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THE APPLICATlON OF ROUNDNESS
AND SS’HEMCITY MEASUREMENTS

TO SUB-SURFACE SAMPLES OF
‘E’HE MARSHALL FORMATION OF
WESTERN MlCHSGAN

Thais far fha» Dayna m? M. 5.
MICHEGAN STATE CQLLEGE

gabmt Acisfbmf Mariam
$9419

 

This is to certitg that the

thesis entitled

"The Application of Roundness and Spherieity
Measurements to Sub-surface Samples of
The Marshall Formation of Western
Michigan"

presented bg

Robert Adelbert Hobbs

has been accepted towards fulfillment

of the requirements for

M- 3. degree mm

 

7— ‘ ,

/ é/ , I, . VN-‘x .& C} Q ._ W‘VM‘
‘ A,

Major IDI‘UlCSSHI‘ 7

 

”we July 22, l9h9

 

0-169

 

 

THE APPLICATION OF ROUNDNSSS ARD SPHERICITY
MEASURERENTS TO SUB-SURFACE SAMPLES OF
THE MARSHALL FORMAPION OF WESTdRN
kICHIGAN

by

Robert Adelbert Hobbs

A Thesis

Submitted to the Graduate School of Michigan
State College of Agriculture and Applied
Science in partial fulfillment of the
requirements for the degree of

MASTER OF SCIENCE

Department of Geology
and GeOgraphy

1949

THE-11.3

Acknowledgements

The writer wishes to express his sincere appreciation
to Dr. B. T. Sandefur for his direction, aid, and criticisms
throughout this problem. Also to Dr. W. A. Kelly for his sug-

gestions and criticisms.

The writer wishes to express his deep thanks to Dr.
S. G. Bergquist for proof reading the manuscript, and to hr.
Rex Grant of the Michigan State Geological Survey for his

cooperation in supplying the samples.

ns‘wnqq‘)
'I-‘II‘.“"'. I "d

ii

Table of Contents

List of Tables ........................................
List of Illustrations .................................
Introduction ..........................................
Location of Area ......................................
General ........................................
Distribution of Wells ..........................
Purpose of Study ......................................
Method of Investigation ...............................
General ........................................
Sieving ........................................
Mounting for Microscopic Study .................
Roundness and Sphericity Measurements ..........
Statistical Methods of Correlation ....................
Quartile measures of the Cumulative
Weight Percentages .............................
Comparison of Quartile Measurements ............
Comparison of Sphericity and Roundness
Measurements ...................................
Conclusions ...........................................

Bibliography 00000oooooooeooooooooooooooo00.000.000.000

iii

Page

iv

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List of Tables
Page
1. Sorting, Skewness and Kurtosis ..................... 26
2. Reduction of Elevations to Sea Level Datum

Plane IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII 54

iv

List of Illustrations

Page
1. Stratigraphic Column ................................ 3
2. Map Showing Garfield Township, Newaygo
County, Michigan .................................... 5
3. Map Showing Location of Wells .......................' 5

4. Wadell's Determination of Shape ..................... 10
5-9. Cumulative Curves of the Weight Percentages
of Samples from Well No. 1 ........................ 14-18
10-14. Cumulative Curves of the weight Percentages
of Samples from'Well No. 2 ...................... 19-23
15. Comparison of Roundness values ..................... 27
16. Comparison of Sphericity values .................... 29
17. PaleogeOgraphic Map of Marshall
Sedimentation ...................................... 32

180 StrUCtural Diagram ooooooooooooooooooooooooooooooooo 34

Introduction

The shape of sedimentary particles for stratigraphic
correlation has not been used extensively in Michigan. Early ob-
servers noted the modification of grain shape that takes place by
transportation and abrasion. Several factors control this "modi-
fication of shape", namely:

(1) cleavage or bedding of the fragment.

(2) the durability of the material.

(5) the rigor of the geologic agent.

(4) the original shape.

(5) the time through which the action is extended.

