Total Element Concentration in 

Soil Within the Northef n 

Great Plains Coal Region

and Reg

Wind River Basins, 

Wyoming and Montana

GEOLOGICAL SURVEY PROFESSIONAL l>At»£R 1134^ A,

Spatial Variation in 

Total Element Concentration in 

Soil Within the Northern 

Great Plains Coal Region

By R. C. SEVERSON and R. R. TIDBALL

GEOCHEMICAL SURVEY OF THE WESTERN ENERGY REGIONS

GEOLOGICAL SURVEY PROFESSIONAL PAPER 1134-A

Geochemical maps or geochemical baselines 

are presented for 40 elements in 

A and C horizons of soils

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1979
UNITED STATES DEPARTMENT OF THE INTERIOR 

CECIL D. ANDRUS, Secretary

GEOLOGICAL SURVEY 

H. WUliam Menard, Director

Library of Congress Cataloging in Publication Data

Severson, Ronald Charles, 1945-

Spatial Variation in Total Element Concentration in Soil Within the Northern Great Plains Coal Region

(Geochemical Survey of the Western Energy Regions) (Geological Survey Professional Paper 1134-A)

Bibliography: p. A17

1. Soil chemistry-Great Plains. 2. Soils Great Plains-Composition. I. Tidball, Ronald R., joint author.

II. Title. III. Series. IV. Series: United States Geological Survey Professional Paper 1134-A 

S599.A1S48 631.4'l'0978 79-22136

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

Washington, D. C. 20402 

Stock Number 024-001-03230-9
CONTENTS

Page

Abstract —————————————————————————————————— A1 

Introduction———————————————————————————————— 1 

Study area ———————————————————————————————— 1 

Sample collection, preparation, and analysis———————————— 3 

Sampling design and statistical methods———————————-——— 3 

Sampled population——————————————————————————— 5

Page

.................... _________...... A 5

........_........—......--—.... 7

................................... 8

Differences between soil horizons —————————————————— 15

Conclusions——————————————————————————————— 16

References cited ———————————————————————————— 17

Variance components

Variance mean ratio

Element distribution summaries

ILLUSTRATIONS

Page

FIGURE 1. Map showing location of the Northern Great Plains and coal region—————-———————————————————————————— A2

2. Diagram of the unbalanced, nested, analysis-of-variance sampling design—————————————————————————————— 3

3. Map showing soil-sample localities in the glaciated terrain of the Northern Great Plains coal region —————————————— 4

4. Map showing soil-sample localities in the unglaciated terrain of the Northern Great Plains coal region ————————————• 4

5. Diagram showing frequency distribution of soil parent materials sampled in glaciated and unglaciated terrains

of the Northern Great Plains coal region ———————————————————————————————————————————————— 5

6. Maps showing regional distribution of elements in A and C horizons of soils of the Northern Great Plains coal region:

6A. Arsenic, C horizon———————————————————————————————————————————————————————————— 10

6B. Calcium, C horizon————————————————————————————————-——————————————————————————— 10

6C. Carbon, A horizon ———————————————————————————————————————————————————————————— 10

6D. Carbon, C horizon--------------------------------------------------------------- 10

6E. Germanium, C horizon————————————————————————————————————————————————————————— 11

6F. Potassium, A horizon —————————————————————————————————————————————————————————— 11

6G. Potassium, C horizon —————————————————————————————————————————————————————————— 11

6H. Magnesium, C horizon ————————————————————————————————————————————————————————— 11

61. Sodium, A horizon———————————————————————————————————————————————————————————— 12

6J. Rubidium, A horizon——————————————————————————————————————————————————————————— 12

6K. Rubidium, Chorizon————————————————————————————————————„——..„———...— 12

6L. Silicon, A horizon————————————————————————————————————————————————————————————— 12

6M. Thorium, A horizon——————————————————————————————————————————————————————————— 13

6N. Uranium, A horizon ——————————————————————————————————————————————————————————— 13

6O. Zinc, A horizon —————————————————————————————————————————————————————————————— 13

6P. Calcium, A horizon—————————————————————————————————————————-———————-—————————— 13

6Q. Iron, A horizon-—————————————————————————————————————————————————————————————— 14

6R. Germanium, A horizon———————————-————————————————————————————————————————————— 14

6S. Molybdenum, A horizon————————————————————————————————————————————————————————— 14

6T. Nickel, A horizon -----------------------------------------------------------------------————————...—....„„...—....... 14

7. Diagram showing discriminate function analysis between A- and C-horizon samples from the Northern Great

Plains coal region————————————————————————————————————————————————————————————— 17

TABLES

Page

TABLE 1. Variance components and variance mean ratio for two soil horizons from the Northern Great plains coal region ————— A6

2. Unbalanced, nested, analysis-of-variance design used in the Northern Great Plains coal region ——————————————— 7

3. Grouping of elements based on significant variance components, variance mean ratios, and analytical error variance—— 9

4. Chemical summaries for elements in soil that exhibit a significant variance component between terrains of the

Northern Great Plains coal region —————————————————————————————————————————————————— 15

5. Chemical summaries for elements in soil that exhibit a non-significant variance component between terrains of the

Northern Great Plains coal region —————————————————————————————————————————————————— 16

III

GEOCHEMICAL SURVEY OF THE WESTERN ENERGY REGIONS

SPATIAL VARIATION IN TOTAL ELEMENT CONCENTRATION IN SOIL 

WITHIN THE NORTHERN GREAT PLAINS COAL REGION

By R. C. SEVERSON and R. R. TIDBALL

ABSTRACT

To objectively determine the changes in chemical character of an 

area subjected to mining and reclamation, prior information is 

needed. This study represents a broadscale inventory of total chemical 

composition of the surficial materials of the Northern Great Plains 

coal region (western North and South Dakota, eastern Montana, and 

northeastern Wyoming); data are given for 41 elements in A and C soil 

horizons.

An unbalanced, nested, analysis-of-variance design was used to 

quantify variation in total content of elements between glaciated and 

unglaciated terrains, for four increasingly smaller geographic scales, 

and to quantify variation due to sample preparation and analysis. 

From this statistical study, reliable maps on a regional basis O100 

km) were prepared for C, K, and Rb in A and C soil horizons; for Na, Si, 

Th, U, and Zn in A-horizon soil; and for As, Ca, Ge, and Mg in 

C-horizon soil. The distribution of variance components for the remaining 29 elements did not permit the construction of reliable maps. 

Therefore, a baseline value for each of these elements is given as a 

measure of the total element concentration in the soils of the Northern 

Great Plains coal region. The baseline is expressed as the 95-percent 

range in concentration to be expected in samples of natural soils.

INTRODUCTION

The present and future role of the Northern Great 

Plains in supplying coal and other minerals to meet 

energy requirements dictates the need for timely information on the chemical character of the soils that will be 

disturbed by mining and reclamation. In order to evaluate the chemical character of soil, or any other natural 

material, its variability needs to be quantified so that 

inferences having known degree of certainty can be 

made from the data that are collected.

Most previous studies to determine variability in soil 

constituents have been related to agronomic or 

taxonomic problems (Beckett, 1967; Beckett and Webster, 1971; Crosson and Protz, 1974; Drees and Wilding, 

1973; Jansen and Arnold, 1976; McCormack and Wilding, 1969; McKenzie, 1955; Oertel, 1959; Protz, Presant, 

and Arnold, 1968; Reynolds, 1975; Walker, Hall, and 

Protz, 1968; Webster and Butler, 1976; and Wilding, 

Jones, and Schafer, 1965). These studies considered different soil properties at different geographic scales from 

those considered in this study. Therefore, their conclusions could not be applied directly at the planning 

stages of, or to the results of, the present investigation. 

However, their results indicate, in general, that soil 

properties tend to exhibit a large local variability 

within the context of the many different sampling designs.

Studies by Connor, Keith, and Anderson (1976); 

Erdman, Shacklette, and Keith (1976); Tidball (1976); 

Tidball and Ebens (1976); and Tourtelot and Miesch 

(1975) addressed variability of total element concentration in soil on the basis of large mapping-units. Information from these studies was used in planning the present 

study. In general, these studies also indicated that variability at local scales is large.

The objectives of the present study were three-fold: (1) 

To provide background information on element concentrations in soil of the Northern Great Plains coal region 

before mining and reclamation. (2) To evaluate the magnitude of the variability in element concentration 

in soil at different geographic scales. Knowing the variability, inferences can be made about the soils with a 

known degree of confidence, and the sample load that 

would be needed to make inferences at a specified level 

of certainty can be determined. (3) Either to prepare 

reliable maps of element concentrations in soil on a 

regional basis, or to determine the number of samples 

that would be required to prepare reliable maps for 

those elements for which adequate data are not available.

STUDY AREA

The study area consists of the part of the Northern 

Great Plains (fig. 1) whose surface is underlain by 

geologic formations that contain large resources of

Ai
A2 GEOCHEMICAL SURVEY OF THE WESTERN ENERGY REGIONS

strippable coal. This area is underlain mainly by finegrained, nonmarine sediments in the Wasatch and Fort 

Union Formations of early Tertiary age (Keefer, 1974). 

The boundaries of this area are modified from a U.S. 

Geological Survey map (1974) for the part within the 

United States, and from Whitaker and Pearson (1972) 

for the part in Canada (fig. 1).

Within this area, the greatest contrast in surface features and soil-parent materials is between glaciated 

and unglaciated areas. Glacial drift generally occupies 

the area to the north and east of the Missouri River (fig. 

1). The glaciated area is an undulating plain having 

local relief of less than 10 m; closed depressions are 

common and a well-developed stream drainage is lacking. Nearly level areas of glacial outwash and locallyoccurring glacial lake deposits are widespread throughout the glaciated areas. Compared to the drift plain, 

areas of moraines have steeper slopes, deeper depressions, and a veneer of gravel and boulders; glacial 

moraines rise above the subdued topography of the drift 

plain, with local relief of 15 to 30 m. Eolian sediments 

that are generally found east of and adjacent to major 

drainages blanket the glacial drift and tend to smooth 

the undulating surface. Some small areas that were not

51 102° 100°

Pierre

Northern Great Plains 

coal region

0 100 200 300 KILOMETERS 

I i I_____I______I

FIGURE 1.—Location of the Northern Great Plains coal region; area 

containing coal deposits of Tertiary age indicated by stipple pattern.

covered by glacial drift or from which the glacial drift 

has been removed by erosion are interspersed throughout the drift plain.

The transitional area between the glaciated and unglaciated landscapes is generally delineated by the Missouri River Valley This area has erosion extending as 

much as 180 m into the soft sediments of the adjacent 

uplands. The valley is generally less than 3 km wide, 

and severely dissected canyons impinge upon the surrounding uplands. The valley contains thick deposits of 

recent alluvium flanked by older terrace deposits.

On the unglaciated plain to the south and west of the 

Missouri River a parallel drainage pattern has formed, 

and some stream valleys are as much as 60 m deep. The 

upland is a gently rolling plain with isolated to closely 

spaced buttes as much as 200 m higher than the adjacent surface. In some localities, mountain outliers are 

flanked with pediments and merge with alluvial fans 

and terraces in the adjacent upland. Between the mountain outliers broad anticlines and synclines control the 

topographic character of the unglaciated plain. Where 

thick units of shale are near the surface, they are highly 

dissected to form "badlands." Spontaneous combustion 

of some lignite beds in the Tertiary formations has 

baked the overlying sediments to form reddish colored 

clinker beds, which are a distinctive feature of the unglaciated area.

The paleogeography of the sediments of Late Cretaceous age in the Northern Great Plains is outlined by Gill 

and Cobban (1973). Paleogeography of deposits of Tertiary and Pleistocene ages for northeastern Montana 

and northwestern North Dakota is detailed by Howard 

(1960). Mineralogy of the major stratigraphic units of 

Tertiary age in the Northern Great Plains is presented 

by Denson and Chisholm (1971).

A general description of soil-development gradients 

by Hunt (1967, p.85-93) indicated that temperature and 

moisture interactions, as they influence the depth of 

water penetration in soil, are the major factors that 

determine the degree of soil development in the Northern Great Plains. Soil moisture and soil temperature 

were also the major criteria used by Aandahl (1972) to 

map major taxonomic soil classes in the Great Plains 

region. The climate of the Northern Great Plains is 

cool-temperate-subhumid to semiarid, and is not conducive to intense soil development. Depth of solum, 

horizonation, and accumulation of salts are properties 

that indicate the intensity of soil development in the 

Northern Great Plains. Soil development and soil pedons are described by Dunnewald (1957) for Wyoming, 

by Omodt and others (1968) for North Dakota, by Southard (1969) for Montana, and by Westin, Puhr, and 

Buntley (1967) for South Dakota.
VARIATION IN ELEMENT CONCENTRATION, NORTHERN GREAT PLAINS COAL REGION A3

SAMPLE COLLECTION, PREPARATION, 

AND ANALYSIS

Samples of A- and C-horizons of soils were collected in 

the Northern Great Plains coal region (fig. 1) in the fall 

of 1974. An A-horizon sample consisted of a channel 

composite of the top 10 cm. A C-horizon sample consisted 

of a channel composite at a depth of from 100 to 120 

cm; if consolidated rock was encountered before this 

depth was reached, the sample consisted of the 10 cm of 

material immediately above the rock zone. All samples 

were collected using a barrel auger that was 10 cm in 

diameter.

