1

In the name of Allah

The most compassionate

and merciful

GRAVIMETERY

METHOD

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

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

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”.

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.

8

Gravimetery vs. Magnetometery

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.

10

Differences:

• Due to gravity’s relatively small and uniform variations in

comparison to magnetic susceptibility’s variations;

Gravity anomalies < Magnetic anomalies

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

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

13

Primary principals and hypothesis

14

Newton’s gravity law :

Gravitational acceleration:

• Is considered as the base of gravity works.

• F=gravity force between m1 and m2

• R= the distance between m1 and m2

• G=universal coefficient of gravity

• ( G= 6.67 * ͳͲ � ଵଵ Nm/ kg in SI)

• (1 N =ͳͲହ dyne )

𝑔=𝐺𝑀𝑒𝑅2

• Acceleration of free falling object = gravity acceleration =>

Applied force from earth to the mass.

• (g) in terms of (m/ݏଶሻ or (cm/ݏଶ)

� ൌܩ��ܯ��ଶ

1 gal = ͳͲଷ mgal = ͳͲ ߤ gal = 1 cm/ ݏ�� ଶ

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

=

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 (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.)

18

Spheroid & Geoid:

Spheroid

Geoidcontinents

oceans

Spheroid

Geoid

A

BN

Strike of vector

Mass anomalyg =(1+ + 2 )=0.0053024 = -0.0000058 =978.0318gals

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

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.

• 0.81 sin (2) mgal/km { =geographical latitude (Radian) }

• Max gravity variations & thus: max latitude correction in altitude (correction:0.01 mgal per 12.2 m)(correction=0 in equator & poles)

(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.

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)

24

D) Altitude correction:

1)Free-air correction

2)Bouguer correction

3)Terrain correction

25

D)1)Free-air correction

• Because: g ;a correction is needed due to: Altitudinal variations between stations.

• g)

• For small altitude differences = =0.3086 h

• + (if measuring point is above datum surface) should be added to data.

- (if measuring point is under datum surface) should be subtracted from data.

• � =amount of gravity in datum surface (Geoid)

• g = amount of gravity in the height of ‘h’ from datum surface

• h = Th

g�� � ሺͳൌ�ଶோ��)

Measuring points

h

29

26

D)2)Bouguer correction:

• In free-air correction it is assumed that:

oThe measuring point is placed in free-air

oThe 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!

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;

28

h

s Measuring point

Bou

guer

pla

te

• 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.

• =0.04191 (=density of Bouguer plate)

• =0.112 mgal/m (if the avg. density of crust’s rocks=2.67 gr/)

29

• Bouguer correction operates the opposite of free-air correction... [ ]:

• (when the station is above the datum surface)

should be subtracted from data.

• (when the station is under the datum surface)

should be added to data.

Bouguer correction a)station broad plateau b)underground stations

30

D)3)Terrain correction:

• In Bouguer correction it is assumed that:

oThe 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.

valley

mountain

h

Measurement point

s

31

Hammer chart :

=

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.

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.)

34

* Airy’s theory:

isostatic level

𝜌1𝜌2

𝜌3

ocean

mountain

Crust

2.7 g /ccMantle

>3.3 g /cc

=antiroot

root

35

*Pratt’s theory:

mountain

ocean

1 3

2>3>1

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.

37

F) Eotvos correction.. ..

• 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.

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.

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

Less density

More density

41

• In igneous rocks; density in: Basic ones > Acidic ones

• In metamorphic rocks: degree of metamorphism density

Density: Marble, Slate, Quartzite > Limestone, Shale, sandstone

• Density of minerals: Metallic ones > Nonmetallic ones

42

AVERAGE DENSITIESMaterial 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 “ “ “ “ .

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.

45

PendulumsFor small angles,

sin = Simple Harmonic Motion

Period = 2 p

Measure period of oscillation and length of pendulum, determine g!

T

𝜃L

mg

𝜃

mg sin

x

Exactness of measuring: 1-1.5 mgal

• 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=

• Measuring ‘g’ by means of: throwing the object vertically upwards

g=

47

• Exactness of relative

measurements0.1mgal

• 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

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

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

.. ..

