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1
GRAVIMETERY
METHOD
2
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
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.
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
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
• 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
Gravimetery vs. Magnetometery
8
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
Differences:
• Due to gravity’s relatively small and uniform variations in
comparison to magnetic susceptibility’s variations;
Gravity anomalies < Magnetic anomalies
10
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
• 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
Primary principals and hypothesis
13
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
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
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)_
+
+
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
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
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
.. ..
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
• 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) _
+
+
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
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
D) Altitude correction:
24
1)Free-air correction
2)Bouguer correction
3)Terrain correction
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
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
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
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
• 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
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
Hammer chart :
𝑑 𝑔 𝑇
= 𝛾𝛿𝜃 𝑟0 − 𝑟𝑖 + 𝑟𝑖
2
+ 𝑧2 − 𝑟0
2
+ 𝑧2
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
• 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
* 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
*Pratt’s theory:

mountain
ocean

 
 > >
• 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
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.
.. ..
• When:
Velocity of vehicle + Velocity of
 The amount of gravity decreases.↓
38
w E
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
*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
• 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
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
Gravity Measurements:
• Base: Differences in density of rocks & minerals.
A)Absolute measuring of gravitational acceleration.
B)Relative “ “ “ “ .
43
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
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
• 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
• 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
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
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.
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
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
Gulf Gravimeter:
52
measuring the rotation of the
spring , instead of its length’s
variation
exploration of oil in America
Boliden Gravimeter:
53
• an electrical detector &
electrical balancer device
• Sensitivity:0.1 mgal.
• airborne measurements
54
b)Unstable
Gravimeters:
Basic elements of an unstable gravimeter
Thyssen Gravimeter:
55
• 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.
Calibration of gravimeters:
• Lacoste-Romberg & Worden gravimeters
• zero-apparatuses.
58
Interpretation of gravitational data:
• Bouguer anomaly map Maps that are the result of gravitational gauging.
59
Salt-dome
>gravity<
Ambiguities in gravimetery:
60
• In case of having similar anomalies such as their
depth and similarity in volume & so forth.
Regional & Residual
Gravity:
61
Graphical techniques & smoothing
62
Empirical gridding method(Griffin):
63
Second derivative & remaining:
64
Polynomial fitting:
65
 based on statistical
theories
 requires the computer
 difficult
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
Gravitational effect of
different structures:
67
Gravity effect of a sphere:
68
Gravity effect of a horizontal rod:
Gravity effect of semi-infinite horizontal sheet:
69
Normal fault: Reverse fault:
70
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
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
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.
GravityandMagneticAnomaliesoverKimberlite(upper)&
Traprock(lower)Intrusives
Legend:1.CarbonateRocks2.Kimberlite3.Traprock
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 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
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).
Trust fault
Trust fault
Symmetric mass
85
Density of rock types from the core
sampling in the study area
86
Determination of Basement
Faults
Determination of a Blind Reef
87
88
89
90
91
Complete Bouguer Anomaly with Overlain Geology of Study Area
92
93
Any question?
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
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
96
Fatemeh Vejdani
M.S. Student of Tectonics
Urmia University
Respectful Professor:
Dr. Ramin Nikrouz
Fall of 2013(1392)
97
Thanks a lot for your
attention….
98

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Geophysics. GRAVIMETERY METHOD

  • 1. 1
  • 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
  • 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
  • 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
  • 55. Thyssen Gravimeter: 55 • Is not used anymore. • sensitivity :0.25 mgal.
  • 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.
  • 62. Graphical techniques & smoothing 62
  • 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
  • 68. Gravity effect of a sphere: 68 Gravity effect of a horizontal rod:
  • 69. Gravity effect of semi-infinite horizontal sheet: 69
  • 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.
  • 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).
  • 84. 85 Density of rock types from the core sampling in the study area
  • 85. 86
  • 87. 88
  • 88. 89
  • 89. 90
  • 90. 91
  • 91. Complete Bouguer Anomaly with Overlain Geology of Study Area 92
  • 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

Hinweis der Redaktion

  1. Not only the exactness of measurements of variable field is much more in magnetometery ,but also the machines used for main field can either be used for small variations of field. While it’s not so in gravity method. Gravity method’s field activities are extravagant and cost more. Gravity probing is used as the mean of exploration of oil.(In spite of high costs , it’s still considerably cheaper than seismographic method.) This method is considered as a secondary method in exploration of minerals.
