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ABSTRACT

A STUDY OF BURIED BEDROCK VALLEYS NEAR
SOUTH HAVEN, MICHIGAN, BY
THE GRAVITY METHOD

by John S. Klasner

A total of 358 gravity stations were observed in an
area of 55 square miles at approximately one-quarter mile
intervals along east-west section line roads. Two detail
gravity profiles were located over the deepest known val-
ley in the area at a station spacing of approximately 300
feet. A density of 2.15 gm/cc was determined for the
glacial drift from a density profile.

Standard procedures were used for the reduction of
the raw gravity data. The least squares profile method,
the three dimensional least squares method, and the cross
profile method were the interpretational techniques used
to isolate the residual gravity anomalies. Each of the
three methods gave essentially the same results although
the magnitude of the residual anomalies varied as much
as 54 per cent.

A quantitative examination of the source of the
residual gravity anomaly minimums was made at four loca-
tions by comparing a theoretically-computed residual grav-

ity anomaly with the observed residual gravity anomaly.

JOHN S. KLASNER

A topographic map of the bedrock surface, utilizing
gravity and well-log data, shows three main bedrock valleys
in the area. One valley trends north-south near the
western edge of the area and the two other valleys lie on
either side of a series of bedrock highs which trend diag-

onally across the area.

THEE“

 

 

A STUDY OF BURIED BEDROCK VALLEYS NEAR
SOUTH HAVEN, MICHIGAN, BY
THE GRAVITY METHOD

By

John S. Klasner

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Geology

1964

ACKNOWLEDGMENTS

The author wishes to express his sincere thanks to
the following people and organizations:

To Dr. William J. Hinze for his unceasing interest
and valuable technical guidance in the preparation of this
manuscript.

To. Dr. H. B. Stonehouse and Dr. J. Zinn for reviewing
the manuscript and for their helpful suggestions.

To the United States Geological Survey for the finan—
cial assistance in the gathering of the field data.

The Messrs G. Hendrickson, K. Vanlier, and P. Giroux
of the Lansing branch of the U. S. Geological Survey for
their encouragement and suggestions during the preparation
of this paper.

To the Michigan State Highway Department for preparing
a seismic profile in the area of this gravity study.

To Mr. D. L. Merritt for his valuable assistance in

the programming of the gravity data for the digital computer.

11

THESIS

 

TABLE OF CONTENTS

Page
ACKNOWLEDGMENTS . . . . . . . . . . . . . 11
LIST OF FIGURES . . . . . . . . . . . . . 1V
LIST OF PLATES . . . . . . . . . . . . . V
INTRODUCTION 1
GEOGRAPHY OF THE AREA . 2
GEOLOGY OF THE AREA . 4
FIELD WORK . . . . . . . . . 6
REDUCTION OF DATA . . . . . . . . . . . . 8
Introduction . . . . . . . . . . 8
Observed Gravity . . . . . . . . . 9
Latitude Correction . . . . . . . . . . . 9
Free-air Correction . . . . . . . . . . . 10
Mass Correction . . . . . . . . . . . . lO
Terrain Corrections . . . . . . . . . . . ll
ACCURACY OF BOUGUER REDUCTIONS . . . . . . . . 12
DISCUSSION OF THE BOUGUER GRAVITY ANOMALY MAP . . . 15
ISOLATION OF THE BEDROCK ANOMALIES . . . . . . 16
Introduction . . . . . . . . . 15
Least Squares Profile Method . . . . . . 20
Three Dimensional Least Squares Method . . . . 20
Cross Profile Method . . . . . 22
Discussion of the Residual Gravity Maps . . . . 23
COMPARISON PROFILES OF OBSERVED AND THEORETICAL
RESIDUAL ANOMALIES . . . . . . . . . . . 25
COMBINED INTERPRETATION FROM WELL- LOG AND GRAVITY
DATA . . . . . . . . . . . . . 37
SUMMARY . . . . . . . . . . . . . . . 39
BIBLIOGRAPHY . . . . . . . . . . . . . . 40

SUPP
M LEMENTARY

IHESIE

 

LIST OF FIGURES

FIGURE PAGE
1. Area of Investigation . . . . . . . . 3
2. Area Location Plat . . . . . . . . . 5

