I
1

7 1 -1 1 ,8 7 6
IBRAHIM, A b d e l w a h i d , 1 9 3 3 THE APPLICATION OF THE GRAVITY METHOD TO
MAPPING BEDROCK TOPOGRAPHY IN KALAMAZOO
COUNTY, MICHIGAN.
M ic h ig a n S t a t e
G e o p h y sic s

U n iv e rs ity , Ph.D.,

1970

U niversity Microfilms, A XEROX C o m p an y , A nn Arbor, M ichigan

THE APPLICATION OF THE GRAVITY METHOD TO
MAPPING BEDROCK TOPOGRAPHY IN
KALAMAZOO COUNTY, MICHIGAN

by

Abdelwahid Ibrahim

A TH ESIS

Subm itted to
Michigan State U niversity
in partial fulfillm ent o f the requirem ents
for the d eg ree of

DOCTOR OF PHILOSOPHY

Departm ent o f Geology
1970

ABSTRACT

The gravity method has been w idely used to d elineate buried bedrock
va lley s in glaciated a r e a s .

The method is based on mapping sp atial

perturbations in the gravity field a sso c ia te d with bedrock topography
which c a u se s horizontal va riation s in d en sity betw een the bedrock and
the generally l e s s d e n se , overlyin g g la cial d r ift.

It is d e sir a b le ,

how ever, in both ground w a te r , geom orphic., and engineering in v esti­
gations to map not only the buried bedrock v a lle y s , but to prepare a
bedrock topography map from the gravity o b se r v a tio n s.

A method of

mapping bedrock topography using gravity m ea su rem en ts in conjunc­
tion with w ell log inform ation has been developed and su c c e ss fu lly
applied to Kalamazoo County, M ichigan.

Depth to bedrock and gravity

observations at w ell s it e s a re used to ca lcu la te a regional gravity
anomaly map which ex clu d es the e ffect o f bedrock above a datum .
This map is subtracted from the Bouguer gravity anom aly v alu es to
obtain a residual gravity anom aly map reflectin g p rim a rily bedrock
topography.

The residual g ravity a n o m a lies obtained by th is method

show a sign ifica n tly im proved c o r re la tio n with bedrock topography
over resid u a ls obtained by the conventional graphical and sta tistic a l
m eth od s.

The residual gravity a n o m a lies a re converted to bedrock

elevation using the a ssu m ed d en sity co n tra st betw een the glacia l
sed im en ts and the bedrock.

The bedrock topography map of Kalamazoo County show s a
prevailing w estw ard slop e with a su p erim p o sed , com plex bedrock
channel s y s te m .

The principal channels g e n era lly trend e a s t—
w est

or north-south.

The map is used to d is c u s s the p reg la cia l and p e r i-

glacial drainage and the ground w ater potential o f the County.

ACKNOWLEDGEMENTS

The author w ish e s to e x p r e s s h is sin c e r e appreciation to the
following individuals and organizations:
D r. W. J . Hinze o f the Departm ent of G eology, Michigan State
U niversity for h is patient gu id an ce, advice and con stru ctive c r itic is m
throughout th is study.
D r. H. Bennett of the Department of G eology, Michigan State
University for h is in te r e s t, su g g estio n s and helpful c r it ic is m .
D r. C. E . Prouty and D r. H. B . S torehouse o f the Michigan
State U niversity Department o f G eology for th e ir su g g estio n s and
cr itic ism concern ing the g eo lo g ica l asp ect of the study.
D r. M. M. M ille r , Chairman of the World Center for Explora­
tion for his su g g estio n s concerning the g la cia l a sp ect of the study.
The City o f Kalamazoo Water Departm ent and the Upjohn Company
of Kalamazoo, Michigan for financial support and providing the w ell
logs needed for the study.

TABLE

OF

CONTENTS

Page
i\

ACKNOWLEDGEMENTS
LIST OF TABLES

v

LIST OF FIGURES

vi

LIST OF PLATES

.

vu

CHAPTER
I.

INTRODUCTION

1

Purpose and Method
C orrelative Investigations
A rea of Study
II.
III.

THE GEOLOGV OF KALAMAZOO COUNTY
BEDROCK TOPOGRAPHY
Introduction
Origin of Buried Bedrock Channels
Bedrock Topography in the Southern
Peninsula o f Michigan
Bedrock Channel D ep osits a s Ground Water
A quifers

IV.

DATA ACQUISITION AND REDUCTION
Introduction
Field S u rvey
Reduction of Field Data
Latitude C orrection
M ass C orrection
F ree A ir C orrection
Terrain C orrection
S o u r ce s of E r ro r s and A ccuracy

V.

ROCK DENSITIES

1
4
6
9
13
13
14
17
20
22
22
23
24
25
25
26
27
27
30

Significance of D en sitie s
F actors C ontrolling D e n sitie s
Published D e n sitie s
iU

30
30
32

Page

CHAPTER
Methods of D ensity Determ ination
Introduction
Laboratory P rocedures for M easuring
D en sities
Density P rofile Methods
Variable D ensity Approach
G eophysical—
G eological Method
VI.

REGIONAL AND RESIDUALS
Introduction
Conventional Method of Isolation R esiduals
Bedrock Topography Residual Bouguer Gravity
Anomaly

VII.

DISCUSSION OF RESULTS
Bouguer Gravity Anomaly
Gravity R esiduals
Bedrock Topography Residual Bouguer
Gravity Anomaly Map
Gravity R esiduals Obtained by Approximating
the Regional by Polynom ial
Bedrock Contour Map

VIII.

INTERPRETATION OF RESULTS
Correlation of Bedrock and Surface Topography
Relation Between Bedrock Channels and
Surface Geology
Reconstruction of the Drainage Pattern Before
and During Glaciation

IX.

GROUND WATER POSSIBILITIES IN
KALAMAZOO COUNTV, MICHIGAN
Introduction
Bedrock Channels in Kalamazoo County as
Ground Water Aquifers

X.

CONCLUSIONS
Applicability of the Gravity Method in
Outlining Bedrock Topography
Suggestions for Further Studies
BIBLIOGRAPHY

35
35
36
36
39
42
52
52
52
64
76
76
78
78
80
82
86
86
88
88

92
92
97
101

101
102
104

LIST

OF

TAB LE S

Page

Table
1

2

3

4

5

Density of glacial sed im en ts near K indersley,
Saskatchewan, Canada (after Hall and Hajnal,
1962)

35

Density of sedim ents near Two H ills, Alberta
(after Lennox and C arlson , 1967)

35

Density values resulting from applying the
geophysical-geologic method to all te st h oles in
Kalamazoo County

45

Density values obtained by applying the geop h ysicalgeological method to te s t h oles located in a rea s
covered with till deposits

45

D ensities of bedrock and glacial sed im en ts
obtained by approximating the two dim ensional
gtacial and bedrock m a s s e s by p o ly g o n s.

49

v

LIST

OF

FIGURES

Page

F ig u r e
1

Area of study

2

Histogram s of sm a ll—
sp ecim en butk d e n sitie s of
sedim entary rocks (from Birch (1942'), by Grant and
W e st(1965)

33

Polygon representation of glacia l and bedrock
sedim ents

48

Relation between c r o s s profile resid u a ls (gR) and
bedrock elevation (E)

56

Relation between Fifth degree polynomial resid u a ls
(gR) and bedrock elevation (E)

62

Relation between Seventh degree polynom ial
residuals (gR> and bedrock elevation (E)

63

Model illustrating the calcuations of geologic
residual gravity anom aly

67

Errors in calcuating the th ick n ess of bedrock
sedim ents above the datum using the infinite slab
formula

72

Relation between geologic residual Bouguer
gravity (gR) and bedrock elevation (E)

74

Salt content of ground w ater and bedrock
topography

95

3

4

5

6

7

8

9

10

8

v’f

LIST

OF

PLATES

Surface Geology and Bedrock Channels in Kalamazoo
County
Gravity Stations and D rill Hole Locations
Contour Map of the Bouguer G ravity Anomaly
Bedrock Topography R esiduals Bouguer Gravity
Anomaly Map
Bedrock Topography Map of Kalamazoo County:
Scale 1 inch = 1 m ile
Bedrock Topography
S cale 1 inch = 2 ,0 0 0 Feet
Map of the Residual V alues from Fifth D egree
Polynomial Approximation to the Bouguer Surface
Map of the Residual V alues from the Seventh
Degree Polynomial Approximation to the Bouguer
Surface
Surface Drainage and Bedrock Channels

vn

CHAPTER

I

INTRODUCTION

Purpose and Method
The sea rch for potable water is one of the o ld est endeavors of m an.
Ancient civ iliz a tio n s thrived where am ple quantities of su rface w ater
were availab le.

The fir s t recorded use of ground w ater dates back

more than five thousand y e a r s (T olm an, 1937).

Ground w ater w as

needed then, even a s it is today, to supplem ent su rface su p p lies of
water for human consum ption and irrig a tio n .

T h e r efo re , the art o f

prospecting and developing ground w ater r e so u r c e s is a s old a s the
e a r lie st civ iliza tio n known to m an.

Today, the exploration and d evel­

opment o f ground w ater su p p lies has becom e an im portant and com plex
s c ie n c e .
During the la st se v e r a l decad es in d u stria liza tio n , w hile demand­
ing m ore w ater, has resulted in ex ten siv e pollution o f s u r fa c e , and
to a certain extent, ground w a ter, through irresp o n sib le w aste d is­
posal p r a c tic e s.

The in creasin g rate of su rface w ater pollution and

the expanding use o f w ater have in crea sed the demand for the develop­
ment of new ground w ater r e s o u r c e s .

T h erefo re, p resen t techniques

of ground water prospecting m ust be rev ised and new m ethods p erfected .

The application of geophysical techniques to ground w ater exp lora­
tion is a com paratively new field with co n sid era b le p oten tial.

This

branch of natural sc ie n c e is being u se d , not only in prosp ectin g for
ground w ater a q u ife r s, but a ls o in th eir evaluation and develop m en t.
A ccordingly, a s in a ll developing f ie ld s , the e ffe c tiv e n e s s o f the geo­
physical m ethods in solvin g d iv e r sifie d h y d ro -g eo lo g ic p rob lem s m ust
be exam ined.

This w ill eventually lead to the m odification of p resen t

methods and the developm ent of new techniques for the a n a ly sis and
interpretation of field data.
In form erly glaciated a r e a s , g la cia l se d im e n ts a re often the only
available sou rce for ground w ater because bedrock form ation s a r e
either im perm eable or contain polluted or sa lin e w a te r .
sedim ents are known for th eir ex tr em e h ete r o g en eity .

G lacial
Both la tera l

and vertical v aria tio n s of th eir physical p r o p e r tie s a r e com m on.
Glacial sed im en ts in bedrock ch a n n els, h o w ev er, have proven to be
favorable s it e s for locating ground w ater a q u ife r s.
this are a s follows:

The rea son for

1) B edrock v a lle y s have a g r e a te r probability

of containing thicker se c tio n s o f sand and gravel b eca u se o f the
increased th ick n ess of g lacia l drift from the la te st glaciation;
2) Bedrock v a lle y s often a r e the loci o f p reserv ed c r buried outwash
deposits from e a r lie r glaciation; 3) Outwash d ep o sits on bedrock highs
are m ore lik ely to be eroded (H orberg, 1950).
In m ost geologic situ a tio n s, the bedrock form ation s have higher

d e n sitie s than the overly in g se d im e n ts.

A s a r e s u lt, d e p r e s s io n s in

the bedrock su rface produce low er gra v ity read in gs than th e se bedrock
a r e a s , which are topographically high.

T h is c o r r e la tio n betw een bed­

rock topography and g ravity ren d ers the method su ita b le for mapping
bedrock topographic fea tu res p a rticu la rly in c a s e s of sig n ifica n t r e lie f
on bedrock su rface or a w ell developed hydrom orphic p attern .

B uried

bedrock channels can be identified by the unique sinuou s pattern w hich
they com m only display on a Bouguer gra v ity m ap.

In few c a s e s , buried

bedrock channels are d ifficu lt to d elin eate b eca u se g la c ia l d e p o sits
have d e n sitie s equal to or slig h tly ex ceed in g that o f bedrock (M cG innis
et a l, 1963).

Lennox and Cc rlso n (1967) conducted lab oratory d en sity

m easurem ents on a lim ited number o f sa m p le s of s i l t , sa n d sto n e, s e n d ,
shale and t i l l .

They concluded that the d e n s itie s o f the fir s t four

m aterials are e s s e n tia lly the s a m e .
appreciably higher d e n s itie s .

The t i l l , on the other hand, showed

In th is c a s e , thickening o f the till a s

encountered in buried channels could produce a high gra v ity trend along
the v a lley a x is .

Hall and Hajnel (1962) have found both high and low

gravity a n om alies a sso c ia te d with the tren d s o f known buried c h a n n e ls.
The gravity method has been applied in d elin ea tin g buried bedrock
channels and defining the c r o s s se c tio n of th ese ch an n els through m odel
studies at location s w here w ell control is a v a ila b le .

The p r e se n t study

aim s at expanding the sco p e of the gra v ity m ethod by developing a
technique of com puting bedrock topography from gra v ity o b se r v a tio n s

4

and w ell c o n tr o l.

A bedrock topography map is valu ab le, not only

in ground w ater stu d ie s, but a ls o in engin eerin g and geom orphic
investigations.

The study w as ca r ried out in K alam azoo County,

Michigan because o f the stron g dependence o f the a rea upon ground
water s o u r c e s , and a ls o b ecau se of the a v a ila b ility o f am ple w ell
data.

C orrelative Investigations
Kalamazoo County has p rev io u sly been stu d ied , p o ssib ly m ore
than on ce, by regional gravity and m agnetic s tu d ie s .

T hese

investigations w ere ca rried out by oil com p an ies for the purpose
of locating oil and gas field s in the buried P a leo zo ic b edrock.

No

major geophysical in v e stig a tio n s, how ever, have been p rev io u sly
undertaken to study the ground w ater r e s o u r c e s o f the g la cia l
sedim ents.

The only geophysical stu d ies ca r ried out for the purpose

of locating ground w ater aq u ifers w ere in the form o f s c a tte r e d , and
rather lim ited r e s is tiv ity m easu rem en ts conducted by consulting
firm s on behalf o f the City of Kalam azoo Water D epartm ent or local
industry.
The Department of Natural R e so u rc e s of the M ichigan G eological
Survey, in cooperation with the United S ta te s G eological S u rv ey
and the City of K alam azoo, r e le a se d Report Number 23 concerning
the "Ground W ater Hydrology and G lacial G eology o f the Kalam azoo
A rea."

T his report is based on an in vestigation which sta rted in

5

1946 and dealt with the a v a ilab ility and quality o f ground w ater in
the Kalamazoo area (D eutsch, V an lier, and G iroux, 1960).

The

investigation involved the c o llec tio n and com pilation o f data p er­
taining to the so u r c e , o c c u r re n c e , and ch em ica l quality o f ground
w ater.

The United S ta tes G eological S u rv ey , in addition, is con­

ducting a hydrological program in Kalamazoo County which is based
4

on well data, pumping t e s t s , and a d rillin g p rogram .

The expected

outcome of this study w ill be the delineation of a q u ife r s, com pilation
of tra n sm issib ility co efficien t and aquifer th ic k n e ss contour m a p s.
A report concerning the findings of th is investigation w ill be r e le a sed
in the near future.
The Michigan Highway C om m ission is conducting a sh allow co rin g
program aim ed at c la ssify in g and delineating su rfa c e glacia l d ep o sits
in Kalamazoo County.

The purpose o f th is investigation is to locate

sand and gravel d ep osits suitable for road construction
General d escrip tio n s of the geology of the Southern Peninsula of
Michigan including Kalamazoo County can be found in papers by Lane
(1895), Leverett (1 912 , 1917) and L everett and T aylor (1915).
Martin (1955) com piled an areal geology map o f the Southern Penin­
sula of Michigan and prepared a sp e c ia l report on the g la c ia l h isto ry
of Kalamazoo County (M artin, 1957).
Reports containing ground w ater data on the Kalamazoo a rea w ere
also made by Lane (1899) and L everett (1 9 0 6 , a , b).

6

Area of Study
The area covered by this investigation is Kalamazoo County,
Michigan.

Located in the southw estern corner of the Southern

Peninsula (F ig . 1), Kalamazoo County lie s between latitudes 4 2 °
05' N and 41° 25' N and longitudes 85° 25* and 8 5 ° 45* W.

The

County is divided into sixteen townships covering T 1S to T4S and
R9w to R 12 W.
The major river in Kalamazoo County is the K alam azoo.
flows from east to w est in the eastern part of the County.

It

At the

City of Kalamazoo it changes direction and flow s northward.
There are sev era l sm a ll c r e e k s , the la rg est of which is Portage
Creek.

It joins the Kalamazoo R iver w here it changes direction

and flows northward.

There are num erous la k e s, m ostly inter­

connected, the largest of which is Gull Lake, located in the north­
eastern corner of the County.
Most of the area is generally flat with a maximum r e lie f o f
fifty feet.

Surface r e lie f in the northwestern part of the County,

however, is appreciably higher due to the Kalamazoo m o ra in es.
The maximum elevation of the m oraines is about 1050 feet above
sea le v e l, and the r e lie f is about 150 fe e t.
The largest m unicipality is the City o f Kalamazoo which has a
population of about 2 0 0 ,0 0 0 .

Industry includes paper m anufacturing,

pharmaceutic products, and transportation equipm ent.

T hese

industries make a c o n sid e r a b le demand upon the lo ca l ground w a ter
so u rces.
The su rfa ce w a te r s o f the County, e s p e c ia lly the K alam azoo
R iver, have becom e polluted through w a ste d isp o sa l o f the paper
companies and oth er in d u s tr ie s .
source of usable w a te r .

T h u s, ground w a ter i s the m ain

I

8

K A L A M A Z O O COUNTY

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FIGURE I

AREA

OF

ST U D Y

CHAPTER

II

THE GEOLOGY OF KALAMAZOO COUNTY

Kalamazoo County Is com p letely covered with glacial sedim ents
ranging in thickness from le s s than 50 to 650 fe e t.

The th ick est

section lie s to the w e st where the Kalamazoo m oraines o v erlie bed­
rock channels.

Throughout the area the glacial sed im en ts are

variable, ranging from w e ll-so r te d len ticu lar outwash d ep o sits to
com pletely unsorted, and m ostly com pact t i l l .
The area was subject to two periods o f P le isto cen e glaciation;
IlUnoian, and W isconsinan which deposited the main body of glacial
sedim ents.

Whether the Nebraskan and Kansan glaciation w as

active in Kalamazoo County is uncertain.

D rilling log s reveal the

presence of a so il profile which v ery often contains tr e e lo g s , brush
ste m s, muck or peat b ed s.

This s o il p rofile is not present e v e ry ­

w here, but it is found in a su fficien t number of p la c e s to e sta b lish
the fact that the glacial sed im en ts in Kalamazoo County w ere deposited
during m ore than one glacia l a g e .

Older g lacial d ep osits a re m ore

indurated and cem ented than the younger and may be separated from
them by w ell developed so il p ro file s or outwash d e p o sits.

10

The W isconsinan drift sh e e t is the youngest and b e st p r e se r v ed
of the P leisto cen e gla cial d e p o s its.

Its m orain es have a v e r y d is ­

tinct pattern reflectin g the lobate nature o f the ic e s h e e t s .

The

pattern r e v ea ls three W isconsinan lob es which invaded the Southern
Peninsula of M ichigan.
the low lands.

The c o u r se of each lobe w as con trolled by

The dominant o n e, the Lake M ichigan lo b e , follow ed

the Lake Michigan basin and p r esse d into Kalam azoo County in a
southeastwardly d ir e c tio n .