It is assumed generally that sand grains become pro-
gressively more round in direct relation to the distance they are
transported by water. If this assumption is correct, and sand
grains along a beach do become more round as they are transported
seaward, a statistical determination of this roundness within a
series of samples taken from a definite horizon within a formation,
should indicate their position relative to an old shore line.
Careful work may reveal a buried beach.

The petroleum geologist is constantly on the search for
buried beaches, since many have proved to be important reservoirs
for oil.

Erickson* showed that the relationship of the heavy
mineral distribution within esker sands was a good criterion for
determining the direction of flow of the parent glacial stream,-and

that shape measurements furnished additional proof to that determination.

 

*Erickson, R. L., A Petrographic Investigation of the Longitudinal
Deposition within the Mason Esker Relative to its Origin. Unpub-
lished Master's Thesis, Department of Geology and Geography,

Michigan State College, 1948.

V’-

From his conclusions it seems logical that shape measurements
could be applied to any'water-transported sand to determine the
direction from which it came.

For the present study, the sand at the top of the
Mississippian Marshall formation in Newaygo County was chosen be-
cause of the readily distinguishable quartz grains with their char-
acteristic reddish iron oxide stain, and the easily identified sedi-
mentary break between these red sands and the overlying Michigan
formation. (figure 1.) The use of such a locally prominent horizon
provided a maximum of control for the investigation which followed.

Although it has been recognized by Monnett* that a red
color in the Marshall deposits is of little value as a regional
stratigraphic marker, and that the red sediments are more character-
istic of the lower Marshall strata, it is significant that they do

occur at the top of the Marshall in local areas of western Michigan.

 

*Monnett, V. B., Mississippian Marshall Formation of michigan:

Bulletin of the American Association of Petroleum Geologists,

 

Vbl. 32, No. 4, April 1948, pp. 661-662

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

System- Formation . . Thick-
Series or Member Section Lithology ness
Quater- . . . E§x?3{?;o revel sand
_pary W13°°n51n a g and 321%: ’ #00'
________ shale,
. . ‘ ———————— gypsum !
Michigan , sand, and 3L5
,. limestone
sand red ,
a Marshall and’white 160
w ......
r4 -.__._
p, _____
Pi ______
H — --
m _ ___..
m — - - ‘- ——-
'3 —;-;T;2:_
.3 l T’l 1 red shale,
2 , gray shale ,
Goldwater ’’’’ limestone,’ 620
;:;::;1;:_ dolomite
{xifix’xx’x
4:5:E:EZE: dark gray ,
Sunbury _____ shale 20

 

 

Figure l.- Stratigraphic Column of Mississippian
Formations, Newaygo County, Michigan.

 

Location 2: Area

 

General
The area involved in this study is limited to a single
section of Garfield Township in Newaygo County, in the west-central

part of the lower Peninsula of Michigan. (figure 2.)

Distribution of Wells

 

 

Three wells were selected in section 11 of Garfield Town-
ship. For convenience they will be referred to as wells No. 1,
No. 2, and No. 3.

Well No. l, is in the sw 1/4, SE 1/4, NW 1/4, section 11,
T. 12 N., R. 13 W., 370' from the south and 990' from the east line
of the quarter section.

Well No. 2, is in the sw 1/4, sw 1/4, ma 1/4, section 11,
T. 12 N., R. 13 Wt, 330' from south and 330 ' from west line of the
quarter section.

Well No. 3, is in the sw 1/4, NE 1/4, sw 1/4, section 11,
T. 12 N., R. 13 W., 990' from north and 990' from east line of the
quarter section.

The plot of the wells is shown in figure 3.

Purpose 2.1:. £21.91
This investigation was undertaken in an effort to prove or
disprove the feasibility of applying shape measurements to sub-sur-
face sands in order to determine the direction of sedimentation and
thus the position and direction of old shore lines along which may

be found stratigraphic traps of economic importance. Also, certain

 

 

/
Bay City.
IH’N waygo
° Grand Rapids
°Lansing

 

 

 

Figure 2.- Map Showing Location of Area. Blacked-in
Portion Represents Garfield Twp., Newaygo
County.

