geophysics. gravimetery method
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In the name of Allah
The most compassionate
and merciful
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GRAVIMETERY
METHOD
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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
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Outline of the lecture :
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• 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.
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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
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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”.
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• 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.
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Gravimetery vs. Magnetometery
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Similarities:
In both of them:
• Little differences are measured in a relatively huge field of force.
• There is the possibility of defining absolute fields.
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Differences:
• Due to gravity’s relatively small and uniform variations in
comparison to magnetic susceptibility’s variations;
Gravity anomalies < Magnetic anomalies
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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
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• 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
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Primary principals and hypothesis
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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
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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
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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)_
+
+
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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.)
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Spheroid & Geoid:
Spheroid
Geoidcontinents
oceans
Spheroid
Geoid
A
BN
Strike of vector
Mass anomalyg =(1+ + 2 )=0.0053024 = -0.0000058 =978.0318gals
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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.. ..
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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
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• 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) _
+
+
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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.
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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)
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D) Altitude correction:
1)Free-air correction
2)Bouguer correction
3)Terrain correction
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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
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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!
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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;
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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/)
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• 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
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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
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Hammer chart :
=
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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.
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• 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.)
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* Airy’s theory:
isostatic level
𝜌1𝜌2
𝜌3
ocean
mountain
Crust
2.7 g /ccMantle
>3.3 g /cc
=antiroot
root
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*Pratt’s theory:
mountain
ocean
1 3
2>3>1
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• 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.
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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.
.. ..
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• When:
Velocity of vehicle + Velocity of
The amount of gravity decreases.
w E
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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.
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*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
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• 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
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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
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Gravity Measurements:
• Base: Differences in density of rocks & minerals.
A)Absolute measuring of gravitational acceleration.
B)Relative “ “ “ “ .
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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.
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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
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• Measuring ‘g’ by means of: free-falling weight:
g=
• Measuring ‘g’ by means of: throwing the object vertically upwards
g=
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• 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
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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
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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.
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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
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a) stable gravimeters:
• First generation of the gravimeters
• Historically worthy
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mm
mg
M(g+)
L L+
F =k m
= displacement of weight : about several
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Gulf Gravimeter:
measuring the rotation of the
spring , instead of its length’s
variation
exploration of oil in America
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Boliden Gravimeter:
• an electrical detector &
electrical balancer device
• Sensitivity:0.1 mgal.
• airborne measurements
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b)Unstable
Gravimeters:
Basic elements of an unstable gravimeter
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Thyssen Gravimeter:
• Is not used anymore.
• sensitivity :0.25 mgal.
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*Lacoste-Romberg Gravimeter:
Askania gravimeter
zero-length spring
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Worden Gravimeter:
made in 1948. sensitivity:0.01mgal.
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Calibration of gravimeters:
• Lacoste-Romberg & Worden gravimeters
• zero-apparatuses.
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Interpretation of gravitational data:
• Bouguer anomaly map Maps that are the result of gravitational gauging.
Salt-dome
>gravity<
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Ambiguities in gravimetery:
• In case of having similar anomalies such as their
depth and similarity in volume & so forth.
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Regional & Residual Gravity:
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Graphical techniques & smoothing
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Empirical gridding method(Griffin):
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Second derivative & remaining:
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Polynomial fitting:
based on statistical
theories
requires the computer
difficult
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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.
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Gravitational effect of different structures:
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Gravity effect of a sphere: Gravity effect of a horizontal rod:
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Gravity effect of semi-infinite horizontal sheet:
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Normal fault: Reverse fault:
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Anomaly of an empty cylinder
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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
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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.
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A,B,C,D: Synclinal structures
E,F,G: Anticlinal structures
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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
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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.
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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.
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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
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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).
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Trust fault
Trust fault
Symmetric mass
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Density of rock types from the core sampling in the study area
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Determination of Basement Faults Determination of a Blind Reef
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Complete Bouguer Anomaly with Overlain Geology of Study Area
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Any question?
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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.
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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
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Fatemeh VejdaniM.S. Student of Tectonics
Urmia University
Respectful Professor:Dr. Ramin Nikrouz
Fall of 2013(1392)
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Thanks a lot for your
attention….
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