3. Profile of Bouguer Gravity Anomaly with Least
Squares Fits . . . . . . . . . . 19

A. Bedrock Valley from Seismic Profile
Interpretation . . . . . . . . . . 26

5. Comparison of Observed and Computed Residual
Gravity Anomaly, Profile A-A' . . . . . 28

6. Theoretical Drift Densities versus Per cent
Sand and Gravel . . . . . . . . . 3O

7. Comparison of Observed and Computed Residual
Gravity Anomaly, Profile B-B' . . . . . 31

8. Comparison of Observed and Computed Residual
Gravity Anomaly, Profile C-C' . . . . . 33

9. Comparison of Observed and Computed Residual
Gravity Anomaly, Profile D-D' . . . . . 34

iv

LIST OF PLATES*

PLATE
1. Bouguer Gravity Map
2. Residual Gravity Map, Least Squares Profile Method

3. Residual Gravity Map, Three Dimensional Least Squares
Method--5th degree fit

4. Residual Gravity Map, Three Dimensional Least Squares
Method—~llth degree fit

5. Residual Gravity Map, Cross Profile Method

6. Topography of the Bedrock Surface

*All plates in pocket in back.

INTRODUCTION

The increasing demand for water has pointed out the
importance of buried bedrock valleys as possible sites for
ground water exploration in the glaciated areas of the
midwestern United States. In areas of adequate well control,
the bedrock valleys can be mapped from well-log data.
However, in areas of inadequate well control, geophysical
methods may serve as useful tools for mapping of the bed—
rock valley systems.

It is the purpose of this study to map the bedrock
valley system in the northwestern part of Van Buren County
by the gravity method, to test several methods for isolating
the residual anomalies caused by the buried valleys, and
to make a quantitative study of the source of the residual

anomalies.

GEOGRAPHY OF THE AREA

The area under study, shown in Figure l, is located
in South Haven, Geneva, and parts of Columbia and Bangor
townships of Van Buren County. It lies between latitudes
42° 19'N and A2° 25'N and longitudes 86° O5'W and 86°
16'w. Most of the area consists of privately owned farm
land which is evenly divided by a network of section-line
roads. Elevations range from the level of Lake Michigan,
579 feet above sea level, to a maximum of 760 feet above
sea level. In general the area is relatively flat with
local relief of 20 to 40 feet along the river valleys.
The Black River and its tributaries constitute the main

drainage system in the area.

 

 

  
   

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AREA OF INVESTIGATION
FIGURE I

 

GEOLOGY OF THE AREA

The area of investigation lies near the southwestern
edge of the Michigan Basin. Goldwater shale forms the bed-
rock, and it is dissected by a system of bedrock valleys
which have been mapped from well-log data (Terwilliger,
unpublished map).

Information from Oil well data indicates the presence
of anticlinal structures within the sedimentary column.
Specifically, there are three anticlinal structures in the
Traverse formation at an approximate depth of MOO feet
below sea level. The closure on these features is approxi-
mately 20 feet. Their location is shown in Figure 2

(Michigan Geological Survey, unpublished maps).

 

 

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FIELD WORK

Two exploration type gravimeters were used for this
study. These are Worden meter number 99 and World Wide
meter number 45. The respective calibration constants of
these two meters are 0.0994(5) and 0.10094 milligals per
scale division. The calibration constants for both
meters were checked at the beginning of the survey to
assure consistant results. Both meters read the relative
acceleration of gravity to an accuracy of 0.01 milligals.
The normal acceleration of gravity at the earth's surface
is 980 gals. Thus, 0.01 mgals is approximately one part
in one hundred million of the normal gravity of the earth.

Although the meters are temperature compensated and
barometrically controlled, they are subject to time
variations or drift. These time variations of the gravi-
meter readings are caused by temperature changes, tidal
variations, spring fatique, and abrupt changes in the
atmospheric pressure. In order to keep track of these
variations, a check reading at one of a series of pre-
established base stations was obtained at least once per
hour during the course of the survey.

A series of gravity base stations were established

throughout the area at easily accessible locations and

tied to a primary base, located near the center of the
area, by the base looping method.

Gravity readings were observed at approximately
one—quarter mile intervals along the east—west section
line roads and tied to the base stations by the hourly
base-check readings.

Two detail profiles were located over the deepest
known valley in the area. The location of these profiles
is shown in Figure 2. The station Spacing on these detail
profiles are approximately 300 feet.