 

 

 

Garfield Township

 

 

 

 

section 11

 

Newaygo-

Well #l-SW l/l-Iv: SE l/t, NW 1/1,
Well #2-sw l/ll, sw l/l, W 1/4
Well #3-sw l/b,, NE l/t, sw l/h

 

 

Figure 3.- Plot of Wells in Garfield Township, Newaygo County.

"shape-horizons" might be found within the sand which may be con-

sistent throughout a limited area and thus used to determine the

 

structure.
Method of Investigation
General

The investigation involved a statistical study of the
quartile measurements, and the measurement of the shape of the
quartz grains. The well samples were taken at vertical intervals of
five feet and placed in bottles of approximately 10 grams each. The
sands in each well were completely separated and did not have to be
disaggregated artificially.

As previously mentioned, the sand grains in the Marshall
formation are stained red by iron oxide. It is possible to remove
the iron stain by treating the grains with a solution of 1:1 hydro-

chloric acid and hydrogen peroxide and heating over a burner.*

 

*Salutsky, Murrellg Graduate Council Fellow, Chemistry Department,

Michigan State College. Personal Communication.

 

The methods described by Krumbein* to remove iron stains were not

successful when applied to the Marshall sands.

 

*Krumbein, W. 0., Manual of Sedimentary Petrography, D-Appleton-

 

Century Company, New York, 1939, pp. 314-315.

 

 

It was found, however, that the iron stain in no way altered
the shape of the quartz grains so it was not absolutely necessary to

remove it before making the shape measurements.

As pointed out by Stearns*, the heavy minerals contained

in the Marshall sands are neither abundant nor diversified.

 

*Stearns, M. D., The Petrology of the Marshall Formation of Michigan:

Journal of Sedimentary Petrology, V51. 3, No. 3, December 1933,

 

pp. 99-112.

 

Therefore, no heavy mineral separation was necessary since minerals
other than quartz were readily discernible with the aid of the petro-

graphic microscope.

Sieving

Owing to the relatively small amount of sample available,
the entire content of each 10 gram bottle was weighed and then
sieved in a Ro-Tap automatic shaking machine for a period of eight
minutes. The shaker was equipped with six sieves having respectively
35, 48, 65, 100, 150, and 200 openings per inch. After sieving, each
sieve size was weighed, placed in an individual vial, and labelled.
The material caught on the 35 mesh sieve was disregarded in the final
analysis as it consisted largely of shale and gypsum which is pre-

sumed to have been due to caving from the overlying Michigan formation.

Mounting for Microscopic Study

 

After a thorough examination of each individual fraction of
one sample, it was found that the 65-100 size proved to be the most
desirable for taking measurements. This is a function of the optical
system of an individual microscope and may not prove the desirable

size in every case. After deciding on the 65-100 size as being the

,‘

most useable, all other fractions were returned to the original
bottles.

Quartz (refractive indices 1.544-l.553) shows little relief
in Canada balsam (n- 1.537) therefore, a synthetic resin (n- 1.66)
was used as a mounting medium in order to produce greater relief and
detail.

A glass slide was heated on a metal plate over a micro-
burner before pieces of the resin (n- 1.66) were placed upon it. Con-
tinued heating of the resin from one to two minutes drove out the
majority of the bubbles while the remaining few could be eliminated
easily by means of a sharp teasing needle.

After the mounting medium had reached the proper consis-
tency, the 65-100 size samples were mounted on slides for roundness

and sphericity measurements.

Roundness and Sphericity Measurements

 

Wadell* defines roundness as the measure of the angularity
of the corners, and Sphericity as the ratio between the length and

breadth of grains. (figure 4.)

 

*Wadell, B., volume, Shape and Roundness of Quartz Particles, Journal

of Geology, Vbl. 43, 1935, pp. 250-280.

 

 

For the measure of roundness'Wadell employs the formula:

"U
I

total degree of roundness.

r- radius of curvature of the corner.