T his lobe w as r e sp o n sib le for the p resen t

surface topography of m ost o f Kalam azoo County.

It form ed a ll the

m orainic rid ges excep t for the north eastern part o f the Tekonsha
moraine which w as deposited by the Saginaw lobe (P la te 1).
The retreat of Lake M ichigan lobe w a s not u niform .

T here w ere

at lea st four m ain in terv a ls during w hich the ic e front w as sta tio n a r y .
This is evident from the a r e a l d istrib u tion o f the m ora in ic r id g e s .
The Tekonsha m orain es w ere form ed during the fir s t and e a r lie s t
halt of the Lake Michigan ice front.
deposited the Battle C reek m o r a in e s.

The second r e c e s s io n a l halt
Part o f th is discontinuous

system lie s in R o s s , P a v ilio n , and Brady T ow n sh ip s.

The third

halt form ed the m orainic b odies located in R ichlano, C ooper and
Prarie Ronde T ow nships.

The fourth, and perhaps the lo n g est s t i l l —

stand of ic e , form ed the K alam azoo m o ra in es which a r e one o f the
most highly developed m orainic r id g e s in the Southern P eninsula o f
Michigan (M artin, 1957).

T his one is com p osed of two w e ll-d e fin e d

11

ridges separated by a narrow , yet n ea rly continuous outwash apron.
The width of each ridge v a r ie s between one and four m ile s .
The Saginaw lobe followed the Saginaw Bay lowland and invaded
Kalamazoo County from the n orth east.

This ice produced the e a ste r n ­

most part of the Tekonsha m oraine and retrea ted fa ste r than the other
two lo b e s.

The third main lobe w as the E rie-H uron lo b e , which cam e

in along the E rie—Huron lowland and did not affect the p resen t topog­
raphy in the County (M azola, 1962).
B esid es the Kalamazoo and Tekonsha m o r a in e s, Kalam azoo
County is covered with outwash d ep o sits and ground m o r a in e s .

The

southeastern corner is c h a ra cterized by drum lins and is d isse c te d by
several sm all c r e e k s and unoccupied str e a m v a lle y s trending northeast-sou th w est.

T h ese channels rela te to the Kankakee torren t which

in early middle W isconsinan tim e drained a ll th ree ic e lob es in the
area of southern M ichigan and northern Indiana (Z um berg, 1960).
The bedrock in Kalam azoo County is im m ed iately o v erla in by a
relatively continuous layer o f d en se p la stic blue c la y with a lm o st no
grains larger than fine san d .

T his d ep osit is g en era lly th ick er at

locations of low bedrock topography and contians block s of Coldwater
shale.

It w as probably deposited by turbid ice-d arrm ed and s e m i-

stagnant w ater.
The P aleozoic bedrock form ation s underlying the g la c ia l d rift a re
formed of two u n its.

The o ld e s t, the C oldw ater sh a le o f M ississip p ia n

12

a g e f is the bedrock form ation in m o st of the County.

The M arshall

sandstone o v e r lie s the Coldwater sh ale in the northeastern co rn er of
the County though it has not been w ell d elin eated .

The Coldwater

shale is light co lo r e d , green ish to bluish black, becom ing san d ier
toward the top and gradually passin g upward into the M arshall sand­
stone.

It o cca sio n a lly contains lim esto n e bands or le n s e s o f M arsh a ll-

type sandstone.

The sh ale is r e la tiv ely im perm eable and is not known

to supply useable w ater in Kalamazoo County.

The M arshall sandstone

in quite fractured and perm eable and is used a s a ground w ater aquifer
in Kalamazoo County and e lsew h ere in M ichigan.

topography and followed m ajor bedrock v a lle y s .

Broad and sh allow

bedrock v a lley s w ere m ore e ffe c tiv e in con tro llin g the d ir e c tio n s o f
ice movement than narrow er and deep er v a lle y s (C h a m erlin , 1888).
Preglacial v a lley s trending in a lm o st the sa m e d ir e ctio n a s the ice
movement w ere m ore effectiv e in the channeling flow than th ose
trending at a n gles to it.

The e ffe c tiv e n e s s of bedrock topography in

controlling glacial m ovem ent a ls o depends on the th ick n ess o f the ice
m a ss.

Thick ice sh e e ts a re l e s s affected by bedrock topography than

thin on es.

A lso , th e o r etica lly ice m a s s e s o f m ore tem p erate g la c io -

thermal character a re m ore m obile and th eir m ovem en ts subsequently
more controlled by bedrock topography than ic e m a s s e s of m ore polar
geophysical ch a r a c ter .
Ice action g reatly m odified the p r e -p le isto c e n e bedrock landscape
in the region of the study.

D ifferen tial g la c ia l scou rin g affected

some a reas m ore than o th e r s .

Soft or jointed bedrock a r e a s a r e

gouged by ice to a g re a ter d egree than hard unjointed r o c k s .

A ls o ,

in periglacial conditions wedging activated by fr e ez in g o f w ater in
exposed bedrock join ts can prom ote future g la c ia l plucking o r m a ss
wastage along v a lley fla n k s.
Preglacial v a lle y s undergo the m ost s e v e r e geom orphic m od ifica­
tion as a resu lt o f g la c ia l a ctio n .

In a r e a s of continental gla cia tio n

tributary v a lley s trending norm al to the ic e front a r e o v errid d en ,
truncated and often d estro y e d .

Those p a ra lle l a r e gouged, w idened,

18

in te r io r .

The bedrock Is m o stly s h a le , sa n d s to n e , and c a r b o n a te .

T hese lith o lo g ies a r e folded and lo c a lly fa u lted .

T h eir d efo rm a tio n

was caused by region al s t r e s s e s , v e r tic a l co m p a ctio n o v e r buried
h ills in the b a se m e n t, faulting o f P r e c a m b r ia n b a se m e n t and s t r a in s
due to solu tion o f underlying w ea k er and m o re so lu b le b ed s (N ew co m b ,
1933; C oh ee, 1965).

Folding in the b ed rock fo r m a tio n s o c c u r s alon g

axial tr e n d s, the m o st prom inent o f w hich sh o w s a p r e v a ilin g north—
w e st-so u th ea st d ir e c tio n .
The p r e g la c ia l d rainage p attern in the S o u th ern P e n in su la and
surrounding a r e a s i s not fu lly u n d ersto o d .

Two h y p o th e se s p rop o sed

regarding p r e g la c ia l d rain age have been su m m a r iz e d by Fennem an
(1938), S p en cer (1 8 9 1 ), and H orberg and A n d erso n (1 9 5 6 ).

T hey

suggest that the p re g la c ia l d ra in a g e in the G reat L akes w as ea stw a rd
and em ptied into the S t . L aw rence R iv e r .

In C o n tr a st, Grabau

(1901) proposed a g en e r a l so u th w e ste r ly d rain ag e d isc h a r g in g into
the M ississip p i probably by way o f the p r e g la c ia l T e a y s v a lle y .
The fo rm er d rainage pattern im p lie s that s t r e a m s w e r e flow ing
into the southward advancing ic e f r o n t .

T h is would r e s u lt in dam ­

ming of drainage and the d evelo p m en t o f la r g e p e r ig la c ia l la k e s ,
with a llied c r o s s d rain age z o n e s and m any d ra in a g e r e v e r s a l s .
Mazola (1962) indicated that the p r e s e n c e o f a d e ep ly b u r ie d , c le a n ,
pebble—
free c la y in the g la c ia l d e p o s its o f th is a r e a is p o s s ib ly an
evidence o f the d rain age b lo c k a g e .

L e v e r e tt (1 8 9 9 ), A r e y (1 9 0 9 ),

19

and U dden, (1 9 0 0 ) s u g g e s t e d th at s i m i l a r c l a y s in Iowa r e p r e s e n t
quiet w a te r d e p o s its fo r m ed a f t e r s u b m e r g e n c e o f the r e g io n , a v ie w
which su p p o rts d a m m in g o f th e s t r e a m s .

B a in (1 8 9 7 ) b e l i e v e s th a t

th e se c la y s a r e c l o s e l y a s s o c ia t e d to l o e s s d e p o s it s and p r o b a b ly
rela ted to it .

A ld en and L eigh ton (1 9 1 9 ) and Kay (1 9 1 6 ) b e lie v e that

th ese c la y s r e s u lte d fro m c h e m ic a l le a c h in g and w e a th e r in g o f
Kansan and Illin o ia n t i l l s .
D r illin g in K alam azoo C ounty r e v e a ls the p r e s e n c e o f an a lm o s t
continuous la y e r o f b lu e c la y d ir e c t ly a b o v e th e b e d r o c k s u r f a c e .
There is no e v id e n c e o f v a r v in g o r s t r a t if ic a t io n in t h is c l a y la y e r .
H owever it c o n ta in s l e n s e s o f sand a n d /o r g r a v e l and in c lu d e s b lo c k s
of bedrock m a t e r ia l.

In s o m e b e d r o c k v a l l e y s , t h is c la y d e p o s it m a y

reach a th ic k n e s s o f 50 f e e t o r m o r e .

E v en in p la c e s w h e r e th e c la y

is co m p a r a tiv e ly th ic k , a g ra d u a l ch a n g e o f c la y to t i l l h a s not b e e n
o b se r v e d .

T h is in fo r m a tio n , p lu s the fa c t that th e c la y la y e r is

notably th ic k e r in b e d r o c k d e p r e s s i o n s , s u g g e s t s th at it m a y h ave
been d ep o sited under sta g n a n t ic e c o n d itio n s due to g la c ia l d a m m in g
or drainage and not due to le a c h in g o f o ld e r t i l l d e p o s i t s .

T he c la y

may a ls o be ou tw ash d e p o s it fo r m e d d u rin g a lo n g in te r v a l o f s t i l l
stand in the in itia l p h a se o f W isc o n sin a n g la c ia t io n .

In t h is c a s e

the c la y m ay be e r o d e d r o c k flo u r p ro d u ced d u rin g th e e a r l y g la c ia l
ad van ce.

20

Bedrock Channel D ep o sits a s Ground W ater A q u ifers
As p reviou sly sta te d , many bedrock ch an n els in o th er a r e a s
contain excep tion ally thick sand and g r a v e l d e p o sits w hich can be
developed into ground w ater a q u ife r s.

S o m e bedrock v a lle y s , how­

ev er, offer a better chance o f containing so rte d g la c ia l se d im e n ts
than o th ers.

G en era lly , the quality of g la c ia l se d im e n ts in a buried

bedrock channel depends on the follow ing:
1.

Age of g la cia l s e d im e n ts .

O l d e r g la c ia l d e p o sits a r e m ore

com pact and cem en ted than younger s e d im e n ts .
2.

D irection o f flow in the channel r e la tiv e to ice a d v a n c e s.
a.

Bedrock ch an n els w hich slo p e in the sa m e d ir e ctio n
a s the ic e advance se r v e d a s s lu ic e w a y s fo r m elt
w a ter,

in th is situ a tio n , the g la c ia l d e b r is tends to

have been so rted resu ltin g in e x c e lle n t ground w ater
a q u ifers (W ayne, 1956).

The exten t o f so r tin g and

quantity o f outw ash d e p o sits in th e se v a lle y s depend
on the duration of the period during w hich the channel
w as a ctiv e and the sed im en t load c a r r ie d by m e lt
w ater (H o rb erg , 1945).
b.

When the d ir e ctio n o f str e a m flow w a s toward the ic e
fron t, the str e a m channel b ecam e dam m ed and g la c ia l
la k e s d ev e lo p e d .

In th is situ a tio n the s tr e a m channel

is m o stly fille d with c la y s i l t , and m ud, thus form ing

a p o o r w a t e r b e a r in g m a t e r i a l ( M a z o la ,
M c G r a in ,

1962;

1948; W a y n e , 1 9 5 6 ).

P e r i g l a c i a l o r p r e g l a c i a l b e d r o c k c h a n n e l s , d e v e lo p e d
p a r a lle l to th e i c e fr o n t w h ile th e i c e fr o n t w a s
s t a t io n a r y , m a y r e m a in a s a c t i v e d r a in a g e c h a n n e ls
fo r a lo n g t i m e .

A c c o r d in g ly , t h e s e c h a n n e ls m a y

c o n ta in a p p r e c ia b le t h i c k n e s s e s o f w e l l —s o r t e d o u t w a s h .

24

of the gravity read in gs a g reed to w ithin 0 .2 s c a le d iv is io n s (about
0 .0 2 m g a ls).

The o b serv ed g ra v ity reading w a s obtained by a v e r ­

aging the co n siste n t r e a d in g s.
The m eter drift w as e stim a te d by reoccu p in g a s e le c t e d b a se
station every hour.

In ad d ition , g r a v ity r ea d in g s at two p r e v io u sly

occupied station s w ere repeated during e a c h hour to add e x tr a p r e ­
cision to the d rift c o r r e c tio n .

A b a se sta tio n (at the in te r s e c tio n o f

Texas D rive and 8th S tr e e t in K alam azoo County) and fo u rteen s u b bases w ere e sta b lish ed for the s u r v e y .

Reduction of F ield Data
The observed gravity r ea d in g s a r e not a b s o lu te , but r a th e r a r e
related to an a r b itr a r ily c h o se n v a lu e .

T h e se r e la tiv e rea d in g s

must be co rrected for v a r io u s in flu en cin g fa c to r s w hich have no
relation with su b su rfa ce g e o lo g y .

The v a lu e s o f th e se c o r r e c t io n s

can be accu ra tely ca lcu la ted and applied to the o b se r v e d r e a d in g .
The correction s are:

(1 ) latitude c o r r e c t io n , (2 ) f r e e —
a ir c o r r e c ­

tion, (3) Bouguer or m a s s c o r r e c t io n , and (4 ) te r r a in c o r r e c tio n .
The corrected g ravity rea d in g s a r e known a s the B ouguer g r a v ity
anomaly which is c a lcu la ted by the fo llo w in g equation:

Gb = Go + G f — G bc + Gt — G e
where
Gj-, is the B ouguer g r a v ity an om aly
G0 is the o b serv ed g r a v ity reading c o r r e c te d fo r m e te r d rift

25

Ge *s the latitude co rrectio n
is the m a ss co rrectio n
Gf is the f r e e -a ir co rrectio n
Gt is the terrain co rrectio n

Latitude Correction
The Earth's gravity field in c r e a se s from the equator to the p o le s .
This increase is caused by a gradual d e c r e a s e of the E arth's radius
and the centrifugal force which op p oses the E arth's gravitational
field from the equator to the p o le s .

The rate o f the gravity field

increase is 1.307 sin 2 9 m gals/W ule, w here 0 is the latitude.

The

area under investigation lie s between latitu d es 4 2 ° 05' and 4 2 ° 2 5 'N .
The corresponding rates of in c r e a se in the gravitational attraction
are 1.3017 and 1.3002 m g a ls /m ile r e s p e c tiv e ly .

The d ifferen ce

between the two rates is v e ry s m a ll, and their average of 1.301
m gals/m ile or 0.0002 464 m g a ls/fo o t w as a ssu m ed for the en tire
area.
The gravity station s w ere placed on the M ichigan coordinate
system established by the U. S . C oast and G eodetic S u rv ey .

A

base latitude was se le c te d at the southern border of Kalamazoo
County and the latitudes of the sta tio n s w ere related to it.

Mass Correction
The m ass or Bouguer c o r re c tio n co m p en sa tes for the g rav ita ­
tional effect of the m a ss e x istin g between the ground su rfa ce and

26

the datum.

The datum w as ch osen to be 700 feet above s e a le v e l

which is the low est su rface elev a tio n in the County.

The m a s s c o r ­

rection is computed from the equation:
Gbc = 2 Xyodh'
where V is the universal gravitational co n sta n t, /© is the overburden
density and dhr is the d ifferen ce betw een the datum and sta tion e le v a ­
tion.

A density of 2 . 15 g m /c c w as a ssu m ed for the overburden

m aterial.

The rationale behind th is s e le c tio n w ill be d isc u sse d in

detail in the section concerning d en sity c a lc u la tio n s.

Free-A ir C orrection
The fr e e -a ir co rrectio n c o m p en sa tes for the e ffe c t on the o b served
gravity readings of the variation o f su r fa c e elev a tio n at ob servatio n
points.

The rate of v e r tic a l g ra vity varia tion can be w ritten as:
= -0 .0 9 4 0 6 - 0 .0 0 0 7 C*o 24> m g a l s / f t . ; w here
0 is the latitude

and

is the rate of v e r tic a l g ravity v a r ia tio n .

The effect of latitude variation on

>9
is sm a ll and can be n eglected ;
3h

accordingly
= 0 .0 9 4 0 6 A h'm gals; w here
is the f r e e - a ir c o r r e c tio n and
Ah

is the d ifferen ce betw een sta tio n and datum e le v a tio n .

r
27

Terrain C orrection
in areas w here topography in the v ic in ity o f g r a v ity sta tio n s is
reasonably flat, the ap p lication of the in fin ite sla b form u la to e s t i ­
mate the m ass c o r r e c tio n is a d eq u a te.

H ow ever, in a r e a s w h ere

the topographic r e lie f is g r e a t , lo c a l topography can introduce
errors in the c a lcu la tio n s of th e se c o r r e c t io n s .

In th e s e a r e a s the

terrain correction i s needed to co m p en sa te fo r lo c a l topographic
effects.
The expected m axim um valu e for the te r r a in c o r r e c tio n is
negligible because su rv ey ed road s w e r e s e le c te d to avoid rough
topography.

This value w a s e stim a te d not to e x c e e d 0 .0 2 m g a ls

in the w estern part o f K alam azoo County w h ere the topography i s
rather com plex.

A s only v e r y few g r a v ity sta tio n s a r e ex p ected

to have terrain e ffe c ts req u irin g th is c o r r e c t io n , the te r r a in
correction is n e g le c ted .
After applying the above d is c u s s e d c o r r e c tio n s to the o b se r v e d
gravity read in gs, the r e su ltin g B ouguer g r a v ity v a lu e s w e r e co n ­
toured.

P lates 3a and 3b sh ow the r e su ltin g con tou r m ap s fo r both

the northern and sou th ern h a lf o f K alam azoo C ounty.

Sources of E r r o r s and A cc u r a cy
The accuracy o f reduced g r a v ity o b s e r v a tio n s d epends on the
magnitude of e r r o r s introduced in s u r fa c e e le v a tio n , and in the

28

t

gravity and latitude m e a su r e m en ts.

A ccuracy is a ls o affected by

the magnitude of the terrain effect which has been assu m ed to be
negligible, and by any significant e r r o r in the assum ed d en sity for
the glacial sedim ents form ing topography.
To examine the accu racy of the gravity o b se r v a tio n s, th irteen
gravity stations, each occupied tw ic e , w ere se le c te d so that the
two gravity observations at each location corresp ond to differen t
drift curves.

The standard deviation for th ese repeated sta tio n s w as

calculated to be 0 .0 2 3 m g a ls.
Surface elevation e r r o r s introduce subsequent e r r o r s in the
calculations of free air and m a ss c o r r e c tio n s .

In a r e a s of detailed

survey, surface elevation s w ere tied to bench m arks to within +
0.01 feet.

Assuming no e r r o r in elev a tio n s of bench m a r k s, the

above error in surface elevation introduces a subsequent e r r o r of
0.0066 mgals in the calculation of fr ee a ir and m a ss c o r r e c tio n s .
In the reconnaissance part of the s u r v e y , su rfa ce e lev a tio n s a re
accurate to + 0.1 of the contour interval of the United S ta te s Geolog­
ical Survey Topographic S h e e ts .
sheets is either 10 or 20 fe e t.