A density profile to determine the in situ density
of the glacial drift was located over a surface feature
with 20 feet of relief. A station spacing of 90 feet was
used on this profile. Its location is shown in Figure 2.

Station elevations and east—west horizontal locations
were surveyed with a Zeiss self-levelirg;level. Elevation
control was established from three U. S. Geological Survey
bench marks and two U. S. Coast and Geodetic Survey bench
marks. All traverses closed to an accuracy of 0.34 feet
or better. East—westhorizontaldistances were determined
by stadia intervals, and the control was carried only from
road intersection to road intersection to eliminate

accumulative error.

REDUCTION OF DATA

Introduction

 

Corrections for the influence of known near surface
and surface conditions must be applied to the raw gravity
data before it is interpreted. These corrections are
applied to each gravity stations and the resulting value
is called the Bouguer gravity anomaly. The Bouguer gravity
anomaly map is an expression of the horizontal variation
in the density of the material within the earth which has
not been accounted for in the Bouguer corrections.

The Bouguer gravity anomaly values were calculated

on a digital computer according to the following formula:

Gb = E0 _ 81 + 8f - Sm + 8t:
where:
Gb = Bouguer gravity anomaly

g = observed gravity

0
g1 = latitude cOrrection
gf = free-air correction

gm = mass correction

gt = terrain correction

9
Observed Gravity

 

The observed gravity values were determined by first
correcting the meter readings for drift, and then multi-
plying these values by the calibration constant of the
meter. The amount of drift for each gravity observation
was determined from graphs of the hourly base-check
readings. If the hourly drift exceeded one scale division,
about 0.1 mgal, the stations that were occupied during

that hour were repeated to insure drift correction accuracy.

Latitude Correction

 

The latitude correction takes into account the
increase in gravity from the equator to the poles. In
this case, latitude corrections were made from latitude
42° 19'N, the arbitrarily selected base latitude. Dis—
tances were measured in feet from the base latitude to
each gravity station on U. S. Geological Survey, 7 1/2
minute, topographic quadrangles. The correction to
be applied to each gravity station was determined by
multiplying the latitude distance by a constant, K.
According to Nettleton (1940), K = 1.307 Sin 2O mgals
per mile, where O is the latitude of the area under

study. In this area K = 0.0002465 mgals per foot.

lO

Free—Air Correction

 

The free—air correction takes into account the decrease
in gravity with an increase in elevation. This correction
was calculated by multiplying the vertical gradient of grav-
ity, 0.09406 mgals per foot, by the elevation differential

between the gravity station and the datum.

Mass Correction

 

The mass correction takes into account the attraction
of the material between the datum and the elevation of each
gravity station. The formula to determine the mass cor-
rection is 0.01276 h mgals per foot, where: a = density
(2.15 gm/cc), and h = the elevation differential between
the datum and the gravity station. In this correction both
the choice of the datum and the density to) are critical
factors. ‘

A 600 foot datum was chosen for this study. This
datum was chosen to minimize the effect on the mass cor—
rection of density variations within the glacial drift.
Both lateral and vertical variations in the density of the
glacial drift result from the heterogeneous nature of the
glacial drift, and from fluctuations in the elevation of
the water table. If the elevation differential (h) is
kept at a minimum, any error in the density (a ) will be

minimized in the mass correction.

11

The density used for the mass correction was 2.15
gm/cc. this value was obtained by a least squares reduction
of the density profile by the method of Jung (1953). One
of the disadvantages of density determination from a den—
sity profile is that in an area of little topographic relief,
very accurate gravity values are needed to make an accurate
density determination. Because this area is relatively
flat, it was difficult to locate an accessible topographic
feature of appreciable relief. However, this disadvantage
is somewhat compensated because a larger error can be toler—
ated in areas of small relief (Nettleton, 1940). Also, the
drift density that was determined from this density profile
was geologically feasible and agrees with other values used

in the reduction of gravity data observed in nearby areas.

Terrain Corrections

 

Because of the lack of appreciable relief in the
area, the effect of variations in the elevation of the land
surface on the acceleration of gravity was checked by com-
puting terrain corrections for those gravity stations that
were located in the areas of maximum relief. The maximum
terrain correction, computed by Hammer's method (1939),

was 0.04 mgals.