The samples were dried at ambient temperature 

under forced air and then were disaggregated in a 

motor-driven ceramic mortar-and-pestle to pass a 2-mm 

stainless steel sieve. These samples were further 

ground to minus-100 mesh (minus 149 /am) in a ceramic 

mill, and splits of this material were used for all chemical determinations.

All analyses were done in the laboratories of the U.S. 

Geological Survey at Denver, Colorado. Analyses were 

performed by James W. Baker, Leon A. Bradley, Isabelle 

Davidson, Andrew Drenick, Jefferey England, Johnnie 

M. Gardner, Patrica Gayle Guest, Raymond G. Havens, 

Claude Huffman, Jr., J. O. Johnson, Lorraine Lee, R. M. 

Lemert, R. E. McGregor, H. T Millard, Jr., Wayne 

Mountjoy Farris D. Perez, Van E. Shaw, George D. Shipley Arthur L. Sutton, Jr., James A. Thomas, Michele L. 

Tuttle, Richard E. Van Loenen, James S. Wahlberg, and 

Thomas L. Yager. The analytical methods employed are 

described in U.S. Geological Survey (1975) by James S.

Wahlberg (p. 69), Claude Huffman, Jr. (p. 71), H. T. 

Millard, Jr. (p. 79), and in U.S. Geological Survey (1976) 

by Arthur L. Sutton, Jr. (p. 131).

SAMPLING DESIGN AND STATISTICAL METHODS

The pattern adopted for collecting soil samples for 

this study (fig. 2) is a six-level, unbalanced, nested, 

analysis-of-variance design (Leone and others, 1968). 

The highest level compares variation in element composition of soil from glaciated terrain with soil from unglaciated terrain. Within the irregular boundaries of 

each terrain, cells 100 km on a side were arranged to 

include as much of each terrain as possible (figs. 3 and 

4). This arrangement resulted in 12 100-km cells 

within the glaciated terrain and 22 100-km cells within 

the unglaciated terrain.

Each of the 100-km cells was partitioned into areas of 

decreasing size, as follows: four 50-km cells, each of 

which was divided into 25 10-km cells, which were then 

divided into 100 1-km cells. Cells to be sampled were 

randomly selected, as follows: two 50-km cells, two 

10-km cells in one 50-km cell and one 10-km cell in the 

other 50-km cell, two 1-km cells in one 10-km cell and one 

1-km cell in each of the two other 10-km cells. This 

resulted in samples of A and C horizons from each of 136 

locations—48 in the glaciated terrain and 88 in the 

unglaciated terrain.

An estimate of variance due to all laboratory procedures (analytical error) was made from data on 28 randomly selected samples (out of a total of 272)—12 

A-horizon samples and 16 C-horizon samples—that were

Terrain 

100-km cell 

50-km cell

10-km cell 

1-km cell [" 

Individual! 

analyses

1

1 ri r

1

i l k \ \ n

Number of units sampled at each level

Cell size, on a side

Terrain

Glaciated 

Unglaciated

100 km

12 

22

50 km

24 

44

10 km

36 

66

1 km

48 

88

Analytical units

A-horizon

12

C-horizon

16

Total 34 68 102 136 148

FIGURE 2.—Diagram of the unbalanced, nested, analysis-of-variance sampling design.

152
A4 GEOCHEMICAL SURVEY OF THE WESTERN ENERGY REGIONS

^ 

MONTANA of glaciationX

NC5RTH 

| SOUTH DAKOTA

LJ____I

100I

200 300 KILOMETERS

FIGURE 3.—Soil-sample localities in the glaciated terrain of the 

Northern Great Plains coal region. Large squares (solid lines) are 

100 km on a side; smaller squares (dashed lines) are 50 km on a 

side. Dots are sampling sites. The limit of glaciation is modified 

from Colton, Lemke, and Lindvall (1963) for North Dakota and 

from Colton, Lemke, and Lindvall (1961) for Montana.

108° 106 10 2° 100°

FIGURE 4.—Soil-sample localities in the unglaciated terrain of the 

Northern Great Plains coal region. Large squares (solid lines) are 

100 km on a side; smaller squares (dashed lines) are 50 km on a 

side. Dots are sampling sites. Modified from U.S. Geological Survey (1974). The limit of glaciation is modified from Colton and 

others (1963) for North Dakota and from Colton and others (1961) 

for Montana.

split and analyzed twice. These duplicate samples were 

randomly interspersed among the original samples, and 

the entire suite of 300 samples was analyzed in a randomized sequence; thus, any systematic analytical error 

would be transformed into a random error.

The components of variance estimated by the sampling design are as follows: the level 1 (terrains) component 

iss«2 ; the level 2 (100-km cells) component isa/s2 ; the level 

3 (50-km cells) component is sy2 ; the level 4 (10-km cells) 

component iss«2 ; the level 5 ( 1-km cells) component issr,2 ; 

and the level 6 (analytical error) component is s*2 .

The statistical model is represented by the following 

equation:

yuk (1)

where JCyWmn is a measure of element concentration in a single sample (the nth analysis, of the mth sample, of the Zth 

1-km cell, and so forth): /t is the mean for the population 

sampled; and a, ft, i//, 8, 17, and e are deviations from the 

mean associated, respectively, with terrains, distances 

of 100, 50, 10, and 1 km, and random errors related to 

sample preparation and analysis. The variance components, as estimated by the analysis-of-variance computation methods following Anderson and Bancroft (1952), 

are expressed as follows:

S,. 2 = Sa2 S/3 S6 (2)

wh ere s* 2 is an estimate of the total observed variation for 

an element in soil, and the remaining terms are the 

variance components described above. All computations 

were done on a computer using statistical programs in 

the U.S. Geological Survey's STATPAC Library (Van 

Trump and Miesch, 1977).

The unbalanced design was chosen in preference to 

a balanced design, because it has the advantage of 

spreading the degrees of freedom almost equally over 

levels 2—6. Also, the number of degrees of freedom 

achieved in the higher levels of the unbalanced design 

is comparable to that achieved in the balanced design, 

but with only one-half the number of samples. Therefore, the power of the F-test at the higher levels of the 

unbalanced design is equivalent to that for a balanced 

design, and yet the cost for sample collection and 

analyses is only about one-half as much.

Concentrations of some elements are below the limit of 

determination by a given analytical method, so they are 

omitted, or "censored." When more than 20 percent of the 

determinations for an element are below the limit of 

detection, the element is omitted from further consideration. Elements omitted include Ag, Au, Bi, Br, Cd, Ce, Cl, 

Cs, Dy, Er, Gd, Hf, Ho, I, In, Ir, La, Nd, Os, Pd, Pr, Pt, Re, 

Rh, Ru, S, Sm, Ta, Tb, Te, Tl, Tm, and W. For elements 

with less than 20 percent censored values, the censored
VARIATION IN ELEMENT CONCENTRATION, NORTHERN GREAT PLAINS COAL REGION A5

values were replaced by small, arbitrary values. These 

replacement values can be justified because their small 

number neither alters the statistical tests nor affects the 

final interpretation of the data.

The data for all elements except Na, Si, Th, and Zn 

were transformed by taking the common logarithm, 

because frequency distributions of the data were more 

nearly log-normal than normal. All data are reported in 

terms of either logarithmic (transformed data) or arithmetic variance, means, and deviations. Unless a statistical term is prefixed by "arithmetic," the term refers to 

logarithmically transformed data.

SAMPLED POPULATION

The population sampled in this study is in the Northern Great Plains coal region and consists of all soils 

developed either from glaciated materials or from rocks 

in the Fort Union and Wasatch Formations of early 

Tertiary age. The 136 sample localities that represent 

the population were randomly selected within the several nested cells. The diversity of sedimentary parent 

materials for the soils sampled is shown in figure 5. If 

indeed the random sampling procedure was unbiased 

and if the number of samples was sufficiently large, 

then figure 5 would also show the proportional distribution of parent materials for soils in the Northern Great 

Plains coal region.

00

D

40

30

20

10

n

GLACIATED

_ TERRAIN

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x |>: ::

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C 

0

...

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c — ;

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UNGLACIATED

TERRAIN

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•X-X;X-: X-X-Xv O 3 01 C —

•:•:•:•:•:•:•: x*:-x* ^ = ^ o n 

Wx$x :::::x:::x :•:•:•:¥:¥ «" o c •£; rJ «:>::::::: W.W.-A <-> ~ -S

::x:::x':;: :x$x$i SSiW: x^?x3 u S S

Sx*3 :Wx':S x?x'::i ^x'WS S^iw .:.:-:.:-:-:.a -2

;iv'x|:|S iiSv'xl? ;:v':x'xv' SxS? ?x5:?: x¥:?:$ oxWx'

SOIL PARENT MATERIALS

FIGURE 5.—Frequency distribution, in percent, of soil parent materials sampled in glaciated and unglaciated terrains of the Northern 

Great Plains coal region.

As suggested by figure 5, a natural division exists 

between glaciated and unglaciated terrains in terms of 

the character of the parent materials. The division is 

significant for two reasons: (1) The total chemical 

character of the soils of the different terrains should be 

distinct because of the different amounts of time over 

which pedologic processes have been acting. (2) The 

mineralogy, source areas, and mode of deposition of parent materials of glacial origin are distinctly different 

from those of the Tertiary sediments. These differences 

should be reflected in the chemical variation between 

the soils of the two terrains. The highest level of the 

sampling design is, therefore, intended to estimate differences in chemical variation between the two terrains. Before discussing terrain differences, however, it 

will be helpful to discuss variance components.

VARIANCE COMPONENTS

Within each terrain, sampling was designed to measure variation over increments of distance expressed in 

terms of cell size. Thus, the total variance was subdivided into components, each associated with a given 

cell size. The distribution of variance components for 41 

elements in both A and C horizons (82 combinations), 

each expressed as a percentage of the total variance, is 

shown in table 1.

Of the 82 entries in table 1, 21 exhibit an analyticalerror-variance component that is greater than 50 percent of the total observed variance. This amount is excessive and these elements are excluded from further 

interpretation. Reduction of the analytical-errorvariance component to an acceptable level requires a 

more precise analytical method or repeated analyses of 

the sample. Generally, as analytical precision or 

number of analyses is increased, the cost rises. It is 

necessary, therefore, to balance the value of the results 

against the increased cost of more precise or repeated 

analyses for each element.

The variance distribution indicates that, for most 

elements, the largest variance occurs at a local level; 

that is, within areas 10 km or less on a side. In fact, it is 

not uncommon for most of the variance to occur within 

distances of 1 km. This could logically be expected where 

a variety of different sample materials are found in a 

small area (for example, outwash gravel and lacustrine 

silt and clay in glacial terrain, or sandstone and shale in 

unglaciated terrain). Naturally, the variance in element 

distribution between soils developed from diverse materials would be greater than variances between soils 

from the same type of material. Independent studies by 

Tidball (1975), Tidball and Ebens (1976), and Keith, 

Anderson, and Connor (1974) of soil in the Powder River
A6 GEOCHEMICAL SURVEY OF THE WESTERN ENERGY REGIONS

TABLE I.-Variance components (expressed as percent of total variance) for 41 elements in A 

and C horizons of soils from the Northern Great Plains coal region, and the variance 

mean ratio for 100-km cells. An asterisk indicates significance at the 0.05 probability 