The contour interval in th e se

T h er e fo re , the e le v a tio n s are con­

sidered accurate within to + 2 .0 fe e t, which co rresp o n d s to an e r r o r
of + 0.132 m gals in the calcu la tio n s o f f r e e - a ir and m a s s - c o r r e c t io n s .
Latitude m easurem ents w ere perform ed on a base map having a
scale of 1:24,000.

Station loca tio n s a re accu rate to +50 fe e t.

The

Factors Controlling D en sities
Density m easurem ents on sam p les taken at different location s in a
geologic formation often reveal that the density of individual form a­
tions varies significantly both la tera lly and v e r tic a lly .

V ariations in

physical properties such as m ineralogy, p o ro sity , com p osition ,
degree of saturation, textu re, and d egree of cem entation, a re a ll
reflected in density variation s.

In r e la tiv ely hom ogeneous form ation s,

the range of density variations is usually sm a ll and an average density
can be easily adopted.
heterogeneous.

But other form ations may be ex trem ely

Thus, the use of an average density in gravity reduc­

tions can distort anom alies and lead to appreciable e r r o r s in inter­
pretation.

The extent of formation h eterogen eity is e sp e c ia lly

critical where the geologically interestin g gravity an om a lies a re of
low amplitude, i. e . , generally le s s than a few m illig a ls .
Glacial sedim ents are a typical exam ple of form ations which may
exhibit a wide spectrum of d en sity.

The pattern of this variation

can be very complex and difficult to p red ict.

A typical glacial deposit

may be composed of a poorly so r te d , inhom ogeneous till which is
made up of particles varying from a cla y to boulder s i z e .

The

boulders are usually randomly d isp ersed in a m atrix of a sm a lle r
size particles.

A s a result o f this conglom eration of different s i z e s ,

composition and textu res, the density o f till m aterial usually v a r ie s
within a rather wide range in contrast to glacial outwash d ep osits

w hich a r e m o r e s o r t e d and h o m o g e n e o u s .

T h e r e f o r e , g la c ia l

outw ash is e x p e c te d to s h o w a m o r e u n ifo r m d e n s i t y .

O u tw a sh

d e p o s its , h o w e v e r , a r e u s u a lly l e n t i c u l a r a n d s e l d o m h a v e g r e a t
la te r a l or v e r t ic a l d i m e n s i o n s .
A ls o , th e e f f e c t o f w a t e r ta b le d e p th c a n b e s i g n i f i c a n t on th e
la tera l d e n s ity v a r ia t io n in g l a c i a l s e d i m e n t s .

T he th ic k n e s s o f

g la c ia l s e d im e n ts ly in g a b o v e w a t e r t a b le in K a la m a z o o C o u n ty
v a r ie s b etw e e n z e r o and o n e h u n d red f e e t .

S i n c e th e d e n s i t y o f

porous s e d im e n t s i n c r e a s e s w ith th e d e g r e e o f w a t e r s a t u r a t i o n ,
la te r a l v a r ia tio n in t h i c k n e s s o f th e g l a c i a l s e d i m e n t a r y s e c t i o n
above the w a te r ta b le i s e x p e c t e d t o c a u s e c o r r e s p o n d i n g l a t e r a l
va ria tio n in d e n s it y .

T h e o r d e r o f m a g n itu d e o f d e n s i t y v a r ia t io n

a s a r e su lt o f s a t u r a t io n c a n b e r e a l i z e d b y n o tin g th a t d r y s a n d s
with tw enty p e r c e n t p o r o s i t y upon s a t u r a t io n s h o w 0 . 2 g m / c c
in c r e a se in d e n s it y .

Published D e n s it ie s
A r e v ie w o f lit e r a t u r e c o n c e r n in g d e s i t y r a n g e s o f d if f e r e n t r o c k
types g iv e s a q u a n tita tiv e p e r s p e c t i v e t o th e p r e c e d in g d i s c u s s i o n
(M anger, 1963; B ir c h ,

1 9 4 2 ).

F o r e x a m p l e , in F ig u r e 2 , w h ic h i s

adapted fr o m B ir c h ( 1 9 4 2 ) by G r a n t an d W e s t ( 1 9 6 5 ) , i n d i c a t e s th a t
d en sity o f s o il and a ll u v ia l m a t e r i a l r a n g e s f r o m
sto n e s from 2 . 0 to 2 . 7 an d s h a l e s f r o m

1 .6 to 2 . 2 ; s a n d ­

1 .9 0 to 2 . 8 g m / c c .

T h is

33

1

03

1

1

\

--------- SOIL AMD A LLUV AL
--------- SANDSTONE
-------- SHALES
----------LIMESTONE! 1

i

\

.

\

I \
t
1

/

0.1

1

1
I__

1
1
1
1
1

iL
V

\

•

\

/
Y

/
1 1
/

/
f

JX

L

•t

\

I

J

\
v
i 1 \
1
\
i
,l

1

1

1
1
T “ K

A

4-1

i

\

/

*

""T

N

V
\
t
\

r

D EN SITY

r _

V
'

G /C M *

FIGURE 2 HISTOGRAM OF SMALL SPECIMEN BULK
DENSITIES OF VARIOUS KINDS OF SEDIMENTARY
ROCKS, fFROM BIRCH (1942) 8Y GRANT AND WEST
(I965)j

34

figure also suggests an extensive den sity overlap among a ll the
sedimentary groups.

Part of this overlap probably r e su lts from

the fact that these rock d en sities a re plotted without regard to age
or depth of burial.
Glacial sedim ents exhibit a sim ila r d en sity d istrib u tion .

A

typical section of glacial sed im en ts may be form ed of outwash or
till deposits, or both.

The outwash or till se c tio n s are usually

formed of thin layers or le n se s of intercalated sand, s i l t , c la y ,
gravel, or mixtures of each apparently arranged at rnadom .

The

density variation produced by such random distribution together
with the possible density variation within the individual sed im en ts
themselves produce a com plex la tera l density variation pattern in
the glacial sedim ents.

To illu str a te , Hall and Hajnal (1962) con­

ducted laboratory density m easurem en ts on d rill c o re sa m p les of
glacial sediments obtained from two t e s t h o les located near
Kindersley, Saskatchewan, Canada.

The r e su lts of th eir m ea su re­

ments are shown in Table 1 .
Table 2 shows a tabulation of d e n sitie s obtained from sa m p les
collected from eighteen d rill c o r e s taken from te st d rillin g near
Two Hills, Alberta, Canada, and in the neighborhood o f Saskatchew an
River (Lennex and C arlson , 1967).

The d e n sitie s of s i l t , sand,

sandstone, and shale are nearly the s a m e .
seems to be appreciable higher.

The density o f till

H ow ever, th ese d e n sitie s a re based

35

Material

D ensity
g m /c c

clay

2 .0

till

2 .1 0 -2 .2 0

silt

1 *80

sand

1•90—
2 . 15

Table 1. Density of glacial sedim ents near K in d ersley, Saskatchew an,
Canada (after Hall and Hajnal, 1962).

Material
silt

Average Saturated D ensity
g m /c c
1.99

N o. of S am p les
3

sandstone

2 .0 0

6

sand

2 .0 4

2

shale

2 .0 5

2

till

2 .2 5

5

Table 2. Density of Sedim ents near Two H ills , Alberta
(after Lennox and C arlson , 1967)

on a very limited number of sam p les and may not be rep resen tative
Of the sedimentary rock types and glacia l d ep osits in the cited a r e a s ,
nor indeed in the area of the present con cern .

Methods of Density Determination
Introduction
The reduction and quantitative interpretation o f gravity
observations requires prior knowledge o f d e n sitie s o f various

36

subsurface form ation s.

The r e lia b ility of gra v ity findings is

largely dependent on the a cc u r a cy with w hich th e se d e n s itie s
are determ ined.

D e fin ite ly , in situ d en sity ca lc u la tio n s give

the best re su lts b ecau se the m ea su rem en ts are c a r r ie d out on
rock sam p les in their natural situ a tio n .

Such m ethods a s

borehole den sity loggin g, N ettleton 's p r o file , variab le d e n sity ,
together with a su ggested method p resen ted below and r eferred
to a s the g r a v ity -g eo lo g ic m ethod, a r e e x a m p les of a vaila b le
techniques for in situ rock d en sity c a lcu la tio n .

Laboratory P ro ced u res for M easuring D e n sitie s
Laboratory d en sity m ea su rem en ts c o n s is t o f ca lcu la tin g the
volume and w eight o f rock sa m p le s obtained by an appropriate
sampling technique.

The procedure is not w ell su ited to uncon­

solidated rocks sin c e the a c q u isitio n , handling, and transportation
of sam ples often disturb them and lead to ch an ges in th eir
physical p r o p e r tie s.

In so m e c a s e s , d en sity m ea su r em en ts a re

preformed on sa m p le s taken at regular in terv a ls in a form ation.
The resulting d e n sitie s a r e then used to ca lcu la te a w eighted
average density o r a sm oothed d ep th -d en sity function.
Commonly, the laboratory m ethods a re used to d eterm in e an
average density for overburden from sa m p le s r e s tr ic te d to su r fa ce

37

outcrops of the form ation.

H ow ever, in g la cia l and g la c io -flu v ia l

material differential com p action , cem en tation and satu ration can
lead to an in crea se of d en sity with depth (A thy, 1930).

To obtain

a representative d en sity o f overburden th is method req u ire s a
considerable amount of sa m p lin g , a la rge number of m e a su r e m e n ts,
and a sampling technique which m in im iz e s sam p le d istu rb a n ce.

Density P rofile Methods
Nettleton's p rofile method in v o lv es ca lcu latin g an overburden
density from gravity rea d in g s.

The e stim a ted d en sity r e p r e se n ts

the density of m a terial constituting the topographic fe a tu r e .

The

procedure c o n s is ts o f taking c lo s e ly -s p a c e d g ra vity readings o ver

a selected topographic fe a tu r e.

Then the gravity read in gs a r e

reduced using different p o ssib le d en sity v a lu es for the m a teria l
forming topography.

The a verag e d en sity o f the overburden is

selected to be the one which g iv e s the le a s t c o r re la tio n betw een
the Bouguer gravity and topography.
The topographic fea tu res em ployed in N ettleton 's method should
not be associated with a stru ctu ra l fe a tu re.

In other w o r d s, the

topographic feature used in th is com putation should not be one
which is anom alous in its physical p r o p e r tie s .

A lso , the r e lie f

of the feature should be ap p recia b le s o that accu rate d en sity
calculations can be a c h ie v e d .

M o r eo v e r, the regional g ra vity

38

surface must be s im p le .

The gravity sta tio n s should be located

along a rela tiv ely straigh t line a c r o s s the fea tu r e, th eir e le v a ­
tions should be m easured a c c u r a te ly , and terra in c o r r e c tio n s
perform ed.
Although th is method d eterm in es the a verage d en sity o f the
m aterial forming the topographic r e lie f , it d oes not give inform a­
tion a s to the density of rocks below the lev el o f the lo w e st point
of topography ( Vaj k , 1956).
Obviously, the Nettleton method req u ires much lab or and
r e lie s on personal judgem ent to determ in e the d en sity em p ir­
ica lly .

To circum vent the drawbacks of the p ro file m ethod,

Siegert (1942) suggested a le a s t square method o f calcu latin g
overburden d e n sitie s.

He a ssu m ed that the o b serv ed gravity

reading along a r e la tiv ely short segm en t o f the p rofile vary
linearly with d ista n ce.

This assu m ed lin ea r ity p er m its the

determination of interpolated gravity and su rfa ce elev atio n at a
station from the straigh t lin e s drawn through the ob served gravity
and surface elevations o f two sta tio n s on e ith e r sid e of the d e sig ­
nated station.

The sa m e p r o c e ss of interpolation is perform ed

on each station of the p r o file .

If g^ and h^ a re the d iffer en ce s

between the interpolated and m easured v a lu es o*1 ob served g rav ity
and elevation at station i then gj = - k hf w here k is the com bined
free air and m ass fa cto r.

The above m athem atical form ulation

9

39

demands that k is chosen so a s to make

(g^ - k h^)^ a m inim um ,

isi
where n is the number of gravity sta tion s along the p r o file .

The

least square procedure is applied to determ ine the value o f k
which makes the gravity profile a s sm ooth a s p o ss ib le .

T his value

of k is readily then converted to the overburden d en sity .

Variable Density Approach
The application of an average den sity is ju stified in situ ation s
where the expected e r r o r due to variab ility of d en sity is n egligib le
when compared with the amplitude of the an om a lies of in te r e s t.
In many applications, the anom alies under investigation have a
low amplitude, thus e r r o r s introduced because of abnorm ally high
density variations may be of su fficien t am plitude to sev en ty d isto rt
or even mask the actual a n o m a lie s.

The se a r c h for Niagaran

reefs in Michigan by gravity provides an exam ple of such a situ a­
tion.

Some of the m ost o il-p r o lific r e e fs do not exceed se v e r a l

tens of feet in th ic k n e ss.
of a few thousand fe e t.

They are buried under an overburden

The gravity a n o m alies a sso c ia te d with

these reefs seldom exceed an am plitude of 0 .3 m g a ls.

In th ese

ca ses if the density of the m aterial form ing the topography v a r ie s
0,1 g m /cc from the se lec ted a v e r a g e, the actual an om alies w ill
be distorted by 0 .1 3 m gals in a r e a s w here a su rfa ce topographic
relief of 100 feet e x is t s .

T his is an appreciable e r r o r com pared

40

to the exp ected a n o m a ly .
The approach o f u sin g a v a r ia b le d e n s ity in the re d u ctio n o f
gravity data h as not r e c e iv e d a s m uch a tte n tio n a s it r e a lly
d eserv es.

Only th ree p a p e r s d e a lin g w ith the s u b je c t a r e known

to the author.

Vajk (1 9 5 6 ) d e m o n str a te d th e n e c e s s it y o f u sin g

a variable d e n sity under c e r ta in c o n d itio n s , h o w e v er he did not
suggest a d efin ite p ro ced u re for c a lc u la tin g the v a r ia b le d e n s it y .
Grant and E lsa h a rty (1 9 6 2 ) c a lc u la te d the v a r ia b le d e n s ity by
m inim izing the c o r r e la t io n s b etw een s u r f a c e e le v a tio n and
Bouguer g ra v ity r e s id u a ls w hich w e r e e x tr a c te d fr o m the B ou gu er
gravity and e le v a tio n s u r f a c e s by a p p r o x im a tin g the r e g io n a l
trends by p o ly n o m ia ls u sin g the m ethod o f le a s t s q u a r e s .

D e n s ity

resid u als at individual s ta tio n s w e r e c a lc u la te d to r e d u c e the
correlation betw een s u r fa c e e le v a tio n and B ou gu er g r a v ity
r e sid u a ls.

T h ese d e n sity r e s id u a ls w e r e added to an a s s u m e d

average d en sity to obtain the v a r ia b le d e n s i t i e s .
This method o f c a lc u la tin g a v a r ia b le d e n s ity m a y p rod u ce
erroneous d e n sity v a lu e s due to the a m b ig u ity o f the p oten tia l
field used in the c a lc u la tio n .

The e r r o r s in c a lc u la te d d e n s it ie s

are expected to be r e la t iv e ly high w hen d e e p ly b u ried m a s s e s
produce g ra v ity a n o m a lie s o f id e n tic a l w idth to chose produced
by lateral d e n sity ch a n g e s in s u r f a c e s e d im e n t s .

It is a ls o

obvious that the g ra v ita tio n a l e f f e c t p roduced by la te r a l v a r ia tio n s

41

in density of su rface se d im e n ts, and the su rfa ce elevation
residuals are determ ined by approxim ating the regional e ffe c ts
by polynomials; a method which takes o b jectiv ity .

Human judge­

ment and experience g reatly influence the outcom e o f the com pu­
tations .
Merritt (1968) su ggested a method of calculating a variab le
density of overburden m aterial by u tilizing ob served g rav ity and
elevation readings.

All sta tio n s located within a predeterm ined

radius of a center station w ere used to calcu late the overburden
density at the station .

The coord in ates of a ll the sta tio n s in each

station group w ere calculated rela tive to the co ord in ates o f the
center station.

The observed gravity v alu es of sta tio n s surround­

ing and including the cen ter station w ere approxim ated with a
polynomial equation.

The polynom ial is a fir s t d eg ree function

of the station elev a tio n , and a

f ir s t , th ird , or fifth d eg ree

function of the station co o rd in a tes.
degree polynomial equation is

For e x a m p le, the fir st

e x p r e sse d as:

gp = ao f a i X xi + a2 S ^ i “ a 3 £ hi
where
gp is the predicted observed g ra v ity ,
is the polynom ial c o e ffic ie n t.
Xj and y^ relative station co o rd in a tes,
and hi is the station elevation with referen ce to the datum .

The

function g p i s c h o s e n s u c h th a t I t g Q - 9 p ]^ i s a m in im u m , w h e r e
gQ is the m easured ob serv ed g r a v ity .

The le a s t square c o e ffic ie n t

associated with the eleva tion te r m is u tilized to c a lc u la te the
overburden d en sity at the c e n te r s ta tio n .

The d e n s itie s obtained by

applying this method g r e a tly depend on the grid radius em p lo y ed .
If a unique den sity pattern is to be c h o se n , a m ethod m ust be d e v ise d
to determ ine the optimum grid ra d iu s.

G eophysical-G eological Method
The method p resen ted here for ca lcu la tin g rock d e n s itie s
is sim ila r to the approach su g g e ste d by Legge (1 9 4 4 ).

He noted

that the Bouguer g ravity anom aly can be r ep resen ted by

where G| is the Bouguer gra v ity anom aly at sta tio n i
aj£ is the polynom ial c o e ffic ie n t
Xj and y^ a re the x and y co o rd in a te s o f sta tio n i.
The Bouguer gravity anom aly a ls o can b e w ritten a s follow s:

9B i = 9i + k ht
where
t

hi is th e d iff e r e n c e b e tw e e n th e s t a tio n e'.ev a tio n and
datum
9B i i s th e B o u g u e r g r a v ity a n o m a ly
k i s th e c o m b in e d m a s s and f r e e - a i r fa c to r

g i i s th e la titu d e c o r r e c t e d o b s e r v e d g r a v it y .

43

The least square principle dem ands that:
N
,
^ [(g. + khi) i= 1

n

j = O

. g
x (J
]

m

/=

= a m inim um .

0

Legge's method is m odified h ere s o that the a vailab le g eo lo g ic
information could be utilized a s additional control in ca lcu latin g
an average density for both the g la cia l se d im e n ts and b edrock.
The geologic information c o n s is ts of the th ic k n e ss e s o f gla cial
and bedrock sedim ents at 256 te s t hole lo ca tio n s a ssu m in g a datum
of 300 feet above sea le v e l.

For each w ell lo ca tio n , a ssu m e that

is the thickness of gla cial se d im e n ts, w hile

r e p r e se n ts the

thickness of bedrock m aterial above the ch osen datum .

Let us

assume, a lso , that the Bouguer g ra vity anom aly can be w ritten as:
n
m

where

is the Bouguer gravity anom aly at t e s t hole i
is a polynom ial c o e ffic ien t
and y. a re the location coord in a tes o f t e s t hole i .
*
4

The mass or Bouguer co rre ctio n which should be added to the
free-air anomaly to obtain the Bouguer gravity anom aly can be
written as:
K f^ h +^ H )
where

K = constant

P \ and /°2 are the d e n sitie s o f g la cia l and bedrock s e d im e n ts,

re s p e c tiv e ly .

44

A ccordingly, we can w r ite
9Bi = 9o1 ' K (n

^ + /*»> Hi)

where gQ| is the f r e e - a ir anom aly at t e s t hole i .

The le a s t

square principle dem ands that:

z

[ goi - K ( ^ h t + /*> Ht ) -

2
$ xi 'A )

= a m inim um

rO

where N rep resen ts the total number o f t e s t h o le s .