ACCURACY OF BOUGUER REDUCTIONS

The main factors that cause errors in the calculation
of the Bouguer gravity anomaly are:

1. Errors in obtaining the observed gravity values.

2. Errors in elevations.

3. Errors in latitude measurements.

4. Errors in the density of the glacial drift.

An estimate of the accuracy of the gravimeter readings
and the drift control was obtained by re—observing several
stations. Nine stations were re-occupied on different days,
and eight stations were re-read on the same day. The stan-
dard deviation for these repeated gravity observations is
I 0.02 mgals.

Errors in station elevations affect the free-air and
mass corrections. The maximum misclosure on any of the
surveyed lOOps was 0.34 feet. By combining the free-air
and the mass effects, at a density of 2.15 gm/cc, a maximum
error in elevation of 0.34 feet would cause a 0.02 mgal
error in the calculation of the Bouguer gravity anomaly.

Errors in the latitude correction depend on the accur-
acy of the latitude measurements. Latitude measurements can
be made to an accuracy of 150 feet or better from 7 1/2
minute U. S. G. S. topographic quadrangles. This gives a
maximum error of 0.03 mgals at 0.0002465 mgals per foot.

12

13

The magnitude of the error due to an incorrect
density value in the mass correction is mainly dependent
on the amount of relief in the area. In this area the
local relief is rarely as great as 40 feet. The hetro—
geneous nature of the glacial drift makes it extremely
difficult to estimate realistically the error caused by
an incorrect value for the density of the glacial drift.
If an average density error of, say, 0.2 gm/cc is assumed
for the glacial drift, it would cause a constant error
over a flat surface. However, in areas of local relief,
this error could cause a critiCal distortion of the Bouguer
gravity anomaly. Thus, it is reasonable to estimate the
error for the density of the glacial drift on the basis of
the maximum local relief of 40 feet. This error is:

E = 0.00l28'Ao-A h

where:

0.00128 = the magnitude of error in milligals
per foot for each 0.1 gm/cc error
in density.

T A0 = error in drift density in gm/cc.
Ah = maximum local relief in feet.

The resulting error is i 0.10 mgals. However, this

error can often be identified because of its direct

correlation with topography.

14

A combination of all sources of possible error gives
a miximum possible error of t 0.2 mgals. However, the
coincidence in sign of all of these possible errors at one

single station is unlikely.

DISCUSSION OF THE BOUGUER GRAVITY ANOMALY MAP

The Bouguer gravity anomaly map (Plate 1) shows
an increase in regional gravity from 37.5 mgals in the
southwest to 52.00 mgals in the northeast. A large
gravity nose points diagonally across the area toward
the southwest. This map shows excellent agreement with
the regional gravity map of Michigan (Hinze, 1963). It
lies on the southwest flank of a regional gravity high
that has 13 mgals of closure.

Two anomalous areas that interrupt the regional
gravity picture are readily apparent. One is the gravity
low that trends in a north—south direction along the
South Haven—Geneva township line. The other anomalous

area lies about two miles north of the city of Bangor.

ISOLATION OF THE BEDROCK ANOMALIES

Introduction

 

The Bouguer gravity anomaly map illustrates the
effect that the horizontal variations in the density of
the material within the earth have on the acceleration
of gravity. To determine the effects of the near surface
features on the acceleration of gravity, the effect of
the deep, broad, regional features must be removed from
the Bouguer gravity anomaly. Three methods were used to
remove the regional gravity effects. These are the least
squares profile method, the three dimensional least squares
method, and the cross profile method. The purpose of
these three methods is to approximate the regional gravity
anomaly. The residual gravity anomaly is then obtained by
taking the difference between the observed Bouguer gravity

anomaly and the regional gravity anomaly at each station.
Least Squares Profile Method

The principle of the least squares method is to
pass a curve through a set of points so that the sum of the

residual errors is a minimum (Smith, 1934).

16

17

To illustrate: z' = a + bx = ex2 is the polynomial

equatiOn for a second degree curve that is to be passed

through a set of points, (x, 2), (x2, 22), . . . . , (Xn’ Zn):
where:
n = the number of points
xi = the horizontal coordinate of the point.
21 = the Bouguer gravity value of the point.

The sum of the squares of the residual errors (Zr2) is
given as follows:

Ere = 2(z-z') = 2(z—a-bx—cx2)2
where:

the observed gravity value

Z

z' the regional gravity value
r(xi, 21) = the residual gravity value at point i.
For the sum of the errors to be a minimum, the total

differential of 2(z—z—bx—cx2)2 is equal to zero.