  2. Gravity field can be shown by levels with fixed potential that are called : Gravitational same-potential levels. The vectors of force are perpendicular on the levels. Along this level, there is no other force component. The surface of a fluid substance can easily deal with the strike of the same-potential level in a gravitational field so, potential is such a quantity that plays a significant role in studying of: The shape of seas’ balance- level on the earth. Spheroid & geoid ( will be elaborated more latter) are two levels that are classified as same-potential ones. These 2 are important in description of earth’s shape & investigation of gravimetric data.
  3. Gravity probing originates from the study of earth’s gravity field by geodesy scientists from 250 years ago in order to determine the shape of the earth.
  4. Reference spheroid: Earth’s surface , based on gravity’s amount in all parts of it, is defined with a mathematical shape. This shape is named reference spheroid. Amount of gravity in every part of this spheroid  g = 𝑔 0 (1+∝ sin 2 ∅ + 𝛽 𝑠𝑖𝑛 2 2∅ ) 𝑔 0 = gravity in equator ∅ = Geographical latitude Geoid : Is defined as the average of free sea’s level that matches the level of oceans & hypothetical channels’ waters’ level which passes through the masses on the lands. Geoid & Spheroid don’t cover each other in all parts; because: geoid: has been deflected upwards under the continental masses ; due to gravity of upper materials. Has been deflected downwards under the oceans. Thoroughly ; their both deviation doesn’t exceed more than 50 meters.
  5. Are applied so as to remove the impacts of different factors which may be included in measurements.
  6. Gravity in poles > Gravity in equator =( gravity is increased with increasing of latitude.)  correction increases with the increasing of latitude. If the station is in the upper or lower than basic station ;the correction is subtracted from or added to the measured amounts.
  7. The total deduction of drift is that during the day or even several hours, there are no unique measured amounts. In order to remove the effects of gravimeters’ drift from data, the curve of gravimeters’ drift is needed to be drawn.( curve of gravity vs. time)
  8. Because of Alternative variations of sun & moon’s gravitational effects, the amount of earth’s gravity varies in terms of time so, tidal correction should be applied. These gravity effects cause: some changes in solid portion of the earth As :variations in seas(=tides)
  9. g ≈ 1 𝑟 2 Because gravity varies with the image of distance’s square; so, a correction is needed due to: altitudinal variations between stations; As : all the data are referred to a datum surface. Base of this correction : Newton’s law that says: g ≈ 1 𝑟 2
  10. The gravity amounts are increased by the impact of the plate between station & datum surface.
  11. Roughness like: The vallies under & hills above the station. It’s obvious that both two mentioned topographical shapes influence the amount of gravity in the same sense of each other. Because pull upward (about hills) & fail to pull downward (about valleys) ; both are the causes of decreasing gravity amounts in measured points. So, the mentioned above is the reason why : Terrain correction is always : 1)positive; 2)it’s added to the measured gravity amount.
  12. There are several graphical patterns for terrain correction. In all of these methods a good topographical map is needed. The usual method is : dividing region into parts & comparing the avg. altitude of every portion with the altitude of survey station. The most usual template is Hammer chart which functions as below: When radius lines of several concentric circles are drawn, some portions are created which their area are increased in accordance with their distance from center. About image: The transparent template is placed on the topographical map so that the center of circles deals with the gravity station. The avg. altitude of each single portion is guessed from the counters which have been placed in it & is subtracted from the known altitude of station. This altitudinal difference stands for ‘z’ in the formula.(The gravitational effect of every single portion is calculated by the mentioned formula .)
  13. If there was no sidelong variations in density of earth’s crust ,a group of gravity data would be the same as each other after applying suitable corrections. Every difference in corrected amounts lead to gravitational anomalies which is called:Bouguer anomaly that is the result f sidelong variations in density. Ba=Bouguer anomaly
  14. Avg. Bouguer anomaly in different places has gotten from gravity measurements in universal scale. Density of substances : under oceans  is more than usual. in mountainous regions of continents  is low
  15. Airy mechanism of isostatic Earth’s crust is formed from some slices which are suspended on the fluid astonosphere & these slices have monotonic density , but with different thickness & less density in comparison to asthenosphere. In this model, mountains have deep roots. The dashed line is an isostatic level; along this line, the weight of the overlying material is the same.
