29 0.33 0.46 0.56 0.49 0.54 

.95 .95 .96 .91 .95 .98 

.97 .84 .69 .77 .97 

.94 .97 .97 .89 

.80 .80 .99 

.97 .91 

.82 

Sample No. 

TABLE 12.-First six eigenvalues of the matrix of cosine 

theta, and cumulative proportions of N (CPN) 

Order of 

eigenvalues 

1 ................................................... . 2 ................................................... . 3 ..................................................... . 4 ................................................... . 

5 ................................................... . 6 ................................................... . 

Eigenvalues 

14.951 

3.277 

1.673 

.080 

.017 

.002 

CPN 

0.748 

.9ll 

.995 

.999 

1.000 

1.000 

TABLE 13.-Composition scores for the three-factor Varimax 

model 

Factor 

Constituent I ~2 3 

A ............................. 29.97 90.33 48.76 

B ............................. 60.77 9.12 -17.84 

c ..................... ~ ....... -12.74 .61 45.91 

D ............................. 7;92 .24 19.42 

£ ............................. 6.46 -.11 2.90 

F ............................. 7.62 -.19 .86 

Sum ................. 10Q.OO 100.00 100.01 

loadings for any sample, the result is an approximation of 

the composition of the sample. For example, the 

composition loadings for sample 1 are 0.05, 0.82, and 0.13 

.92 .82 .89 .73 .77 .49 .54 .57 .67 .60 .65 

.97 .60 .76 .51 .60 .28 .35 .20 .33 .24 .31 

.79 .91 .90 .83 .83 .62 .65 .76 .85 .79 .80 

.93 .76 .88 .68 .75 .47 .52 .31 .46 .36 .40 

.91 .73 .77 .62 .63 .34 .38 .62 .70 .64 .70 

.67 .96 .94 .93 .91 .77 .80 .80 .89 .84 .84 

.82 .79 .-81 .72 .70 .46 .51 .77 .83 .78 .83 

.75 .86 .66 .72 .42 .48 .39 .52 .43 .48 

.69 .43 .so .15 .22 .27 .38 .30 .38 

.98 .98 .89 .90 .73 .83 .78 .74 

.97 .82 .85 .58 .71 .64 .62 

.95 .96 .72 .82 .78 .73 

.95 .61 .74 .68 .63 

.60 .69 .66 .58 

.70 .66 .59 

.99 

.98 

TABLE H.-Composition loadings for the three-factor Varimax model 

Sample Factor Sample Factor 

No. No. 

1 ............... 0.05 0.82 0.13 11 ............... .31 .47 .22 

2 ............... .12 .73 .15 12 ............... .28 .59 .13 

3 ............... . 09 .91 .00 13 ............... .!18 .!18 .24 

4 ............... . 15 .61 .24 14 ............... .!18 .46 .16 

5 ............... .15 .82 . 0!1 15 ............... .64 .II .25 

6 ............... .05 .74 . 21 16 ............... .59 .19 .22 

7 ............... . 22 .5!1 .25 17 ............... .18 .18 .64 8 ............... .08 .65 . 27 18 ............... .21 .29 .50 

9 ............... .II .81 . 08 19 ............... .21 .21 .58 

10 ............... . 02 .92 .06 20 ............... .15 .29 .56 

(table 14). When the three sets of composition scores of 

table 13 are combined, respectively, in these proportions, 

the result is· an approximation of the composition of 

sample 1 as given in table 8. The combination of scores 

referred to an the composition of hypothetical sample 1 are 

given for comparison in table 15. 

Inspection of the factor scores in table 13 reveals that 

individual samples with high composition loadings (table 

14) on factor 1 tend to be relatively rich in constituents B, 

E, and F and deficient in constituent C; samples with high 

loadings on factor 2 tend to be rich in constituent A and 

contain little else; samples with high loadings on factor 3 

tend to be rich in constituents C and D and are especially 

deficient in constituent B. Hence, maps of the three 
METHODS OF SAMPLING, LABORATORY ANALYSIS, AND STATISTICAL REDUCTION OF DATA A35 

0.8 

('I 

i..""' 

ci 

0 

u.. 0.7 

0 

w 

1-

z 

::> 

0 0.6 u 

u 

<l: 

w 

u 

z 0.5 

~ 

a: 

<l: 

> 

u.. 0.4 

0 

z 

0 

~ 

a: 0.3 0 

a.. 

0 

a: 

a.. 

0.2 

NUMBER OF FACTORS IN MODEL 

FIGURE 6.-Factor-variance diagram for the hypothetical data in table 

8. The diagram shows the proportion of the total variance in each 

constituent that can be explained by Q-mode models containing 

one to six factors (end members). 

TABLE 15.-0riginal hypothetical data for sample 1 (from 

table 8) and a combination of the three sets of composition 

scores (table 13) in the proportions indicated by the composition loadings (0.05, 0.82, and 0.13; table 14) 

Constituent 

A ............................ . B ............................ . 

c ............................ . D ............................ . 

£ ............................ . £ ............................ . 

Sum ................ . 

Original 

data 

82 

8 

6 

3 

1 

0 

100 

Combination 

of scores 

81.9 

8.2 

5.8 

3.1 

.6 

.3 

99.9 

columns of factor loadings in table 14 tend to show the 

same compositional variations as do maps of· the six 

individual constituents represented in table 8. This is 

illustrated by comparison of figures 7 and 8. Figure 7 

shows six maps of the individual constituents, and figure 8 

shows maps of the three columns of composition loadings. 