level

hori

Al — ——

As — ——

B —— ——

Ba —— --

Be ———

Ca — ——

Co — ——

Cr -----

Cu -----

F —— ——

Fe —— —

Ga — ——

Ge — ——

Hg — ——

K ______

La -----

Li ———

Mg —— ~

Mn -----

Mo —— —

Na —— -

Nb —— —

Ni ————

p ______

Pb —— —

Rb —— —

Sb — ——

Sc -----

Se ———

Si2 ———

Sn -----

Sr —— ~

Th ————

Ti 2 -——

u — —

V ______

Y —————

Yb ————

Zn —— -

Zr ———

zon variance

0 . 0069

.0106 

1338

.1290 

.0446

.0466

.0175

.0629

.0340

.0477

.0444 

.1293

.1586

.1166

.0400

.0411

.0434

.0679

.0470

.0877

.0827 

.0693

.0329

.0291

.0287

.0565

.1546

.0746

.0672

.0736

.0038

.0083

.0353

.0508

.0209

.0440

.0477

.0620

.1851

.2361

.1068

.1860

.0774

.1249

.0510

.0600

.0275

.0519

.0319

.0281

.0396

.0826

.0093

.0186

.4064

.4376

.0622

.0772

.3418

.2549

9.531

12.61

.1690

.1662

0295

.0372

.0094

2 .0208

0023

.0041

.0131

0288

.0171

.0449

.0369

.0361

.0296

0347

540.2

413.5

.0594

0406

terrains

11.7*

11.0*

0 

0

0 

.7

0

0

6.4*

1.3

25.6* 

21.2*

0

26.4*

0

.6

0

.7

.7

0

2 .4* 

.1

0

0

3.0

2.0*

0

0

6.4*

3.8

43.7*

39 .6*

2.7

.4

3.0

0

0

10.7*

22.6*

10.6*

0.5

0

7.7

1.6

.7

0

0

3.8*

0

0

1.9

.1

25.0*

31.2*

0

.8

0

2.2

3.2*

2.1

0

6.9*

.9

5.1

8.8*

9.3*

17.7*

13.3*

0

1.3

31.7*

17.7*

7.3*

10.7*

2.2

0

6.4*

1.2

3.3

0

4.6*

0

Between

100-km cells

0

0

11.9 

31.8* 

8.8

10.2

6.3

9.0*

.03

0

20.7* 

12.5*

18.8*

4.0

0

0

17.2*

0

0

0

11.8* 

0

18.1*

0

0

0

14.4*

29 . 2*

4.8

3.7

0

0

0

0

4.1

0

5.2

17.2*

0

0

7.8*

0

19.5*

7.2

0

0

11.0*

0

1.1

0

0

0

11.1*

0

0

0

9.1

0

0

0

27.0*

9.3

2.3

8.3

2.1

6.1

5.5

0

11.2

0

10.2*

0

0

0

7.1

0

0

0

19.0*

0

8 8

5.0

Between

50-tan cells

32.3*

16.2

0 

0 

0

0

0

0

6.4

52.1*

0 

0

0

4.6

49.0*

24.9

0

32.2*

22.7

17.8

5.4 

0

0

20.2*

10.4

29.2*

0

0

0

6.3

13.3

21.6*

0

15.9

11.1

25.4

40.3

0

0

34.1*

11.1

32.5*

10.1

0

19.1*

21.3

0

20.8

5.7

17.9

9.9

39.6*

0

3.3

0

3.1

0

22.9

1.9

6.6

0

0

0

0

0

0

0

2.2

0

6.4

0

10.6

3.1

17.5*

0

0

9.0

0

0

10.7

0

4.2

Between

10-kn cells

3.3

0 

0

7.4 

48.9*

12.1

3.1

21.9*

0

0 

4.7

13.6

21.3

7.2

3.5

0

0

0

2.8

0 

0

26.2*

62.9*

0

0

0

29.4

0

55.0*

0

4.4

2.4

9.4

0

.1

0

18.8

27.6*

33.0*

4.2

0

0

0

29.2

0

18.8

12.3

0

0

0

0

0

29.2*

9.4

14.8

0

6.9

0

0

0

7.6

7.3

43.4*

0

37.5*

0

29.2*

16.5

39.9*

0

18.0

11.5

12.6

0

0

30.9*

0

26.7*

13.4

0

10.0

0

Between

1-kra cells

31.7*

66.9* 

83.7*

56.8* 

18.4

69.7*

3.2

0

55.7*

28.9* 

48.5*

52.1*

59.5*

57.4*

25.0

58.5*

15.3

42.0*

44.5*

48.2* 

0

0

18.6*

79.5*

42.5

41.3*

54.5*

65.5*

2.9

82.9

36.6*

35.9*

30.3

45.3*

79.1

68.2*

35.5*

44.4*

8.2

24.3

44.4

25.7

62.2*

61.1*

24.5

0

40.6

58.2*

0

4.9

26.6

35.4*

24.8*

49.3*

0

39.2

21.3

5.8

61.5*

7 6

52.0*

64.7*

34.5*

71.5*

33.4*

75.8*

23.5

17.1

32.2*

87.4*

37.6*

57.9*

22.1

60 6*

47.2

29.1

3.3

24.5

62.4*

74.9*

0

22.9

Analytical

error

21.0

5.9 

4.4

4.0 

23.9

7.3

87.5

69.1

31.4

17.6 

.5

.6

.4

.4

22.5

16.0

67.5

25.1

29.4

34.0 

80.4

73.7

.4

.3

44.0

27.6

1.7

5.3

30.9

3.3

2.0

.5

57.5

38.4

2.6

6.4

.2

.1

36.2

26.8

36.2

41.8

.5

.9

55.7

59.9

36.0

17.2

93.2

77.2

61.6

24.9

9.9

6.8

85.2

56.9

62.2

69.1

33.4

83.7

13.4

11.8

18.8

15.1

18.3

8.8

24.1

50 9

16.7

4.9

2.5

2.3

54.9

11.2

43.5

40.1

81.3

47.6

1.9

14.4

76.6

67.9

!

m

0.34

.39 

.52

1.68 

.30

.46

.26

.35

.25

.03 

3.3

1.8

.82

1.5

0

.02

.83

.02

.02

0 

.60

<0.01

.64

0

.11

.06

.55

1.58

.39

.29

2.2

1.7

.11

.01

.26

0

.13

1.3

.96

.30

.31

0

1.2

.33

.02

0

.46

.12

.04

0

.07

<0.01

1.8

1.6

0

.03

.39

.07

.13

.08

1.4

.74

.10

.60

.40

.73

1.0

.54

.41

.05

2.5

.68

.28

.37

.41

0

.24

.04

1.1

0

.59

2.0

ance mean rati af Miesch (1976a).
VARIATION IN ELEMENT CONCENTRATION, NORTHERN GREAT PLAINS COAL REGION A7

Basin of Wyoming (fig. 1) showed a significant portion of 

the total variation to be at distances of from 0.3 to 1 km for 

many of the elements evaluated in this study.

Each variance component was tested against the null 

hypothesis that the component does not significantly 

differ from zero using the conventional F-test at the 0.05 

probability level (table 2). If a component fails to differ 

from zero, then it is impractical to map the observed 

variation over intervals associated with that component 

because of the high probability that no variation exists. 

On the other hand, a significant variance component at 

the terrain level suggests that the concentrations of 

elements in samples from one terrain differ from those of 

the other terrain.

Our principal interest is in using variance components to calculate the variance mean ratio, to calculate 

the minimum number of samples required to estimate a 

cell mean with a given degree of certainty, and to determine the presence and magnitude of regional variance 

as a basis for making regional maps. (We define "regional variance" as variation that occurs between areas 

of 100-km on a side or greater.) The large local variation

indicates that mapping within smaller areas would require an excessive number of samples and would result 

in more map detail than is necessary.

VARIANCE MEAN RATIO

The variance mean ratio, vm , of Miesch (1976a) provides an index of the relative stability of an estimate of 

the mean for any cell size on the basis of the data already 

collected. In particular, we use vm (table 1) to evaluate the 

feasibility of mapping the regional distribution of 

total concentration of elements in soil. The equation for 

vm has been modified from that of Miesch (1976a) to 

account for the unbalanced, nested design, as follows:

(3)

ny sy ss

se2 )

where the numerator is the variance between 100-km 

cells and the denominator is the variance within 100-km 

cells. The s,'s are the variance components at each level,

TABLE 2. —Unbalanced, nested, analysis-of-variance design used in the Northern Great Plains coal region

Level Source of variation

Degrees of 

freedom Mean square estimates F-ratio2

Variance 

component

1 Between terrains MS. = S 2 +1.2s 2 +1.8s 2 +2.8s 2 +4.5s 2 +68.6s 2 MS./MS.

1 e n S a 1 2

- MS 2

S a 68.6

Between 100-km cells 

within terrains

32

Between 50-km cells 34 

within 100-km cells

22222 MS 0 = s -t-l.ls +1.7st+2.7s +4.3s

2 e n 5 B

2222 MS. = s -t-l.ls +1.3s~+l. 6s

3 e n 6

MS 2 - MS3 

4.3

MS3 - MS4

Between 10-km cells 

within 50-km cells

34 22 2 MS. = s +s +1.4s

4 e n 6

2 s, =

- MS 5

1.4

Between 1-km cells 

within 10-km cells

34 2 2 MS = s£ +l.lsn MS,/MS, j b

2 MS 5 - MS6 _ 2

Between analyses of:

A-horizons within 

1-km cells

12 MS, = sf

o b

C-horizons within 

1-km cells

16 MS, = s. b b

2-2

s = a 

c e

^ean-square estimates are for A horizons; the coefficients for C horizons may vary by 0.1 unit because of the 

different numbers of samples for A and C horizons at the "Between analyses" level.

-Leaders ( ), no F-ratio exists.
A8 GEOCHEMICAL SURVEY OF THE WESTERN ENERGY REGIONS

and the /i,'s are coefficients that represent the average 

number of samples in each level. These coefficients are 

developed from a more general expression of Leone and 

others (1968, p. 725). A value of 1.0, which is taken as a 

threshold value, is approximately equivalent to an 

F-test at the 80 percent probability level. For values of 

vm less than about one, a map of total concentration of an 

element in soil, based on limited sampling, tends not to 

faithfully reproduce the true chemical pattern (Miesch, 

1976b,p.l02). Asi>TO increases beyond 1.0, however, a map 

based on limited sampling reveals more clearly the true 

chemical pattern. The observed values of vm range 

from a low of zero to a high of 3.3 (table 1). Eight elements in the A horizon and eight in the C horizon have a 

vm greater than one and, therefore, these data are presented cartographically

ELEMENT-DISTRIBUTION SUMMARIES

The decision as to which method of reporting the 

distributions of element concentrations is best depends 

on the magnitude of variation present in the data. A 

distribution map based on the means of rather small 

areas is the most ideal display, because the element 

concentrations can be related to geographic locations. 

However, this requires highly reproducible data. Where 

such data are not available, then the means must be 

summarized over larger areas, with the result that local 

differences tend to disappear. The data have been subdivided, therefore, into five groups on the basis of variance components at the terrain, 100-km-cell, and 

analytical-error levels, and on the basis of whether or 

not the variance-mean ratio exceeds the threshold of 1.0.

The five distinct groups of elements are presented in 

table 3. Group-1 elements are those that exhibit a significant variance component at either the terrain or the 

100-km-cell level and that have a uw >1.0. For these 

elements, we can prepare reliable maps of their concentration in soil on the basis of the means of samples 

within each 100-km cell. These maps represent values 

from a minimum of 22 percent of the total observed 

arithmetic variation (Zn in A horizons) to a maximum of 

46 percent of the total observed logarithmic variation (C 

in A horizons). Maps showing regional distribution of 

amounts of 15 elements in soil are presented in figures 

6A through 6Q. The resolution, or the amount of detail, 

is dependent on the sampling interval (cell size) shown 

on the map. Greater resolution and increasing detail of 

element distributions in soil can be obtained if the mapping interval is decreased to 50,10, and 1 km, respectively, and if a significant variance component is associated with each of these smaller geographic scales. However, the reliability of data on maps of smaller areas will

depend on the variance mean ratio (Eq. 3). For example, 

mapping Ge in the C horizon of a 10-km unit would 

result in no increase in either reliability or resolution 

over mapping a 100-km unit, because the components of 

variance at 50 and 10 km are both zero (table 1). However, mapping K in the C horizon at a 50- rather than a 

100-km unit should enhance both the reliability and the 

resolution of the map, because the variance component 

at 50 km is significant and it accounts for an additional 

21.6 percent of the total variation. The value of vm is 

increased from 1.7 (100-km unit) to 5.3 (50-km unit); the 

resulting map of K in the C horizon would be much more 

reliable. The variation explained by the map based on 

100-km units is 39.6 percent of the total variation and 

would be 61.2 percent of the total variation for a map 

based on a 50-km unit. In addition, the map of a 50-km 

unit would show more detail of the element distribution 

than the map of a 100-km unit. However, maps of less 

than 100-km units are not presented because of the 

nature of our unbalanced sampling design and the resulting distribution of data points.

The entries in Groups 2, 3, and 4 (table 3) have a um<1.0 

and, therefore, the lines on a map for any of these 

elements would not be considered reliable when compiled for a 100-km unit using the present data. Group-2 

elements exhibit significant variance components at the 

terrain level but not at the 100-km-cell level (table 3). 

For these elements, the means and expected ranges in 

concentration of the samples within each terrain give the 

best estimate of element distribution in soil for the area. 

This type of estimate has been referred to as a "regional 

geochemical baseline" by Tidball and Ebens (1976). The 

baselines for elements of Group 2 are presented in table 4 

for each of the two terrains, glaciated and unglaciated. 

The expected range is computed after adjusting the gross 

deviation for analytical error, which makes up a portion 

of the gross deviation (Connor, 1976). An estimate was 

also computed for nr, the number of random samples 

needed within each 100-km cell to raise the value ofi>m to 

1.0 and, thereby, provide data that can be expressed by a 

reliable map.

Group-4 elements have no significant variance component at either the terrain or the 100-km-cell levels 

(table 3). A single estimate of the mean and expected 

range for each of these elements over the entire study 

area is the best estimate of a baseline. The estimates are 

presented in table 5. The value of the baseline for each 

element in Groups 2 and 4 represents an expected range 

in concentration that we consider to be of use in making 

extrapolations from one location to another, either over 

the entire study area (Group-4 elements) or within the 

area of each terrain (Group-2 elements). In addition, 

any new data may be compared to the baseline to identify extreme values in element concentration.
VARIATION IN ELEMENT CONCENTRATION, NORTHERN GREAT PLAINS COAL REGION A9

TABLE 3 -Grouping of elements based on significant variance components (sa_ e2), variance mean ratios (v,J, and analytical-error variance (sfz) 

[Asterisk indicates significance at the 0.05 probability level. (—) indicates no element included in that grouping]

100-km Soil 

cell horizon

s2 * A

6 c

4 p A

C

s 2* A p 

3 C

c *- A

PR

c

v >1 . 0

m

Group 1 Group 2

C, Rb, U

C, Mg

K, Th Al, Be, Hg,

Mn , Se , Sr ,

Ca, K, Rb Al, Ga, Mn ,

Ni, Si, Sr,

U, V

Na, Si, Zn ——

As , Ge ——

_ — ——

—— ——

Group-3 elements (table 3) exhibit a significant component of variance between 100-km cells but not between terrains. The regional distribution of these elements, therefore, is best estimated by each 100-km-cell

mean. These means are both given in table 5 and plotted

on maps in figures 6P—6T. The values on the maps are

v <1.0 s2>50 pet. m e

Group 3 Group 4 Group 5

Terrain, s2 *

a

—— —— F

—— —— ——

—— —— Yb, Zr

—— —— Th, V

Terrain, s2

a

Ca, Fe, Ge —— Cr

Mo, Ni —— Ba

—— As, B, Ca, Ba, La, Nb,

Co, Ga, Li, P, Pb, Sb,

Mg, Sn, Ti, Sc

Y

—— B, Be, Co, F, Nb, P,

Cr, Cu, Fe, Sb , Sc , Se ,

Hg , La , Li , Zr

Mo, Na, Pb,

Sn, Ti, Y,

Yb, Zn

not contoured because the data are judged to be unreliable (um <1.0).