Thus:
2
d(Zr2) = 3(Er2) da + 3(2r2) db + BIZP I dc = 0,
3a ab BC
or:

22(z—a-ox—cx2) = 0

Z2x(z—a-bx-cx2) = 0

22x2(z-a-bx—cx2) = 0.

Q) Q) Q)
Q) o: 0)
0"3 U"'S QJI'S

I'D R) m

II

It then follows that:

Zz = na + be + che

l8

sz aZx + be2 + cfx3

erz aZx2 + be3 + chu.

To determine the coefficients (a, b, c), the three

simultaneous equations can be solved by matrices as follows:

 

 

 

 

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2x 2x2 2x3 = sz
er 2x3 2x“ c x2z

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2 -1
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In a similar manner higher degree equations can be
computed to fit a set of gravity values. A digital com-
puter was used to calculate least squares equations from
the first to the twentieth degree. Figure 3 illustrates
how the least squares curves of various degrees fit a
Bouguer gravity anomaly profile. The third degree fit
was chosen as the best approximation to the regional
gravity anomaly.

Plate 2 shows the residual gravity anomaly map for
the third degree fit. Three main residual gravity lows
occur in the area. One trends in a north-south direction
along the South Haven—Geneva township line. The two other
residual lows lie on either Side of a series of residual

gravity highs which trend diagonally across the area in a

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northeast—southwest direction. Several tributary residual

lows Join these three gravity lows at various locations.

Three Dimensional Least Squares Method
The three dimensional least squares method is a
technique by which the regional gravity anomaly is approx-
imated by a three dimensional surface. In contrast to the
least squares profile method which uses a system of two

coordinates, (xl zl) (x2 Z2),....(Xn zn), the three dimen-

sional least squares method utilizes a system of three

coordinates, (x1 y1 zl), (x2 y2 z2),....(xn yn Zn)’ where

x and y1 are the east-west and north-south horizontal

i
coordinates of the gravity station, and Zi is the Bouguer

gravity anomaly value of the station. The polynomial
equations for the three dimensional least squares method
Iwere solved by matrices on a digital computer in a manner
sijnilar to the least squares profile technique.

Seven three dimensional least squares surfaces were
(xxnputed to fit the Bouguer gravity anomaly. These in—
volved equations of the first, third, fifth, seventh,
ninifll, eleventh, and thirteenth degree. After an examin-
atixni of the various degree fits, the fifth degree surface

was cfllosen as the best approximation to the regional
STaVity'anomaLy.
The residual gravity anomalies from the fifth degree

surfknze are shown on Plate 3. A comparison with the results

21

of the least squares profile method illustrates that the
two methods give essentially the same results. The three
main residual lows are present at the same locations, and
the series of residual graviQJhighstrend diagonally across
the area.

Plate 4 shows the residual gravity anomalies from
the eleventh degree surface. In general this map is similar
to the two previous interpretations. However, the size and
configuration of the residual anomalies are changed

appreciably.
Cross Profile Method

The cross profile method for the approximation of
the regional gravity anomaly is a personal interpretation
technique. It involves the selection of two series of
Bouguer gravity profiles at right angles to each other.
A regional gravity profile is drawn along each of the
selected profiles from an examination of the Bouguer
gravity anomaly. These regional profiles are inspected
and adjusted wherever necessary so that the regional
gravity values are equal at the points of intersection
of any two profiles, and that the resulting regional gravity
profiles are geologically reasonable. The residual gravity
values are obtained by subtracting the value of the regional
gravity anomaly from the value of the Bouguer gravity

anomaly at each station.

22

Plate 5 shows the residual gravity map which was
obtained from the cross profile interpretation. Similar
to the two previously discussed methods, the cross profile
technique gives the three main residual gravity lows and
the series of residual gravity highs trending diagonally

across the area.

Discussion of the Residual Gravity Maps

The residual gravity lows are attributed to bedrock
valleys that are filled with glacial deposits. Because
of its greater amount of pore space, the glacial material
filling the bedrock valleys is less dense than the adja-
cent bedrock. This decrease in density in the bedrock
valleys causes the acceleration of gravity to be less
over the buried valleys. These deviations in the acceler—
ation of gravity from the regional gravity anomaly are
shown as residual lows on the residual gravity maps.