  16. The Pratt mechanism of isostatic Another type of balance (model), known as Pratt isostacy. The density of the overlying material varies throughout a topographic feature. The isostatic level here is the boundary between crust and mantle The density of the crust varies with topography. Its amount for mountainous regions is low & for oceanic regions that crust is thin there, is high.
  17. Isostasy correction isn’t that much significant in small-scale gravity surveys. Because rarely are developed measuring regions that application of such correction will be required.
  18. This time correction is applied on such data that have been measured on a moving vehicle; such as: airplane or ship. In accordance with the strike of motion, the movement of vehicle will make a center-wards acceleration that whether enhances the gravity or the opposite, decreases its amount.
  19. When the ship moves Eastwards its velocity is added to the velocity of the earth’s rotation around itself. The result is that : the amount of gravity decreases.
  20. Formerly we talked about differences in amounts of gravity & the ways that are applicable for getting the correct data & extract the reliable amounts from our measurements. But, what makes such varieties in gravity? This is the question that we want to answer in this section. As a whole; a clear factor in gravimetery ( the source of gravity anomalies)local variations in density of rocks & minerals. Changes in density of rocks & minerals is relatively low in comparison to other parameters mentioned in the slide.
  21. In igneous rocks; density in: Basic ones is more than acidic ones. ????In metamorphic rocks ; density is enhanced by the degree of metamorphism. WHY???? Because under the metamorphism , the empty places are filled & recrystallization happens in the rock. ?????As the explanations that I gave, which group is denser in your idea? Density: Marble, Slate, Quartzite > Limestone, Shale, sandstone Metallic minerals are denser than nonmetallic ones. I’m not sure !but I think it’s due to their atomic number!
  22. It means that if the density of mineral or rock-mass is more or less than surrounding rocks’ density, the amount of gravitational acceleration on the earth’s surface & above the  aforementioned mass is more (positive anomaly + ) or less ( negative anomaly - ) than normal gravitational acceleration. We have 2 ways for measuring gravitational acceleration .In latter slides we’ll expand on the uttered ideas
  23. .
  24. Absolute measuring of gravitational acceleration by means of pendulum that is based on the time of period of a simple pendulum’s oscillation . Kater was the first person who used the pendulum in 1818. Some samples of these pendulums are in Potsdam , Washington & Teddington. The gravitational acceleration (g=981.274 gal) that has been gotten by means of pendulum in Potsdam in 1906 is still used nowadays. In 1967 : g modified to :981.260gal
  25. Measuring of gravitational acceleration by means of free-falling weight relies on the measuring the time of free-fall of the object. In the uttered formula h1 & h2 :the distances that falling object traverses during t1 & t2 intervals. Another method that nowadays is used is: to throw the object vertically upwards. In this form , the object passes twice from one level ; once when going upwards & once again when coming back. t1 & t2 the moments that the object passes the h1 & h2 when going upwards ;; t3 & t4 when coming down.
  26. Difference of gravitational acceleration from one point to another is measured. The most gravimetric surveys are from this type. Exactness of relative measurements is about 0.1 mgal Relative measurements of gravity are done by means of such machines which not only have high operating speed in comparison to physical pendulums , but also are much more exact. These machines are called gravimeter. Here is that the tractate of portable pendulum & torsion balance appears.
  27. Modified samples of this machine has been used for gravity probing from 1915-1950. Nowadays torsion balance is historically worthy.
  28. They had been the first generation of the gravimeters. There is a very sensible spring that a weight which is in stable equilibrium, has been attached to & has been hung from it. When gravitational acceleration varies ; the position of the weight varies, too. Gravimeter is unbalanced! It should be said that displacement of weight is a little bit (about several 𝐴 0 )  It should be strengthened with electronical or optical-mechanical methods , then be measured. K=coefficient of springs hardness 𝛿𝐿≈𝛿𝑔 ( spring’s length variations is proportional with gravity’s variations) 𝛿𝐿 ≈ F
  29. This machine measures the rotation of the spring that has been made from flat bar, instead of its length’s variation. This has been broadly used for exploration of oil in America.
  30. In this gravimeters an electrical detector & electrical balancer device has been used. Sensitivity of this machine is about 0.1 mgal. Some kinds of such gravimeters are used for airborne measurements. By means of them, the altitudinal gravity gradient can be measured , too.