R- radius of the maximum inscribed circle.
N- number of corners measured.

lO

r=lO wadell's Roundness (P):

13%): 13.49 = .49

 

Wadell's Sphericity (¢):

.R .2.
Wm? 5'°63

 

D«=35

D‘sradius of circumscribed circle.'
R =radius of inscribed circle.

r =radius of curvature of corner.

N =number of corners measured.

Figure h.- Wadell Method of Determination of Shape
and roundness.

11

For the measurement of sphericity he uses the formula:

_d.

D.
fi- degree of sphericity.
d.-diameter of a circle equal in area to the area of the
grain obtained by planimeter measurement.
D.-diameter of the smallest circle circumscribing the
particle.
The measurements were made with the aid of a concentric
circle protractor drawn on transparent plastic.
This method of measuring roundness and sphericity is ac-
curate but very time-consuming because each individual grain must
be drawn before any measurements can be made.

Riley* devised a method for measuring sphericity which is

both accurate and fairly rapid.

 

*Riley, N. A., Projection Sphericity, Journal of Sedimentary

 

Petrology, Vbl. 11, 1941, pp. 94-97.

 

A concentric circle protractor is placed in the occular of the micro-
scope. Measurements may be read directly, thus eliminating the draw-

ing of individual grains. Riley used the formula:

M:

fl? degree of sphericity.

i- diameter of the largest inscribed circle of the grain.

D.-diameter of the smallest circumscribed circle.

The accuracy thus obtained closely approached that of
Vadell.

The writer, however, used a combination of Riley's method

for measuring sphericity and Wadell's method for measuring roundness

as devised by Schmitt*.

12

 

*Schmitt, G. T., A Petrographic Investigation of the Relationship
of Deposition of Sediments in a Group of Eskers Related to the
Charlotte Till Plain. Unpublished master's Thesis, Department of

Geology and Geography, Michigan State College, 1949, p. 47.

 

A camera lucida attached to the occular of the microscOpe projected
the grains on Wadell's concentric circle protractor which had been
drawn on a sheet of white paper rather than plexiglass. The various
measurements could then be made simultaneously without drawing the
individual grains.

Using this method, the writer measured the roundness and
sphericity of fifty quartz grains per slide of each 5 foot sample

taken from the three wells. A total of 1,700 grains were measured.

Statistical Methods of Correlation

 

 

Quartile Measures of the Cumulative Weight Percentages

 

 

Quartile measures are widely used for describing and come
paring sediments statistically. The first use of quartile measures

in sedimentary data was by Traskt in 1930.

 

*Trask, P. D., hechanical Analysis of Sediments by Centrifuge:

Economic Geology, V61. 25, 1930, pp. 581-599.

 

 

Three expressions of quartile measures can be used to de-

scribe a sediment. They are quartile deviation, quartile skewness,

and quartile kurtosis.

13

The first and second quartile, the median, and the tenth
and ninetieth percentiles are used in the computations of these
measurements. The great advantage of quartile measures is that each
can be read directly from the cumulative curves of the weight per-
centages as shown in figures 5-14.

The median diameter, N, is defined as that diameter which
is larger than 50 percent of the diameters in the distribution, and
smaller than the other 50 percent. The quartiles lie on either side
of the median and are the diameters which correspond to the fre-
quencies of 25 and 75 percent.

The tenth and ninetieth percentiles correspond to the
diameter values at the intersection of the ten and ninety percent
lines with the cumulative curve. They are the diameters which corre-
spond to frequencies of 10 and 90 percent.

Trask* used the geometric quartile deviation as a “sorting

coefficient", applying the formula:

‘I Q.
Q.-
So- sorting.

09- first quartile (the larger size).
Qt‘ third quartile (the smaller size).

 

*Trask, P. D., Origin and Environment of Source Sediments of Petro-

leum, Houston, Texas, 1932, pp. 67ff.

 

In general, 'So' is a convenient measure to use for de-
scribing the spread of the curve because it is a ratio and eliminates

the size factor and the units of measurement.

1h

 

01" 03 02 o].
sieve size in mm.