The three gravity highs that trend diagonally across
the area in a northeast—southwest direction could be attri—
buted to either structures within the sedimentary column
of high areas on the bedrock surface. The large residual
high that lies near the center of Geneva township appears
to be related to a structural high in the Traverse formation
as shown by comparing Figure 2 and Plate 6. The other
gravity high that is located in the northeast corner of

Geneva township does not appear to be related to a

23

structural high in the Traverse formation. Both of these
residual gravity highs, however, do correspond to high
areas on the bedrock surface as shown on Plate 6. It thus
appears that the residual gravity highs are the results of
the effects from both the bedrock surface and deeper

structures within the sedimentary column.

COMPARISON PROFILES 0F OBSERVED AND THEORETICAL
RESIDUAL ANOMALIES

Talwani (1959) has outlined a method for the computa—
tion of the acceleration of gravity due to two dimensional
bodies. These are bodies which have finite dimensions only
in one direction; the dimension normal to the finite dimen-
sion is considered to be infinite. By approximating the
shape of the two dimensional body with a vertical polygon,
analytical expressions can be obtained for the gravitational
attraction of the polygon. The computed gravitational attrac-
tion of the two dimensional body is compared with the ob—
served gravitational attraction of the body. The closeness
of the comparison depends on how closely the dimensions
and depth of the theoretical body corresponds to those
of the actual body, and on how accurately the density con-
trast between the body and the host rock is estimated.

By logarithmic potential, the gravitational attrac-
tion for a two dimensional body is equal to 2G péde which
is the line integral taken along the periphery of the body.
In the above formula G is the gravitational constant,p
is the density of the body, and z and O are the respective
distance and angle parameters to define the dimensions of
the body. By setting up a coordinate system to locate the

ground points at which the gravity is being computed, and
24

25

to define the location of the vertices of the polygon,
Talwani developed a method by which the above integral can
be solved on a digital computer. The formula for the
gravitational attraction due to the whole polygon at any
point along the profile is:
n
v = 2G 02 z.,
i=1 1
where:
G and p are the same as above,
zi = the results of the evaluation of the
line integral over the ith side of the
polygon,
n = the number of the sides of the polygon
v = the total gravitational effect of the
polygon.

Four comparison profiles were drawn across the bedrock
valleys. The locations of the comparison profiles are shown
in Figure 2. All four profiles were located in areas of
depth control. Three of the comparison profiles were
selected over oil well locations, and the other profile was
located over a seismic profile which was observed by the
Michigan State Highway Department (Figure 4).

These profiles involved a comparison between an
observed residual gravity profile, taken fromifluacross pro-

file interpretation, and the residual profile computed from

a two dimensional body by the method outlined above. The

26

 

 

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Observed residual anomalies were taken from the cross pro-
file interpretation because the residual anomalies of
interest are clearly defined and are not subject to smooth-
ing effects in the cross profile method as they are in the
least squares methods.

Comparison profile A—A' (Figure 5) was selected at
the location of coincident seismic and detail gravity
profiles. The first approximation for the shape and depth
of the theoretical bedrock valley was made on the basis of
the results of seismic data. To obtain the desired fit
between the observed and computed gravity anomalies, the
width of the body from the seismic interpretation was
altered as shown by comparing Figures 4 and 5. The dashed
line in Figure 4 illustrates an Observed reversed seismic
dip. Although this was unexplained in the seismic inter—
pretation, it does support the presence of the bench on
the west side of the bedrock valley as shown in Figure 5.

Control for the depth and general shape of the bed-
rock valley from the seismic profile permitted a reasonable
estimate to be made of the density differential between the
material filling the valley and the adjacent bedrock. This
density differential was used as a guide in calculating the

three remaining comparison profiles.

28

 

 

 

I I

 

T

WEST

A SURFACE A

 
     
   
 

   
  

FEET

BEDROCK
VALLEY
G‘ IO.224 amt/cc.

DEPTH CONTROL TAKEN FROM SEISMIC PROFILE

 
  
     

BSERVED ANOMALY
COMPUTED ANOMALY

\J

.1

RESIDUAL GRAVITY ANOMALY

EAST

 

-0.0
--O.l
--02
”0.3

--O.4

r-O.5
--O.6
”0.7
--O.8
--O.9
--I.O

 

h--I.I

COMPARISON OF OBSERVED AND COMPUTED

FIGURE 5

FEET ABOVE SEA LEVEL

MILLIGALS

 

 

29

A density differential of 0.224 gm/cc was obtained
from comparison profile A-A'. The density of the Coldwater
shale is estimated at 2.65 gm/cc (Michigan State University,
unpublished data). This gives 2.43 gm/cc as the density
of the material filling the bedrock valley.