Group-5 elements (table 3) exhibit excessive analytical error. Therefore, no interpretation is presented

for these elements.

FIGURE 6 (following pages}—Regional distribution of elements in A and C horizons of soils of the Northern Great Plains coal region. Values are 

means of cells 100-km on a side. Contour lines for figures A through O are the geometric mean (GM) or the arithmetic mean (AM) and the upper 

or lower expected 95-percent values. No contours are given for figures/* through T because the analysis of variance indicates that such contour 

lines would tend not to be reproducible.
A10

50'

108°

GEOCHEMICAL SURVEY OF THE WESTERN ENERGY REGIONS

106° 104° 102° 100 i——i——i——i——n—i——f

SASKATCHEWAN I MANITOBA

CANADA

UNITED 

STATES

48°l

Bismarc

46°

'Billings 

_MONTANA

WYOMING"

44°

GM 6.5 -5 

Range 2.5-17

KOTA

108°

I-As in C horizon

106° 104° 102° 100°

50°

1——i——i——i——n—i——r

SASKATCHEWAN I MANITOBA 

o i 

Regina \ 

\

48

44

46°

Pier

42'

GM 1.9 

Range 1.0-3.7

0.8 1.1

'•.~:~.:1

\ \ NEBRASKA

C--C(pct.) in A horizon

50°

I——i——r~i

SASKATCHEWAN | MANITOBA 

Regina

8--Ca(pct.) in C horizon

108° 106° 104° 102°

50°

D-C(pct-) in C horizon

0 100 200 300 400 KILOMETERS

EXPLANATION

Frequency distribution, in percent

<5 5-50 50-95 >95

FIGURE 6.—Continued
VARIATION IN ELEMENT CONCENTRATION, NORTHERN GREAT PLAINS COAL REGION

108° i —— i —— r- 106°

I

104° 102

1 ——— I" 1 1 

SASKATCHEWAN

0 100°

T 'I I , 

I MANITOBA

50°

42°L___i

E--Ge in C horizon

108° 106° 104° 102° 100°

50

SASKATCHEWAN I MANITOBA) 

o Regina

I

48°

Pierre I

GM 1.7 

Range 1.3-2.2 

42°l———LI |

1.9 1.9

\ I NEBRASKA

G--K(pct.) in C horizon

108°

All

100°

106° 104° 102°

SASKATCHEWAN | MANITOBA

F--K(pct.) in A horizon

108° 106° 104° 102°

50

i———i———r——i———I—«

SASKATCHEWAN MANITOBA

H--Mg(pct.) in C horizon

0 100 200 300 400 KILOMETERS

I.I I I I

EXPLANATION

Frequency distribution, in percent

<5 5-50 50-95 >95

FIGURE 6.—Continued
A12 GEOCHEMICAL SURVEY OF THE WESTERN ENERGY REGIONS

108

50

SASKATCHEWAN | MANITOBA 

O Regina

/--Na(pct.) in A horizon

108° 106" 104" 102" 100°

50°

SASKATCHEWAN I MANITOBA

Ci

Regina

8..4.«ii::::::::::::::::::::::: Bismarck

\ I NEBRASKA

K--Rb in C horizon

50°

_ 108" 106 n———r——|———i- 104 102° 100" i——i——i—~~n—i——r"

SASKATCHEWAN! MANITOBA

^CANADA

UNITED"

STATES

Billings

MONTANA 

WYOMING

440!

GM 72 -74 

Range 58-90

-I———__L I I il

J--Rb in A horizon

106° 104° 102° 100°

50

SASKATCHEWAN I MANITOBA 

o Regina

I

46°

44°

AM 31 

Range 28-34

42" I —— I ——— _] |

L--Si(pct.) in A horizon

0 100 200 300 400 KILOMETERS

EXPLANATION

Frequency distribution, in percent

<5 5-50 50-95 >95

FIGURE 6.—Continued
50 C

VARIATION IN ELEMENT CONCENTRATION, NORTHERN GREAT PLAINS COAL REGION 

J08" 106° 104° 102° 100

A13

i —— i —— i —— n i

SASKATCHEWAN I MANITOBA 

Regina

48°

46°

44°

GM 8.4 

Range 6.5-10

—L————L 1

r i———.

NEBRASKA 

9.1

Af--Th in A horizon

108° 106° 104° 102-°

50°

48°

SASKATCHEWAN I MANITOBA

f I NEBRASKA

42°

O--Zn in A horizon

50°

108° ~l———I

106 104" 102" 

——I———I———T~*~ 

SASKATCHEWAN! MANITOBA

100°

—r~

48°

46°

44°

42<

2.3

GM 2.3 2.2 

Range 1.7-3.1

N~\J in A horizon

106° 104° 102°

50°

48°

440

I———i———I———I———I—I

SASKATCHEWAN 1 MANITOBA

Regina

I 

I

1.0 «1.2 .'0.8 1.0.9

x •—r • • • x

1^8 1.3 1.7 .2.1 .0.9 1

2.6 .0.7 .0.7

46°

42°

P--Ca(pct.) in A horizon

100 200 300 400 KILOMETERS

EXPLANATION

Frequency distribution, in percent

<5 5-50 50-95 >95

FIGURE 6.—Continued
A14 GEOCHEMICAL SURVEY OF THE WESTERN ENERGY REGIONS

100 108° 10°°

50

106° 104° 102° __ "i——i——i——i——\——i——n—r

SASKATCHEWAN | MANITOBA

Regina

I

- "?1.5. Jl.7"V-?

CANADA

48°

ANADA

UN7TBD 

STATES

.2.3 .2.4 .2.4 .1-8

.2.3 ^.2.5 .2.4 .2-4 ^

I Bismarck

I ~ '

.1.7 .1-2 .1-6 .1-6

.3.1 .3.5 V2J .2.0 1.8 .0.8

___ N DAKOTA C~S""DAKO TA

2.3

N DAKOTA 

DAKOTA Billings

MONTANA 

WYOMING!

Billing

MONTANA 

WYOMING

GM 1.6 "1.5 

Range 1.1-2.4

Q--Fe{pct.) in A horizon

I___y___i____L

fl--Ge in A horizon

50"

48°

104° 102" 100 i——r~T—i

SASKATCHEWAN I MANITOBA

O

Regina

I

SASKATCHEWAN I MANITOBA 

o 

Regina

I

.2.0 .3.3 .4.4

.17 .18 .24 .16

.15 ^19 .18 .25

I Bismarck 

I

.. .. .. ..

.3.4 5.3 .3.8 .5.5 \

.3-6 2,0 .2.3 .5.0 .22 4 .16 .18

Billings 

MONTANA

WY"OMING

17 .25^.16 .15 .24

^———^ NEBRASKA 

1-9 1.9 S———/. NEBRASKA

11 15

S--Mo in A horizon 7"--Ni in A horizon

0 100 200 300 400 KILOMETERS

I , I_____I_____I_____|

FIGURE 6.—Continued
VARIATION IN ELEMENT CONCENTRATION, NORTHERN GREAT PLAINS COAL REGION A15

TABLE 4. -Chemical summaries for elements in soil that exhibit a significant variance component between terrains of the Northern Great Plains

coal region (Group-2 elements) 

[G. glaciated terrain; U. unglaciated terrain. *. element measured in percent; other elements measured in parts per million except Hg. parts per billion]

Element Soil

Geometric 

mean

horizon 

G

Al* ——— 

Be ————

Ga ————

TJ Hg _ ———— 

Mn ————

Ni ————

C 0 _ ___ _

Si* 4 —

CT- _____ JL

U —————

v ———

A 

C 

A 

C 

A

A 

C 

C 

A 

C

A 

C 

C 

C

5.3 

5.3 

1.5 

10 

26

720 

440 

22 

.5 

27

180 

240 

2.2 

64

U

5.8 

5.9 

1.7 

11 

21

330 

180 

18 

.4 

29

150 

190 

2.8 

50

Geometric 

deviation Geometric

G

1.17 

1.22 

1.46 

1.58 

1.40

1.83 

2.37 

1.44 

2.45 

2.74

1.24 

1.24 

1.42 

1.45

1 

1 

1 

1 

1

2 

4 

1 

2 

3

1 

1 

1 

1

U

.18 

.22 

.38 

.51 

.48

.76 

.20 

.67 

.93 

.59

.54 

.56 

.41 

.43

error

1. 

1. 

1. 

1. 

1.

1. 

1. 

1. 

2. 

1.

1. 

1. 

1. 

1.

09 

06 

27 

33 

05

81 

79 

24 

18 

22

18 

14 

06 

18

4. 

3. 

0. 

5 

13

570 

120 

12 

0. 

22

140 

170 

1. 

33

Baseline value 1

G

1- 6.9 

6- 7.8 

8- 2.6 

- 21

- 51

- 910 

-1600 

- 40 

2- 1.1 

- 32

- 240 

- 380 

1- 1.4 

- 120

4 

4 

1 

6 

9

60 

10 

7 

0 

22

70 

80 

1 

26

U

.4- 7.7 

.0- 8.6 

.1- 2.6 

- 21 

- 44

-1700 

-2500 

- 46

.1- 1.9 

- 36

- 340 

- 450 

.4- 5.5 

- 99

7 

7 

11 

34 

7

5 

8 

16 

n.d. 3 

5

7 

6 

5 

7

Expected 95-percent range.

2 Minimum number of random samples per 100-km cell needed to map regional ... variation.

q

Not determined.

Values computed on arithmetic basis.

DIFFERENCES BETWEEN SOIL HORIZONS

In the unbalanced, nested, analysis-of-variance design, the sixth (or lowest) level consists of samples that 

were analyzed in duplicate to estimate variation associated with sample preparation and analysis (table 2). 

This was done because splits of a single sample, when 

subjected to repeated chemical analysis, do not yield 

identical results. The variance associated with sample 

preparation and analysis should be estimated and included as part of the total variation observed in a sample 

of a population, because, in some cases, it exceeds the 

variation from any other source.

Initially each element was assumed to have a common analytical-error variance that could be estimated 

from sample determinations irrespective of soil horizons. Although the reproducibility of a measured value

is subject to interferences that arise from differing matrix effects, these effects were expected to be common to 

both surface and subsurface horizons. However, the possible analytical errors shown in table 1 suggest that, for 

many elements, the analytical reproducibility differs 

widely in the two soil horizons. For most elements, the 

portion of the total observed variance associated with 

sample preparation and analysis of the A horizon exceeds that of the C horizon (table 1). In fact, logarithmic 

variance estimates of analytical error for B, Ba, C, Hg, 

Li, Na, Th, and Zn differ significantly between horizons 

as indicated by an F-test at the 5 percent probability 

level. (The F-ratio is computed by dividing the variance 

of the A or C horizon, whichever is larger, by the smaller 

variance.)

Because the data for 29 elements do not show significant differences in analytical error between horizons, it
A16 GEOCHEMICAL SURVEY OF THE WESTERN ENERGY REGIONS

TABLE 5.—Chemical summaries for elements in soil that exhibit a 

non-significant variance component between terrains of the Northern Great Plains coal regions (Group-3 and -4 elements)

[*, element measured in percent; all others measured in parts per million except Hg, parts

per billion]

Element Soil 

horizon

Geometric Geometric Geometric 

mean deviation error

Baseline1 

value

As ———

Be ——— 

Ca* ———

Co ———

Cr ——— 

Cu ———

Fe* ———

Ga ———

Ge ———

Hg ———

La ———

Li ———

Mg* ———

Mo ————

Na*" ——

Ni ———

Pb ———

Sn ———

Ti* 1* ——

y —————

Yb ————

Zn ———

A

A

C

£

A

A

C

C

A 

C

A

C

A

A

C

C

A

C

A

A

C

C

A

C

A

C

A

C

A 

C

C

C

7.1 

41

43

1.6 

1.0

6.4

6.6

42

19 

17

2.1

2.2

11

1.6

27

23

19

21

.7

3.8

4.0

.9

18

15

.9

.9

.25

.25

1 ft 10

17

2.1

59

1 AO . 07

1.59

1.61

1.44

2.14

1.48

1.49

1.66 

1.64

1.82

1.41

1.40

1.44

1.27

1.74

1.55

1.40

1.48

1.67

1.68

1.72

.33

1.46

1.71

1.86

1.94

.023

.058

1.46 

1.47

1.49

19

1.19 

1.27

1.14

1.23

1.06

1.24

1.21

1.35 

1.31

1.49

1.02

1.02

1.30

1.13

1.12

1.38

1.06

1.13

1.02

1.57

1.90

.034

1.26

1.39

1.51

1.44

.019

.014

1.34 

1.32

1.34

7.7

2.6 — 19

18 - 96

16 -115

0.6 - 4.0

0.2 - 4.6

2.8 - 14

2.8 - 16

15 -120 

8 - 43

6 - 52

1.1 - 4.2

1.1 - 4.3

6 - 19

1.1 - 2.4

10 - 80

10 - 51

10 - 37

10 - 46

0.2 - 1.8

1.1 - 13

0.9 - 18

0.2 - 1.5

10 - 32

5 - 47

0.3 - 2.2

0.3- 2.8

0.22- 0.28

0.14- 0.36

10 - 36 

9 - 33

1.1 - 3.9

23 - 94

7 

9

7

n.d. 3

5

n.d.

n.d.

n.d.

n.d. 

n.d.