Cumulative Curve, Well No. 1, 780-785'

15

 

‘ _ A M ii v .11 1.1-..4-‘ 1 - I: H N w _ . . _

_ m a a . a _

1‘ A I I l r 1| 1| . ll. 1 \ .c II. V) o l ' . H l
and . a . M M m _ . d
. :7; - -;‘:E-.--~;57é:;a:-: -n1;; I..- m -1 .1
1.. _ v w .1 - W I: w - m W a
. . _ m _ _
. - L - ..... . r l l 111 F [iii L”. I . 1: .H

m

 

 

 

 

- .1
O
...... O
n
.1
..... e
Z
.1
2 S
. 7;; 1:. |_--H.1...-. a
$9-.." .__- i hit... 9
”thi. ..... . LIEr. v
”1.. .3 .L _ 21.....1. e
ltliir- .1
: S

 

.ri.

Cumulative Curve, Well No. 1, 785-790'

16.

 

.1. .3 .2 .1
sieve size in mm.

Cumulative Curve, Well No. 1, 790-795'

 

90V,

75'

50

25'

10

 

1?

    

ellv 03 .02' e

sieve size in mm.

Cumulative Curve, Well No. 1, 795-800'

 
  

90'_

75'

50‘

25'

10 '

18

 

'l" 03 .2 el
sieve size in mm.

Cumulative Curve, Well No. 1, 800-805'

19

 

m .. H . a - a .7 - . a a 1 i «.1.1
. _ H u 1 .
— L a
l a . F - . i m
¢ . . ._ w . .—
1 a . a ., _ u
.l i r .- -Iuvl- :-I,_.. .l, v: I-“ #17 .1 s 4 a - ..
i 1 _ i
| l I 1| N 9 ~ .

m
1
U _ _ _
1
a

 

i

l

i
in mm.

 

. V

..,llt,|l'l.ioil¢ 1. ..

fl _

.14. .9' T11? . - I...
. _

vlm 'T-.§laln .
l _ _

sufaVL a.

.2
Sieve Size

lxbll 41"] 0 Cl 1 .IB':

a?

90
75
SO
25
10

Cumulative Curve, Well No. 2, 780-785'

20

 

01" .3 .2 .1
sieve size in mm.

Cumulative Curve, Well No. 2, 785-790'

21

1 ll: I.:|!Tl|.lu I!

M
M
_
-1
i

 

 

OI .‘ll .7;

 

2
Sieve size in mm.

.3

Curve, Well No. 2, 790-795'

Cumulative

22

 

oll' 03 02 01
sieve size in In.

Cumulative Curve, W011 No. 2, 795-800'

23

 

.h .3 .2 .1
sieve size in mm.

Cumulative Curve, Well No. 2, 800-805'

24

Quartile skewness is a measure of the departure of the
arithmetic mean of the quartiles from the median. The quartile skew-

ness may also be expressed in geometric form as shown by Krumbein*.

 

*Krumbein, W. C., op. cit., p. 23“.

 

The equation is as follows:

1, . _, Q. Q.
3&6- T
Skg-— skewness.

Q. — first quartile.
third quartile.
'1 ‘— Hiediane

2‘?
I

The geometric skewness has the same advantages as the
geometric quartile deviation in that it eliminates the size factor
'and the units of measurement. When a frequency curve is symmetrical,
the value of skewness is unity. Other values obtained will range from
numbers less than one, which Show a greater concentration in the fine
sizes, to nunbers larger than one, which indicate a larger percent of
coarse sand.

Quartile kurtosis essentially involves a comparison of the
spread of the central position of a frequency curve to the spread of
a curve as a whole. It is the measure of the degree of peakedness of
the curve. A well sorted sand would show marked kurtosis, whereas, a
poorly sorted sediment would have negligible peakedness. Quartile

kurtosis can be obtained from Kelley's equation* which is as follows:

25

an— kurtosis.

Q. — first quartile.

Q: -third quartile.

R. — tenth percentile.

Rn - ninetieth percentile.

