PETROLEUM GEOSCIENCE PROGRAM

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PETROLEUM GEOSCIENCE PROGRAM
Offered by GEOPHYSICS DEPARTMENT IN COROPORATION
WITH GEOLOGY,
PHYSICS, CHEMISTRY, AND MATHEMATICS DEPARTMENTS
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Newton's First Law of Motion

• I. Every object in a state of uniform motion
  tends to remain in that state of motion unless an
  external force is applied to it.

Law of Inertia"
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Newton's Second Law of Motion

• II. The relationship between an object's mass m,
  its acceleration a, and the applied force F is
• F ma.
• Acceleration and force are vectors in this
  law the direction of the force vector is the same
  as the direction of the acceleration vector.

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The net force can be expressed as Fnet m a

• a unit of force is equal to a unit of mass times
  a unit of acceleration. By substituting standard
  metric units for force, mass, and acceleration
  into the above equation, the following unit
  equivalency can be written.
• One Newton is defined as the amount of force
  required to give a 1-kg mass an acceleration of 1
  m/s/s.

1 Newton 1 kg(m/s2)
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Quick Quiz

• Using the equation Fnet m a
• and solve for the unknown quantity shown in
  the following table

• Fnet 10 N, Fnet m a , Fnet (2 kg) (5
  m/s/s), Fnet 10 N
• m 1 kg, m Fnet / a , m (10 N) / (10 m/s/s),
  m 1 kg
• a 5 m/s/s, a Fnet / m , a (10 N) / (2 kg),
  a 5 m/s/s
• a 10 m/s/s, a Fnet / m , a (20 N) / (2 kg),
  a 10 m/s/s
• a 5 m/s/s, a Fnet / m, a (20 N) / (4 kg), a
  5 m/s/s

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Newton's Third Law of Motion

• III. For every action there is an equal and
  opposite reaction.

• i.e., there is a pair of forces acting on the two
  interacting objects.
• The size of the forces on the first object
  equals the size of the force on the second
  object.
• The direction of the force on the first object is
  opposite to the direction of the force on the
  second object.

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Universal Mutual Gravitation

• Isaac Newton, in his Principia, formulated the
  Law of Universal Mutual Gravitation
• Gravity is an Attractive force
• It draws massive objects closer together
• Gravity is a Universal force
• It operates everywhere in the Universe.
• Gravity is a Mutual force
• It works between pairs of massive objects.

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• Gravity Survey - Measurements of the
  gravitational field at a series of different
  locations over an area of interest.
• Gravity survey is divided into three types
• 1- land survey. 2- airborne
  survey
• 3- ship born survey
• Gravity techniques measure minute variations in
  the earth's gravity field. Based on these
  variations, subsurface density and thereby
  composition can be inferred.

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GRAVITY SURVEYINGMethodology and Instrumentation
Gravity observations are either
RELATIVE
ABSOLUTE
it is necessary to measure the actual gravity
that exists at the observation point.
it is necessary to measure only the difference
between the gravity at the base station and the
gravity at the field stations.
Our concern here with the relative measurements
Instruments used for relative gravity
observations are portable gravimeters
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• Gravimeters are basically spring balances
  carrying a constant mass. Variations in the
  weight of the mass caused by variations in
  gravity cause the length of the spring to vary
  and give a measure of the change in gravity. The
  extension of the spring is proportional to the
  extending force (Hooke's Law)

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How do we Measure Gravity?
1. Falling Body Measurements (Galileo Galilei)

• The gravitational acceleration can be measured
  directly by dropping an object and measuring its
  time rate of change of speed (acceleration) as it
  falls.
• In this experiment, Galileo is supposed to have
  dropped objects of varying mass from the leaning
  tower of Pisa and found that the gravitational
  acceleration an object undergoes is independent
  of its mass.
• It is easy to show that the distance a body falls
  is proportional to the time it has fallen
  squared. The proportionality constant is the
  gravitational acceleration, g. Therefore, by
  measuring distances and times as a body falls, it
  is possible to estimate the gravitational
  acceleration.

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How do we Measure Gravity?
2. Pendulum Measurements

• Another method for measuring the acceleration due
  to gravity is to observe the oscillation of a
  pendulum, such as that found on a grandfather
  clock.
• If we were to construct a simple pendulum by
  hanging a mass from a rod and then displace the
  mass from vertical, the pendulum would begin to
  oscillate about the vertical in a regular
  fashion. The relevant parameter that describes
  this oscillation is known as the period of
  oscillation.

The period of oscillation is the time required
for the pendulum to complete one cycle in its
motion.
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How do we Measure Gravity?
3. Mass and Spring Gravity Measurements
The most common type used in exploration surveys.

• If we hang a mass on a spring, the force of
  gravity will stretch the spring by an amount that
  is proportional to the gravitational force. It
  can be shown that the proportionality between the
  stretch of the spring and the gravitational
  acceleration is the magnitude of the mass hung on
  the spring divided by a constant, k, which
  describes the stiffness of the spring. The larger
  k is, the stiffer the spring is, and the less the
  spring will stretch for a given value of
  gravitational acceleration.

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• Instruments of this type are produced by several
  manufacturers, including LaCoste and Romberg,
  Scintrex (IDS), and Texas Instruments (Worden
  Gravity Meter).

LaCoste and Romberg Gravity Meter
Worden Gravity Meter
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Factors that Affect the Gravitational Acceleration
Spatial variations
Temporal variations

• These are changes in the observed acceleration
  that are time dependent

• These are changes in the observed acceleration
  that are space dependent

Drift Effect
Latitude
Elevation
Tidal Effect
Slab
Topographic
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Gravity Data Reduction

• is the process of removing effects of surface
  features which mask the true gravity value at any
  given location.
• A gravity survey will show variation in gz caused
  by the following
• a) changes in latitude
• b) changes in elevation
• c) local topography
• f) earth tides
• g) variation in subsurface density.

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Instrument drift and tides

• Drift - A gradual and unintentional change in the
  reference value with respect to which
  measurements are made.
• Tidal Effect - Variations in gravity observations
  resulting from the attraction of the moon and sun
  and the distortion of the earth so produced.

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Strategy of correction