5

n.d.

28

6

10

n.d.

11

n.d.

14

9

n.d.

9

7

n.d.

30

6

7

32

n.d.

n.d.

n.d.

Expected 95-percent range.

2 Minimum number of random samples per 100-km cell needed to map 

regional variation.

3 Not determined. 

Values computed on arithmetic basis.

appears that some properties or factors in addition to 

matrix composition are affecting the reproducibility of 

the analytical determinations. If the analytical technique is at fault, then we would expect that a group of 

elements determined by a single technique should consistently exhibit either significant or nonsignificant 

variation between horizons. However, the elements that 

exhibit significant differences between errors in the two 

horizons were determined by several procedures (see 

U.S. Geological Survey, 1975, fig. 2). Therefore, differences in analytical reproducibility between soil horizons are related to matrix effects, analytical methods, 

and other unknown factors. However, from the data it is 

not clear which effect dominates.

The investigator should be aware of the possibility of 

significant analytical variability between soil materials and should plan to account for it. The cost of reducing the analytical variability, however, must be balanced against the cost of deriving an adequate estimate

of the analytical variation either by repeated analysis of 

a sample or by a more precise analytical technique.

Discriminate-function analysis of data was also performed between A and C horizons. The results, which 

are presented in figure 7, show that an adequate function can be obtained to discriminate between A and C 

horizons using only three variables (Ca, Mg, and C). In 

general, a discriminate-function analysis using only 

trace-element data would be of little value in separating 

A- from C-horizon samples. For future studies that concentrate on describing the geographic distribution of 

elements occurring in trace amounts, a more productive 

use of available resources may be to sample and analyze 

only a single soil horizon or a composite sample of several soil horizons. Just as much, or possibly more, information useful in constructing maps of element concentration in soil may be obtained in this way as is 

obtained by dividing available resources between samples of more than one soil horizon.

CONCLUSIONS

An attempt has been made to determine the spatial 

variability of soil chemistry in the Northern Great 

Plains coal region for 41 elements on the basis of their 

total concentrations in A and C horizons. Using an unbalanced, nested, analysis-of-variance design, maps 

showing dependable data were prepared based on 

100-km cells (100 km on a side) for three elements (C, K, 

and Rb) in both A and C horizons, for an additional five 

elements (Na, Si, Th, U, and Zn) in the A horizon, and 

C horizon. By doubling the number of random samples 

from four to eight per 100-km cell, an additional 20 

elements in either A- or C-horizon soil would be mappable for the 100-km cell. Baseline values can be assigned, however, for elements that were not dependably mappable. The baseline value is a probable range 

in concentration to be expected in natural soils. The 

baseline can be applied to soil materials throughout 

the study area.

Most of the total observed variation in element concentration for most elements is within cells of less than 

10 km on a side. Therefore, while baseline values can be 

used as an overview, additional sampling is necessary to 

evaluate local variability.

Repeated analytical determinations on samples of A 

and C horizons of soils vary significantly for several 

elements. It is not clear from the data whether the 

varying matrix compositions of the samples or the analytical techniques, or both, are responsible for these 

variations.

Discriminate-function analysis shows that analyses 

for only three elements (Ca, Mg, and C) are needed to 

adequately distinguish between A- and C-horizon soil 

samples in the Northern Great Plains coal region.
VARIATION IN ELEMENT CONCENTRATION, NORTHERN GREAT PLAINS COAL REGION A17

VARIABLES DELETED

<———————————————

Ca Mg C Hg Sr K U Y Ti Ni Si Li Sn Co Al Ge Na Ba As Cu Mo Fe Zn Ga B Mn Rb 160

10 12 14 16 18

NUMBER OF VARIABLES

20 22 24 26 28

FIGURE 7.—Discriminate function analysis, for elements with analytical error less than 50 percent, between A- and C-horizon samples from

the Northern Great Plains coal region.

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172-179.

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scale 1:500,000.

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Geochemical survey of the western energy regions, 3rd annual 

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variation in soils and sagebrush in the Powder River Basin, 

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Crosson, L. S., and Protz, R., 1974, Quantitative comparison, of two 

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and lithologic characteristics of Tertiary sedimentary rocks in 

the middle Rocky Mountains and the northern Great Plains, in 

Geological Survey Research 1971: U.S. Geological Survey Professional Paper 750-C, p. 117-126.

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sampling unit: Soil Science Society of America Proceedings, v. 37, 

p. 82-87.

Dunnewald, J. J., 1957, Wyoming soils and soils materials, Wyoming 

University Agricultural Experiment Station Bulletin 349,24 p.

Erdman, J. A., Shacklette, H. T., and Keith, J. R., 1976, Elemental 

composition of selected native plants and associated soils from 

major vegetation-type areas in Missouri: U.S. Geological Survey 

Professional Paper 954-C, 87 p.

Gill, J. R., and Cobban, W. A., 1973, Stratigraphy and geologic history 

of the Montana group and equivalent rocks, Montana, Wyoming, 

and North and South Dakota: U.S. Geological Survey Professional Paper 776,37 p.

Howard, A. D., 1960 [1961], Cenozoic history of northeastern Montana and northwestern North Dakota with emphasis on the Pleistocene: U.S. Geological Survey Professional Paper 326,108 p.

Hunt, C. B., 1967, Physiography of the United States: San Francisco 

and London, W. H. Freeman and Co., 480 p.
A18 GEOCHEMICAL SURVEY OF THE WESTERN ENERGY REGIONS

Jansen, I. J., and Arnold, R. W., 1976, Defining ranges of soil characteristics: Soil Science Society of America Journal, v. 40, no. 1, p. 

89-92.

Keefer, W. R., 1974, Geologic map of the Northern Great Plains, in 

Regional topography, physiography, and geology of the Northern 

Great Plains: U.S. Geological Survey Open-file Report 74-50, 

Plate A-3, scale 1:1,000,000.

Keith, J. R., Anderson, B. M., and Connor, J. J., 1974, Trace metal 

variation in the Powder River Basin, in Geochemical survey of 

the western coal regions, 1st annual progress report, July 1974: 

U.S. Geological Survey Open-file Report 74-250, p. 14-29.

Leone, F. C., Nelson, L. S., Johnson, N. L., and Eisenstat, S., 1968, 

Empirical studies of unbalanced nested designs, pt. 2 of Sampling 

distributions of variance components: Technometrics v. 10, no. 4, 

p. 719-737.

McCormack, D. E., and Wilding, L. P., 1969, Variation of soil properties within mapping units of soils with contrasting substrata in 

northwestern Ohio: Soil Science Society of America Proceedings, 

v. 33, p. 587-593.

McKenzie, R. M., 1955, Sampling variations in the concentrations of 

elements in soils: Australian Journal of Agricultural Research, v. 

6, p. 699-706.

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sampling, laboratory analysis, and statistical reduction of data 

with sections on laboratory methods by 11 others: U.S. Geological 

Survey Professional Paper 954-A, 39 p.

____, 1976b, Sampling designs for geochemical surveys—syllabus 

for a short course: U.S. Geological Survey Open-file Report 

76-772,138 p.

Oertel, A. C., 1959, Estimation of the trace element status of large 

areas of soil: Australian Journal of Agricultural Research, v. 10, 

p. 58-70.

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1968, The major soils of North Dakota: North Dakota State University Agricultural Experiment Station Bulletin 472,60 p.

Protz, R., Presant, E. W., and Arnold, R. W., 1968, Establishment of 

the modal profile and measurement of variability within a soil 

landform unit: Canadian Journal of Soil Science, v. 48, p. 7—19.

Reynolds, S. G., 1975, Soil Property variability in slope studies — 

suggested sampling schemes and typical required samples sizes: 

Zeitschrift fur Geomorphologie, v. 19, no. 2, p. 191-208.

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Agriculture Experiment Station Bulletin 621,42 p.

Tidball, R. R., 1975, Sampling requirements for mapping soil 

geochemistry in the Powder River Basin, in U.S. Geological Survey, Geochemical survey of the western coal regions, 2nd annual 

progress report, July 1975: U.S. Geological Survey Open-file Report 75-436, p. 20-28. 

_, 1976, Chemical variation of soils in Missouri associated with

selected levels of the soil classification system: U.S. Geological 

Survey Professional Paper 954—B, 16 p.

Tidball, R. R., and Ebens, R. J., 1976, Regional geochemical baselines 

in soils of the Powder River Basin, Montana-Wyoming, in 

Laudon, R. B., ed., Geology and energy resources of the Powder 

River: Wyoming Geological Association Guidebook, 28th annual 

field conference, p. 299-310.

Tourtelot, H. A., and Miesch, A. T., 1975, Sampling designs in environmental geochemistry: Geological Society of America Special 

Paper no. 155, p. 107-118.

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Great Plains, Montana, Wyoming, North Dakota, and South 

Dakota: U.S. Geological Survey Miscellaneous Field Studies Map 

MF-590, scale 1:1,000,000.

___, 1975, Geochemical survey of the western coal regions, 2nd 

annual progress report, July 1975: U.S. Geological Survey Openfile Report 75-436,132 p. 

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reduction of geochemical data: Computers and Geoscience, v. 3, 

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America Proceedings, v. 29, p. 711—717.
Regional Soil Chemistry in 

the Bighorn and 

Wind River Basins, 

Wyoming and Montana

By R. C. SEVERSON

GEOCHEMICAL SURVEY OF THE WESTERN ENERGY REGIONS

GEOLOGICAL SURVEY PROFESSIONAL PAPER 1134-B

Baseline values for 38 elements characterize

the composition of soils

overlying major geologic units in each Basin

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1979
UNITED STATES DEPARTMENT OF THE INTERIOR 

CECIL D. ANDRUS, Secretary

GEOLOGICAL SURVEY 

H. William Menard, Director

Library of Congress Cataloging in Publication Data

Severson, Ronald Charles, 1945-

Regional Soil Chemistry in the Bighorn and Wind River Basins, Wyoming and Montana

(Geochemical Survey of the Western Energy Regions) (Geological Survey Professional Paper 1134-B)

Bibliography : p. B'9

1. Soil chemistry—Bighorn Basin, Mont, and Wyo. 2. Soil chemistry—Wyoming—Wind River Basin.

3. Soils—Bighorn Basin, Mont, and Wyo.—Composition. 4. Soils—Wyoming—Wind River Basin—Composition.

5. Bighorn Basin, Mont, and Wyo. 6. Wind River Basin, Wyo. I. Title. II. Series. III. Series: United States

Geological Survey Professional Paper 1134-B 

S599.W8S48 631.4'l'09787 79-607781

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

Washington, D. C. 20402 

Stock Number 024-001-03230-9
CONTENTS

Page

Abstract——————————————————————————Bl

Introduction———————————————————————————————— 1 

Study area———————————————-———————————————— 1 

Sampling design————————————————————————————— 2 

Samples and analysis --—-————————......——........—...... 2

Page

Analytical error variance ———————————————————————B4 

Baseline values —————————————————————————————— 5 

Mapping requirements—————..—.......——.————————.— 6

Conclusions———————————————————————————————— 8 

References Cited —————-—..—.„.„—.—.———.—————.— 9

ILLUSTRATIONS

Page

FIGURE 1. Geologic and sample locality map of the Bighorn and Wind River basins of Montana and Wyoming —————————B3

2. Diagrammatic representation of a barbell design with sampling localities shown as X's--——-—-———————-——-———— 3

TABLES

Page

TABLE 1. Analysis-of-variance design for the Bighorn and Wind River Basins—————————————————————————B2

2. Variance analysis of total element concentrations in soil in the Bighorn Basin———————————————————— 3

3. Variance analysis of total element concentration in soil in the Wind River Basin—-—————-——-------—————————— 4

4. Statistical summary for elements that lack regional variation in soils of the Bighorn Basin—————————————— 4

5. Statistical summary for elements that lack regional variation in soils of the Wind River Basin———————————— 5

6. Statistical summary for the element having regional variation in soils that overlie the three major geologic units in the 

Bighorn Basin —————————————————————————————————————————————————————————————— 5

7. Statistical summary for elements having regional variation in soils that overlie the three major geologic units in the Wind 

River Basin —————————————————————————-—————————————————————————————————————— 5

8. Average concentrations of elements in soils and surficial materials in the Bighorn, Wind River, and Powder River Basins 

and in the Western United States ———————————————————————————————————————— 7

9. Minimum number of samples needed in a 10-km square to map total element concentrations in soils of the Bighorn and Wind 

River Basins at the 80 percent confidence level ——————-——-————————————-———————————~—————-— 7

in

GEOCHEMICAL SURVEY OF THE WESTERN ENERGY REGIONS

REGIONAL SOIL CHEMISTRY IN THE BIGHORN AND 

WIND RIVER BASINS, WYOMING AND MONTANA

Bv R. C. SEVERSON

ABSTRACT

A reconnaissance study of total concentrations of 38 elements in 

samples of soils (0—40 cm deep, composite) from the Bighorn and Wind 

River Basins of Montana and Wyoming indicates that the geographic 

variation for most elements occurs locally (5 km or less). However, in 

the Bighorn Basin, Zn exhibits significant regional variation (between 

geologic units); and in the Wind River Basin, Al, Cr, K, Mn, Mo, Ni, U, 

and V exhibit similar variation. For the remaining elements, the lack 

of regional variation suggests that a single summary statistic can be 

used to estimate a baseline value that reflects the range in concentration to be expected in samples of soils in each basin. The concentrations 

of most of these elements in both basins are not much different from 

those measured independently in the Powder River Basin of Wyoming 

or in the Western United States. In addition, data from an analysis of 

variance provide an estimate of the number of random samples within 

an area of specified size (10 km square, approximately a township) that 

are needed to prepare a reliable map of total element concentration in 

soils for each of the elements in each of the basins.

