Gravimetry uses measurements of variations in Earth's gravitational field to obtain information about subsurface density variations. It has applications in hydrocarbon exploration, geological mapping, and other fields. Gravity measurements are based on Newton's law of universal gravitation. Instruments used include stable gravimeters like pendulums and torsion balances, as well as portable unstable gravimeters. Measurements require corrections for factors like latitude, altitude, tides and drift. Density differences between rock types are the source of gravitational anomalies that can be interpreted.

1. 1

2. GRAVIMETERY
METHOD
2

3. List:
• Outline of the lecture
• Some of the applications of gravity
surveying
• Preface
• Gravimetery vs. Magnetometery
• Primary principals and hypothesis
• Gravity corrections
• The density of rocks & minerals
• Gravity Measurements
• The instruments of measuring gravity
• Interpretation of gravitational data
• Ambiguities in gravimetery
• Regional & Residual Gravity
• Gravitational effect of different
structures
3

4. Outline of the lecture :
4
• Gravity method is used for recognition of rocks’ gravitational
variations or the density of earth’s layers.
• Indeed, measuring changes in earth’s gravity field and Sidelong
variations in density of subsurface rocks are required for gravity
surveys which gives valuable information about different
structures beneath the earth.

5. Some of the applications of gravity surveying:
• Hydrocarbon exploration
• Regional geological studies
• estimation of, mineral deposits
• Detection of sub-surface cavities (micro-gravity)
• Location of buried rock valleys
• Determination of glacier thickness
• Tidal oscillations-
• Shape of the earth(geodesy)
• Monitoring volcanoes 5

6. Preface:
• Gravimetery method fundamentally is based on Newton’s law of
gravity.
• According to this law , everything with the mass of “M” can apply
such a force to every other substances that have been placed in
a definite distance from it and is called “gravity force”.
6

7. • The rocks with higher density  Earth’s gravity field is
more on them and vice versa.
• These variations in the earth’s gravity field ,due to existence
of environmental anomalies , are called gravitational
anomalies.
7

8. Gravimetery vs. Magnetometery
8

9. Similarities:
In both of them:
• Little differences are measured in a relatively huge field of force.
• There is the possibility of defining absolute fields.
9

10. Differences:
• Due to gravity’s relatively small and uniform variations in
comparison to magnetic susceptibility’s variations;
Gravity anomalies < Magnetic anomalies
10

11. Differences
• Sensitivity of the machines used for measurements in:
Gravimetery > Magnetometery
• Complexity in time changes in related fields in :
Gravimetery < Magnetometery
• Complexity of corrections for measured data in:
Gravimetery > Magnetometery
11

12. • The exactness of variable field’s measurements in:
Gravimetery < Magnetometery
• The price of machines for:
Gravimetery > Magnetometery
• The proficiency of experts should be more in:
Gravimetery > Magnetometery
Differences
12

13. Primary principals and hypothesis
13

14. Newton’s gravity law :
Gravitational acceleration:
• Is considered as the base of gravity works.
𝐹 = 𝐺
𝑚1 𝑚2
𝑟2
14
• F=gravity force between m1 and m2
• R= the distance between m1 and m2
• G=universal coefficient of gravity
• ( G= 6.67 * Nm/kg in SI)
• (1 N = dyne )
𝑔 = 𝐺
𝑀𝑒
𝑅2
• Acceleration of free falling object= gravity acceleration =>
Applied force from earth to the mass.
• (g) in terms of (m/ 2 or (cm/ 2 )
𝑔 = 𝐺
𝑀𝑒
𝑅2
1 gal = mgal = gal = 1 cm/ 𝑒 2
g = a vectorial quantity

15. Gravitational potential:
• Gravitational field is usually
defined in terms of gravitational
potential.
• Gravitational potential = Work
done by the gravitational force
to the test unit mass to bring it
from infinity to the point ‘p’.
• U = G
𝑚
𝑟 15
p
m
M=1
Same-potential level
U= a scalar quantity

16. Shape of the earth:
• Earth is not an absolute sphere  gravitational acceleration :: is not fixed all
over the earth’s surface.
• Based on geodetic measurements & satellites’ data  Earth is a spheroidal
oIn equator  raised
oIn poles flattened  Polar flattening
• Due to polar flattening : (g) in equator < (g) in poles
16
(g)_
+
+

17. Magnitude of gravity relies on:
1) Geographical latitude
2) Altitude
3) Surrounding topography
4) Earth tides
5) Subsurface gravity changes  (*The only important factor in gravity
method.)
17