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

a) stable gravimeters:

• First generation of the gravimeters

• Historically worthy

51

mm

mg

M(g+)

L L+

F =k m

= displacement of weight : about several

52

Gulf Gravimeter:

measuring the rotation of the

spring , instead of its length’s

variation

exploration of oil in America

53

Boliden Gravimeter:

• an electrical detector &

electrical balancer device

• Sensitivity:0.1 mgal.

• airborne measurements

54

b)Unstable

Gravimeters:

Basic elements of an unstable gravimeter

55

Thyssen Gravimeter:

• Is not used anymore.

• sensitivity :0.25 mgal.

56

*Lacoste-Romberg Gravimeter:

Askania gravimeter

zero-length spring

57

Worden Gravimeter:

made in 1948. sensitivity:0.01mgal.

58

Calibration of gravimeters:

• Lacoste-Romberg & Worden gravimeters

• zero-apparatuses.

59

Interpretation of gravitational data:

• Bouguer anomaly map Maps that are the result of gravitational gauging.

Salt-dome

>gravity<

60

Ambiguities in gravimetery:

• In case of having similar anomalies such as their

depth and similarity in volume & so forth.

Regional & Residual Gravity:

61

62

Graphical techniques & smoothing

63

Empirical gridding method(Griffin):

64

Second derivative & remaining:

65

Polynomial fitting:

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.

Gravitational effect of different structures:

67

68

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

69

Gravity effect of semi-infinite horizontal sheet:

70

Normal fault: Reverse fault:

71

72

Anomaly of an empty cylinder

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

Gra

vit

y

Distance

High Gravity

3.1 2.7 2.3 2.6 3.2

Low density

Gra

vit

y

Distance

Low Gravity

2.1 2.1 2.1 2.1 2.1

Constant density

Gra

vit

y

Distance

Constant Gravity

74

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

A,B,C,D: Synclinal structures

E,F,G: Anticlinal structures

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.

Gra

vit

y a

nd M

agneti

c A

nom

alie

s over

Kim

berl

ite

(upp

er)

& T

rap

rock

(lo

wer)

Intr

usi

ves

Legend:

1. C

arb

onate

Rock

s 2.

Kim

berl

ite 3

. Tr

apro

ck

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.

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.

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 mountainoustopography, 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

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 microgravitymeasurements are required in order to provide such detail.

It shows negative gravity anomalies related to depositsof bauxite and bauxite-clays in a contact zone between limestonesand siltstone, which are covered with overburden. (Unfortunately, no distancescale is given for these two sections).

Trust fault

Trust fault

Symmetric mass

85

Density of rock types from the core sampling in the study area

86

87

Determination of Basement Faults Determination of a Blind Reef

88

89

90

91

92

Complete Bouguer Anomaly with Overlain Geology of Study Area

Any question?

94

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.

95

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

کتب فارسی:,مرکز نشر 1369گارلندوجورج د.؛آشنایی با ژئوفیزیک؛ترجمه میرعباس رحمتی,جعفرشجاع طاهری,•

دانشگاهی تهران,انتشارات عمیدی1364آستیه,ژ.ل؛آب یابی؛ترجمه دکتر علی اصغر موحد دانش,•�؛ژئوفیزیک کاربردی؛ترجمه دکتر حسین • تلفورد,دبلیو.ام.؛جلدارت,ال,پی؛شریف,ار.ای.؛کیز,دی.ا

؛انتشارات دانشگاه تهران1387زمردیان,دکتر حسن حاجب حسینیه؛؛انتشارات دانشگاه پیام نور1388توکلی,شهاب؛ژئوفیزیک؛•زمین شناسی زیرسطحی,انتشارات دانشگاه پیام نور•

Other:• Several lectures & numerous websites

Fatemeh VejdaniM.S. Student of Tectonics

Urmia University

Respectful Professor:Dr. Ramin Nikrouz

Fall of 2013(1392)

Thanks a lot for your

attention….