INTRODUCTION

This reconnaissance study provides data on spatial 

variation in total element concentrations in soil in the 

Bighorn and Wind River Basins. The data provide 

chemical baseline values for the two areas. The baseline 

values enable the monitoring of any changes that might 

result from disturbances of the geochemical environment by activities such as energy development. The 

baseline value for each element accounts for the natural 

chemical variability of soils and may be defined as the 

95-percent range in concentration to be expected in 

samples of soils in these basins. In addition, differences 

between cell averages may be used to determine the 

feasibility of mapping regional variation in concentrations of elements in soils at a mapping interval greater 

than 10 km.

STUDY AREA

The Bighorn and Wind River Basins are structural 

basins formed in late Cretaceous and early Tertiary 

time (Keefer, 1965). During Eocene time, the basins

became progressively filled; by Oligocene time, the bordering mountain ranges were largely buried; and by 

Pliocene time, only the highest parts of the ranges stood 

above a broad depositional plain (Love, 1970).

In early Eocene time the basin fill was obtained from 

erosion of the surrounding mountains made up of Precambrian, Paleozoic, and Mesozoic rocks. The western 

border of the Bighorn Basin is east of the Absaroka 

Range at the border of the erosional scarp of the Absaroka volcanic plateau; these volcanic rocks of Eocene 

and younger ages contributed debris for the later filling 

of the basin but contributed little to the earlier deposits. 

The eastern border of the Wind River Basin is the Powder River lineament, a sharply folded belt of Cretaceous 

and Paleozoic rocks that contributed little debris to the 

basin fill. The Granite Mountains along the southern 

margin of the Wind River Basin mark the structural 

boundary of the basin but are buried by strata of 

Miocene and Pliocene age; this region is included in this 

study in order to obtain data on the general composition 

of these younger rocks, which are markedly different 

from the lower Eocene rocks that make up the oldest 

levels of the basin fill. Distribution of rock units is taken 

from Andrews, Pierce, and Eargle (1947) for the Bighorn 

Basin and from Whitcomb and Lowry (1968) for the 

Wind River Basin.

Coal occurs in rocks of Cretaceous and Paleocene age 

in both basins. Although small amounts of coal have 

been mined in each basin in the past (Keefer, 1965), it 

seems unlikely that energy resource development in the 

Bighorn and Wind River Basins (except for uranium in 

the Wind River Basin) will be comparable to that foreseen for the Powder River Basin (U.S. Bureau of Land 

Management, written commun., 1973).

Data on the composition of soils of the two basins are 

useful for comparison with each other and with data 

from the Powder River Basin. The data are also used in 

establishing a chemical background against which any 

changes can be measured in regions where development 

has taken place.
B2 GEOCHEMICAL SURVEY OF THE WESTERN ENERGY REGIONS

SAMPLING DESIGN

Chemical variation between geologic units within basins, and within geologic units across different distances, was estimated from an unbalanced, nested 

analysis-of-variance design. The analysis-of-variance 

design used in this study is shown in table 1. Sampling 

sites were randomly located using a barbell design 

within each of the primary geologic units within each of 

the basins (fig. 1).

The major axis of the barbell was 25 km long, and the 

sequentially smaller axes of each barbell were 10,5, and 

1 km long, respectively. All axes were oriented by selecting a compass direction at random. A barbell design is 

shown in figure 2. In each of the six barbells, 12 samples 

were collected for a total of 72 samples. Also, for each set 

of 12 samples, 4 samples were randomly selected to be 

split and analyzed twice, yielding a total of 24 samples 

split and analyzed in duplicate. These sample splits 

represent the analytical-error level of the sampling design (tables 2 and 3).

Soils on the geologic unit of Paleocene age (Fort 

Union Formation) were sampled only in the Bighorn 

Basin, and those on the geologic units of Miocene and 

Pliocene age (Moonstone and Arikaree Formations, respectively) were sampled only in the Wind River Basin. 

Soils on the geologic units of Eocene age (Wind River 

and Indian Meadows Formations in the Wind River 

Basin and Willwood Formation in the Bighorn Basin)

and on deposits of Quaternary age were sampled in both 

basins. Soils on the pre-Tertiary geologic unit were not 

sampled.

SAMPLES AND ANALYSES

The material collected at each sample location consisted of a composite sample of soil, excluding coarse 

fragments, from 0 to 40 cm in depth. In the laboratory, 

all samples were dried under forced air at ambient temperature. The samples were disaggregated using a mechanical, ceramic mortar and pestle, and the fraction 

passing a 10-mesh (2-mm) sieve was saved. The saved 

fraction was further ground to pass a 100-mesh (150/tm) 

sieve; this material was used for all chemical analyses. 

The 96 total samples (72 samples plus 24 splits) were 

analyzed in a random sequence, so that any systematic 

errors in sample preparation and analysis would be 

effectively converted to random errors and not bias the 

interpretation of results.

Analyses for some elements present in trace quantities commonly result in censored data, because part of 

the normal range of concentrations is smaller than the 

lower limit of determination for the analytical method. 

Because statistical tests require a complete numeric 

data set, censored values were replaced by arbitrary 

concentrations equal to 0.7 times the value that represents a lower limit of determination for the analytical 

method. This replacement is justified by the fact that

TABLE 1.—Analysis-of-variance design for the Bighorn and Wind River Basins

[Eachs, 2 is an estimate of the variation associated with the sources of variation: for example, s,, 2 is variation between geologic units ands,, 2 is the variation between duplicate analyses;

—, no F-ratio exists]

Source of variation

Between geologic units

10-25 km distance — - —

Degrees 

of 

freedom

2

3

6

Mean square estimates

MS, = s^l.5s 2 -i-2.3sc-i-4.1s 2 n -i-8.1soc-i-16s 121

la 1 j 10 LJ u

z a i j lu ij 

MS, = s 2 -i-1.4s 2 -i-2.3sr-i-4.0s 2 n

J a 1 J 1 U

F-ratio

MSj_

MS 2

MS 3

MS4

Variance 

component

2 MS 1 -MS 2

s u 

16

2 MS 2 -MS 3

7.9 

2 MS 3 -MS4

S 10 

4.0

~ 2

~ °u

~ 2

010

1-5 km distance- 12 MS, =

0-1 km distanceBetween analyses12

12

MS 5 -

MS 6 - s a

MS

MS, 

MS,

MS-MS 0

1.7

MS-MS

1.2

,2 ^ 0 2 'a °a
REGIONAL SOIL CHEMISTRY, BIGHORN AND WIND RIVER BASINS, WYOMING AND MONTANA B3

1

45 

44° 

43° 

42°

I

[

[ 

f

FlGl 

W 

fr 

L(

the £ 

with 

sign 

How 

part 

men 

stud 

Br,C 

Pr,F 

El 

teria 

quer 

form 

used 

cent

10° 109° 108° 107° 106°

I I I I

_^HZ&^ MONTANA

V°J^PI % WYOMING

\- \r-"' ' "' ;''%V

% \i v.'.T* •'-' ~7l\

%^ j^^^L-Tma"---"-^^ %

WIND RIVER BASIN ——— ^^^^^i^^^j0

I I I I

0 25 50 100 KILOMETERS

EXPLANATION 

o(fe;.;j Quaternary deposits \/ *v/i Paleocene Fort Union Formation

-Tma^j M^o'cene A°ikareee formations K^'l pre" Tertiary formations

'T*°S''3 Eocene Wind River and \^ 

"•„...'] Indian Meadows Formations / Sample localities *i.*.»iii yX r

-.Tw'- ] Eocene Wlllwood Formation

JRE 1. — Geologic and sample locality map of the Bighorn and 

ind River Basins of Montana and Wyoming. Geology modified 

om Andrews, Pierce, and Eargle (1947), and Whitcomb and 

nvry (1968).

mall number of replaced values (affecting samples 

detection ratios of <1:1 in tables 4-7) does not 

ificantly alter the results of the statistical tests, 

ever, when one-quarter or more of the analyses for a 

icular element were censored, the data for that elet were discarded and, therefore, not reported in this 

y. The highly censored elements were Ag, Au, Bi, 

Id, Cl, Cs, Dy, Er, F, Gd, Hf, Ho, I, In, Ir, Nd, Os, P, Pd,

>t, Re, Rh, Ru, S, Se, Sm,Ta, Tb, Te, Tl, Tm, and W. 

ements occurring in trace quantities in natural mails commonly tend to exhibit positively skewed freicy distributions. Therefore, a logarithmic transation of the data prior to statistical analysis was 

to improve the estimate of the most probable conration of an element in natural materials. The freX

| x

x Y^- 6^-^ x

5 ' A/ ^yy 25km

X--X ^^N'* 

1km x

FIGURE 2.— Diagrammatic representation of a barbell design with 

sample localities shown as x's.

TABLE 2. — Variance analysis of total element concentration in soil in 

the Bighorn Basin

[The sample consisted of a composite of soil from a 0- to 40-cm depth; total variance is 

computed on logarithmically transformed data; *. variance component is significantly 

different from zero at the 0.05 probability level; estimates based on analyses of 48 

samples]

Percent of total variance

Element variance Between Analytical 

geologic 10-25 km 5-10 km 1-5 km 0-1 km error 

units

Ce ——— .0314 0 27.9* 0 0 17.7 54.4 

Co ——— .0183 16.5 0 10.1 34.6 20.8 18.0 

Cr ——— .0434 5.4 0 0 77.7* 8.8 8.2

Fe ——— .0239 23.0 0 8.8 46.3* 17.9* 4.0

Mo ——— .0396 7.6 0 0 43.2 26.9 22.2

N i ——— .0229 12.7 0 0 41.5 34.4* 11.4 

Pb ——— .0337 3.6 0 00 46.5 49.9

v ———— .0253 0 2.2 0 61.6* 30.7* 5.5

quency distribution of the log-transformed data more 

nearly resembles a normal distribution, one of the basic 

assumptions for the analysis of variance. 

Chemical analyses were done in the U.S. Geological 

Survey analytical laboratories in Denver, Colorado.
B4 GEOCHEMICAL SURVEY OF THE WESTERN ENERGY REGIONS

TABLE 3—Variance analysis of total element concentration in soil in 

the Wind River Basin

[The sample consisted of a composite of soil from a 0- to 40-cm depth; total variance is 

computed on logarithmically transformed data; *, variance component is significantly 

different from zero at the 0.05 probability level; estimates based on analyses of 48 

samples]

TABLE 4.—Statistical summary for elements that lack regional variation in soils of the Bighorn Basin

[Detection ratio, number of samples in which the element was found in measurable concentrations relative to the number of samples analyzed; *, elements measured in percent; 

other elements measured in parts per million]

Element

Ce ————

C U ———— 

Fe ———— 

Ga ———

Hg ————

Mg ————

Nb ————

Pb ————

V ____.«.