18. Spheroid & Geoid:
18
Spheroid
Geoid
continents
oceans
Spheroid
Geoid
A
B
N
Strike of vector
Mass anomaly
g =𝑔0 (1+∝ sin2
∅ + 𝛽 𝑖𝑛2
2∅ )
𝛼=0.0053024 𝛽= -0.0000058 𝑔0 =978.0318gals

19. 19
Gravity
corrections:
A) Geographical
latitude correction
B) Drift correction
C)Tidal correction
D)Altitude correction
1.Free air
correction
2.Bouguer
correction
3.Terrain
correctionE) Isostasy correction
F) Eotvos correction
.. ..

20. A) Geographical latitude correction
• Rotation of the earth & Slight equatorial bulge are the
causes of enhancing gravity with geographical latitude.
• Centrifugal acceleration <> Gravitational acceleration
• Centrifugal acceleration in  equator > poles :due to
• Polar flattening   gravity in equator < poles
20
Polar radius
Equatorial radius
Angular velocity
vector

21. • Centrifugal acceleration 
• This effect is partly removed with increasing of snatcher mass in
equator; thus, geographical latitude correction is essential for
north-south measurements.
• C 𝐿 ≈ 0.81 sin (2𝜃) mgal/km { 𝜃=geographical latitude (Radian) }
• Max gravity variations & thus: max latitude correction  in
altitude450
(correction:0.01 mgal per 12.2 m)(correction=0 in equator & poles)
21
(g) _
+
+

22. B)Drift correction:
• In all gravimeters amounts of gravity varies
with time!  Due to: creep of spring in
gravimeters.
• Drift correction in a time like ‘t’ is a deal like
‘d’ that is subtracted from observed amount.
22

23. C)Tidal
corrections
• Although : moon’s mass < sun’s mass ;;;
gravitational effect of: moon >> sun
Because : distance between: Earth &
Moon << Earth & Sun
• Max amplitude of gravitational variations
caused by tidal effects≈ 0.3mgal in 12 hours.
• While drift corrections tidal effects are
removed(due to their smooth & slow variations)
23

24. D) Altitude correction:
24
1)Free-air correction
2)Bouguer correction
3)Terrain correction

25. D)1)Free-air correction
• Because: g ≈
𝑟2 ;a correction is needed due to: Altitudinal variations between
stations.
• g≈ 𝑔0( −
2ℎ
𝑅𝑒
)
• For small altitude differences 𝐶 𝐹=
2 𝑔0 ℎ
𝑟𝑒
=0.3086 h
• 𝐶 𝐹 (if measuringpointisabove datumsurface) 𝐶 𝐹 should be added to data.
(if measuringpointisunder datumsurface) 𝐶 𝐹 shouldbesubtracted fromdata.
25
• 𝑔0 =amount of gravity in datum surface (Geoid)
• g = amount of gravity in the height of ‘h’ from datum surface
• h = Th
g≈ 𝑔0( −
2ℎ
𝑅𝑒
)
Measuring points
h
29

26. D)2)Bouguer correction:
• In free-air correction it is assumed that:
o The measuring point is placed in free-air
o The mass between that point & datum surface does not affect on the
measurements.
WHILE; in fact, this mass exists!!  so, its effect should be taken into account!
26

27. Bouguer correction is needed.
High amount of mass between measuring point & datum surface!
Due to:
The more the amount of measured gravity.
The more the altitude of the measuring point;
27

28. h
s Measuring point
Bouguerplate
• In Bouguer correction:
 All the measuring points are on the: flat & smooth plate
with infinite horizontal expansion. (Bouguer plate)
 Thickness & density of the mass between datum
surface & measuring surface are totally monotonic.
• 𝐶 𝐵=0.04191 𝜌 (𝜌=density of Bouguer plate)
• 𝐶 𝐵=0.112 mgal/m (if the avg. density of crust’s rocks=2.67 gr/ 𝑚 )
28

29. • Bouguer correction operates the opposite of
free-air correction...
[ 𝐶 𝐵 ]:
• (when the station is above the datum surface)
𝐶 𝐵 should be subtracted from data.
• (when the station is under the datum surface)
 𝐶 𝐵 should be added to data.
29
Bouguer correction a)station broad
plateau b)underground stations