T h is

equation is a fir st d eg ree function o f the th ic k n e ss o f the g la c ia l
and bedrock sed im en ts above the datum .

D ividing each te r m o f

the equation by K, the le a s t sq u are c o e ffic ie n t o f hj and
the glacial and bedrock a v era g e d e n s itie s d ir e c t ly .

y ie ld

D en sity

values w ere computed for up to fourth d e g r e e function o f the
station co o rd in a tes.
The elevation datum w as ch o sen to be the lo w e st known
bedrock elev a tio n .

F r e e - a ir a n o m a lie s at t e s t h o le s w here

direct gravity o b serv a tio n s w ere not made w ere ca lcu la ted by
interpolation from a p r e v io u sly com p iled Bouguer g ra v ity contour
map using an arbitra. ily c h o s e n d e n sity o f 2 .1 5 g m / c c .
This method w as applied to a ll e x istin g te s t h o le s which
reached or penetrated the bedrock su r fa c e and the r e s u lts a r e
shown in Table 3 .

th is table sh ow s the d e n s itie s o f g la c ia l and

bedrock sedim ents corresp on d in g to a reg io n a l trend r e p r e se n ta ­
tion of up to the fourth d eg ree p o ly n o m ia l.

A lso show n a r e the

45

su m s o f th e s q u a r e d r e s i d u a l s .

1 st

4 th

2n d

3rd

1 .9 0

1 .9 5

2 . 15

2 .0 9

/°2 g m / c c ( b e d r o c k s e d i m e n t s ) 2 . 0 8

1 .9 5

2 .4 3

2 .3 0

248

156

130

D e g r e e o f P o ly n o m ia l
/° 1 g m /c c ( g l a c i a l s e d i m e n t s )

Sum o f s q u a r e d r e s i d u a l s
Table 3 .

435

D e n s it y v a l u e s r e s u l t i n g f r o m a p p ly in g th e g e o p h y s i c a l g e o l o g i c a l m e th o d to a l l t e s t h o l e s in K a la m a z o o C o u n t y .

It i s a p p a r e n t f r o m T a b le 3 th a t f a i r l y r e a s o n a b l e d e n s i t y
v a lu e s w e r e o b ta in e d b y u s in g a t h ir d d e g r e e f u n c t io n o f th e x
and y c o o r d i n a t e s .

T h e fo u r th d e g r e e fu n c t io n r e p r e s e n t a t i o n

r e su lte d in a n a b n o r m a ll y lo w b e d r o c k d e n s i t y w h i le t h e s u m o f
the r e s id u a ls i s th e l o w e s t .
T a b le 4 s h o w s th a t th e r e s u l t s w h ic h w e r e o b t a in e d w h e n
c a lc u la tio n s w e r e s t r i c t e d to 2 5 t e s t h o l e s c h o s e n in a r e a s
c o v e r e d w ith t i l l ty p e g l a c i a l s e d i m e n t s .

M ost o f th e s e w e lls

a r e lo c a te d in th e K a la m a z o o M o r a i n e .

D e g r e e o f P o ly n o m ia l

1 st

2n d

3rd

4 th

2 .4 4

2 . 16

1 .9 5

2 . 10

g m /c c (b e d r o c k s e d im e n t s ) 2 .9 5

2 .2 9

1 .9 8

2 .0 8

0 .2 6

0 .0 6

0 .0 2

A*| g m / c c ( g l a c i a l s e d i m e n t s )

Sum s o f sq u a red r e s id u a ls
Table 4 .

0 .5 6

D e n s it y v a l u e s o b t a in e d b y a p p ly in g th e g e o p h y s i c a l —
g e o l o g i c a l m e th o d t o t e s t h o l e s l o c a t e d in a r e a s
c o v e r e d w it h t i l l d e p o s i t s .

The first d egree r e p r ese n ta tio n in x and y o f the B ouguer
gravity produced d e n sity e s t im a t e s w hich ap p ear

to be in b e st

agreement with v a lu e s an ticip ated from p r e v io u s s t u d ie s .
e v e r,

How­

the sum o f the sq u ared r e s id u a ls is la r g e r than that obtained

from the higher d eg ree e q u a tio n s.

To fu rth er in v e stia g e the

extent of density dependence on the type o f g la c ia l se d im e n t,
Kalamazoo County w as divided into s e v e r a l o verlap p in g a r e a s
depending on the nature o f s u r fa c e g la c ia l d e p o s it s .

The a r e a s

were also delineated to in su re that enough r e lie f on the b ed rock
surface existed within ea ch a r e a (m in im u m o f 50 fe e t) to a llo w
a reliable estim a te o f d e n s it ie s .

T he r e s u l t s , h o w e v e r , did not

show a coherent rela tio n sh ip betw een the d e n s itie s obtained and
the type of glacial d e p o sit.
The failure of the m ethod m ay be accou n ted fo r by the lim ite d
data and the interpolation p r o c e s s em p loy ed to obtain g r a v ity
values at test hole lo ca tio n s w here d ir e c t g r a v ity o b se r v a tio n s
were not availab le.

A ls o , the p olyn om ial r e p r e s e n ta tio n o f the

Bouguer gravity anom aly m ay not e lim in a te the r e g io n a l e f f e c t s

quantitatively.
The assumption that K-j (^ ih | +Z32 ^ i) r e p r e s e n t the g r a v ita ­
tional effect of both the bedrock and g la c ia l s e d im e n ts ab ove the
(latum implies that topography o f the ground and b ed ro ck s u r fa c e s
are sufficiently horizontal that g la c ia l and b ed rock s e d im e n ts

47

above the d a tu m c a n b e r e p r e s e n t e d b y in f in it e s l a b s .

H ow ever,

in c a s e s w h e r e th e b e d r o c k and s u r f a c e to p o g r a p h y e x h ib it c o n ­
sid era b le r e l i e f th e in f in it e s l a b a s s u m p t io n m a y le a d to e r r o n e o u s
r e s u lts .

In t h e s e s i t u a t i o n s , a n a l t e r n a t i v e p r o c e d u r e i s s u g g e s t e d

based on a m e th o d d e v is e d by T a lw a n i, e t a l ( 1 9 5 9 ) f o r th e c a l c u l a ­
tion o f the g r a v it a t io n a l e f f e c t o f i r r e g u l a r tw o d im e n s i o n a l b o d i e s .
The c r o s s s e c t i o n o f th e d r if t and b e d r o c k l a y e r s a r e a p p r o x im a t e d
by p o ly g o n s a s s h o w n in F ig u r e 3 .

T h e c o m b in e d g r a v it a t io n a l

e ffe c t o f th e g l a c i a l a n d b e d r o c k m a t e r i a l a b o v e th e d a tu m c a n b e
w ritten a s;
f , ( X , Z )/® !

+

f2 ( X , Z ) ^

w here f^ ( X , Z ) and fg ( X , Z ) a r e th e g r a v it a t io n a l e f f e c t s o f g l a c i a l
and b e d r o c k l a y e r s r e s p e c t i v e l y a s s u m i n g a d e n s i t y o f 1 .O g m / c c .
I
Z p+ !
They ca n be e x p r e s s e d a s :
f ( X ,Z ) = 2
( a p +bp
p = i
* -

w h e re

ap =

XP +1

~ *jp

Zp+1

— Zp

bp = Xp Z p + i
Zp + )

_

X p +1 Z p
Zp

In t h e s e e q u a t io n s ( F i g u r e 3 ) p r * e p r e se n ts th e p o ly g o n s i d e
n u m b e r, X and Z a r e t h e c o o r d i n a t e s o f p o ly g o n c o r n e r s .
su m m a tio n i s c a r r i e d o v e r th e [ s i d e s o f t h e P o ly g o n .

The

A c c o r d in g ly ,

the le a s t s q u a r e p r in c ip l e d e m a n d s that:
1= N

>
i * 1

.

tgoi-Lfi (x,z)

n

m

+ f2 cx.z)^] 21 21 ajk
j= o

i

k 2

yi 1 =

k=o

a m in im u m w h e r e g 0 ^ i s th e f r e e —a i r g r a v it y a n o m a ly a t w e l l

48

■IDBQClt

SEDIMENTS
______________

FIGURE

3

_Otp»*p)___

__________

POLYGON REPRESENTATION
OF
AND
BEDROCK
SEDIMENTS

DATUM____

GLACIAL

49

number i and other sym b ols are a s defined a b o v e .

The ch oice o f

a density of unity for the d en sity o f both the g la cia l and bedrock
sediments in calculating f-, (X ,Z ) and f2 (X ,Z ) m akes th eir le a st
square coefficients equal the d en sity o f the g la cia l and bedrock
sedim ents.

This modified approach has been applied to profile P

shown in Plate 2a which is esta b lish ed by six w e lls .

The profile

is located in Com stock and Kalamazoo Townships w here the su r fa c e
sediments are m ostly outwash g la cia l d e p o s its .

Table 5 show s

the densities calculated by fitting p olynom ials of up to the fourth
degree to the Bouguer gravity an om ly.

/° 1

Degree of polynomial

1st

2nd

3rd

4th

gm /cc (glacial sed im en ts)

1.80

1 .9 0

2 .2 7

1 .43

g m /cc (bedrock sed im en ts) 1 .7 0

2 . 16

2 .6 0

1 .76

1 .9 4

0 .9 5

0 .5 5

Sum of squares of resid u als
Table 5 .

1 0 .50

D en sities of bedrock and g la cia l se d im e n ts obtained by
approximating the two d im ensional g la cia l and bedrock
m a sse s by polygons.

The third degree polynom ial is shown to yield the b e st d en sity
values.

It is a ls o c le a r that the fourth d eg ree polynom ial, w hile

showing the sm a lle st su m s o f the square of the r e s id u a ls , does
not yield r e a listic d e n s itie s .
Attempting to a ssig n an av erage den sity to the g la cia l and
bedrock sedim ents using the above liste d r e su lts ap p ears to be

50

a risky v en tu re.

The sum o f the sq u a re s o f the r esid u a ls cannot

be used a s c r ite r io n for se le c tin g the m ost suitable equation to
represent the regional e ffe c t.

The d en sity v a lu es corresponding

to the sm a lle st sum o f the sq u a res o f the re sid u a ls in m ost c a s e s
do not fall within the known range of d en sity va ria tio n .

A cco rd in gly,

a reasonable average den sity w as se le c te d for the g la cia l and bed­
rock m a te r ia ls, based on published d ata.

Unconsolidated san d ,

gravel, and cla y d ep o sits u su ally have a d en sity ranging between
1.9 and 2 .1 g m /c c depending on com p action , cem en tation and the
degree of satu ratio n .

T ill m a te r ia ls , on the other hand, have

generally higher d e n sitie s which vary betw een 2 .1 to 2 .3 g m /c c .
An average d en sity of 2 .1 5 g m /c c w as assu m ed for the g la cia l
sedim ents b ecau se se d im e n ts could be till or outwash type d ep o sits
or a combination of both.

T his value la y s m idway between the

normal density o f the till m ateria l and that of sa n d , g r a v e l, and
clay d e p o sits.

T his d en sity value a ls o w as determ ined by K lasner

(1963) using N ettleton 's p rofile method in the New Haven, M ichigan
area which is im m ed iately to the w e st of Kalam azoo County.

The

use o f two sep a rate d en sity valu es in the reduction o f g ravity data
depending on whether we are dealing with a r e a s co v ered with till
or outwash d ep o sits appears v er y ap p ealin g.

H ow ever, g la cia l

deposits often change nature at d ep th s, and u n le ss proven oth er­
w is e , the use o f an av era ge d en sity s e e m s to be s a f e s t .

The density o f the C oldw ater sh a le w a s a ssu m e d to be 2 .5 5 g m / c c .
This value w as obtained by lab oratory m e a su r e m e n ts at the D epart­
ment o f Geology o f M ichigan S ta te U n iv e r sity and a p p e a r s to be a
reasonable e s t im a t e .

CHAPTER

VI

REGIONAL AND RESIDUALS

Introduction
One of the m ost unfortunate facts about geop h ysical m ethods of
exploration is that the m ea su rem en ts a re not v e r y s e le c tiv e in
nature.

Consequently they portray not only the d istribution and

physical c h a r a c te r istic s o f fea tu res of in te r e s t, but a ls o anom alous
bodies creating m easu reab le e ffe c ts at the point o f m ea su rem en t.
Surface inhom ogeneities and random reading e r r o r s often add to
the com plexity o f the situ a tio n .

The ex tra ctio n of the anom aly of

interest from th is com plex sp ectru m o f overlapping e ffe c ts i s ,
therefore, a c r itic a l and c e rta in ly frustrating task en tru sted to
the geo p h y sicist.

Much of th is fru stration has been laid upon the

ambiguity inherent in the m athem atical rep resen tation of the
potential fie ld .

T his fact hoc been pointed out s e v e r a l tim e s in

literature (S k e e ls , 1947; N ettleton , 1954).

Conventional Methods of Isolation R esiduals
The developm ent of techniques for extractin g resid u al g ravity
effects from the total e ffe c ts has been the su b ject of in ten sive study
for the la st s e v e r a l d e c a d e s.

S e v e r a l m ethods have been su g g ested
52

fo r

this purpose.

In th is connection, two com p lem en tary te r m s

have been introduced in literatu re; the "regional" and " resid u al" .
The "regional" or trend (G rant, 1954) is defined a s the Bouguer
gravity value which would have been obtained had the a n o m a lies
of interest been a b sen t.

The a n o m a lies of in te r e st a r e ca lled

"residuals" and are obtained by subtracting the regional from the
Bouguer gravity.

T h e re fo re , depending on what we define a s

residual, numerous regional valu es can be obtained, and v ic e v e r s a .
The term "regional" by it s e lf has no m eaning u n le ss the exp ected
anomalies are co m p letely defined.
From the p ractical point of v ie w , the regional is often recogn ized
as those smooth broad v aria tion s which have low cu rv a tu r e , su g­
gesting deep-seated d istu r b a n c e s.

A d m itted ly, th is definition o f

the regional could be m isle a d in g .
The e a r lie st method of regional elim in a tion w as by contour o r
profile sm oothing.

The ju stifica tio n of th is procedure is that the

smooth variations a re attributed to anom alous m a s s e s which are
considered to be too deep o r broad to be of in te r e st for ex p lo ra tio n .
This is the m ost em p irica l approach o f defining the r e g io n a l.

T his

method may be useful in p articu lar c a s e s when the ''egional is sim p le
and has a uniform gradient.

H ow ever, in a r e a s w here the regional

is complex, the method b eco m es v e r y d ifficu lt to apply (N ettleto n ,

54

A m ore refined v e r sio n o f the above m ethod is often ca lle d " c r o s s
profiling” .

T his in v olves plotting g ra v ity p r o file s in a netw ork of

intersecting lin e s .

The sp a cin g o f th e se lin e s and th e ir orien tation

depends on the d e g ree of co m p lex ity and trend of the r e g io n a l.

The

advantage of the c r o s s p ro filin g m ethod is that the region al v a lu e s
at each point o f in te r se c tio n have to be the sa m e fo r the two in te r ­
secting p r o file s by adjusting and m odifying the region al c u r v e s .
This method is s t ill e m p ir ic a l and can lead to e r r o n e o u s r e s u lt s .

It

is sim ila r to the method of d ir e c t contour o r p ro file sm oothing
except that the c r o s s p rofilin g m ethod is done along two s e t s of p ro­
f ile s .

This ex tra d im en sio n m ay im prove the a c c u r a c y o f e stim a tin g

the region al, e s p e c ia lly in c a s e s w h ere the region al is ra th er co m ­
plicated .
To evaluate c r o s s p rofilin g a s a method o f elim in a tin g the
regional gravity trend and producing g r a v ity r e sid u a ls in d ica tiv e o f
bedrock topography, the m ethod w as applied to the B ouguer g ra v ity
map of Kalamazoo County ( P la t e s 3 a , 3 b ).

One s e t o f p a r a lle l pro­

files w as esta b lish e d in the n o r th e a st-so u th w e st d ir e c tio n p a r a lle l
to the general Bouguer g ra v ity g ra d ien t.

The seco n d s e t o f p a r a lle l

profiles w as taken norm al to the f i r s t , w ith the sp a cin g betw een
lines estab lish ed at about th re e m ile s in both s e t of lin e s .

A fter the

cro ss profile rou tin es w ere c o m p le te d , the resid u a l g r a v ity v a lu e s
at 39 randomly ch o sen te s t h o le s w e r e plotted v e r s u s bedrock

elevation (Figure 4 ).

The s e le c tio n o f the 39 te s t h oles w as per­

formed by drawing at random , ten percen t of the te s t h o les of each
township with a minimum o f two h oles from each Tow nship.

Figure

4 shows that the sc a tte r of points on eith e r sid e of the le a st square
line is appreciable.

A value of 0 .2 1 w as obtained for the co r re la tio n

coefficient, resulting in a co effic ie n t o f determ ination of 0 .0 4 indi­
cating that only 4 percent of the ob served variation s o f the g ra vity
residuals obtained by c r o s s profiling is attributed to bedrock topog­
raphy.

A test of sig n ifica n ce at the 5% and 1% le v e ls in d icates that

the above correlation c o e ffic ie n t d o es not d iffer from z e r o .

The

points in Figure 4 which a r e en closed in sq u a r e s rep resen t m axim um
negative deviation from the le a s t square lin e s .

M ost o f th e se points

correspond to te s t h oles located o v er v ery prom inent, broad, r e la ­
tively low Bouguer gravity a n o m a lies which are caused by deep
seated m ass d istrib u tio n s.

O bviously, the c r o s s p ro file method did

not remove these an o m alies co m p letely and the r e sid u a ls w ere
accordingly low er than ex p ected .

S im ila r ly , the c ir c le d points of

Figure 4 show anom alously higher v a lu e s o f r e s id u a ls .

T hese points

correspond to te s t h oles located o v er aprom inent broad gravity high
which was not co m p letely elim inated a s a regional e f fe c t .

A cco rd -

ingly, m ost o f the sc a tte r of points in F igure 4 in d icates that the
cro ss profile method can produce d istorted g ravity r e sid u a ls in
terms of this a n a ly s is .

To produce m eaningful r e sid u a ls by applying

56

1.0

oo

0.0

-to

B.0

RESNMJAL

IN

MOALS

-to

SRAVfTY

-4 0

•0 0
TOO
•00
BEDROCK ELEVATION IN FEET ABOVE SEA LEVEL
500

FIBURE 4 — RELATION BETWEEN CROBB PROFILE
RESIDUALS C p ,) AND BEDROCK ELEVATION ( E )

the cross profile m ethod, the in terp reter m ust be fa m ilia r with
the geology of the a r e a .

A lso , he should know the approxim ate

amplitude, width and shape of gravity a n o m a lies which are to be
defined as r e sid u a ls.
All the methods o f contour or p rofile sm oothing depend on the
experience and judgement of the in te r p r e te r .

In e x tr em ely co m p li­

cated situations, different in terp reters might a rriv e at totally
different regional m aps.
The apparent inadequacy o f the sm oothing technique has led
various workers to the other approaches for regional evaluation.
These techinques w ere designed in such a way that the in ter p r e te r's
judgement is rem oved, as much a s p o s s ib le , from affectin g the
outcome of the regional ca lcu la tio n s.

Griffin (1949) su ggested

defining the regional a s the weighted mean o f the ob served v a lu es
at a number of points in the surrounding a r e a .

Using cy lin d rica l

coordinates he defined the regional according to the following
equation:
G-

where G is the regional and g ( r ,9 ) is a gravity value at a point
on a circle of radius

r centered at the data point.

that this approach elim in ates human b ia s.

He pointed out

P e te r s (1949) and

Elkins (1951) indicated that the residual obtained by applying th is
rc^thod could be equivalent to the second d e r iv a tiv e .