 

*Kelley, T. L., Statistical kethods, London, 1924, p. 77.

 

Comparison of Quartile Neasurements

 

 

A summary of the quartile measures of the samples examined
in this study may be seen on table 1. The quartile measures of the
samples from well No. 2 may now be compared with those from well
No. 1.

0n the basis of approximately 200 analyses, Trask found
that an '80' value less than 2.5 indicates a well sorted sediment.
From the results shown in table 1, it is apparent that the harshall
sand from the wells examined is very well sorted.

The values for kurtosis are quite consistent and Show a
maximum deviation of only .08, which is considered insignificant.

The skewness values of the samples from well No. l are
slightly greater.than one, indicating sorting toward the larger sizes.
The skewness of samples from well ho. 2 is just less than one. This
would indicate that the sorting of the sand in well No. 2 is in the

smaller grain sizes.

Comparison of Sphericity and Roundness Measurements

 

 

A graphic presentation of the roundness is shown in

figure 15. It is readily seen that the roundness of the quartz

26

 

Depth

Q.

Q.

R0

Ru

So

Skg

an

 

760-765

2.85

1.92

2.29

3 011']-

1.36

1.22

1.02

0.26

 

765-770

2.82

1.88

2.26

3oh2

1.58

1.23

1.02

0.25

 

770-775

2.70

1.75

2.13

3.33

l.h7

1.2h

1.02

0.25

 

775-780

2.74

1.80

2.17

3.39

1.52

1.2a

1.02

0.25

 

780-785

2.52

1.84

2.09

3.09

1.54

1.18

1.03

0.22

 

785-790

2.h1

1.80

2.08

2.96

1.39

1.16

1.00

0.19

 

790-795

2.65

2.00

2.19

3.28

1.65

1.15

1.05

0.20

 

795-800

2.61

1.99

2.20

3.2h

1.66

1.15

1.0a

0.20

 

800-805

2.57

1.89

2.16

3.13

1.52

1.17

1.02

0.21

 

805-810

2.60

1.92

2.19

3.20

1.57

1.16

1.02

0.21

 

810-815

2.41

1.96

2.12

3.08

1.66

1.12

1.02

0.16

 

815-820

2.58

1.87

2.18

3.18

1.51

1.18

1.01

0.21

 

820-825

2.99

1.86

2.38

3.58

1.51

1.27

0.99

0.27

 

 

825-830

 

2.99

 

1.92

 

2.39

 

3.55

 

1.58

 

1.25

 

1.00

 

0.27

 

Well

No. 1

 

Depth

Q.

Q.

M.

B.

Ru

So

Skg

an

 

780-785

3.27

2.21

2.72

3.7h

1.77

1.22

0.99

0.27

 

785-790

3.13

2.07

2.58

3.66

1.66

1.23

0.99

0.26

 

790-795

3.39

2.33

2.87

3.80

1.91

1.21

0.98

0.28

 

795-800

3.37

2.28

2.82

3.79

1.85

1.22

0.98

0.28

 

 

800-805

 

3.36

 

2.28

 

2.81

 

3.79

 

1.84

 

1.22

 

0.98

 

0.28

 

Table 1.- Summary of Quartile Measures.

Well

No. 2

 

 

27

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

35
30 x”z
l
f\
.’ ‘. /\
7 Y \ i \
1 \ 1
25 \ / I ‘
. / \
I L \
£
, 1
20 f
I
I
\i
1
5o 15 30 as 60 75
Well #1-————__ .
Well #2 ------

W'ell #3 see...

Figure 15.- Graphic Comparison of the Roundness of
the Marshall Sand, Newaygo County.

28

particles in well No. 2 closely follows the pattern of those in well
No. 1, but in almost every instance, is greater. Also, the roundness
values for the 25 feet examined in well No. 3 again reflect the general
pattern of the other two. The curve representing well no. 3, however,
more closely resembles that of well No. 2 than that of well No. 1.