30. D)3)Terrain correction:
• In Bouguer correction it is assumed
that:
o The surrounding topography of the
measuring point is flat & tabulate.;
While, indeed it is not like that.
• Terrain correction considers the
adjacent surface roughness of survey
stations.
• Terrain correction is always:
Positive +
It is added to the measured gravity
amount. 30
valley
mountain
h
Measurement point
s

31. 31
Hammer chart :
𝑑 𝑔 𝑇
= 𝛾𝛿𝜃 𝑟0 − 𝑟𝑖 + 𝑟𝑖
2
+ 𝑧2 − 𝑟0
2
+ 𝑧2

32. E)Isostasy correction:
• Ba=[corrected gravity – theory gravity]
• Ba  A base for interpreting of the gravity data on the lands.
• Ba for deep parts of the seas! instead, using: free-air correction
for interpreting the gravitational data.
32

33. • Avg. of Ba:
0 = in land nearby the sea-level
+ = in oceanic regions
- = in regions with high altitude
• This severe oscillation is due to: variations in density in the crust.
• For justification of the mentioned large scale variations  Airy’s
& Pratt’s theories (The base of isostasy theory.) 33

34. 34
* Airy’s theory:
isostatic level
𝜌 𝜌2 𝜌
ocean
mountain
Crust
2.7 g /cc
Mantle
>3.3 g /cc
𝜌 = 𝜌2 =𝜌
antiroot
root

35. 35
*Pratt’s theory:

mountain
ocean

 
 > >

36. • The contact level of suspended
slices of asthenosphere as:
 Airy’s theory  sharp & uneven
 Pratt’s theory  flat & even
• Isostasy correction : in small-scale
gravity surveys.
36

37. F) Eotvos correction
37
.. ..
• Time correction  on data measured on a moving
vehicle
• Needed factors for Eotvos correction:
The velocity of moving vehicle.
Geographical latitude of measuring point.
.. ..

38. • When:
Velocity of vehicle + Velocity of
 The amount of gravity decreases.↓
38
w E

39. The density of rocks & minerals:
• the source of gravity anomalies  local variations in density of rocks &
minerals.
• Changes in :
o density << magnetic susceptibility; Electrical transduction; Ratio of
radio-activity & plasticity coefficients of rocks & minerals.
39

40. *Density: Sedimentary rocks < Igneous & metamorphic rocks
• In sedimentary rocks
density varies with their:
Formation
Age
Porosity
Depth
• Age ↑  porosity ↓
• Depth ↑  density ↑
Conglomerate & sandstone
Shale
Limestone
dolomite
40
Less
density
More
density

41. • In igneous rocks; density in: Basic ones > Acidic ones
• In metamorphic rocks: degree of metamorphism↑  density ↑
41
Density: Marble, Slate, Quartzite > Limestone, Shale, sandstone
• Density of minerals: Metallic ones > Nonmetallic ones

42. AVERAGE DENSITIES
42
Material Density
(g/cm3)
Air 0
Water 1
Sediment 1.7-2.3
Sandstone 2.0-2.6
Shale 2.0-2.7
Limestone 2.5-2.8
Granite 2.7-3.1
Basalt 2.6-3.0

43. Gravity Measurements:
• Base: Differences in density of rocks & minerals.
A)Absolute measuring of gravitational acceleration.
B)Relative “ “ “ “ .
43

44. A) Absolute measuring
of gravitational acceleration:
• Fixed machines are
used.
• Pendulum’s oscillation
period or the time of free-
fall of a weigh is required.
44

45. Pendulums
For small angles,
sin 𝜃 = 𝜃
Simple Harmonic Motion
Period = 2p L/g
Measure period of
oscillation and length
of pendulum,
determine g!
T
𝜃
L
mg
𝜃
mg sin 𝜃
x
Exactness of
measuring: 1-1.5
mgal
45
• Kater, in 1818
• Potsdom, Washington,
Teddington
• g = 981.274 gal , in 1906
• g = 981.260 gal, in 1967

46. • Measuring ‘g’ by means of: free-falling weight:
g=
2 ℎ2 𝑡1 ℎ1 𝑡2
𝑡2 𝑡1 𝑡1 𝑡2
• Measuring ‘g’ by means of: throwing the object vertically upwards
g=
8 ℎ2 ℎ1
𝑡4 𝑡1
2 𝑡3 𝑡2
2
46

47. • Exactness of relative
measurements≈0.1mgal
• Relative measurements of gravity:
by means of such machines
with:
 high operating speed
much more exactness
 (gravimeter)
B)Relative measuring of
gravitational acceleration:
• Portable pendulum
• Torsion balance
47

48. Portable pendulum:
• Geodesy purposes & exploration works
• Assessing ‘g’ in:
 Earth’s surface
Seas
• Vening Meinesz three-pendulum machine  submarine operations
• In early 1930  exploration of oil
• Pendulum instruments  huge & complicated 48

49. Torsion balance:
• Cavendish, in1791,an
exact sample of torsion
balance, assessing earth’s
gravity
• Baron Ronald von Eotvos,
Hungarian physicist, in
1880,Geodesy purposes
.. ..
49
gravity probing:1915-1950.