N ettleton (1954),

58

Swartz (1954) Dean (1959), and Ray and Jain (1961) indicated that
the approach leads to different r e su lts depending on the grid spacing
and the formula u sed .

It is apparent that human judgem ent is not

completely elim inated because the ch oice of the grid configuration
and dimension is not based on any th eo retica l co n sid eration .
In addition to the sm oothing and griding m ethods of calculating the
regional, a group of analytical methods has been introduced in the
geophysical litera tu re.

T hese methods commanded a great deal of

popularity in recent y e a r s .

The polynom ial approxim ation o f the

regional by the method of lea st sq u ares has proved to be one o f the
most popular of analytical m ethods.

The e a r lie s t v e r sio n w as

employed by Numerov (1929) on gravity data obtained over a la k e.
He assum ed the regional to be a fir s t d eg ree polynom ial o f the form
a + bh + dy + cx; where x and y are C artesian co o rd in a tes, h is the
depth of water in the la k e, and the co n sta n ts, a , b, c , and d are
determined by the le a st square m ethod.

A gocs (1951) dem onstrated

the applicability of the method for the rem oval of a plane regional
superimposed on the gravitational e ffe c t of a sp h e r e .

He rem arked

that the method can be used to approxim ate a m ore com plicated
regional by using a higher o rd er polynom ial.
a higher order polynom ial.

Sim pson (1954) used

He conceded that large am plitude local

anomalies or blunders in observation s could lead to local u n r ea listic
estim ates of the reg io n a l.

59

While the idea of using polynom ials s e e m s to keep human bias at a
minimum, som e assum ptions have to be made a s to the p ro p erties or
behavior of the raw data.

T hese assu m p tion s are usually em ployed to

establish checks and co n tro ls through which the equation that best
fits the data can be s e le c te d .

It is usually assu m ed that the re sid u a ls

occur at random and that p ositive and negative local d isturban ces have
about equal probability of o c c u r re n c e.

T h erefo re, the sum o f r e sid ­

uals should be a m inim um .
In the traditional way of executing the le a st square fitting o f a
polynomial, a low order polynom ial equation is in itia lly u se d , and
the least square method is applied to ca lcu late the c o e ffic ie n ts .
More term s are then added to produce a higher o rd er equation which
is subjected again to the le a st square a n a ly s is .

T his p r o c e ss of add­

ing more term s and calculating c o e ffic ie n ts is usually repeated until
a polynomial equation which produces a minim um sum o f the squared
values of resid u als is obtained.
to several polynomial eq u ation s.

O bviously, certa in te r m s are com m on
The co effic ie n t of each one of th ese

term s is determ ined once for each equation in which it e x is t s because
the coefficient o f a certain term m ay depend on the polynom ial equa­
tion in which it e x is t s .

To avoid the added labor of calculating the

coefficient of som e te r m s se v e r a l t im e s , the approach can be m odi­
fied in such a way that the e ffec t o f any term in the polynom ial can
be separately investigated so that, step by ste p , a check o f the goodness

60

of fit can be a c h ie v e d .

T his approach w a s d e sc r ib e d by Oldham and

Sutherland (1955), and Grant (1 9 5 7 ), who a ssu m e d a r eg io n a l equa­
tion of the form:
G = t)Qp0 + b ip-j + .................................................................+t>nPj
where the
and

*s a r e p o ly n o m ia ls in x and y , the b 's a r e c o e f f ic ie n t s ,

being of d eg ree j .
= O when j*k.

values of x and y .

The p o ly n o m ia ls a r e d eterm in ed s o that

The su m m ation is taken o v e r a ll the o ccu p ied

T h is m odified v e r s io n is s u p e r io r to the co n v en ­

tional polynomial approxim ation b ec a u se the c o e ffic ie n ts and the
standard e r r o r a re independent of the d e g r e e o f the polynom ial fitte d .
The com putations can be c a r r ie d out fa s te r and w ith l e s s la b o r .

T h is

is e sp e c ia lly advantageous in c a s e o f high d e g r e e p o ly n o m ia ls.
The re sid u a ls obtained by fitting a polynom ial to the reg io n a l a r e
not particularly su ited for quantitative in te r p r e ta tio n .

The s t a t i s ­

tical b a sis behind the method a s s u m e s that the a v e r a g e valu e o f the
residual is z e r o .

In oth er w o r d s , the p ro b ab ility o f o c c u r r e n c e o f

positive and negative r e sid u a ls is eq u a l.

In the m a jo r ity o f actu al

c a s e s , this assu m p tion s e e m s to be hardly te n a b le .

When w e , fo r

exam ple, w ish to d elin ea te p r e g a lc ia l v a lle y s o r lo ca te s a lt d o m e s ,
we are expecting to com pute a reg io n a l w hich w ill y ie ld p red o m i­
nately negative r e s id u a ls .
The extraction o f gra v ity r e sid u a ls by approxim ating the region al
gravity trend by a polynom ial applying the m ethod o f le a s t s q u a r e s

performed on the B ouguer g r a v ity m ap o f K alam azoo C ounty.
Th# gravity r e sid u a ls co r re sp o n d in g to the fifth and se v e n th d e g r e e
polynomial rep resen ta tio n of the reg io n a l w e r e c a lc u la te d at the 39
test hole locations d e sc r ib e d in the d is c u s s io n o f the c r o s s p r o file
method.

These resid u al v a lu e s plotted v e r s u s b ed rock e le v a tio n s

and the results a re shown in F ig u r e s 5 and

6

w hich c o r r e sp o n d

respectively to the fifth and se v e n th d e g r e e p olyn om ial r e g io n a l.
It is apparent that F igure 5 d is p la y s l e s s s c a t t e r o f p oin ts than
Figure

6

.

This is a ls o apparent from the v a lu e s o f the c o r r e la tio n

coefficients of 0 .4 4 for the fifth and 0 .3 4 fo r the se v e n th d e g r e e
polynomial rep resen tation of the r e g io n a l.

The c o r re sp o n d in g

coefficients of d eterm in a tio n s a r e 0 .1 9 and 0 . 12 r e s p e c t iv e ly .
These values of the c o e ffic ie n t o f d e te r m in a tio n s a ls o in d ica te th a t,
in this study, the g ra v ity r e s id u a ls obtained by ap p roxim atin g the
regional trend by p o ly n o m ia ls is s u p e r io r to th o se from c r o s s p ro ­
filing in reflecting bedrock top ograp h y.

T e s ts o f s ig n ific a n c e o f

the correlation at the 5% le v e l in d ic a te s that the c o r r e la tio n b etw een
bedrock elevations and p olyn om ial r e s id u a ls is s ig n ific a n t.

At the

1%level the c o r r e la tio n b etw een fifth d e g r e e p olyn om ial r e s id u a ls
and bedrock e le v a tio n s is sig n ific a n t w h ile the se v e n th d e g r e e p o ly ­
nomial residuals a r e not sig n ific a n tly c o r r e la te d to b ed ro ck e le v a ­
tions.

The deviations o f the r e s id u a ls fro m the le a s t sq u a r e lin e s

in Figures 5 and

6

in d ic a te s that the m ethod o f r e p r e s e n tin g the

naglonal trend by polynom ial a n a ly s is o ften r e s u lt s in d isto r te d

IN MGALS
RESI0UAL8
GRAVITY
500
600
700
800
BEDROCK ELEVATION IN FEET ABOVE SEA LEVEL
FIGURE 5 RELATION B ETW EEN F IF T H D E G R E E POLY­
NOMIAL RESIDUALS (g R ) AND BEDROCK ELEVATION (E).

OO

05

OO

06

9R4VITY

RESIDUALS

IN

00

900
600
700
600
500
BEDROCK ELEVATION IN FEET ABOVE 8EA LEVEL
FIGURE 6 - RELATION BETWEEN SEVENTH DEGREE
POLYNOMIAL R E SID U A L S (g R ) AND BEDROCK
ELEVATION ( E ) . _______________________________________

64

residuals as in the c a s e o f the c r o s s p r o file r e s id u a l.
The above d isc u ssio n co n cern in g the a v a ila b le m ethods fo r the
e x t r a c t i o n of the resid u a l an om aly from the o b se r v e d potential f ie ld ,

point out that, although the m ethods a r e num erou s and d iv e r s if ie d ,
none of them s e e m s to o ffe r a to ta lly o b je ctiv e r e s id u a ls .
some are m ore o b jective than o t h e r s .
tive and e m p ir ic a l.

H o w ev er,

The grid m eth od s a r e s u b je c ­

The lab elin g o f th e ir r e s u lts a s r e s id u a ls is

questionable.
The polynomial ap p roxim ation o f the regio n al m ay lead to a m ore
realistic evaluation o f the region al than the grid m e th o d s, e s p e c ia lly
in situations w here the region al is s im p le and can be r e p r e se n te d by
a low degree p olyn om ial.

In m o st c a s e s , h o w e v e r , the resid u a l pat­

tern obtained is only su ited for lo ca tin g tr en d s ra th er than fo r quan­
titative interpretation.
The c r o ss-p r o filin g m ethod is g e n e r a lly favored in producing the
most re a listic r e s id u a ls , e s p e c ia lly when the in te r p r e te r h as a fa ir ly
thorough knowledge o f the su b su r fa c e g e o lo g y o f the a r e a , and par­
ticularly, of the stru ctu re he is e x p lo r in g .

Geologic Residual G ravity A nom aly
The above d is c u s sio n d e m o n str a te s the fact that g r a v ity r e s id u a ls
obtained by em ploying any o f the d e sc r ib e d m eth od s can be e x tr e m e ly
inaccurate in defining the b edrock top ograp h y.

The a p p lica tio n of

these resid u als in ca lcu la tin g the d im e n sio n s and d epths o f m a s s

65

distributions ch aracterized by sm a ll am plitude a n o m a lie s in a r e a s
of c o m p le x regional gravity m ay lead to e rro n eo u s r e s u lt s .

The

a c c u r a c y of the r e su lts is c e rta in to be enhanced when known geology

is incorporated.

It is the goal o f th is su g g ested method to apply the

geologic information av ailab le in K alam azoo County, and the o b served
Bouguer gravity in calculating g ravity regional and resid u a l e f f e c t s .
The available geologic inform ation c o n s is ts of 256 te s t h o le s reach ­
ing or penetrating the bedrock su rfa ce tog eth er with 50 additional te s t
holes which penetrated a co n sid era b le th ic k n e ss o f g la c ia l s e d im e n ts .
To apply this m ethod, it is e s s e n tia l to a ssu m e that the regional
gravity effect is broad, and the te s t h o le s a r e located s o that the
interpolation of calculated regional g ra vity at te s t hole lo ca tio n s
completely defines the regional g ravity e ff e c t.

The a ssu m p tion that

the regional effect is sim p le and regional a n o m a lie s rather broad is
justified because the regional a n o m a lie s a r e cau sed by d e e p e r , and
generally broader d en sity v aria tion s in the P a le o z o ic se c tio n and
underlying ro ck s.
The regional gravity e ffe c t at a s p e c ific location is h ere defined
as the observed Bouguer g rav ity which would be obtained had the
bedrock m ateria l, above a datum , been rep laced by g la c ia l s e d i­
ments. The datum w as ch o sen to be the lo w est e le v a tio n point on
the bedrock su rface in Kalam azoo County, and is 300 fe e t above s e a
level. A ccordingly, the resid u a l Bouguer g ra v ity anom aly is defined
as the gravitational effec t of the su rp lu s m a ss due to the e x is te n c e o f

d e n s e r

bedrock above datum e le v a tio n r a th er than g la c ia l s e d im e n t s .

To illustrate the m e th o d , le t u s a s s u m e that at a s p e c if ic t e s t h ole
location^,
a

n

d

/® 2

and

H a r e the d®n s i t i e s artd t h ic k n e s s e s o f g la c ia l

bedrock sed im en ts r e s p e c t iv e ly (F ig u r e 7 ) .

At th is lo c a tio n the

surplus mass caused by the p r e s e n c e o f H fe e t o f b ed ro ck m a te r ia l
instead of glacial se d im e n ts c o n tr ib u te s
to the gravity reading.
Bouguer gravity.

g = 2fTtf H

( /° 2

“

) m illig a ls

T h is e f fe c t h e r e d efin ed a s the r e sid u a l

F or a c o n sta n t d e n sity c o n t r a s t , the r e sid u a l

Bouguer gravity is d ir e c tly p rop ortion al to the th ic k n e s s o f the bed­
rock section above the a ssu m e d datum e le v a t io n .

The reg io n a l

Bouguer gravity at the lo c a tio n is obtained by su b tr a c tin g th e r e s id u a l
Bouguer gravity from the o b se r v e d B ou gu er g r a v ity .

It m u st be

emphasized here that the su r p lu s m a s s e f fe c t o r r e sid u a l B ou gu er
gravity is alw ays p o sitiv e a s lon g a s H is p o s it iv e .

H o w e v e r , in

locations where bedrock s u r fa c e i s b elo w the a s s u m e d datum e le v a ­
tion, H is negative and the r e sid u a l B ou gu er g r a v ity a ls o i s n e g a tiv e .
A density c o n tra st o f 0 . 4 g m /c c w a s a s s u m e d fo r the d e n sity
contrast C ^ 2 ~

and the reg io n a l g r a v ity e f f e c t at e a c h t e s t h o le

location w as ca lcu la ted a s d e s c r ib e d a b o v e .

T he r e g io n a l v a lu e s

which w ere com puted at w e ll lo c a tio n s w e r e in terp o la ted to d e fin e
the regional s u r f a c e .

A su ita b le a p p roach w ould be to fit a p o ly ­

nomial using the m ethod of le a s t sq u a re to the r e g io n a l v a lu e s o r to
contour them d ir e c t ly .

D ir e c t co n to u rin g w a s s e le c t e d b e c a u s e

r
67

GLACIAL DAIFT

BEDROCK SURFACE
* *•

BEDROCK

FRURE 7

MODEL

ILLUSTRATING

RESIDUAL

GRAVITY

THE

CALCULATION

ANOMALY

OF

GEOLOGIC

68

many te st h o le s , not reach ing b ed ro ck , have been em ployed a s ex tr a
control in the contouring p r o c e s s .

The m axim um depth o f p en etra­

tion of th ese t e s t h o le s w as u sed in the sa m e m anner to c a lc u la te a
minimum value o f the region al w hich w as used a s a regio n al con ­
touring g u id e.

The B ouguer gra v ity v a lu e s at the t e s t hole lo ca tio n s

were computed from d ir e c t g r a v im e tr ic read in gs o r interpolated from
the Bouguer gra v ity contour m ap.

The g ra v ity reg io n a l contour map

was em ployed to e stim a te the g ra v ity region al at e v e r y g ra v ity s ta tio n .
The gravity region al value w a s su b tra cted from the B ouguer g ra v ity
anomaly value at each g ra v ity sta tio n to produce the r esid u a l g ra v ity
anomaly v a lu e.

T h ese w ere contoured to produce the r e sid u a l g r a v ity

contour map show n in P la te s 4a and 4 b .
mgals was s e le c t e d .

A contour in terval o f 0 .2

The c o n v e r sio n o f r esid u a l g r a v ity to bedrock

elevation can be ach ieved usin g the follow in g equation:

EB = g R / f 2 t f > C / ° 2 -

^1>]+

D

where
9R is the value o f the r esid u a l g r a v ity at a g r a v ity sta tio n
y is the u n iv ersa l g rav itation a l con sta n t
D
/® 2

is the ch o sen datum ele v a tio n (300 fe et above s e a le v e l)

“ ^°i *s the d en sity c o n tr a st betw een bedrock and g la c ia l
se d im e n ts ( 0 .4 g m /c c )
E g is bedrock e le v a tio n r e la tiv e to s e a le v e l.

It is apparent from th is eauation that a r esid u a l valu e o f z e r o r e p r e ­
sents a bedrock ele v a tio n o f 300 fe e t above s e a l e v e l .

P o sitiv e and

69

ttve residual valu es rep resen t bedrock elev a tio n s g re a ter o r le s s
i^apectively.

Bedrock elev a tio n s w ere calculated a t each gravity

gMtton and contoured to obtain the bedrock topography map (P la te s 5 ,
Ǥ*and

6

b).

Because of the density of the glacial d rift in particular may vary
■Considerably, the ex p ressio n (

Aj) is a lso expected to v a r y .

The

.^effect of this variation on the accu ra cy o f the method of calculating
' gravity residuals depends on the range o f d en sity v a riation .

In a r e a s

where local density co n tra sts a re m ore than the a ssu m ed 0 .4 g m /c c ,
calculated bedrock elev ation s a r e expected to be higher than true
'values, and vice v e r s a .
The assum ption that the bedrock upper su rfa ce is a gently 'undulating
Surface to ju stify the approxim ation o f bedrock m a s s e s by infinite
•labs, is another p o ssib le sou rce of e r r o r .

G lacial e r o sio n certa in ly

Smoothed and reduced the r e lie f on the bedrock su rface; y e t, som e
glaciated v a lle y s may have su fficien tly ste ep s id e s to im pair the
validity of the assu m p tion .

To evaluate the e ffe c t of an irregu lar

k

bomplex bedrock su rface on the a ccu ra cy of our c a lc u la tio n s, le t us
gwsume a situation a s shown in Figure 7 .
The glacial drift is shown to o v erla y a flat bedrock su rface excep t
the p resen ce of a bedrock ch an n el.

Suppose that the elevation

the bedrock su r fa c e is to be calculated at points A , B , C , D , and
employing the residual gravity v a lu es at each location .

The e r r o r s

In tro d u c e d in the c a lc u la tio n s o f the r e g io n a l, r e s id u a l, and b ed rock

elevations at any point betw een A and E can be exp la in ed a s fo llo w s:
( 1 ) At point A lo ca ted at a la r g e d ista n c e from the edge o f the v a lle y ,
the errors introduced a r e in sig n ific a n t.

(2 ) At B , d ir e c tly above the

edge of the v a lle y , the e r r o r is ex p ected to be m a x im u m .

Its m agn i­

tude depends on the d ep th , and the s t e e p n e s s o f the v a lle y s i d e s .

The

application of the in fin ite sla b fo rm u la to the r e s id u a ls in th is lo c a tio n
to calculate bedrock e le v a tio n im p lie s that the v a lle y is n e g le c te d .
The presence o f the v a lle y r e n d e r s the va lu e o f the r e sid u a l g r a v ity
at location B l e s s than w hat it would be in the a b se n c e o f the v a lle y .
Therefore, the a p p lica tio n o f the in fin ite sla b form u la to c a lc u la te
the bedrock e le v a tio n s at B from the r e sid u a l g r a v ity va lu e r e s u lt s
in bedrock e lev a tio n w hich a r e l e s s than the tru e v a lu e s .
the error is a ls o m a x im u m .

(3 ) At D ,

The in fin ite sla b a ssu m p tio n im p lie s

the absence o f the b ed rock m a te r ia l ab ove the v a lle y f lo o r .

The

presence of su ch m a te r ia l r e n d e r s the r e sid u a l g r a v ity at lo ca tio n
D more than its valu e if the bedrock m a te r ia l ab ove the v a lle y flo o r
was absent.

T h e r e fo r e , at lo c a tio n D , the c a lc u la te d b ed ro ck e l e ­

vation is expected to be h ig h er than the a ctu a l v a lu e s .

(4 ) A s we

move towards E , the e r r o r s d e c r e a s e until th ey r e a c h a m inim um
at the cen ter of the v a lle y .

(5 ) At lo c a tio n C betw een B and D , the

absolute value o f the e r r o r is l e s s than that at e ith e r p o in t, B o r D .
In this region applying the in fin ite s la b fo rm u la im p lie s that w e a r e

71

a d d in g the bedrock m a s s la b eled

1

and at the s a m e t im e , ign o rin g

the presence of the m a s s la b eled 2 (d o tted ).