McGinnis, Kempton, and Heigold (1963) made a theoreti—
cal study of the density of the glacial drift, assuming
spherical grains, as a function of percentage of sand and
gravel. The study was made in connection with a gravity
study of bedrock valleys in northern Illinois. In refer-
ence to their results as shownillFigure 6, a density of
2.43 gm/cc gives either 48 or 87 per cent sand and gravel
for the saturated material in the bedrock valley. The
energy levels in this diagram refer to the type of packing
of the glacial material. The lowest energy level refers
to the situation in which the Spherical grains are packed
to give the least amount of pore space. The highest energy
level refers to the situation in which the Spherical grains
give the greatest amount of pore space. A value near the
lowest energy level (saturated) was chosen for the material
filling the valley since it is buried by several hundreds
of feet of glacial drift.

Comparison profile B-B' (Figure 7) was located over
a detail gravity profile two miles north of profile A-A'.

The shape of the valley was determined through repeated

30

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POINT or DEPTH CONTROL
FROM WELL-LOG "’ '00

 

(COMPUTED ANOMALY

   
    

" .. OBSERVED ANOMALY

 

COMPARISON OF OBSERVED AND COMPUTED
RESIDUAL GRAVITY ANOMALY

FIGURE 7

FEET ABOVE SEA LEVEL

MILLIGALS

 

 

32

alterations of an initial, arbitrary approximation. A
value of 0.225 gm/cc for the density differential was
used in this approximation.

Profile C-C' (Figure 8) was located over the bedrock
valley that trends in a northwest—southeast direction in
the northwest corner of Geneva township. The shape of
the valley was approximated in the same manner as profile
B—B'. A value of 0.224 gm/cc was used as the density
differential for the calculation of the theoretical valley.

Profile D-D' was located in the southeast corner of
the area across the northwest-southwest trending bedrock
valley. The shape of the bedrock valley was approximated
in the same manner as profiles B—B' and C-C'. Figure 9
illustrates the results that were obtained. The bench on
the northeast side of the valley is based on a depth obtained
from an oil well log. The observed residual anomaly appears
to be incorrectly estimated because a reasonable comparison
cannot be made with the well—log depth. The incorrect
estimate of the magnitude of the residual anomaly is
attributed to the fact that this is near the edge of the
area of gravity control. In order to obtain a better estim—
ate of the size of the residual anomaly, the gravity control
would have to be extended outside of the present area of
control.

Without the depth control that was available for

each profile, a unique solution for the size and shape of

33

 

 

SOUTHWEST NORTHEAST
c SURFACE ‘ c'

_ (W 030.224omucs. BEDROCK -4m
L POINT OF DEPTH CONTROL VALLEY haoo

FROM WELL - LOG

 

 

 

 

I
§
FEET ABOVE SEA LEVEL

fOMPUTED ANOMALY
......... oBSERVED ANOMALY

    

 

I

p

01
MILLIGALS

 

 

COMPARISON OF OBSERVED AND COMPUTED
RESIDUAL GRAVITY ANOMALY

FIGURE 3

 

 

31+

 

 

FEET
O 5000
L 4 L 42 l J

SOUTHWEST NORTHEAST

*- [W' - TOO

 

 
     
   
 
   

BEDROCK
VALLEY

0' IO.23O mice.

POINT OF DEPTH CONTROL FIOO
FROM WELL-LOG

 

 

    

I P-0.0
r-OJ
L'02
-'O.3
--04

OMPUTED ANOMALY

OBSERVED ANOMALY

" -036

 

 

COMPARISON OF OBSERVED AND COMPUTED
RESIDUAL GRAVITY ANOMALY

FIGURE 9

 

FEET ABOVE SEA LEVEL

MILLIGALS

 

35

the bedrock valley could not be obtained. A series of
theoretical valleys could be computed by changing one or
more of the three variables, depth, size, and density. For
example, if the theoretical valley for profile B-B' was
lowered 40 feet, and the dimensions and density of the

body were increased, a new comparison could be obtained .
between the observed and computed residual gravity anomalies.
This process could be repeated at several different depths
until the depth factor would make it impossible to attain
an agreement between the computed and observed residual

anomalies.

