Subject 1: Introduction (Gravity)
Lecturer: Dr. Bakhtiar Q. Aziz
Objective: The gravitation law of attraction was discovered by Isaac Newton in
1685 Gravity is an attractive force between all pairs of massive objects in the
universe, this introduction will explain to the students in detail.
Scientific contents
1- Gravity and Geology, Gravitational Force, Earth Gravity Field
2- Universal Mutual Gravitation.
3- Mass and Weight.
References
1.
2.
3.
4.
5.
Applied and environmental geophysics, 1999, Sharma,V.,P.
Introduction to geophysical prospecting, 1988, Durbin, M. B.
An introduction to applied and environmental geophysics, 1997, Reynolds, J. M.
www.1728.com/gravity.htm
www.physicsforums.com
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Gravity & Magnetic
By
BAKHTIAR QADER AZIZ
Assistance professor
2010-2011
The Second Semester
Gravity Method
Magnetic Method
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Syllabus of the Gravity Method:
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Introduction
Theoretical background
Data Reduction
Survey procedure
applications
Instruments for measuring gravity
Interpretation
Separation of Anomaly
Regional and Residual gravity
Methods of separation
Ambiguities in gravity
modeling
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References:
1. Applied Geophysics,1996 , Telford, W.,M.
2. An introduction to applied and environmental
3.
4.
5.
6.
geophysics, 1997, Reynolds, J. M.
Introduction to geophysical prospecting, 1988, Durbin,
M. B.
Applied and environmental geophysics, 1999,
Sharma,V.,P.
www.Geophysics.Com
www.Geophysics.net
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The gravitation law of attraction was discovered by Isaac Newton in 1685
Gravity: It is an attractive force between all pairs of massive objects in the
universe.
Newton is referred to “Universal Mutual Gravitation”
Universal: Gravity works every where in the universe, not just on the earth.
Mutual: Gravity works between pairs of objects.
The force of gravity depend on:
1- Mass
2- Distance
Mass and weight:
In popular language mass and the weight refer to the same thing.
Weight= Mass x Gravity
Mass is a measure of how much materials are in an object, while weight is a
measure of the gravitational force exerted on that material.
Mass= Density x Volume
Note: Mass is constant for an object.
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Gravity in Physics:
It is a rate of increase of velocity measured by cm/Sec2
It is constant :
1- The earth is perfect sphere
2- The earth is uniform or homogenous
Newton’s Law of Gravitation states that the force of attraction F between two
masses m1 and m2 is directly proportional to the product of the masses and
inversely to the square of distance between them.
m1 x m2
r2
m xm
F G 1 2 2
r
F
r
m1
m2
G: is a gravitational constant equal to the force between two unit mass (1 Gram)
separate by a distance of 1 cm. = 6.67x10-8 Dyne. Cm2/gm2
The relation between force and distance is known as “Inverse Square law”
F
1
r2
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Acceleration of Gravity: It is a force acting on a unit mass
G m1m2
2
F
r
g

m2
m2
m
g  G 21
r
m2
r
Earth
m1
When making measurements of the earth's gravity, we usually don't measure the
gravitational force, F. Rather, we measure the gravitational acceleration, g. The
gravitational acceleration is the time rate of change of a body's speed under the
infuence of the gravitational force.
Units Associated With Gravitational Acceleration
Units Associated with Gravitational Acceleration As described earlier, acceleration is
de¯ned as the time rate of change of the speed of a body. Speed, sometimes
incorrectly referred to as velocity, is the distance an object travels divided by the time
it took to travel that distance (i.e., meters per second (m/s)). Thus, we can measure
the speed of an object by observing the time it takes to travel a known distance, If
the speed of the object changes as it travels, then this change in speed with respect
to time is referred to as acceleration. Positive acceleration means the object is
moving faster with time, and negative acceleration means the object is slowing down
with time. Acceleration can be measured by determining the speed of an object at
two different times and dividing the speed by the time difference
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between the two observations ,Therefore, the units associated with acceleration is
speed (distance per time) divided by time; or distance per time per time, or distance
per time squared.
If an object such as a ball is dropped, it falls under the influence of gravity in such a
way that its speed increases constantly with time. That is, the object accelerates as
it falls with constant acceleration. At sea level, the rate of acceleration is about 9.8
meters per second squared. In gravity surveying, we will measure variations in the
acceleration due to the earth's gravity.
As will be described next, variations in this acceleration can be caused by variations
in subsurface geology. Acceleration variations due to geology, however, tend to be
much smaller than 9.8 meters per second squared. Thus, a meter per second
squared is an inconvenient system of units to use when discussing gravity surveys.
The units typically used in describing the graviational acceleration variations
observed in exploration gravity surveys are speci¯ed in milliGals. A Gal is de¯ned as
a centimeter per second squared. Thus, the Earth's gravitational acceleration is
approximately 980 Gals. The Gal is named after Galileo Galilei. The milliGal (mgal) is
one thousandth of a Gal. In milli- Gals, the Earth's gravitational acceleration is
approximately 980,000.
1 gal = 10-2 m/s2 = 10-2 newton/m2
1 mgal = 10-5 m/s2 = 10-3 gal
1ugal = 10-8 m/s2 = 10-3 mgal
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Figure 1: The concept of velocity.
Figure 2: The concept of acceleration.
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The fundamental physical property of gravity is density
Density = Mass / Volume
Low
Gravity
High
density
Constant
Gravity
Distance
Distance
2.1 2.6 3 2.4 2.1
Gravity
High
Gravity
Gravity
Gravity
Observe the following cases:
3.1 2.7 2.3 2.6 3.2
Low
density
Distance
2.1 2.1 2.1 2.1 2.1
Constant
density
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Gravity and Geology
How is the Gravitational Acceleration, g, Related to Geology?
Density is defend as mass per unit volume. For example, if we were to calculate
the density of a room filled with people, the density would be given by the average
number of people per unit space (e.g., per cubic foot) and would have the units of
people per cubic foot. The higher the number, the more closely spaced are the
people. Thus, we would say the room is more densely packed with people. The
units typically used to describe density of substances are grams per centimeter
cubed (gm/cm3); mass per unit volume. In relating our room analogy to
substances, we can use the point mass described earlier as we did the number of
people.
Consider a simple geologic example of an ore body buried in soil, Figure 3. We
would expect the density of the ore body, d2, to be greater than the density of the
surrounding soil, d1.
The density of the material can be thought of as a number that quantifies the
number of point masses needed to represent the material per unit volume of the
material just like the number of people per cubic foot in the example given above
described how crowded a particular room was. Thus, to represent a high-density
ore body, we need more point masses per unit volume than we would for the
lower density soil3, Figure 4.
Now, let's qualitatively describe the gravitational acceleration experienced by a
ball as it is dropped from a ladder, Figure 5. This acceleration can be calculated by
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measuring the time rate of change of the speed of the ball as it falls.
Figure 3: Earth density model of an ore body. Figure 4: Point mass representation of
the ore body density model.
Figure 6: Building a
gravity profile.
Figure 5: More point masses mean
more acceleration.
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