The two e r r o r s red u ce

each others e ffe c t, and the net r e s u lt is a s m a lle r e r r o r .

At a c e r -

1

tain location C , betw een B and D , the g ra v ita tio n a l e ff e c t o f the added
mass is equal to that o f the ig n ored m a s s , and the net e r r o r is z e r o .
Because the number two m a s s is a lw a y s c l o s e r to the s u r fa c e than
f

mass number o n e, point C is a lw a y s c l o s e r to B than D .
The magnitude o f e r r o r s introduced in the c a lc u la tio n s o f bed­
rock topography by applying the in fin ite s la b form u la in a r e a s o f
complex bedrock topography ca n be v is u a liz e d by a m o d el stu d y .
The model em ployed i s show n in the upper right hand s id e o f
Figure

8

.

The m odel in d ic a te s a fla t-la y in g b ed rock s u r fa c e m odi­

fied by a ste e p -sid e d b ed ro ck c h a n n e l.
valley sid es w as a ssu m e d to be

1 0

The s lo p e o f the b ed ro ck

° and it s flo o r w idth

The glacial se d im e n ts w e r e a ss u m e d to be

1 0 0

1 0 0 0

fe e t.

fe e t th ick and the

valley depth was v a r ied betw een 25 and 125 f e e t , at 25 fe e t in te r ­
vals.

For each v a lle y d ep th , the g r a v ita tio n a l e f f e c t r e s u ltin g

from the e x c e s s m a s s produced by the p r e s e n c e o f b ed ro ck s e d i­
ments instead o f g la c ia l s e d im e n ts above the datum w a s c a lc u la te d
at several su r fa ce s ta tio n s u sin g the m ethod su g g e ste d by T a lw a n i,
at al (1959).

U sing a d e n sity c o n tr a s t o f 0 .4 0 g m / c c , t h e s e g r a v i-

tational valu es c o r re sp o n d to w hat h a s b een defin ed e a r l i e r a s the
residual Bouguer a n o m a ly .

The s u g g e s te d ap p roach fo r c a lc u la tin g

AXIS

0*0

GLACIAL SEDIMENTS
•EOMOCl
1000 FT

h= 1 0 0

FEET
u.

UO

-0.5
0-5

. _

A X I S ( D I S T A N C E FROM MID
P O I N T OF S L O P I N O
I N T E R F A C E IN K I L O F E E T )

20

FIGURE 8

ERRORS IN CALCULATING THE TH IC K N ESS
OF BEDROCK SEDIMENT8 ABOVE DATUM USING
THE INFINITE SLAB FORMULA

the bedrock e le v a tio n fr o m the r e s id u a ls w a s th en a p p lie d to e a c h
r e s i d u a l value at e a c h s u r f a c e s t a t io n .

The e r r o r s in tro d u ced in the

calculations o f b ed ro ck e le v a t io n s fr o m th e g r a v it y r e s id u a ls by
applying the in fin ite sla b fo r m u la w a s o b ta in ed a t e a c h s u r f a c e s t a ­
tion by su b tractin g the known b e d r o c k e le v a t io n s at e a c h s u r f a c e
s t a t i o n (r e la tiv e to datum D) fr o m th e c a lc u la t e d v a lu e s .

F ig u r e

8

shows the m a g n itu d es o f the e r r o r s in t e r m s o f d is t a n c e fr o m m id ­
p o in t on the s id e o f the b e d r o c k c h a n n e l.

A s d is c u s s e d a b o v e , th e

g r a p h s show that the e r r o r s in c a lc u la tin g b e d r o c k e le v a t io n s fr o m

the residual g r a v ity v a lu e s a r e m in im u m a t g r e a t d is t a n c e fr o m the

adga of the v a lle y and a p p r o x im a te ly h a lf w a y down i t s s i d e s .

E rrors

a r a , h o w ev er, m a x im u m at th e u p p er and lo w e r p o in ts on th e v a lle y
s id e s .
To d em o n stra te the s u p e r io r it y o f t h is g e o lo g ic m eth od o f is o l a t —
ing gravity r e s id u a ls r e f le c t in g b e d r o c k to p o g r a p h y , th e 39 t e s t
holes p r e v io u sly u se d to e v a lu a te th e r e s id u a l m a p s w e r e a s s u m e d
nonexistent.

The r e g io n a l g r a v ity v a lu e s a t e a c h o n e o f t h o s e t e s t

holes w as e s tim a te d by in te r p o la tin g the r e g io n a l g r a v it y v a lu e s
obtained by the g e o lo g ic m eth od a t th e su r r o u n d in g t e s t h o l e s .

T he

Interpolated r e g io n a l g r a v ity v a lu e a t e a c h t e s t h o le w a s s u b tr a c te d
from the c o r r e sp o n d in g B o u g u e r g r a v it y v a lu e s to ob tain r e s id u a l

g ra v ity v a lu e s .

T h e s e r e s id u a l g r a v it y v a lu e s a r e p lo tte d v e r s u s

b sd ro c k e le v a tio n in F ig u r e 9 .

T h is fig u r e s h o w s th a t the p o in ts in

■

1

*

500
600
700
800
BEDROCK ELEVATION IN FEET ABOVE SEA LEVEL
FIGURE 9 - RELATION BETW EEN GEOLOGIC
RESIDUAL BOUGUER GRAVITY (gR ) AND
BEDROCK ELEVATION (E ) .

75

the graph exh ib it a p p r e c ia b ly l e s s s c a t t e r around the le a s t s q u a r e s
line tf»n th ose in F ig u r e s 4 , 5 and

6

.

A c o e ffic ie n t o f d eterm in a tio n

of 0.83 was ca lcu la te d fo r the p oin ts o f F ig u re 9 .

The c o r r e la tio n

between bedrock e le v a tio n s and g e o lo g ic r e sid u a l B ouguer g r a v ity
is highly sig n ifica n t at the 1% le v e l.

T h is sh o w s that the g e o lo g ic

method is far s u p e r io r to the m ethods o f c r o s s p ro filin g and p oly­
nomial approxim ation o f r e g io n a ls by the m ethod o f le a s t sq u a r e in
producing resid u a l g r a v ity v a lu e s w hich r e fle c t b ed rock topography.
Most of the points in F ig u re 9 w hich sh ow a p p r e c ia b le d ev ia tio n from
the least sq u a r e s lin e c o r re sp o n d to t e s t h o le s lo ca ted in a r e a s w h ere
additional bedrock c o n tr o l is v e r y s c a r c e .

The r eg io n a l v a lu e s a t

these test h o les w e r e thus obtained by in terp olatin g fro m reg io n a l
gravity values located a t la r g e d is ta n c e s fro m the t e s t h ole s i t e s .

CHAPTER

VII

D ISC U SSIO N O F R E S U L T S

B o u g u er Gravity A nom aly

Tire Bouguer g ra v ity a n o m a ly con to u r m ap o f K alam azoo County
is shown in P la te s 3 a and 3 b .

A s m en tion ed p r e v io u s ly , a d e n s ity

of 2.15 g m /c c w as a ssu m e d for the g la c ia l s e d im e n t and an e le v a tio n
of 700 feet above s e a le v e l w a s taken a s the d atu m .

The B o u g u er

gravity contour map r e p r e s e n ts the g r a v ita tio n a l e ffe c t o f a ll d i s ­
turbing m a sse s beneath the ground s u r f a c e .

T h e se e f f e c t s in clude

lateral density v a ria tio n and the lo c a l th ick en in g and thinning w ithin
the glacial s e d im e n ts , and the e f f e c t o f str u c tu r e and d e n s ity v a r ia ­
tions in the P a le o z o ic s e c t io n and b a se m e n t c o m p le x .
The Bouguer g r a v ity a n o m a ly m a p s e x h ib it the fo llo w in g broad
features:
1.

A general n o r th e a s t-s o u th w e s t g ra d ien t o f rou gh ly 0 . 8
m a g ls /m ile is a p p a re n t, w ith v a lu e in c r e a s in g to th e so u th .

2.

A gravity high is c e n te r e d in the so u th w e ste r n c o r n e r o f
Com stock T ow n sh ip .

It e x te n d s e a stw a r d a c r o s s c e n tr a l

C harleston T ow nsh ip to the e a s t e r n b o r d e r o f th e c o u n ty .
This g r a v ity high s e e m s to d is a p p e a r to w a r d s the w e s t in
76

77

west cen tra l K a la m a zo o T o w n sh ip , due to the p r e s e n c e o f
a bedrock c h a n n e l.

It b e c o m e s n o t ic e a b le a g a in in s e c t io n

22 and b ro a d en s in O sth e m o and A la m a T o w n s h ip s .
3

.

A prom inent g r a v ity high c o v e r s P r a ir i e R o n d e, S c h o o l­

cra ft, and the s o u th e r n h a lf o f P o r ta g e and T e x a s T o w n s h ip s .
This g r a v ity high tr e n d s n o r th -n o r th w e s t and d is p la y s it s
stron gest e x p r e s s io n in N o r th w e s t S c h o o lc r a f t T o w n s h ip .
4.

A gravity high is lo c a te d a t the s o u t h e a s t e r n c o r n e r o f th e
County and a p p e a r s to e x te n d s o u th e a s tw a r d in to C alh ou n
and S t . J o se p h C o u n tie s .

5.

A prom inent a r e a w h e r e th e g e n e r a l B o u g u e r g r a v it y g r a d ­
ient is v e r y lo w tr e n d s n o r t h w e s t - s o u t h e a s t fr o m th e
northern b o u n d a r ie s o f R ich a ln d and C o o p e r to c e n t r a l R ic h ­
land and C h a r le s to n T o w n s h ip s .

It c r o s s e s th e K a la m a z o o

County lin e at th e s o u t h e a s t e r n c o r n e r o f C h a r le s t o n T ow n­
sh ip .

In t h is a r e a a b ro ad lo w a n o m a ly s e e m s to be r e s p o n ­

sib le fo r c a n c e llin g o r g r e a t ly r e d u c in g th e lo c a l g r a v it y
g r a d ien t.

T h is fe a tu r e c o in c id e s w ith a v e r y p r o m in e n t lo w

in the to ta l m a g n e tic f i e l d .
6

.

A g r a v ity lo w c e n t e r e d in e a s t —
c e n t r a l C lim a x T o w n sh ip
exten d s e a s tw a r d a c r o s s so u th P a v ilio n and s w in g s to the
n o rth w est in P o r ta g e T o w n sh ip .

F r o m t h e r e , it e x te n d s

w estw a rd c r o s s i n g th e c o u n ty lin e in w e s t T e x a s T o w n sh ip .

I

r
I

78

Most of the a n o m a lie s d isc u sse d above g e n e r a lly have c o r r e ­
sponding magnetic a n o m a lie s (H in ze, 1963).

T h is c o r r e la tio n is

very important in identifying the c a u sa tiv e b o d ies of th e se a n o m a lie s
and the isolation o f g ra v ity r e s id u a ls .

The g la c ia l and P a le o z o ic

sediments are known to have little or no m agnetic e f f e c t s .

T h e r e fo r e ,

we can conclude that th e se broad fe a tu r es in the Bouguer anom aly
map are caused by stru ctu ra l and lith o lo g ic v a r ia tio n s in the b a se­
ment complex and hence should be elim in a ted a s r e g io n a l.

T h is

interpretation is sub stan tiated by the g e n e r a lly low g ra d ien ts o f the
gravity a n o m a lie s, which again indicate a deep s o u r c e .
In addition to th ese broad fe a tu r e s , the map a ls o in d ica tes the
presence of local lin ea r tren d s o f r e la tiv e ly low B ouguer g ra vity
values.

T hese tren d s a r e cau sed by bedrock ch an n els and w ill be

described in detail in the s e c tio n regard ing the gra v ity r e sid u a ls
and bedrock topography.

Gravity R esiduals
Bedrock Topography R esid u al B ouguer G ravity A nom aly Map
Plates 4a and 4b show the g ra v ity r e sid u a ls ca lcu la ted by
employing the w ell log inform ation and the B ouguer g ra vity
anomaly contour m ap.

The resid u a l v a lu e s r e p r e se n t the g r a v i­

tational effect of the e x c e s s m a s s r esu ltin g from the p r e se n c e
of denser bedrock se d im e n ts above the datum ele v a tio n (300 fe e t

79

above s e a le v e l) in ste a d o f g la c ia l s e d im e n t s .

D efin ed in t h is

m anner, the r e s id u a l g r a v ity v a lu e s a r e p o s it iv e a s lon g a s
the bedrock e le v a tio n i s g r e a t e r than the datum e le v a t io n .

N eg a ­

tive resid u a l g r a v ity v a lu e s in d ic a te b e d r o c k e le v a t io n s l e s s than
the datum e le v a t io n .
Insp ection o f the r e s id u a l c o n to u r m ap r e v e a l s the p r e s e n c e o f
se v e r a l lin e a r tr e n d s c h a r a c t e r iz e d by lo w e r g r a v ity r e s i d u a l s .
T hese tr e n d s r e s e m b le a flu v ia l d r a in a g e p a tte r n and a r e b e lie v e d
to be c a u se d by b e d r o c k c h a n n e ls .

The m o s t p r o m in e n t lin e a r

low r e sid u a l a r e a i s lo c a te d ju s t e a s t o f th e w e s t e r n b o u n d ary o f
K alam azoo C o u n ty .

H ere it g e n e r a lly tr e n d s n o r t h -s o u th .

T h is

trend e n t e r s th e C ounty at th e n o r th w e s te r n c o r n e r and c r o s s e s
the so u th ern b ou n d ary at so u th —c e n t r a l P a r a r ie R onde T o w n sh ip .
The lo w e st r e s id u a l g r a v ity v a lu e s o f z e r o m g a ls o c c u r a t tw o
lo c a litie s a lo n g the a x is o f the tr e n d a t the s o u th w e s te r n c o r n e r
of O shtem o and the w e s t - c e n t r a l p o r tio n o f T e x a s T o w n s h ip s .
S e v e r a l a d d itio n a l low r e s id u a l tr e n d s a r e a p p a r e n t and have
an e a s t - w e s t o r n o r t h w e s t - s o u t h e a s t d ir e c t io n .

The m o s t p r o m ­

inent e x te n d s g e n e r a lly e a s t - w e s t a c r o s s c e n tr a l K a la m a zo o
County.

It e n t e r s th e C ounty a t th e n o r th e a s te r n c o r n e r o f

C h a rlesto n T o w n sh ip , c o n tin u e s n o r th w e stw a r d to c e n t r a l R o s s
Township w h e r e it tu r n s so u th w a r d , th en w e s tw a r d and c o n tin u e s

r
80

in this d ir e c tio n a c r o s s C o m sto c k , K alam azoo, and O shtem o
Townships.

T h is m ajor trend i s join ed by s e v e r a l tr ib u ta r ie s

trending n o r th w e st-so u th e a st and n o r th e a s t-s o u th w e s t.

The

drainage s y s te m of th is trend a p p ea r s to be v e r y co m p le x in and
west of the C ity o f K alam azoo.
Other m inor tr e n d s include an e a s t —
w e st b ed rock channel and
its two tr ib u ta r ie s .

T h is trend o c c u p ie s the n o rth w estern and

north-central part o f K alam azoo C ounty.
In addition to the above m entioned low r e sid u a l g r a v ity t r e n d s ,
sev era l resid u a l g r a v ity high s a ls o e x i s t .

The m o st p rom in en t o f

these a r e lo c a te d in n o rth w estern NAfakeshma, so u th w e ste r n C lim a x ,
and so u th e a ste r n P a v ilio n T o w n sh ip s.

S e v e r a l ad d ition al a r e a s of

high r e sid u a ls a r e apparent in n o rth w estern K a la m a zoo, sou th ­
eastern O sh te m o , n o r th ea ste rn R ich lan d , and n o rth w estern R ose
T ow nsh ips.

T h e se high g r a v ity r e s id u a ls r e fle c t r e la t iv e ly high

bedrock top ograp h y.

Gravity R e sid u a ls Obtained by A pproxim ating the R egional by
P oly n o m ia ls
A s m entioned p r e v io u s ly , g r a v ity r e s id u a ls obtained by fittin g
a polynom ial to the g r a v ity data fo r the p u rp ose o f sep a r a tin g
regional tr e n d s m ay not be su ita b le fo r q u an titative in te r p r e ta tio n .
They a r e u s e fu l, h o w e v e r , fo r v isu a l stu d y o f a n o m a lo u s t r e n d s .
With th is in m in d , g r a v ity r e s id u a ls w e r e com puted for g ra v ity

81

regionals approximated by p o ly n o m ia ls of fifth and se v e n th d e g r e e s .
The County was divided into two p a rts by an e a s t - w e s t tine in su ch
a way as to perm it a re a l o v e r la p .
separately on these two h a lv e s .

The c a lc u la tio n s w e r e p erform ed

R e sid u a ls co rresp o n d in g to the fifth

and seventh degree polynom ial r e g io n a ls a r e illu str a te d in P la te s 7 a p
7bf and 8a, 8b.
Examination o f the resid u al contour m aps r e v e a ls the c lo s e s im i­
larity between the fifth and sev en th d e g r e e r e s id u a ls .

H ow ev er, a s

expected, the seventh d e g ree r e s id u a ls a n o m a lie s a r e g e n e r a lly o f
less amplitude than the fifth .

A ls o , the se v e n th d e g r e e r e s id u a ls show

better resolution o f a n o m a lie s than the fifth .
A careful com parison betw een r e s id u a ls obtained by approxim ating
the gravity regional by a sev en th d e g r e e polynom ial and the b ed rock
topography residual Bouguer g ra v ity an om aly d e m o n str a te s the a b ility
of the least square technique to ou tlin e a n om a lou s a r e a s .
the method fails to define the reg ion a l q u a n tita tiv ely .

H ow ev er,

The r e s u lt is

that gravitational e ffe c ts o f d e ep er b o d ie s a r e not c o m p le te ly e lim in a te d ,
thus causing d istortion s to the g ra v ity r e s id u a ls .

F or e x a m p le , the

gravity high located in southern C om stock i s s t ill v e r y prom inent
in the fifth and seventh d e g r e e polyn om ial r e s id u a ls .

T h is an om aly

is caused by basem ent e f fe c t s and should be elim in a ted a s a r e g io n a l.
•*hne situation is rep eated in sou th ern T e x a s and n orthern
Preire Ronde Townships w here a g r a v ity high ca u sed

by the basem ent is not c o m p le t e ly e lim in a te d a s r e g io n a l.

Som e

n e g e t t v e gravity a n o m a lie s c a u s e d by a n o m a lo u s fe a t u r e s in the

p a le o z o ic se c tio n o r the b a se m e n t a r e a l s o a p p a ren t in the r e s id u a l
m ep e. T hese n eg a tiv e a n o m a lie s cou ld g iv e a f a ls e in d ic a tio n o f a
b ed ro ck channel.

T h is ca n be illu s tr a t e d by an a r e a in W akeshm a

Tow nship w here it a p p e a r s from the r e s id u a ls ob tain ed by a s e v e n th
d e g re e polynom ial r e g io n a l that th e "F" v a lle y (p la te s 5 ) e x te n d s
farther south into B ra d y and w a k e s h m a T o w n sh ip s, than s u g g e s te d

by g eo lo g ic in fo r m a tio n .

B edrock Contour Map
P la te s 5 , 6 a and 6b sh ow the b ed r o ck to p ograp h y m ap o f
K alam azo o C ounty.

T he co n to u r lin e s a r e d ash ed in a r e a s w h e r e

b e d ro c k control and g r a v ity c o v e r a g e i s in s u ffic ie n t to p e r m it
a c c u r a te outlining o f b ed ro ck to p o g r a p h y .