Total 

variance

0.0069 

.1012 

.0272 

.0082 

.0184

.0494 

.0987 

.1290 

.0333 

.0566

.0731 

.0228 

.0229 

.1575 

.0267

.0042 

.1116 

.0359 

.0528 

.0305

.0441 

.0115 

.0340 

.0492 

.0395

.0240 

.0342 

.0011 

.2108 

.0258

.0238 

.0098 

.0097 

.0195 

.0410

.0639 

.0163 

.0247

Between 

geologic 

units

33.1* 

3.2 

14.0 

0 

11.4

5.4 

11.8 

1.0 

15.2 

65.4*

11.7 

7.9 

12.4 

0 

0

12.0* 

0.6 

3.4 

37.1 

26.3*

22.1* 

0 

0.2 

47.9* 

0

15.6* 

16.6 

0 

0 

2.5

33.8 

12.6 

15.6* 

10.6* 

0

0 

24.0 

9.4

10-25 km

0 

0.4 

0 

0 

0

0 

0 

1.3 

0 

0

0 

0 

6.2 

0 

23.6

0 

1.4 

0 

0 

0

0 

0 

0 

0 

0

0 

0 

2.3 

0 

32.6

12.2 

0 

0 

0 

4.4

5.1 

0 

0

5-10 km

2.8 

0 

0 

4.9 

24.4

20.8 

21.6 

0.2 

8.4 

0

0 

29.4 

0 

5.4 

0

0 

4.8 

14.7 

15.1 

0

0 

16.4 

0 

0 

0

6.8 

22.3 

9.5 

0 

31.4*

0 

25.9 

0 

0 

0

0 

2.8 

0

1-5 km 0-1 km

5.9 43.2* 

62.7* 13.1 

27.1 44.7* 

17.9 0 

21.7 0

13.7 50.9* 

37.6* 28.8* 

0 0 

34.9 28.9* 

5.9 25.2*

22.6 38.5* 

0 59.2* 

51.0* 9.7 

15.9 14.0 

10.2 23.4

67.6* 5.7 

0 0 

21.8 57.6* 

0 46.9* 

34.9 26.2*

16.9 42.4* 

69.8* 12.8* 

33.9 0 

14.9 29.2* 

8.2 0

0 14.0 

14.3 22.3 

53.7* 14.0 

13.0 16.7 

7.5 14.7

30.1* 16.0* 

13.3 40.4* 

0.6 79.7* 

18.9 59.5* 

11.8 0

11.7 0 

10.4 55.2* 

0 0

Analytical 

error

15.0 

20.6 

14.2 

77.2 

42.5

9.2 

0.3 

97.5 

12.6 

3.5

27.2 

3.5 

20.7 

64.7 

42.8

14.7 

93.2 

3.1 

1.0 

12.6

18.6 

1.0 

65.9 

8.1 

91.8

63.6 

24.5 

20.6 

70.3 

11.4

7.9 

7.8 

4.2 

11.0 

83.9

83.2 

7.5 

90.6

Element

Al* ——— 

Be ————

C* ———— 

Ca* ———

Co ————

Cu ———— 

Fe* ———

Ga ———— 

Hg ————

K*— TM~ TM

La ———— 

Li*~ •""••— 

Mg* — —

Mn ————

Mo —— — 

Na* ———

Pb ————

Sc ———— 

Si* ———

Sr ———

Ti* ———

U —— ——

Yb ————

Zr— -•-•—•

Geometric Geometric 

mean deviation

4.0 1.32 

50 1.33 

2.0 1.40 

1.5 1.72 

3.0 1.78

6.3 1.33 

59 1.55 

20 1.65 

1.8 1.38 

11 1.47

0.026 1.33 

1.5 1.19 

36 1.20 

18 1.31 

0.86 1.41

400 1.38 

4.8 1.47 

0.53 1.53 

22 1.37 

8.6 1.44

55 1.32 

5.9 1.59 

32 1.10 

230 1.39 

8.5 1.27

0.26 1.22 

2.7 1.25 

68 1 . 34 

20 1.28 

2.7 1.33 

320 1.35

^Expected 95-percent range.

ANALYTICAL

Geometric 

error

1.09 

1.14 

1.23 

1.17 

1.03

1.14 

1.15 

1.29 

1.07 

1.19

1.16 

1.07 

1.15 

1.11 

1.04

1.11 

1.24 

1.03 

1.13 

1.35

1.25 

1.19 

1.03 

1.08 

1.13

1.05 

1.05 

1.09 

1.15 

1.11 

1.29

ERROR

Baseline 

value

2.4 - 4.8 

30 - 83 

1.2 - 3.4 

0.53 - 4.2 

0.95 - 9.5

3.8 - 10 

26 -135 

8.4 - 47 

0.96 - 3.4 

5.5 - 22

0.016- 0.042 

1.1 - 2.1 

28 - 45 

11 - 30 

0.4 - 1.7

220 -740 

2.5 - 9.1 

0.23 - 1.2 

12 - 39 

5.7 - 13

40 - 77 

2.5 - 14 

27 - 38 

120 -440 

5.6 - 13

0.18 - 0.38 

1.7 - 4.2 

39 -120 

13 - 30 

1.6 - 4.6 

230 -440

VARIANCE

Detection 

ratio

36:36 

36:36 

36:36 

36:36 

36:36

36:36 

36:36 

36:36 

36:36 

36:36

36:36 

36:36 

36:36 

36:36 

36:36

36:36 

35:36 

36:36 

36:36 

36:36

36:36 

32:36 

36:36 

36:36 

36:36

36:36 

36:36 

36:36 

36:36 

36:36 

36:36

Sample preparation and analyses were performed by 

James S. Baker, A. J. Bartel, E. L. Brandt, J. G. Crock, 

I. C. Frost, Johnnie M. Gardner, Patricia Gayle Guest, 

Raymond G. Havens, J. P. Hemming, Kathryn E. 

Horan, Claude Huffman, Jr., J. O. Johnson, R. J. 

Knight, R. M. Lemert, R. E. McGregor, Violet M. Merritt, H. T. Millard, Jr., Wayne Mountjoy, G. O. Riddle, 

V. E. Shaw, M. W. Solt, J. A. Thomas, Michele L. Tuttle, 

R. E. Van Loenen, R. J. Vinnola, J. S. Wahlberg, and 

R. J. White. The analytical methods are described in a 

previously published report (U.S. Geological Survey, 

1975).

All computations were done on a HoneywellMULTICS computer using statistical programs in the 

U.S. Geological Survey's STATPAC Library (Van 

Trump and Miesch, 1977).

The distributions of variance components for 38 elements in soils from the two basins are shown in tables 2 

and 3. For 6 elements in the Bighorn Basin and 11 

elements in the Wind River Basin, the variance due to 

analytical error accounts for more than 50 percent of the 

total observed variation. This error is judged to be excessive and, therefore, any interpretation of the data for 

these elements must be made with extreme caution.

Excessive analytical errors result in duplicate samples being reported as having widely different concentrations. The analytical procedure, rather than splitting errors or particle effect, is probably the best explanation for this excessive error. If splitting errors or particle effect were responsible, then a larger number of 

elements would exhibit excessive error. Concentrations 

of all elements, except Rb, that exhibit excessive analytical error were determined by multi-element emission spectrography or X-ray fluorescence. Atomic ab-
REGIONAL SOIL CHEMISTRY, BIGHORN AND WIND RIVER BASINS, WYOMING AND MONTANA B5

TABLE 5.—Statistical summary for elements that lack regional variation in soils of the Wind River Basin

[Detection ratio, number of samples in which the element was found in measurable concentrations relative to the number of samples analyzed; *, elements measured in percent; 

other elements measured in parts per million]

TABLE 7.—Statistical summary for elements having regional variation in soils that overlie the three major geologic units in the Wind 

River Basin

[Detection ratio, number of samples in which the element was found in measurable concentrations relative to the number of samples analyzed; *, elements measured in percent; 

other elements measured in parts per million]

Element Geometric Geometric Geometric Baseline Detection 

mean deviation error value 1 ratio

As ——— 3.6 1.90 1.39 1.2 - 10.8 36:36

B ———— 28 1.38 1.15 16 - 50 36:36

Be ——— 2.4 1.29 1.23 1.8 - 3.2 36:36 

C* ——— 0.85 1.62 1.17 0.34 - 2.1 36:36

Ca* ——— 2.2 1.93 1.04 0.59 - 8.2 36:36

Co ——— 5.5 1.49 1.16 2.6 - 12 36:36

Cu ——— 15 1.70 1.38 6.5 - 35 36:36 

Fe* ——— 1.5 1.36 1.07 0.82 - 2.7 36:36

Ga ——— 15 1.32 1.17 9.5 - 24 36:36

Hg ——— 0.020 1.45 1.28 0.011- 0.035 35:36

Li ——— 15 1.49 1.08 6.9 - 33 36:36 

Mg* ——— 0.63 1.54 1.05 0.27-1.5 36:36 

Na* ——— 1.3 1.26 1.03 0.8-2.1 36:36

Sc ——— 5.3 1.47 1.23 2.8 - 10 34:36 

Si* ——— 31 1.07 1.03 28 - 35 36:36

Sr ——— 340 1.42 1.13 180 -660 36:36

Th ——— 12 1.43 1.10 6.0 - 24 36:36 

Ti* ——— 0.22 1.22 1.07 0.15 - 0.32 36:36

Zn ——— 43 1.31 1.08 26 - 72 36:36

^Expected 95-percent range.

TABLE 6. — Statistical summary for the element having regional variation in soils that overlie the three major geologic units in the Bighorn 

Basin

[Detection ratio, number of samples in which the element was found in measurable concentrations relative to the number of samples analyzed; *, elements measured in percent; 

other elements measured in parts per million]

.-., . Geometric Geometric Geometric Baseline Detection Llement . , mean deviation error value 1 ratio

Willwood Formation

Zn ——— 51 1.32 1.11 30-85 12:12

Fort Union Formation

Zn ——— 66 1.36 1.11 37-118 12:12

Quaternary deposits

Zn ——— 55 1.26 1.11 36-83 12:12

1 Expected 95-percent range.

sorption was used for the determination of Rb concentration.

BASELINE VALUES

A total of 31 elements in soils from the Bighorn Basin 

(table 2) and 19 elements in soils from the Wind River 

Basin (table 3) do not exhibit statistically significant

.-., .. Geometric Geometric Geometric Baseline Detection Llement . i mean deviation error value ratio

Moonstone and Arikaree Formations

Al* ——— 4.4 1.18 1.08 3.3- 5.9 12:12 

Cr ——— 27 1.45 1.11 13 - 55 12:12

K JL. *> 1 1 1 T 1 f\f. IT *>£ 1 •> • 1 •>

Mo ——— 3.7 1.64 1.23 1.5-9.1 11:12

Mn ——— 270 1.50 1.15 130 -580 12:12 

Ni ——— 12 1.56 1.16 5-28 12:12

U ———— 2.6 1.15 1.05 2.0- 3.4 12:12 

v ———— 43 1.44 l.il 21 - 86 12:12

Wind River and Indian Meadows Formations

Al* ——— 5.0 1.16 1.08 3.9- 6.4 12:12 

Cr ——— 52 1.36 1.11 29 - 93 12:12

Mo ——— 5.0 1.43 1.23 2.8- 9.0 12:12 

Mn ——— 320 1.29 1.15 210 -490 12:12

Ni ——— 21 1.39 1.16 12 - 38 12:12

U ———— 2.9 1.27 1.05 1.8- 4.6 12:12 

V ———— 48 1.22 1.11 34-67 12:12

Quaternary deposits

Al* ——— 5.5 1.17 1.08 4.2- 7.2 12:12 

Cr ——— 61 1.24 1.11 42 - 89 12:12 

K* ——— 1.9 1.12 1.06 1.6- 2.3 12:12

Mo ——— 5.8 1.43 1.23 3.2- 10.0 12:12

Mn ——— 420 1.32 1.15 260 -680 12:12

Ni ——— 23 1.25 1.16 16 - 32 12:12

U

OQ IT/, 1 H R *>*> T £ 1 *> • 1 *>

v ———— 53 1.26 1.11 35-80 12:12

1 Expected 95-percent range.

(0.05 probability level) variability between geologic 

units and do not exhibit excessive analytical error. 

Thus, a single baseline value is the optimum estimate to 

describe the total concentrations of these elements in 

soils from each of these basins (tables 4 and 5). The 

results of analysis of variance (tables 2 and 3) suggest 

that the composition of soil samples taken from within 

different geologic units within a basin are expected to 

vary little more than the composition of soil samples 

taken at distances of 5 km or less apart. The baseline 

value is defined by Tidball and Ebens (1976) as the 

expected 95-percent range in concentration in samples 

of soils in these basins. The expected range is estimated 

from the residual variation after analytical error has 

been removed. This residual variation is the natural 

chemical variation measured between samples and excludes variation due to sample preparation and 

analysis.
B6 GEOCHEMICAL SURVEY OF THE WESTERN ENERGY REGIONS

Rocks of Paleocene age in the Bighorn Basin consist of 

thin-bedded, light-colored sandstone and conglomerate 

with drab to olive-brown shale and some red shale in the 

upper part (Andrews and others, 1947). The rocks of 

Eocene age in the Wind River Basin are made up of 

varicolored claystone and siltstone interbedded with 

white to gray, fine- to medium-grained arkosic 

sandstone (Keefer, 1965); about half the soils sampled on 

the Wind River Formation lay on a drab-colored 

sandstone and shale sequence and the other half, on 

varicolored mudstone. In the Bighorn Basin, the rocks 

of Eocene age are typically a variegated shale with 

abundant beds of white and yellow sandstone composed 

of unsorted grains whose mineralogy represents crystalline rather than sedimentary rocks as source material (Van Houten, 1944). The Miocene and Pliocene rocks 

in the Wind River Basin consist of medium- to coarsegrained, gray to buff, massive to coarsely crossbedded 

sandstone with common limestone beds, algal reefs, and 

pumicite beds, and also consist of stratified gray arkosic 

conglomerate containing boulders of granite and 

Paleozoic rock (Love, 1970). These rocks of Miocene and 

Pliocene age are different in composition from strata of 

Eocene age in the Wind River Basin. The deposits of 

Quaternary age are highly variable; the soils at the 

sampling localities on the western end of the barbell in 

the Wind River Basin are mostly developed in finegrained alluvium (Thompson, 1954) in the nearly undrained part of the Wind River Basin in which Ocean 

Lake was formed when irrigation began. Two of the 

localities at the southeastern end of the same barbell 

are on low terrace deposits along the Wind River north 

of the city of Riverton, and four are on erosional remnants of coarse-grained, bouldery, high-terrace deposits 

(Thompson, 1954). On Quaternary deposits in the 

Bighorn Basin, three sampling localities are on the 

Powell terrace 50 to 80 m above present stream level; 

five are on high, dissected gravelly pediment surfaces 

older than the Powell terrace; and four are on gravelly 

pediment surfaces younger than the Powell terrace 

(Andrews and others, 1947).