50. The instruments of measuring gravity:
• Are the tools for  measuring gravity’s vertical component
directly
• Are very sensitive mechanical scales that a mass is kept & is
hung by a spring in them.
• Are in two types:
a) stable gravimeters
b)Unstable gravimeters
50

51. a) stable gravimeters:
• First generation of the gravimeters
• Historically worthy
51
m
m
mg
M(g+𝛿 𝑔)
L L+𝛿𝐿
F =k 𝛿𝐿 = m 𝛿𝑔
𝛿𝑔=
𝑘
𝑚
𝛿𝐿
displacement of weight : about several 𝐴0

52. Gulf Gravimeter:
52
measuring the rotation of the
spring , instead of its length’s
variation
exploration of oil in America

53. Boliden Gravimeter:
53
• an electrical detector &
electrical balancer device
• Sensitivity:0.1 mgal.
• airborne measurements

54. 54
b)Unstable
Gravimeters:
Basic elements of an unstable gravimeter

55. Thyssen Gravimeter:
55
• Is not used anymore.
• sensitivity :0.25 mgal.

56. 56
*Lacoste-Romberg Gravimeter:
Askania gravimeter
 zero-length spring

57. 57
Worden Gravimeter:
 made in 1948.
 sensitivity:0.01mgal.

58. Calibration of gravimeters:
• Lacoste-Romberg & Worden gravimeters
• zero-apparatuses.
58

59. Interpretation of gravitational data:
• Bouguer anomaly map Maps that are the result of gravitational gauging.
59
Salt-dome
>gravity<

60. Ambiguities in gravimetery:
60
• In case of having similar anomalies such as their
depth and similarity in volume & so forth.

61. Regional & Residual
Gravity:
61

62. Graphical techniques & smoothing
62

63. Empirical gridding method(Griffin):
63

64. Second derivative & remaining:
64

65. Polynomial fitting:
65
 based on statistical
theories
 requires the computer
 difficult

66. The prominent factors in opting the
method for elimination of regional impact:
The whole work that should be done;
Complicacy of gravitational map;
Density & distribution of stations;
Quality of data.
66

67. Gravitational effect of
different structures:
67

68. Gravity effect of a sphere:
68
Gravity effect of a horizontal rod:

69. Gravity effect of semi-infinite horizontal sheet:
69

70. Normal fault: Reverse fault:
70

71. 71

72. 72
Anomaly of an empty cylinder

73. 73
The fundamental physical property of gravity is density
Density = Mass / Volume
Observe the following cases:
2.1 2.6 3 2.4 2.1
High
density
Gravity
Distance
High
Gravity
3.1 2.7 2.3 2.6 3.2
Low
density
Gravity
Distance
Low
Gravity
2.1 2.1 2.1 2.1 2.1
Constant
density
Gravity
Distance
Constant
Gravity

74. 74

75. 75
Bouguer Microgravity Profile over Paleokarst Collapse Structure
Figure shows a
Bouguer microgravity
profile over a aleokarst
collapse structure. In
this case, stations
were at 30m intervals
on the profile.

76. 76
 A,B,C,D:
Synclinal
structures
 E,F,G:
Anticlinal
structures

77. 78
differentiating between intrusives of kimberlite (upper
example) and trap rock (lower example) into limestones.
Both intrusives show up as positive magnetic anomalies
(∆Z).
However, the kimberlite :negative gravity anomaly, ∆g,
while the trap rock :positive gravity anomaly.
(no scale is given for the gravity profiles).
The density of:
kimberlites (2.33 – 2.60 g/cm3) <carbonate rocks (2.40
– 2.65 g/cm3),
which is still less than that of trap rocks (2.7 – 3.1
g/cm3).
In addition, kimberlite weathers readily near surface,
which reduces its mean density still further.
GravityandMagneticAnomaliesoverKimberlite(upper)&
Traprock(lower)Intrusives
Legend:1.CarbonateRocks2.Kimberlite3.Traprock

78. 79

79. 80
Chromite[(Fe ،Mg)Cr2O4] has a
mean density of 4.36 g/cm3,
which is about 1.4 g/cm3 higher
than the basic intrusive rocks in
which it normally is found.