The co n to u r m ap

in d ic a te s a p r e v a ilin g w e stw a r d s lo p e o f the b e d r o c k s u r f a c e .
B ed ro c k e le v a tio n s a s high a s 8 5 0 fe e t a r e e n c o u n te r e d in the
e a s te r n part o f the C ounty w h ile t h e s e a t the w e s t e r n part a r e
u n d e r 350 fe e t at c e r t a in lo c a t io n s .

S u p e r im p o s e d on t h is g e n e r a l

b e d ro c k s u r fa c e s lo p e a r e s e v e r a l p ro m in e n t high to p o g ra p h ic
f e a tu re s w hich a r e lo c a te d in s o u th w e s te r n S c h o o lc r a f t , so u th ­
w estern O sh te m o , n o r th e a ste r n T e x a s , n o r th w e ste r n R o s s , and
n o r th e a s te r n C o m sto c k T o w n sh ip s.

L oca l low e le v a t io n s on

the bedrock su r fa c e e x i s t s alo n g the a x e s o f b ed rock c h a n n e ls .

A c lo s e exam ination o f the b ed rock topography m ap in d ic a te s
the p r e s e n c e of a v e r y c o m p lic a te d b ed ro ck channel s y s t e m .

The

m ain b e d ro c k ch an n els s e e m to tren d g e n e r a lly e a s t - w e s t o r n o r th so u th . H ow ever, the tr ib u ta r ie s o f the m ain b ed rock c h a n n e ls trend
northw est-southeast.

B ed ro ck ch a n n e ls a r e d e sig n a te d in p late 5

by alphabetic sy m b o ls fo r e a s y r e f e r e n c e .
The "A" v a lle y tr e n d s w estw a rd a c r o s s K alam azoo C ou n ty.

It

p o s s e s s e s fa ir ly ste e p s id e s and a rounded flo o r in d icatin g the
p o ssib le e ffe c t o f g la c ia tio n , o r indeed co m b in ed g la c ia l and
fluvial e r o sio n .

Its channel e x h ib its a p p r e c ia b le m ea n d erin g

in dicatin g stron g flu v ia l e f f e c t s .

S e v e r a l co n to u r c lo s u r e s alon g

the axis of the channel and lo c a l r e v e r s a ls o f s lo p e a r e a p p a r e n t,
f u rth e r su g g estin g g la c ia l o r g la c io - f lu v ia l in f lu e n c e s .
The m ost p rom in en t fea tu re o f the "A" ch an n el is the fa c t that
most of its tr ib u ta r ie s in K alam azoo County s e e m to jo in the r iv e r
from the sou th .

The la r g e s t o f th e s e tr ib u ta r ie s i s the "F"

Channel which o r ig in a te in c e n tr a l B ra d y T o w n sh ip .

The "F"

-Channel has a v e r y broad ch an n el and a r a th e r s tr a ig h t c o u r s e .
Its s id e s show v e r y g en tle s l o p e s .

The "G" channel is an oth er

tr ib u to a ry to the "A" b ed ro ck c h a n n e l.

It s e e m s to join th e "A"

Channel near the sa m e point at w hich th e " A " and "F" c h a n n e ls
m e et.

The "j" v a lle y is a n o th er tr ib u ta r y to the "A" c h a n n e l.

ft tea a n a r r o w e r c r o s s s e c t i o n a n d v e r y s t e e p s i d e s .
The "E" c h a n n e l j o i n s t h e "A" c h a n n e l a t t h e c e n t e r o f
Comstock T o w n sh ip a n d t r e n d s w e s t w a r d p a r a l l e l to t h e "A"
ctannel.

Its c h a n n e l c o i n c i d e s w it h t h e MG" c h a n n e l f o r a b o u t a

mile in s o u t h e a s t e r n K a la m a z o o T o w n s h ip a n d s w i n g s w e s t w a r d
to meet the "F" c h a n n e l in s o u t h w e s t e r n K a la m a z o o T o w n s h ip .
It changes c o u r s e to s o u t h w e s t w a r d a n d m e e t s th e 11K*1 c h a n n e l
in w e s t-c e n tr a l T e x a s T o w n s h ip .
*
M
The "C* and ,fC M c h a n n e l s a r e t r i b u t a r i e s t o t h e "C" c h a n n e l
which w as flo w in g w e s t w a r d in n o r t h e r n A la m o T o w n s h ip .

I ts

direction o f f lo w b e c o m e s n o r t h w a r d in s e c t i o n 4 o f t h e T o w n s h ip
and c r o s s e s th e K a la m a z o o b o r d e r in t o A l l e g a n C o u n t y .

T h is

channel and i t s t r i b u t a r i e s a r e b r o a d w it h g e n t l y s l o p i n g s i d e s .
The "K" and "B" s e g m e n t s r e p r e s e n t t h e d e e p e s t b e d r o c k
channels in K a la m a z o o C o u n t y .
have ste e p s i d e s .

T h e ir c h a n n e ls a r e n a r r o w and

T h e l o w e s t b e d r o c k e l e v a t i o n in K a la m a z o o

County e x i s t s a lo n g th e a x i s o f th e "K" s e g m e n t a n d o c c u r s in
w e st-c e n tr a l T e x a s an d s o u t h e a s t O s h t e m o T o w n s h i p s .
The "M" c h a n n e l i s t h e s o u t h e r n m o s t b e d r o c k c h a n n e l in
Kalamazoo C o u n ty .

Its d i r e c t i o n o f f lo w w a s w e s t —n o r t h w e s t w a r d .

This channel m a y n o t b e v e r y a c c u r a t e l y d e l i n e a t e d b e c a u s e o f
lack o f a c c u r a t e g r a v i t y a n d w e l l lo g in f o r m a t io n in t h i s p a r t o f

85

the County.

H ow ever, its e x is t e n c e i s e s ta b lis h e d by th e p r e s e n c e

of a bedrock channel in Van B u ren County w h ich s e e m s to be a
continuation o f the s a m e d ra in a ge (G iro u x , e t a l , 1964).

CHAPTER

VIII

IN TER PR ETA TIO N O F R E S U L T S

C o r r e l a t i o n o f B ed rock and S u r f a c e T o p o g ra p h y

In areas co v ered w ith a thin g la c ia l d e p o s it , s u r f a c e to p o g ra p h y
very often r e fle c ts b e d r o ck to p o g r a p h y .

In K a la m a z o o C o u n ty , h o w e v e r ,

glacial sedim ents a r e s u f f ic ie n t ly th ic k th a t m u ch o f the b e d r o c k to p o g ­
raphy is masked by the g la c ia l c o v e r .

T h u s , w h ile the b e d r o c k s u r ­

face generally s lo p e s dow nw ard to the w e s t , s u r f a c e to p o g ra p h y i s
highest at the w e s t s id e o f th e c o u n ty .

S u r f a c e to p o g r a p h y i s g r e a t ly

influenced by the a r e a l d is tr ib u tio n o f t e r m in a l m o r a in e s in th e
County. The d istr ib u tio n d o e s not s e e m to be r e la te d t o b e d r o c k
topography.
Because a c o r r e la tio n b e tw e e n s u r f a c e to p o g ra p h y and b e d r o c k
topography is la c k in g , th e c o r r e la t io n b e tw e e n s u r f a c e d r a in a g e and
the bedrock channel s y s t e m i s e x p e c te d to be v e r y p o o r .

T he a v a il­

able bedrock in fo rm a tio n in th e s o u t h w e s t e r n p a r t o f th e S o u th e r n
Peninsula of M ichigan in d ic a te s a p r e v a ilin g w e s tw a r d s lo p e o f th e
bedrock su r fa ce .

A s s u m in g p o s t - g l a c i a l rebound to be l e s s than th e

relief difference in b e d r o c k , th e p r e v a ilin g d ir e c t io n o f p r e g la c ia l
86

d rain ag e 1°

area (w hich in c lu d e s K a la m a zo o C ounty) w ould p r e ­

sum ably have been w estw ard to w a r d s the Lake M ich ig a n L ow lan d .

It

is alao apparent that p r e s e n t s u r f e c e d r a in a g e i s to the w e s t , but lit t le
of its coincides with the p r e g la c ia l d r a in a g e l i n e s .

C o in c id e n c e b e­

tween the present su r fa c e d r a in a g e and b e d r o c k c h a n n e ls e x i s t o n ly
in areas where d ifferen tia l c o m p a c tio n o f th ic k g la c ia l d e p o s it s h a s
occurred in bedrock c h a n n e ls , o r w h e r e g la c ia l d e p o s it s a r e in su f­
ficient to fill these c h a n n e ls.
There are se v e r a l e x a m p le s in K ala m a zoo C ounty w h e r e b e d r o c k
channels (as proven by d r illin g ) h a v e s u r f a c e e x p r e s s i o n .
channels are shown in P la te 9 .

T h ese

T h e m o s t p r o m in e n t e x a m p le a r e th e

tributaries of Pine C reek in K a la m a zo o C ounty w h ic h s e e m to be flo w ­
ing over the "C” and the n o r th e rn p a rt o f th e MB n b e d r o c k c h a n n e ls .
The "B" channel c o in c id e s w ith a tr ib u ta r y

o f P in e C r e e k w h ich

joins Rupert, M urry, H ip p s, and B a rb o u r L a k es to the m ain c r e e k .
Southward the su rfa ce e x p r e s s io n o f the MB ,? ch a n n e l d is a p p e a r s
beneath the g lacial d e p o s its o f the K a la m a zo o m o r a in e s w h ich c o n c e a l
its surface e x p r e s s io n .

P a r t o f th e "E" ch a n n el lo c a te d b e tw e e n the

W
F" and "K" channel a ls o c o in c id e s w ith the s u r f a c e d r a in a g e lin e a —
tion of the w est fork o f P o r ta g e C r e e k and C r o o k e d , D u ck , and P r e tty
Lakes. A third ex a m p le o f b e d r o c k ch a n n el b ein g r e o c c u p ie d by
„
M
surface stream s is the b e d r o c k "C" ch a n n e l w h ic h g e n e r a lly c o in c id e s

with Spring and Brook C r e e k s .

T he a s s o c ia t io n o f the p r e s e n t

88
Kalamazoo R iver to seg m en ts of the "A", "D", and "C" channels is
a ls o apparent.

T his su g g e s ts the p o ssib ility that the Kalamazoo

R iver follow s su rface d ep ressio n s along bedrock ch an n els.

Relation Between Bedrock Channels and S u rface Geology
Plate 1 show s the distribution o f bedrock channels and su rfa ce
geology in Kalamazoo County.

It is apparent from the m ap, that

the two distributions are totally independent and u nrelated.

This

su g g ests that bedrock topography was not a m ajor factor in con trol­
ling the m ovem ent of g la c ie r s .

Exam ination o f the bedrock topog­

raphy map (P late 5) and Plate 1 a ls o indicates no apparent relation
between bedrock channel distribution and bedrock su rfa ce geology.

R econstruction o f the Drainage Pattern B efore and During Glaciation
Before d isc u ssin g the c la ssific a tio n of bedrock channels in Kala­
mazoo County, a few pertinent facts a re worth restating:

(1)

P re-

glacial bedrock channels flow in the general d irection of the bedrock
surface s lo p e .

T heir c o u r s e s , however may be controlled by str u c ­

ture and differen tial hardness o f bedrock.

(2)

The bedrock su rface

of the southw estern part of the Southern Peninsula of M ichigan,
which includes Kalamazoo County, slo p e s w estw arc towards Lake
M ichigan.

The structural trend i s , how ever, to the northw est.

(3) P reg la cia l channels n ever c r o s s drainage divides which may be
formed o f m ore resista n t bedrock form ation s.

89

A careful study of Plate 5 indicates that w ater in bedrock channels
”CMand its trib u taries "C" and "C", a s w ell a s the "A" and MM"
channels, generally flow in a prevailing w e ste r ly direction towards
the Lake Michigan B a sin .

T hese channels appear to have r ela tiv ely

broad floors up to a m ile wide and exhibit noticeable m eandering.
These facts su ggest that the above m entioned bedrock channels may
have represented the p reglacial fluvial drainage in Kalamazoo County,
Michigan.

The "F1*, "G", and "J" channels appear to have been

tributaries to the "A" channel and a r e believed to be p reg lacia l as
w ell.
In term s of th ese configurations the follow ing sequence of even ts
is postulated.

When the ice front of the Lake Michigan lo b e, which

invaded Kalamazoo County from the northw est, covered the north­
w estern corner of the County, it blocked the westward flowing m aster
"C" channel.

The dammed w ater began to r is e until it reached the

elevation of the drainage b a r rie r between the "A" and "C" ch an n els.
The dammed w ater then breached the drainage b a r r ie r in Kalamazoo
Township to form the MD" segm en t o f the bedrock drainage channels
which w as flowing southward.

Thus, the p reg alcial drainage in the

"CMand part of the "C" w as seem in g ly diverted to -low southward
and join the "A” ch an n el.

This drainage pattern apparently did not

last v ery long because the floor elev a tio n s o f the f,C M, "C" and M
D”
channels a re appreciably higher than that o f the "A" channel.

90

Apparently, the "B" channel w as a ls o form ed a s a c r o s s drainage
by the glacial m elt w ater from the southward advancing and eastw ard
spreading Lake Michigan ice front to the "A” channel.

This channel

is appreciably deep er than the "CMand "D" channels indicating that
it was carrying a la rger load of w ater southward.
The ice front seem in g ly advanced farther southward and continued
to spread to the ea st; eventually blocking the "A" channel.

The

damming of the p reglacia l "A" channel probably created an a ltern a­
tive route for drainage farther south.

T his drainage is suggested

on Plate 5 a s the "E" channel which trended sou th w est.

S m a ll s e g ­

m ents of the p reg a lcia l "G" and "F" trib u ta ries o f the "A" channel
were incorporated in th is new p erig la cia l strea m ch an n el.

As a

result of this drainage d iv e r sio n , drainage o ffse ts occurred in the
w estern part of the "A" channel, and in the northern parts of the
"G" and "F" bedrock ch an n els.
The "K" channel may a ls o have been created by glacia l m elt
w aters flowing southward from the advancing Lake Michigan ice
front towards the "M" p reg lacial channel which w as not yet dammed
by the advancing ice front.

T his segm en t "K", like the "B" channel,

is appreciably deeper than the "A" o r "C" channels and has steep
sided v a lley w a lls accentuated probably by p o st-g la c ia l down cutting.
This evidence su g g e sts that the MB" and "K" channels a re p e r ig la c ia l.
It is a lso p o ssib le that the "K" channel w as the locus for a northw est

91

flowing w ater in p reglacial tim e , then a r e v er sa l in drainage
occurred during g laciatio n .

A s the ic e front advanced further south

and e a s t, presum ably the "E" channel drainage w as dammed and the
"I" and "H" channels w ere form ed to c a r ry the w estw ard advancing
drainage to the "K" and hence to the "M" channel.

CHAPTER

IX

GROUND WATER PO SSIBILITIES IN
KALAMAZOO COUNTV, MICHIGAN

Introduction
The City of K alam azoo's m unicipal w ater n e e d s, in addition to
industrial and d o m e stic w ater consum ption in K alam azoo County,
is totally dependent on ground w ater s u p p lie s .

M ost of th is needed

supply co m es from aq u ifers in the g la c ia l s e d im e n ts .

The rem ain­

ing portion is supplied by w e lls com pleted in the M arshall sandstone
aquifers and located in the n orth eastern co r n er o f the County.
The ch em ical quality o f the ground w ater produced from the
glacial and sandstone a q u ife r s is quite v a r ia b le .

The m o st com m on

sa lts are the b icarbonates of ca lciu m and m a gn esiu m .

A ccording

to Deutch, V a n lier, and Giroux (1 9 6 0 ), the bicarb on ates a r e derived
from p a r tic le s o f lim esto n e and sandston e w hich a r e the m ajor con­
stituent of g la cia l s e d im e n ts .

In so m e a r e a s , h o w ev er, the m ost

abundant d isso lv e d m a teria l is ca lc iu m s u lfa te .

The su lfa te s a r e

more com m on in the ground w ater produced from w e lls com pleted
in sand and g ravel a q u ife rs which a r e in contact with sh a le o r basal
t ill.

It w as noted by D eutch, V a n lie r , and Giroux (1960) that lo w er­

ing the w ater table r e s u lts in an upward m igration o f the c a lciu m
92

93

sulfate w aters from the Coldwater shale to the aq u ifers in gla cial
sedim ents.

Iron and m anganese a re a ls o a com m on constituent in

the ground w ater o f Kalamazoo County.

Their concentration is

variable depending on the lo c a lity .
The author b e lie v e s that the m igration p r o c e ss is fa ste r in a r e a s
occupied by bedrock channels e s p e c ia lly w here a local d ep ressio n
in the floor of the bedrock channels e x is t s .

Figure 10 show s the

normalized concentration (highest concentration taken a s

1 0 0

) of

several chem ical compounds in the ground w ater pumped from five
w ells belonging to the Upjohn Company and located along profile
"S" (P late
Township.

6

a ) c r o s sin g the a x is of the MF" channel in Portage
The graph has been constructed from w ater a n a ly sis

data supplied by the Upjohn Company.

It is obvious that ground

w aters obtained from w e lls located along the a x is of the bedrock
channel is the highest in sa lt content.

The in creased rate o f upward

migration of d isso lved s a lts from bedrock sed im en ts to glacial
aquifers located in bedrock channels m ay be caused by the com bined
effect of th ese suggested factors:

(1) The effectiv e area through

which sa lin e w ater m igration takes place is g re a ter in a r e a s o f bed­
rock d ep ressio n s than in flat a r e a s .

(2) Bedrock c e p r e s s io n s a re

possible site for upward m igration o f w a ters o f r e la tiv e ly higher
salinity content because the sa lin ity of bedrock sed im en ts g en erally
in creases with depth.

(3)

Som e o f the bedrock channels in

94

Kalamazoo County may be estab lish ed along the troughs of m inor
folds in the bedrock su rfa c e .

It is a lso p o ssib le that som e o f them

follow minor faults or fracture zon es in the bedrock su rface where
the resistance to stream ero sio n is m inim um .

Whether the channels

are established o ver fault z o n e s , fr a c tu r e s, or m inor fo ld s, the
rate of upward m igration of sa lin e w a ters from the bedrock to the
glacial sedim ents is expected to be enhanced.

The evidence of high

salinity in ground w aters produced from aq u ifers located at the center
of bedrock channels is dem onstrated in one location a s se e n in
Figure 10.
unknown.

Whether this situation e x is t s in other a r e a s or not is
More stu d ies a re w arranted.

The glacial sed im en ts in Kalamazoo County range in th ick n ess
between 50 fe e t, m ostly in the vicin ity of the Kalamazoo R iv e r , to
650 feet in the w est sid e o f the County w here the Kalamazoo m orain es
are underlain by bedrock ch an n els.

The saturated th ick n ess in a r e a s

where the glacial sed im en ts are thin is v e r y sm a ll and the p o ssib ility
of developing aquifers suitable for sa tisfy in g the needs of m unicipal­
ities or indu stries is m in im al.

A ccord in gly, a r e a s underlain by a

thick section of saturated glacial sed im en ts a re m ore favorable for
locating aquifers of appreciable th ick n ess and suitable y ie ld .

A rea s

which are covered with thick outwash and recent channel d ep o sits
are e sp e c ia lly favorable for locating ground w ater a q u ife r s.

B e sid e s

having high p e r m e a b ilitie s, aquifers developed in the channel d ep osits

95

8
M

s

CA**

t

TOTAL HARDNESS
HCOJ

\

CD

FE *~

111

X

2

MQ + +

I

NA*

50
s

F
<
BC
UJ

O

s

o

J

IfcJ

>

5

_i
a

PROFILE (3)

R O R TH

—*■

650
BEDROCK TOPOGRAPHY

ieoo-

:>

a
W550

FIGURE

io

SALT CONTENT OF GROUND WATER
BEDROCK
TOPOGRAPHY

AND

of recent s tr e a m s , v e r y o ften , r ep le n ish the w a ter lo s t to pumpage

5y direct recharge from su r fa c e w a te r s .