It should be noted that the maximum roundness values differ
somewhat in each well. The maximum value for the samples from well
No. 1 is .26, for well No. 2, .29, and well No. 3, .34. It is inter-
esting to note that the horizons that gave maximum roundness values
in each case are not at the same depths. In well No. l, the maximum
value of .26 is found 45 feet below the t0p of the harshall. In well
No. 2, the maximum value of .29 is located 40 feet below the top of
the formation. A raximum value of .34 was found 30 feet below the
top of the formation in well No. 3. This shows, that with an increase
in the maximum roundness value, the position of the horizon is nearer
the top of the formation. The significance of the position change
of maximum roundness will be discussed in the conclusions.

The sphericity results are shown graphically in figure 16.
The results of the Sphericity measurements do not exhibit the same
clear-cut comparisons that are shown by the roundness. However, it
may be seen that the sphericity of the samples from well To. 2 is
less than those of well No. 1. host authorities agree that with an

increase of roundness the sphericity decreases*.

 

*Wentworth, C. K., The Shapes of Pebbles: U. S. Jeol. Survey Bull.

 

730‘0, 1922, pp. 91‘1140

 

Ԥ

29

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

85
/ \ /\
x f 1" \ l \
l/ \‘ / I \\
[I \ I \\
3 f
XI
I
75
51 201 hO' 601 75:
Well #1 __._.—
Well #2 ------

well #3 00000.

Figure 16.- Graphic Comparison of the Sphericity of
the Marshall Sand, Newaygo County.

30

The curve for the 25' of samples examined from well No. 3 does not
seem to bear any relation to the other two, although it appears to
be less than well No. 1 and greater than well No. 2.

The sphericity values obtained in this limited study appear

to have little significance.

Conclusions

 

It is concluded from the data accumulated for this problem
that roundness and sphericity measurements can be applied to sub-sur-
face samples to determine the direction of the sedimentation and thus
the direction of old shore lines.

It is generally accepted that sediments near the source are
blocky or angular with a very low roundness value but with relatively
high sphericity. As the sediments are transported farther from their
source, abrasion tends to remove sharp corners thus causing the frag-
ments to become more round. On the contrary, the particles tend to

flatten by abrasion, the result of which is a decreased sphericity.*

 

*Wentworth, do Kc, Op. Cit.

 

The degree of roundness of water-borne quartz grains is a
direct function of the distance transported. The degree of sphericity,
conversely, is an inverse function of the distance the grains are
transported.

Following this line of evidence, the sand from well No. 1,
having the lowest roundness values, the highest degree of sphericity,
and maximum sorting in the coarse sizes, is obviously the nearest of

the three wells to the source of sand supply in the area.

31

The sands of well No. 2 have a greater degree of roundness, lower
values of sphericity and maximum sorting in finer sizes. These factors
indicate that the sands are farther removed from the source than are
those of well No. 1.

The maximum roundness values are found in the samples from
well No. 3, indicating that they are the farthest from the source.
The sphericity is higher than expected. This may be due to a secon-
dary increase caused by the wearing away of the thin peripheral edges
of the grains thus causing them to become more equidimensional. The
fact that the roundness curve of the fractions from well No. 3 more
closely resemble the curve of the samples from well No. 2, would in-
dicate that it is in the line of sedimentation from well No. 2 rather
than from well No. 1.

The "shape-horizons", depicted by the apices of the round-
ness curves, occur at a different depth in each of the three wells.
It is interesting to note that, with an increase in the maximum
roundness values, the "shape-horizons" are located nearer the top of
the formation. This evidence might also be an indication of increa-
sing distance from the source of the sediments.

Figure 17 is a paleOgeOgraphic map of Marshall sedimenta-
tion as constructed from the roundness values shown in figure 15.

The exact shoreward distance to the source material is not definitely
known. however, the excellent sorting, the high degree of roundness,
together with the paucity of heavy minerals which possibly may have

been destroyed by abrasion, would seem to indicate the source to be a

considerable distance away.

32

 

:2
\
/

#3)

Scale- 1" 1/8 mile

 

 

 

Figure l7.- Paleogeographic Map of Marshall Deposition
Indicating Shore Line and Source to the
North-west.