The rock types described for the various geologic units 

differ from one another in ways that suggest they should 

differ also in chemical composition. The nonsignificant 

variability between the soils on the geologic units for 

most elements in both basins suggests that the soils on 

strata of different ages are not chemically distinct from 

one another. This implies that either the soils are not 

genetically related to the rock units which they overlie 

or, if the soils represent the compositions of the rock 

units, that the rock units are not chemically distinct 

from one another. Possibly, the soils are not genetically 

related to the geologic units because soil composition 

reflects surficial geology and geomorphology of

Holocene age rather than rock-stratigraphic units of 

Tertiary age. However, for the Wind River Basin, several elements exhibit significant variability between 

soils on the various map units.

Zinc is the only element that exhibits a significant 

variability in soil between map units from the Bighorn 

Basin (table 2). The soils sampled on the Fort Union 

Formation had the highest average Zn concentration, 

and those on the Willwood Formation and deposits of 

Quaternary age were about equal. However, in the Wind 

River Basin, eight elements (Al, Cr, K, Mn, Mo, Ni, U, 

and V) exhibit variability between geologic units that is 

significant at the 0.05 probability level; Rb was eliminated because of excessive analytical error. All these 

elements, except K, were highest in average concentration in soils on deposits of Quaternary age and lowest in 

average concentration on those soils developed in the 

Miocene Moonstone and Pliocene Arikaree Formations. 

For K, the trend was reversed. Concentrations of these 

elements are best described by individual estimates of a 

baseline for each mapping unit, because the differences 

between mapping units are greater than the differences 

between samples within the mapping units. Statistical 

summaries and baseline values for these elements are 

given in tables 6 and 7.

Summary data on the average composition of soils of 

the Bighorn and Wind River Basins, of soils and surficial materials of the Powder River Basin, and of surficial materials of the Western United States are presented in table 8. The data show that, for most elements, 

the average composition of the soil differs little between 

the Bighorn Basin, the Wind River Basin, the Powder 

River Basin, and the Western United States. Concentrations of Na in soil in the Wind River Basin; B, C, and Ca 

in the Bighorn Basin; and Ba, Be, Mo, and Sr in both 

basins are 50 to 100 percent higher than in soils in either 

the Powder River Basin or the Western United States. 

Li is the only element in the Wind River and Bighorn 

Basins that is about 50 percent lower in concentration 

than in either the Powder River Basin or the Western 

United States. However, concentrations that differ by a 

factor of one to two are generally within a 95-percent 

expected range and should not be considered as anomalous values that warrant special consideration.

MAPPING REQUIREMENTS

This geochemical survey is preliminary in character; 

it is conducted mainly to measure chemical variability 

and to estimate the magnitude of the sampling effort 

that will be required to assess the present, natural 

geochemical status of the soils in each basin. Data from 

the analysis of variance are useful for estimating the
REGIONAL SOIL CHEMISTRY, BIGHORN AND WIND RIVER BASINS, WYOMING AND MONTANA B7

TABLE 8.— Average concentrations (geometric means) of elements in 

soils and surficial materials in the Bighorn, Wind River, and 

Powder River Basins and in the Western United States 

[All elements in Bighorn and Wind River Basins are included regardless of the magnitude of 

analytical error; *, element measured in percent; other elements measured in parts per 

million; — , no data available]

Wind Powder River Basin Western

Basin Basin Subsurface B horizon States

Al* —— 4.0 5.0 —— 5.6 5.4 

As ——— 4.7 3.6 —— —— 6.1

Ba ——— 1300 1500 720 660 560

Be ——— 2.0 2.4 .99 —— .6

Ca* ——— 3.0 2.2 —— .87 1.8 

Ce ——— 57 54 —— —— 74

Co ——— 6.3 5.5 6.3 7.6 8

Cr ——— 59 52 49 46 88

Cu ——— 20 15 16 17 21 

Fe* —— 1.8 1.5 —— 2.2 2.0

Ga ——— 11 15 13 —— 18

/""*•» Q "7 Q Q

Hg ———— .25 .020 .023 .022 .055

La ——— 36 33 28 —— 35 

Li ———— 18 15 24 5 27 23 

Mg* ——— .86 .63 —— .67 .78 

Mn ——— 400 320 230 270 389

Mo ——— 4.8 5.0 <3 -— 

Na* —— .53 1.3 —— 4 .45 1.0 

Nb ——— 8.9 6.9 6.2 —— 11

Ni ———— 22 21 15 17 16 

Pb ——— 8.6 13 17 18 18

Rb ——— 55 63

OU 1 £ O Q

Sc ——— 5.9 5.3 7.8 8.6 9 

Si* —— 32 31 —— 5 34 

Sn ——— .71 .87

Sr ——— 230 340 160 160 210

Ti* ——— .26 .22 —— 5 .29 .21

U ———— 2.7 2.9 3.0 

v ———— 68 48 87 78 66

W* O "7 O & 1 Q "3

Zn ——— 57 43 61 5 66 51 

Zr ——— 320 230 140 200 170

Connor, Keith, and Anderson (1976). 

riidball and Ebens (1976). 

Surficial material, from Shacklette and others (1971a, b, 

1973, 1974). 

Arithmetic mean of four geometric means. 

Arithmetic mean.

number of samples that would be required within an 

area of specified size to prepare a reliable map of total 

element concentration. 

Sampling cells 10 km on a side were arbitrarily chosen to illustrate the concepts used in interpreting the 

analysis of variance and applying it to the preparation

of maps of regional variation. Such variation may easily 

be mapped as differences between cell averages, if an 

adequate number of random samples are taken within 

each cell to produce a stable average. The methods for 

estimating the minimum number of random samples 

(nr) required in each cell, based on the concept of a 

variance ratio (v), were developed by Miesch (1976). The 

variance ratio is a ratio of the variance measured between increments of distance (in this case 10 km) to the 

variance measured within increments of distance. The 

minimum number of random samples that need to be 

collected in each 10-km cell is determined from the following equation: 

F = I + nr u (1) 

where nr is adjusted so that the sum, (1 +nr v), exceeds 

the critical F-statistic (F) at the 80 percent confidence

interval with 1 and 2nr —2 degrees of freedom. 

Table 9 summarizes the number of mappable elements in each basin for increasing n,. values. Maps 

showing regional distribution of C and Na concentration in soil in the Bighorn Basin and Cr in the Wind 

River Basin would require a minimum sampling intensity of two random samples per 10-km cell to describe 

more than half of the natural variation. At the other 

extreme, it would not be feasible to attempt a mapping 

program based on 10-km cells for several elements in 

each basin (elements labeled "n.d." in table 9) . For these

TABLE 9. — Minimum number of random samples needed fnr) in a 

10-km square to map total element concentrations in soils of the 

Bighorn and Wind River Basins at the 80 percent confidence level

[— , no element can be mapped in a basin using this n, value; n.d., not determined because n,. 

is infinitely large]

Mappable elements

Bighorn Basin Wind River Basin

2 C, Na Cr 

3 —— Al, Mg, Ni, Sr, Th 

4 Ca, Ce, Fe, Mn, Sr Hg, Mn, Mo, Zn 

5 Co, Si Ga 

6 As, Ni, Rb, Sc, Zn B, Co, Rb, Sc, Ti, U

7 Ba, Ga Be, Ca, Cu, K 

8 Al, Li, Mg V, Zr 

9 Cu —— 

10 K, Mo Fe 

12 Nb C

13 B, Be, Cr, Hg —— 

14 —— Yb 

17 —— Li, Y 

20 Pb 

25 —— As

n.d. Ge, La, Sn, Th, Ti , Ba, Ce, Ge , La, Na, 

U, V, Y, Yb, Zr Nb, Pb, Si, Sn
B8 GEOCHEMICAL SURVEY OF THE WESTERN ENERGY REGIONS

elements, variation estimated at distances of 10 km or 

greater was very small or nonexistent, so a minimum 

sampling intensity could not be calculated. The sampling intensity necessary to map the regional distribution of single elements differs between the Bighorn and 

Wind River Basins. For example, if there is interest in 

mapping the regional distribution of Mo in the Bighorn 

Basin, it would require a minimum of 10 random samples per 10-km cell. To map the regional distribution of 

Mo in the Wind River Basin would require a minimum 

of four random samples per cell. The geographic variability of element concentration is unique for any single 

element in the sampling area.

The previous paragraphs have illustrated the 

methods for determining minimum sampling intensity 

for mapping variation in element concentration between 10-km cells. Similar tables of minimum sampling 

intensities can be constructed for each element in each 

basin for 5- or 1-km cells by using the analysis-ofvariance data in tables 2 or 3 to compute the variance 

ratios and by using Equation 1 to compute nr values. The 

analysis-of-variance data can also be used to estimate 

the portion of the total variation explained by the size of 

the geographic unit selected for mapping regional distribution. The proportion of the total variation explained for mapping at a 10-km cell size is determined 

by summing the analysis-of-variance values for "Between Map Units" and "10-25 km" (tables 2 or 3). For 

example, mapping Mo at a 10-km interval with a sampling intensity of 10 samples per cell in the Bighorn 

Basin and 4 samples per cell in the Wind River Basin 

would describe only about 8 percent of the natural variation of this element in the Bighorn Basin (table 2) and 

only about 22 percent of the natural variation in the 

Wind River Basin (table 3). To describe more than half of 

the natural variation of an element concentration, add 

together the percent of total variance at each level of the 

sampling design, starting with the "Between Map Unit" 

level (tables 2 or 3), until a value of 50 percent is exceeded. To describe more than half of the natural variation of Mo, it would be necessary to sample at a 1-km 

interval in the Bighorn Basin and at an interval of <1 

km in the Wind River Basin. At either of these intervals, 

the sampling load and costs would be very high.

Because of the dominant local variation for most 

elements, the baseline value is more practical than a 

map of regional variation. For most elements, maps 

prepared at an interval requiring a reasonable sample 

load would explain a very small portion of the total 

natural variation, whereas, at the other extreme, maps 

that explain a reasonable portion of the total natural 

variation would require such a large sample load as to 

be impractical at present.

CONCLUSIONS

This reconnaissance study of spatial variation in total 

concentration of elements in soils in the Bighorn and 

Wind River Basins suggests the following:

1. Geographic variation in total concentration of elements in soil occurs mainly at distance intervals of 

less than 5 km.

2. Because of the large local variation, individual measurements of total element concentration in soil cannot be extrapolated over great distances.

3. The summary data for a group of samples, however, 

expressed as a baseline value, may be extrapolated 

over great distances (geologic units or whole basins) 

depending on the magnitude of the regional variation.

4. The lack of significant variation between geologic 

units for most elements suggests that soils mask the 

presumed variation between rock differences that 

make up the mapping units and possibly indicates 

that the soil materials are not genetically related to 

the geologic mapping units. This lack of significant 

relations between soil composition and geologic 

units seems reasonable, because soil composition 

probably reflects differences in surficial geology and 

geomorphology of Holocene age rather than rockstratigraphic units of Tertiary age.

5. The average concentration for most elements in soil 

is not greatly different between the Bighorn, Wind 

River, and Powder River basins or the Western 

United States. The geometric means for Ba, Be, Mo, 

and Sr in soil, however, in both the Bighorn and Wind 

River Basins are 50 to 100 percent greater than in the 

Powder River Basin or the Western United States. 

Concentrations of Na in soil in the Wind River Basin 

and B, C, and Ca in soil in the Bighorn Basin are also 

slightly higher than in the other areas. Lithium in 

soil in the Bighorn and Wind River Basins has an 

average concentration that is about half that in the 

Powder River Basin or the Western United States; 

however, these values generally lie within an expected 95-percent range in concentration and should 

not be considered anomalous values.

6. The analysis of variance indicates that it is possible 

to map regional variation in element concentration 

in soil as differences among 10-km cell averages for C 

and Na in the Bighorn Basin and for Cr in the Wind 

River Basin; with only two random samples per cell, 

a large portion of the natural variation would be 

described. At the other extreme, it is not feasible to 

even attempt to map regional variation for several 

elements, because analysis of variance indicates that 

little or no variation is expected to exist at 10-km or 

greater distances. Therefore, for most elements in
REGIONAL SOIL CHEMISTRY, BIGHORN AND WIND RIVER BASINS, WYOMING AND MONTANA B9

soil in both basins, a mapping program designed to 

describe more than half of the natural variation in 

element concentration is impractical.

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GOVERNMENT PRINTING OFFICE: 1979-677-026/7