T his is the r e a so n w h y

many of the pumping s ta tio n s o f the C ity o f K alam azoo W ater D epart­
ment are located along su r fa c e d r a in a g e .

The w a te r s o f the K alam azoo

River, which is the la r g e s t su r fa c e d rain age in K alam azoo C ounty,
are highly polluted.

A c c o r d in g ly , no attem p t w a s m ade to d evelop

g ro u n d water a q u ifers in its channel d e p o s it s .

G lacial till se d im e n ts

in Kalamazoo County a r e m o stly form ed o f red o r blue com p act and
impervious se d im e n ts which a r e form ed o f p a r tic le s having a w ide
range of s i z e s .

H ow ever, in so m e a r e a s , t ill d e p o sits a r e form ed

Of fine grained c la y type se d im e n ts w hich a r e g r e y , brow n, o r g r e y ­
ish blue in c o lo r .

Both v a r ie t ie s o f t ill d e p o s its a r e un su itab le a s

aquifers.
Exploration d r illin g in the sp r in g o f 1968 ind icated that the o u twash apron located betw een the ou ter and inner K alam azoo M orain es
la underlain by v e r y th ic k , highly p erm ea b le sand and g r a v e l d e p o s its .
An exploration te s t hole w as attem pted a t the c e n te r o f s e c tio n 21 o f
Oshtemo Township w h ere the mud c ir c u la tio n w a s lo s t at a depth of
860 feet a fter penetrating 50 fe e t o f v e r y c o a r s e g ra v el a n d /o r sand
deposits.

The d r illin g w a s d iscontinu ed b e ca u se the c ir c u la tio n

oould not be r e sto r e d and heaving o f the outw ash d e p o s its m ade
drilling im p o s s ib le .

The r e s u lt s in d icate an upper aq u ifer o f 90 fe e t

Of sand a n d /o r g r a v el and a lo w er aq u ifer beginning at a depth o f 207

foet below the su r fa c e .

The total th ic k n e ss o f the lo w er aquifer

could not be determ ined b eca u se o f the term in ation o f d r illin g at the
site. The lower and upper a q u ifer s a r e sep a rated by 30 fe et o f till
deposits.
The existence of th is e x tra o rd in a r ily thick seq u en ce of outw ash
deposits in the apron m ay be accounted for a s follow s:

W hile the

Lake Michigan ice front w as sta tio n a ry during the fo rm a tio n s o f the
imer Kalamazoo m o r a in e s , the g la c ia l m elt w ater w a s confined
between the ice front and the ou ter K alam azoo m orain e to the e a s t ,
which was already p r e se n t.

T h is r e su lte d in the confinem ent o f

deposition of the g la c ia l outw ash d e p o s its to the a r e a betw een the two
Kalamazoo m o r a in e s.

T hick outwash d e p o sits m ay a ls o e x is t d ir e c tly

to the east of the ou ter K alam azoo m oraine .

The g la c ia l slu ic e w a y

which was flowing eastw ard away from the ic e front during the
formation of th e se m o r a in e s is exp ected to have d ep o sited the c o a r s e r
datrttus directly to the e a s t o f th e se ou ter m o r a in e s .

B ad rock

Channels in K alam azoo County a s Loci fo r Ground W ater
Aquifers
Ground w ater exp lo ration in bedrock ch an n els in Ohio ( S c h a e f e r ,

Write, and V anTyl, 1946), Illin o is (H o rb erg , 1950; P isk in and
Bergstrom, 1967; S tep h en , 1967) and Indiana (W ayne, 1956) indicate
that bedrock ch an n els a r e e s p e c ia lly favorab le fo r lo ca tin g ground
water aq u ifers.

H ow ever, in s e v e r a l in s ta n c e s , bedrock ch an n els

98

were found to contain fine grained d ep o sits such a s c la y , s i l t , and
impervious sedim ents o r till d ep o sits (M cG rain, 1948; W ayne, 1956).
Fine grained glacial d ep o sits m ay be form ed under stagnant conditions
due to damming of drainage by ice fr o n ts.

In so m e situ a tio n s, it is

also possible that p r e -e x is tin g outwash d e p o sits in bedrock channels
were excavated and d estro y ed by the advancing ic e , o r a sso c ia te d
torrential outwash w a te r s , and then the ch an n els r e filled with poorly
sorted till or even fine grained fluvial o r la cu str in e d e p o s its .

Under

these circu m sta n ces, g la cia l se d im e n ts in bedrock ch an n els u su ally
possess low perm eab ility and cannot be developed a s a q u ife r s .
The available w ell log inform ation in K alam azoo County is not
sufficient to e sta b lish the nature of the g la c ia l d e p o sits in a ll bedrock
channels.

The C ity of K alam azoo Water D epartm ent undertook a

drilling program in 1968 and 1969 to in v estig a te the nature o f g la c ia l
deposits in se le c te d lo c a tio n s.

About 30 d r ill h o le s w e r e com pleted

during this p erio d , m o stly in C om sto ck , R ichland, and O shtem o
Townships.

H ow ever, few o f th e se te s t h oles w ere located o v e r

bedrock c h a n n e ls.

B ased on ava ilab le d r ill log in form ation , the

following gen eral c o n c lu sio n s a r e drawn regard ing the nature of
glacial d ep osits in the bedrock channels o f K alam azoo County:

(1)

Ths "A” channel (P la te 5) a p p ears to be g e n e r a lly billed with till
type d ep o sits.

T his co n clu sio n is based on sc a tte r e d d r ill log infor­

mation in C o m sto ck , K alam azoo, and O shtem o T ow n sh ip s.

It is

possible that the p reg la cia l d e p o s its in th is channel have been
e x c a v a te d and d estroyed by g la c ia l a c tio n and then rep la ced by u n sorted
till o r even r e la tiv ely unsorted g la c io -flu v ia l d e p o s it s .

(2 )

The " F "

end "G" bedrock channels appear to contain outw ash d e p o s its .

E a st-

central Portage Township is e x te n s iv e ly d r ille d by the Upjohn C om pany.
Several aquifers w ere developed alon g the se g m e n t o f the " F " v a lle y
located in the a r e a .

The b etter a q u ife rs in th is a r e a a re lo ca ted along

the sides of the bedrock c h a n n e l.

A few in fe r io r w e lls w e r e develop ed

along the axis w here the g la c ia l outw ash d e p o sits a r e fin e -g r a in e d and
less sorted.

The w a ter pumped from th e se w e lls sh o w s a r e la tiv e ly

higher percentage o f d is s o lv e d s a l t s .

(3 )

The "E" bedrock channel

is known to contain e x te n siv e outw ash d e p o s it s .

T h e se d e p o s its a r e

especially thick in the se g m e n t o f the channel to the so u th w est o f the
City of Kalamazoo w h ere the bedrock channel c o in c id e s w ith the s u r ­
face drainage lin e s o f the w est fork o f P ortage C r e e k , C rook ed , D uck,
and Pretty L a k es.

The th ick outw ash d e p o sits in th is se g m e n t probably

consists of both g la c ia l outw ash and r e c e n t p o s t-g la c ia l channel
deposits.

(4)

S p rin g and B rook C r e e k s flow south w estw ard and

overly the "C" trib u tary o f "C" bedrock c h a n n el.

F low g a u g es

placed at s e le c te d lo ca tio n s along the c r e e k indicate that during d ry
periods ap p reciab le su r fa c e w ater flow i s su sta in e d by ground w a te r .
This su g g ests that the p r e se n c e o f p erm ea b le outw ash and channel
it

deposits in the a r e a surrounding the C re ek and in the "C" bedrock

channel* As a r e s u lt, four e x p lo r a tio n d r ill h o le s w e r e co m p leted
along the sid e s of the channel in R ichland T ow nship in e a r ly sp r in g o f
1968.

The r e su lts indicated the p r e s e n c e o f up to 170 fe e t o f outw ash
If

deposits underlain by c la y and o th e r la c u s tr in e d e p o s it s .

The "C"

"C" tributaries o f the "C" ch an n el have not b een d r ille d e x te n ­
sively.

However, an ex p lo ra tio n d r ill h ole w a s co m p leted in north­

west Cooper Township about 1200 fe e t south o f the a x is o f the M
C"
channel which encountered 9 0 fe e t of s u r fa c e outw ash d e p o s its und er­
lain by clay and lake type d e p o s it s .

M ore d r illin g i s need to d efin e

the nature o f g la c ia l d e p o s its in the channel in o th e r a r e a s .

(5 )

The

glacial sed im en ts in the "B" and "K" v a lle y s a r e the th ic k e s t in
Kalamazoo County.

The nature o f the d e p o s its is not known in d e t a il.

Besides s e v e r a l o il t e s t h o le s w h ich do not in d icate the nature o f
glacial d ep osits in the "B" v a lle y , on ly one e x p lo r a tio n t e s t h o le w a s
drilled by the C ity o f K alam azoo W ater D ep a rtm en t.

T h is t e s t hole

was drilled o v e r the a x is o f the "B" v a lle y in c e n tr a l A lam o T o w n sh ip .
The resu lts in d icate the p r e s e n c e o f 55 fe e t o f outw ash d e p o sit in the
form of thin la y e r s o f sand a n d /o r g r a v e l and c la y .

T h is s e c t io n o f

oub*ash i s u n d erlain by t ill and lake type d e p o s it s .

The th ick g la c ia l

sediments in the "B" and "K" v a lle y s a r e apt to co n ta in th ick outw ash
deposits and fu rth er ex p lo r a tio n d r illin g is str o n g ly reco m m en d ed in
these a r e a s .

( 6 ) M ore stu d y i s a ls o needed to a c c u r a te ly d efin e the

axis and nature o f g la c ia l s e d im e n ts in the "M" v a lle y .

CHAPTER

X

CONCLUSIONS

Applicability of the G ravity Method in O utlining B ed rock Topography
The resu lts of the g ra v ity in v e stig a tio n in K alam azoo C ounty,
Michigan, warrant the follow in g c o n c lu sio n s:

(1 )

The g ra v ity

method can be s u c c e s s fu lly em p loyed in K alam azoo County to ou tlin e
bedrock topographic fe a tu r e s and map the b ed rock s u r f a c e .

The

density of the g la cia l s e d im e n ts in the a r e a w hich w a s e s tim a te d to
be 2.15 g m /c c , is a p p r e c ia b ly lo w er than the rep orted 2 .5 5 g m /c c
value for the d en sity o f C oldw ater s h a le .

T h is la r g e d e n sity c o n tra st

permitted the application of the g ra v ity m ethod to outline b edrock
topography.

(2)

The p roced u re d evelo p ed for iso la tin g the resid u a l

gravity anom alies cau sed by buried bedrock topography h as been
successfully used to obtain a fa ir ly d eta ile d bedrock topography map
of the County.

(3)

The d e ta il in the c o m p iled bedrock topography

map made it p o ssib le to r e c o n str u c t the p r e g la c ia l and p e r ig la c ia l
drainage in K alam azoo C ounty.

(4 )

The p rop osed approach o f c a l­

culating the av era ge d e n sity o f the g la c ia l and bedrock s e d im e n ts
using the f r e e - a ir an o m aly and w ell log in form ation produced d e n sity
estimates com parable to m ea su red v a lu e s .

101

H o w ev er, the r e s u lt s

r

' '
art inconclusive because of the wide range o f d en sity v a lu e s ob­
tained and the lack o f c o r r e la tio n betw een f r e e - a ir anom aly v a lu es
and various types of g la cia l s e d im e n ts .

The interpolation of the

fTea-air anomaly valu es to w ell lo ca tio n s w h ere d ir e c t g ra v ity obser—
vetions were not availab le and the d ifficu lty o f defining the polynom ial
equation which b est app roxim ates the regional trend w ere the m ain
sources of inaccuracy.

(5)

The g ravity r e sid u a ls obtained by

approximating the regional trend by a polynom ial applying the method
of least squares is useful in delin eatin g bedrock c h a n n e ls.

The

method however, did not r e su lt in a quantitative d efin ition o f the
residual Bouguer gravity a n o m a lie s .

The r e sid u a ls obtained by

approximating the regional by a polynom ial o f up to the seven th
degree appeared to be d istorted by the gravitation al e ffe c ts o f deep
structures which should have been elim in a ted a s part o f the r eg io n a l.
Accordingly, th ese r e sid u a ls w ere not su ita b le for quantitative
interpretation.

Suggestions

for Further S tu d ies

Additional gravity o b se r v a tio n s and exp lo ra tio n s! d r illin g is
desirable in S ch oolcraft and P r a ir ie Ronde T ow nsh .ps to define
accurately the "MMv a lle y and its tr ib u ta r ie s .

The "A" v a lle y in

Ross and C harleston T ow nships is defined on the b a s is o f only a few
gravity o b serv a tio n s.

F urther g ra v ity and exp lora tion d r illin g in

103

t a r e a is thus a ls o ju stified for defining the a x is o f the v a lle y and
pure o f its glacial se d im e n ts.
Very little is known about the g la cia l sed im en ts in the "BMand MK"
Hays and so m ore exploration d rillin g is d esira b le here a s w e ll.

The glacial d ep o sits o f the outwash apron located between the inner
J outer Kalamazoo m orain es appear to be form ed m o stly o f th ick ,
(hiy perm eable sand a n d /o r gravel h o r iz o n s.

B ecause of the

mmercial im plications th is area is highly recom m ended for fu r I#**' exploration d r illin g .
T h e im plications for detailed g la cia l g eolo gical study in such
using geophysical techniques a r e c o n sid e r a b le .

They a re not

academ ically o f in te r e s t, but can lead to locating further and

bStter sources of uncontaminated w ater for future co m m er cia l and
municipal u s e .

B IB L IO G R A P H Y

Agees* W. B - ,

1 9 5 1 , L e a s t s q u a r e r e s id u a l a n o m a ly d e t e r m in a tio n :
G e o p h y s i c s , V . 13, p . 6 8 6 —
696.

Alden, VV. M ., and L e ig h to n , M . M . , 1 9 1 7 , T h e Iow an D r ift: A
review o f th e e v i d e n c e s o f th e Iow an s t a g e o f G la c ia tio n : Iow a
G eological S u r v e y , V - 2 6 , p . 5 0 - 2 1 2 .
A le x a n d e r , H . S . ,

1 9 3 2 , P o th o le e r o s i o n :

J o u r . G e o l. V . 4 0 ,

p. 3 0 5 - 3 3 7 .
A rey, M . F . , 1 9 0 9 , G e o lo g y o f D a v is C ounty:
Survey, V . 2 0 , p. 5 1 1 .

Iow a G e o lo g ic a l

Athy, L . F .> 1 9 3 0 , D e n s it y and p o r o s i t y o f s e d im e n t a r y r o c k s :
B u ll. A m . A s s o c
P e t. G e o l., V . 14, p . 1 -2 5 .
Bain, H. F . , 1 8 9 7 , G e o lo g y o f D e c a t i e r C ounty:
Survey, V . 8 , p . 2 9 2 .

Iow a G e o lo g ic a l

Birch, F . , 1 9 4 2 , H andbook o f P h y s i c a l C o n s ta n ts :
s p e c ia l p a p e r s 36„

G e o l. S o c . A m . ,

Brown, R . E . , 1 9 6 3 , B e d r o c k t o p o g r a p h y , lit h o l o g y , and g l a c i a l d r if t
th ic k n e ss o f L a p e e r an d S t . C la ir C o u n t i e s , M ic h ig a n : M a s t e r ’s
T h e s is , M ic h ig a n S t a t e U n i v e r s i t y , p . 2 9 - 3 2 .
Coffey, G. N . , 1 9 3 0 , P r e g l a c i a l , i n t e r g l a c i a l , and p o s t g l a c i a l
c h a n g es o f d r a in a g e in n o r t h e a s t e r n O h io w ith s p e c i a l r e f e r e n c e
to the U pper M u sk in g u m D r a in a g e B a s in : O h io J o u r n a l o f
S c ie n c e , V . 3 0 , p . 3 7 3 - 3 8 4 .
Cohee, G. V . , 1 9 6 5 , G e o lo g ic h i s t o r y o f th e M ic h ig a n B a s in :
Journal o f th e W a sh in g to n A c a d e m y o f S c i e n c e , V . 5 5 ,
p. 2 1 1 -2 2 3 .
Cotton, C . A . , 1941 , T h e lo n g itu d in a l p r o f i l e s o f g la c ia t e d v a l l e y s :
Jour. G e o l., V . 4 9 , p . 1 1 3 -1 2 8 .

Chamberlin, T . C . , 1 8 8 8 , T h e r o c k s c o r i n g o f th e g r e a t i c e in v a s io n :
United S t a t e s G e o lo g ic a l S u r v e y , 7 th A n n . R e p t . , p .
104

1 4 7 -2 4 8 .

105

Dean, W* C ., 1958, F req u en cy a n a ly s is fo r g r a v ity and m a g n etic
interpretation: G e o p h y s ic s , V 2 3 , p . 9 7 - 1 2 7 .
Deutsch, M , V a n lie r , K. E . , and G ir o u x , P . R . , 1960, Ground
water hydrology and g la c ia l g e o lo g y o f the K a la m azoo A reaMichigan: United S t a t e s G e o lo g ic a l S u r v e y P r o g r e s s R ep ort
Number 2 3 , p . 122 .
Elkins, T. A . , 1951, The se c o n d d e r iv a tiv e m ethod o f g r a v ity in te r ­
pretation: G e o p h y s ic s , V . 2 7 , p. 2 9 - 5 0 .
Fenneman, N. M. , 1938, FTiysiography o f E a s te r n U nited S ta te s ;
McGraw-Hill Book C om p an y, p . 4 6 8 - 4 7 2 .
Fidler, M. M. , 1943, The p r e g la c ia l T e a y s V a lle y in Indiana:
Jour. G eol. V 5 , p . 4 1 1 -4 1 8
Giroux, P. R . , H en d rick so n , G . E . , S to im e n o ff, L . E .» and
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Htnze, W. » 1963, Regional g ra v ity and m agnetic anom aly m ap, the
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107

Leverett, F . , 1906, W ater su p p lie s o f K alam azoo C ounty, in
L everett and o th e r s , Flow ing w e lls and m unicipal w a ter
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* Leverett, F . , 1906b, G eological con d ition s o f m unicipal and in sti­
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?
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j Nettleton, L. L . , 1954, R e g io n a ls, r e s id u a ls , and stru ctu re:
i:
G eop h ysics, V . 19, p . 1 -2 2 .
£
^fcimerov, B . , 1929, R e su lts o f g r a v im e tr ic o b se r v a tio n s on S h u v a ?
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f.;

OfcJham, C . H. G . , and S u th erla n d , D . B . , 1955, O rthogonal p oly­
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*
V . 2 0 , p . 2 9 5 -3 0 6 .
t;

108

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ft A . , and J a in , S . , 1961, A sim p le in tegral tran sfo rm and its
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275.

|

tefer, E . J . , W hite, G. W. , and Van T y l, D . W. , 1946, The
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in sou th eastern M ichigan: P h. D . T h e s is , M ichigan S tate
|
U n iversity .
;
$
p a g e r t, A . J . F . , 1942, D eterm ination o f the Bouguer c o r r e c tio n
I
constant: G e o p h y sic s, V . 7 , p . 2 9 -3 4 .
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109

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M cG raw -H ill.

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G eop h ysics,

Vfcr Steeg, K . , 1934, The buried topography of N orth-C entral Ohio
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58 5 .
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T ra n s. III. A cad.

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