COMBINED INTERPRETATION FROM WELL-LOG
DATA AND GRAVITY DATA

The residual gravity maps, discussed above, are not
bedrock surface maps as such. They represent the effects
of the near surface materials on the acceleration of gravity
after the regional gravity effects have been removed from
the Bouguer gravity anomaly. A map of the elevation of the
bedrock surface was made from a combined interpretation of
the gravity data and well—log data (Plate 6). In the areas
of adequate well control, the gravity interpretation was
supported by the well—log data, and in areas of poor well
control the gravity data aided in the mapping of the bed-
rock surface.

There are three major bedrock valleys in the area.
One of these valleys trends along the South Haven—Geneva
township line. The two other valleys lie on either side of
bedrock high which trends diagonally across the area in a
northeast-southwest direction. A low area, or saddle, with
about 150 feet of local relief joins these two oppositely
trending valleys. The directions from which the tributary
valleys enter the main valleys indicate the probable direc-
tion of former stream-flow in the bedrock valleys.

The depths of the bedrock valleys vary considerably.

The north-south trending valley is a maximum of 400 feet
36

37

deep. The valley which lies on the northwestern SIOpe of
the bedrock divide is approximately 180 feet deep at the
location of profile B—B'. The valley which lies on the
southwestern Slope of the bedrock divide is of the order
of 600 feet deep, however, an accurate depth approximation
cannot be made at this location because it is near the

edge of the area of gravity control.

SUMMARY

The bedrock valley system has been successfully
mapped by the gravity method in the northwestern corner of
Van Buren County. Three main bedrock valleys were delini-
ated. These are a north-south trending valley along the
South Haven-Geneva township line, and two valleys which lie
on the Opposite slopes of a northeast-southwest trending
bedrock divide. A tOpographic map of the bedrock surface
has been made from a combined interpretation of the gravity
and well—log data.

The three interpretation techniques, the two least
squares methods, and the cross profile method have success-
fully isolated the anomalies caused by the bedrock valleys.
The least squares equations below the sixth degree approxi-
mate the regional gravity anomaly more closely than the
higher degree equations.

A quantitative study of the residual gravity anomalies
was made at four locations by the method of Talwani. Two
profiles were calculated for the north—south trending
valley, and a profile was computed for each of the two
northwest-southeast trending anomalies. All of the com-
parison profiles were selected in an area of depth control
so that unique solutions could be obtained for the dimen—
sions of the bedrock valleys.

38

39

The quantitative studies of the shape and approximate
density differentials of the bedrock valleys proved success—

ful and were supported by the known geology in the areas.

 

BIBLIOGRAPHY

HALL, D. H., and HAJNAL, Z. (1962) The gravimeter in
studies of buried valleys: Geophysics, v. 27,

pp- 939-951.

HAMMER, SIGMUND. (1939) Terrain corrections for gravi-
meter stations: Geophysics, v. 4, pp. 184—194.

HINZE, W. J. (1963) Regional gravity and magnetic maps
of the Southern Peninsula of Michigan: Michigan
Dept. of Conservation, Geological Survey Division,
Report of Investigation 1.

JUNG, KARL, (1953) Some remarks on the interpretation of
gravitational and magnetic anomalies: Geophysical
Prospecting, v. 1, pp. 29-35.

MCGINNIS, L. D., KEMPTON, J. P., and HEIGOLD, P. c. (1963)
Relationship of gravity anomalies to a drift—filled
bedrock valley system in northern Illinois: Illinois
State Geological Survey, Circular 354.

NETTLETON, L. L. (1940) Geophysical Prospecting for Oil:
McGraw-Hill Book Co., Inc., New York and London.

SMITH, J. G. (1934) Elementary Statistics: Henry Holt
and Co., Inc., New York.

TALWANI, MANIK, WORZEL, J. L., and LANDISMAN, MARK, (1959)
Rapid gravity computations for two—dimensional bodies
with application to the Mendicino submarine fracture
zone: Hour. Geophysical Research, v. 64, pp. 49—59.

TERWILLIGER, F. W. (1954) The glacial geology and ground
water resources of Van Buren County, Michigan in_
Occasional Papers on the Geology of Michigan:
Michigan Dept. of Conservation, Geological Survey
Division, Publication 48, pp. 14—95.

40

 

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