  31. Unstable Gravimeters consist of a mass (m) & a spring. In this machine , there is an arm that is attached to the hinge & to weight from other side. The arm has been supported by the spring versus the torque caused by gravitational acceleration. Magnitude of the torque exerted by the spring on the arm depends on: spring’s tension & sin𝜃. Such condition leads ‘m’ to be in unstable balance. If gravity is increased , the arm will be pulled downwards & spring will be expanded more.
  32. This gravimeter isn’t used anymore. It was relatively big & heavy with the sensitivity about 0.25 mgal.
  33. The most famous unstable gravimeter is the “ Lacoste-Romberg” gravimeter. The most significant point of it: using a very sensitive spring which is named: ’zero-length spring’. This spring has been stretched in such a way that its restoring force is proportional to its physical length & doesn’t have any proportion with its extension. It has known with different names , too. Such as: Askania, Frost , Magnolia & North American.
  34. It was made in 1948. Its sensitivity is about 0.01 mgal.
  35. Nowadays Lacoste-Romberg & Worden gravimeters are the only gravimeters which are used in explorations. Both of them are zero-apparatuses.
  36. After different corrections on the measured gravitational data, the amount of anomaly is defined in every station. After defining bouguer anomaly of each station ,its amount is written in related station on the map & points with the same amount of gravity are joined to each other  Bouguer anomaly map. The bouguer gravity map in terms of appearance resembles to the map of total field of magnetism. Of course it should be said that the contours of gravity are much smoother than those ones in magnetic maps. BECAUSE: Variations  in gravity field are less than magnetic susceptibility. Variations  in gravity are slower than magnetic dipole field. Of course , simplicity of gravity map causes easier interpretation of them in some cases. I’ve brought this picture to sample one of these maps. This map shows a salt-dome that gravity decreases center-wards in it.
  37. Interesting anomalies in gravity maps are often hidden by deep structures. Elimination of the gravity’s impact that is deduced from these deep structures & is called Regional gravity; is much more serious & significant problem in gravimetery rather than other geophysical methods. These activities ( the act of wiping out the regional gravity) resembles to filtering process (optic-electrical) Regional effects equals with low frequencies & the opposite; residual impacts are related to high frequencies. But these low frequencies are not easily removed by using a high pass filter. So, high local geological information is the most prominent useful factor in interpretation of data in geophysics. There are several ways in order to eliminate the unwanted regional impacts. Some of these techniques are graphical & the others are analytical.
  38. Graphical techniques & smoothing: About a) in first one there is a profile that apparently reflects two disturbances with totally different sizes. Picture b) in this picture , the contours show such a difference , too. In this way the differences are apparently separable. In some cases the discrepancies may not be that much apparent; so we should use another methods to smooth the data. - In one of the methods ; several profiles are drawn for lines which are almost perpendicular to regional contours……………………………………………….
  39. This technique has been described by Griffin . In this method, regional effect is considered as the average amount of gravity around the station & is taken by averaging of observed amount of gravity in a circular surroundings (circumference) when the station is considered as center. By having the regional amount in access , the residual effect will be understood from the difference between the average gravity & the amount of gravity in the center of the circle.
  40. Another method for separating regional & residual gravity is to use a method which is named: Second derivative & remaining. In picture shown here is a sample that is used in this method. In this method some special mathematical formulas are used that you can search more about it so as to get more information.
  41. Till now , the mentioned methods were graphical, but this one is completely analytical. The procedure is based on statistical theories. Anyhow, this procedure requires the computer & is difficult to some extent.
  42. For example; in case of having less data or simple regional impact, the application of graphical method is preferred.
  43. SPHERE: In this profile, the seen anomaly is somehow symmetric. The shape of sphere is guessed whenever there is a symmetry in 3-dimensional anomalies. HORIZONTAL ROD: As you see , because g varies proportional to 1 𝑥 2 the profile is more elongated than sphere’s profile.
  44. This is such an asymmetric profile.
  45. A fault structure can be shown by two semi-infinite horizontal sheets that one of them has been displaced relative to another. As it’s clear , the profiles are asymmetric & whenever the dip is far from 90 0 , the profiles increasingly tend to be asymmetric.
  46. shows the use of the gravity method to differentiate between intrusives of kimberlite (upper example) and trap rock (lower example) into limestones. Both intrusives show up as positive magnetic anomalies (ΔZ). However, the kimberlite shows up as negative gravity anomaly, Δg, while the trap rock shows a positive gravity anomaly. (Unfortunately, no scale is given for the gravity profiles).