80. 81
all types of coal have very low
densities ranging
from about 1.19 g/cm3 for lignite
to 1.5 g/cm3 for anthracite.
Other
things being equal, therefore,
the areas of larger negative
Bouguer gravity
anomalies, within the
sedimentary basin, are more
favorable for the occurrence
of the thicker coal beds.

81. 82
It shows the application of this
interpretive approach to a gravity profile
across the Salmon glacier in British
Columbia.
The observed gravity profile, after
corrections for the mountainous
topography, was curve-fitted, to
achieve an excellent fit, as shown.
The interpreted cross section of the
glacier is shown, as well as the
cross section based on drilling.
Bouguer Gravity Profile, Observed and Theoretical over the Salmon Glacier

82. 83
It shows a much smaller (0.01 mgal) anomaly,
marking a single vertical dis-solutioned joint (alluvium filled) in
the limestone,
within a broader gravity depression. Clearly, very precise
microgravity
measurements are required in order to provide such detail.
It shows negative gravity anomalies related to deposits
of bauxite and bauxite-clays in a contact zone between limestones
and siltstone, which are covered with overburden. (Unfortunately,
no distance
scale is given for these two sections).

83. Trust fault
Trust fault
Symmetric mass

84. 85
Density of rock types from the core
sampling in the study area

85. 86

86. Determination of Basement
Faults
Determination of a Blind Reef
87

87. 88

88. 89

89. 90

90. 91

91. Complete Bouguer Anomaly with Overlain Geology of Study Area
92

92. 93
Any question?

93. Conclusion:
Gravimetery, that is one of the branches of geophysical methods, is vastly
used in lots of scientific & geological fields. Use of such methods will
lead the experts to figure out more practical knowledge in every related
scientific filed which involves tectonics, too.
As a whole geophysical methods are faster in comparison to other ways in
order to get the structures beneath the earth. 94

94. References:
English Books:
• Lowrie, William, fundamentals of geophysics ,2007
• Milsom, John, Field Geophysics,2003
• Seigel, H.O.; a guide to high precision land gravimeter surveys;1995
‫فارسی‬ ‫کتب‬:
•‫د‬ ‫گارلندوجورج‬.‫رحمتی‬ ‫میرعباس‬ ‫ژئوفیزیک؛ترجمه‬ ‫با‬ ‫؛آشنایی‬,‫جعفرشجاع‬
‫طاهری‬,1369,‫تهران‬ ‫دانشگاهی‬ ‫نشر‬ ‫مرکز‬
•‫آستیه‬,‫ژ‬.‫دانش‬ ‫موحد‬ ‫اصغر‬ ‫علی‬ ‫دکتر‬ ‫یابی؛ترجمه‬ ‫ل؛آب‬,1364,‫عمیدی‬ ‫انتشارات‬
•‫تلفورد‬,‫دبلیو‬.‫ام‬.‫؛جلدارت‬,‫ال‬,‫پی؛شریف‬,‫ار‬.‫ای‬.‫؛کیز‬,‫دی‬.‫؛ژئوفیزیک‬ ِ‫ا‬
‫زمردیان‬ ‫حسین‬ ‫دکتر‬ ‫کاربردی؛ترجمه‬,‫حسینیه؛‬ ‫حاجب‬ ‫حسن‬ ‫دکتر‬1387‫؛انتشارات‬
‫تهران‬ ‫دانشگاه‬
•‫توکلی‬,‫شهاب؛ژئوفیزیک؛‬1388‫نور‬ ‫پیام‬ ‫دانشگاه‬ ‫؛انتشارات‬
•‫زیرسطحی‬ ‫شناسی‬ ‫زمین‬,‫نور‬ ‫پیام‬ ‫دانشگاه‬ ‫انتشارات‬
Other:
• Several lectures & numerous websites 95

95. 96
Fatemeh Vejdani
M.S. Student of Tectonics
Urmia University
Respectful Professor:
Dr. Ramin Nikrouz
Fall of 2013(1392)

96. 97
Thanks a lot for your
attention….

97. 98