33

The outstanding peaks on the roundness graphs indicate a
horizon that could be picked out readily at least locally, (figure
15). The elevations of these peaks are reduced to a sea level datum
plane in table 2, and plotted on a structural diagram as shown in
figure 18. This diagram.shows a slight increase in elevation from
well No. 1 to well No. 2, and a greater increase to well No. 3. This
indicates a local high just to the south of well No. 3 which is

actually the case in this area.*

 

*Grant, R., Oil and Gas Geologist, Michigan State Geological Survey,

1949. Personal Communication.

 

A summary of the conclusions is as follows:

1. Sphericity and roundness measurements have proved to be of
practical value when applied to sub-surface sands of the Marshall
formation of western Michigan. These factors indicate the direc-
tion of source material from which the sediments were derived in
the sedimentation process.

2. Cumulative curves and quartile measures as prepared give addi-
tional proof of the value of roundness and sphericity in deter-
mining the direction of source material for the Marshall sands.

3. The determination of the direction of the source material focuses
attention to a limited area, such as an old shore line, which may
prove of economic importance in the deep seated storage of petro-
leum.

4. Locally prominent "shape-horizons" may be recognized and contoured
in such a manner as to suggest the presence of structure within

limited and restricted areas.

1‘

o

o

3h

 

 

 

 

 

 

 

 

 

 

 

 

 

Elevation Elevation Elevation
Well of Peak of Surface from Datum
#1 800 842.2 42.2
#2 800 8h8.0 48.0
#3 765 836.3 71.3
Table 2.
. #1 ll #3 II
' ll " N ‘____-
I #2 I: ll ||
: :I II "
i ': H ,:
I
I u /
I ll |p/' / II
I ll 1 II II
: H //l / II
' / ,4 ll
, lkv' H
: II " II
. H II II
. ll H II
I II N
I | I II
I II ' II
,J— --- - -II----n---—-I I-----—-- ——---- - --
lx’ :: ~sea level datum-
I

 

 

Figure l8.- Diagrammatic View of Marshall Structure

in Garfield Twp., Newaygo County.

 

35

Bibliography

*Erickson, R. L., A PetrOgraphic Investigation of the Longitudinal
Deposition within the Mason Esker Relative to its Origin.
Unpublished Master's Thesis, Department of Geology and
Geography, Michigan State College, 1948. '

*helley, T. L., Statistical kethods, London, 1924, p. 77.

*Krumbein, W. C., manual of Sedimentary Petrography,

D-Appleton-Century Company, New York, 1939, pp. 314-315.

 

*Monnett, V. B., hississippian harshall Formation of michigan:

Bulletin of the American Association of Petroleum Geologists,

 

Vbl. 32, No. 4, April 1948, pp. 661-662.

*Riley, N. A., Projection Sphericity: Journal of Sedimentary

 

Petrology, V01. 11, 1941, pp. 94-97.

*Schmitt, G. T., A Petrographic Investigation of the Relationship
of Deposition of Sediments in a group of Eskers Related to
the Charlotte Till Plain. Unpublished Master's Thesis,
Department of Geology and Geography, Michigan State College,
1949, p. 47.

*Stearns, M. D., The Petrology of the harshall Formation of

kichigan: Journal of Sedimentary Petrology, Vbl. 3, No. 3,

 

December 1933, pp. 99-112.
*Trask, P. D., Mechanical Analysis of Sediments by Centrifuge:

Economic Geology, vol. 25, 1930, pp. 581-599.

 

O

36

*Trask, P. D., Origin and Environment of Source Sediments of
Petroleum, Houston, Texas, 1932, pp. 67ff.
*Wadell, H., volume Shape and Roundness of Quartz Particles:

Journal of Geology, Vbl. 43, 1935, pp. 250-280.

 

*Wentworth, C. K., The Shapes of Pebbles: U. S. Geological

 

Survey Bulletin, 730-0, 1922, pp. 91-114.

 

 

 

 

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293