The patterns of variation for the six constituents (fig. 7) 

display several prominent features that are repeated, to 

some extent, among the six maps. One of these features is a 

preponderance of high values in the upper-left portion of 

the map (constituent A); another isaclusterofhigh values 

in the lower right (constituents C and D); another is a 

cluster of high values in the lower-central part of the maps 

(constituents B, E, and F). The repetition of these features 

among the maps occurs because of linear correlations 

among the six constituents, and it results in partial 

redundancy. Each of the features also occurs in one of the 

factor maps of figure 8. Thus, the factor maps tend to show 

the same . patterns of geochemical variations, but 

redundancy is avoided. The map of factor 1, for example, 

shows that samples from the lower/ central part of the map 

area tend to be rich in constituents B, E, and F and 

deficient in constituent C. The other two factor maps can 

be interpreted in a similar manner. 

Although the principal purpose of Q-mode factor 

analysis, as used in the geochemical survey of Missouri, 

has been to summarize data and to show patterns of variation in general geochemical character across the State, the 

results can, in some cases, be interpreted in terms of geochemical processes. In the hypothetical problem treated 

here, for example, one may infer that factor I represents 

some process that acts to enrich the samples in constituents B, E, and F and removes constituent C. The samples 

that have been subjected to this process to the greatest 

extent are those with high loadings on factor 1 (tabie 14), 

and the degrees to which they have been subjected to it are 

proportional to the magnitudes of the loadings. Whether 

or not interpretations such as this are plausible in actual 

field studies, however, does not bear on the usefulness of 

the factor maps for summarizing the data in a convenient 

map form. 

In conventional factor analysis the factor loadings and 

scores are in normalized form and the signs of these values 

are somewhat arbitrary. That is, the signs of the entire kth 

column of loadings may be changed if one also changes 

the signs of the entire kth row of scores. With the extended 

method, however, it is required that each set of scores (that 

is, the scores for each factor) sum to the same constant as do 

the variables for each sample. This prohibits changing 

signs of the scores and, therefore, prohibits changing signs 

of the loadings also (Miesch, 1975). As a result, in the 

interpretation of loadings in terms of geochemical 

processes a negative loading must imply the depletion of 

constituents with positive scores and enrichment of 

constituents with negative scores. 

Most of the data matrices examined by Q-mode factor 

analysis in the Missouri study contain variables 

representing all of the major constituents in the materials 

(rocks, soils, and water) except oxygen and HzO. Because 
A36 GEOCHEMICAL SURVEY OF MISSOURI 

0 

0 0 0 

® 

0 0 

® 

0 

0 0 

0 0 0 

Constituent A Constituent B 

0 0 

0 0 0 0 0 

0 0 

0 0 ® 0 

0 0 ® 0 

0 

® 0 

0 0 0 

0 0 0 ® 

Constituent C Constituent D 

0 0 

0 0 0 0 0 

0 0 

0 ® 0 

® ® 

0 0 

0 ® 0 

Constituent E Constituent F 

FIGURE ?.-Distribution patterns for 6 constituents in 20 samples used in the Q-mode experiment (see hypothetical data in table 

8). A solid dot indicates that the value is in the upper third of the range for the constituent, a circled x indicates that . the 

value is in the middle third, and an open circle indicates it is in the lower third of the range. The regions of high values 

are shaded. 
METHODS OF SAMPLING, LABORATORY ANALYSIS, AND STATISTICAL REDUCfiON OF DATA A37 

0 

0 0 0 

0 

0 0 

0 0 

0 

0 0 

0 0 0 

Factor 1 

0 0 

0 

0 0 0 

Factor 2 

0 

0 0 0 

0 

0 0 

0 0 

0 

0 

0 0 

0 0 

Factor 3 

FIGURE B.-Distribution patterns for the composlUon 

loadings from the Q-mdde experiment (table 14) on three 

sets of composition scores (table 13). Solid dot indicates 

a score from 0.67 to 1.0, circled x indicates a score from 

0.33 to 0.67, and open circle indicates a score from 0 to 

0.33. The regions of high values are shaded. 

these two constituents are not represented, the variables for 

each sample do not sum to a constant as is required for use 

of the extended Q-mode method, and some adjustment 

was necessary. For constituents in rocks and soils reported 

by the analysts in elemental form, the reported values were 

converted to oxide forms if the element occurs in oxygenbearing minerals. Thus, reported values for Ba were converted to BaO and values of Cr were converted to Cr20 3, for 

example. The particular oxides used depended on the 

common valence states for the element in the surficial 

environment. Reports for elements such as organic carbon 

and Hg, which occur in elemental form in the rocks and 

soils, were not converted to the oxide form. All data on 

rocks and soils reported as parts per million were then converted to percentages, and the final adjustment consisted 

of dividing the variables for each sample through by their 

sum and multiplying through by 100. 

The chemical data for each ~ample of water were 

adjusted to sum to 106 by converting all values to parts per 

million and summing. The sum was then subtracted from 

I 06, and the difference was taken as an estimate of H 20 in 

parts per million. Although the values for H 20 are overwhelmingly greater than the values for any other constituent in the samples, they all ranged from zero to one, just 

as for the other constituents, after the data were transformed to proporrions of the variable ranges. The 

procedure led to parts per million data with a constant 

sum for each sample as is required for the extended Qmode method. 

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*U.S. GOVERNMENT PRINTING OFFICE: 1976-677·340/68