Structural Geology Basics
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Transcript of Structural Geology Basics
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Structural Geology BasicsStructural Geology Basics
• We need to review fundamental We need to review fundamental information about physical properties information about physical properties and their units.and their units.
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Exponents
• aman = am+n am/an = am-n
• (am)n = amn (ab)m = ambm
• (a/b)m = am/bm a-n = 1/an
Suppose m and n are rational numbers
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Logarithms
• Logarithms (Logs) are just exponents
• if by = x then y = logb x
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Scalars and VectorsScalars and Vectors• A scalar is a quantity with a size, for
example mass or length
• A vector has a size (magnitude) and a direction.
http://www.engineeringtoolbox.com/average-velocity-d_1392.html
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VelocityVelocity• Velocity is the rate and direction of
change in position of an object.
• For example, at the beginning of the Winter Break, our car had an average speed of 61.39 miles per hour, and a direction, South. The combination of these two properties, speed and direction, forms the vector quantity Velocity
http://www.engineeringtoolbox.com/average-velocity-d_1392.html
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Vector ComponentsVector Components• Vectors can be broken down into components
• For example in two dimensions, we can define two mutually perpendicular axes in convenient directions, and then calculate the magnitude in each direction
• Vectors can be added
• The brown vector plus
the blue vector equals
the green vector
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Vectors 2: Acceleration.Vectors 2: Acceleration.• Acceleration is the change in Velocity during
some small time interval. Notice that either speed or direction, or both, may change.
• For example, falling objects are accelerated by gravitational attraction, g. In English units, the speed of falling objects increases by about
g = 32.2 feet/second every second, written g = 32.2 ft/sec2
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SI Units: SI Units: Kilogram, meter, secondKilogram, meter, second
• Most scientists and engineers try to avoid English units, preferring instead SI units. For example, in SI units, the speed of falling objects increases by about 9.81 meters/second every second, written
g = 9.81 m/sec2
• In geology, both english and SI units are used. We must learn to use both.
http://en.wikipedia.org/wiki/International_System_of_Units
Système international d'unités pron dooneetay
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What’s in it for me?What’s in it for me?
• Petroleum Geologists trained in Structural Geology and Stratigraphy make more money than other Geology job centers.
• http://jobs.bhpbilliton.com/jobDetails.asp
• The mining industry also employs many Structural Geologists, e.g.
• http://www.na.srk.com/en/page/na-geology-resource-jobs
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Data and Conversion FactorsData and Conversion Factors
• In your work as a geologist, you will be scrounging for data from many sources. It won’t always be in the units you want. We convert from one unit to another by using conversion factors.
• Conversion Factors involve multiplication by one, so nothing changes.
• 1 foot = 12 inches so 1 foot = 1
12 “
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ExampleExample
• Rock is flowing at a velocity of 3 x 10-14 meters per second at a depth of 35km. What is this speed in feet per second?
• Steps: (1) write down the value you have, then (2) select a conversion factor and write it as a fraction so the unit you want to get rid of is on the opposite side, and cancel. Then calculate.
• (1) (2)• 3 x 10-14 meters x 3.281 feet = 9.843 x 10-14 feet
second meter second
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Momentum (plural: momenta)Momentum (plural: momenta)• Momentum (p) is the product of velocity and mass, p =
mv• In a collision between two particles, for example, the total
momentum is conserved.
• Ex: two particles collide and m1 = m2, one with initial speed v1 ,
the other at rest v2 = 0,
• m1v1 + m2v2 = constant
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ForceForce• Force is the change in momentum with respect to time.
• A normal speeds, Force is the product of Mass (kilograms) and Acceleration (meters/sec2), so Force F = ma
• So Force must have SI units of kg . m
sec2
• 1 kg . m is called a Newton (N)
sec2
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StaticsStatics
• If all forces and Torques are balanced, an object doesn’t move, and is said to be static
• Discussion Torques, See-saw
• Reference frames
F=2
F=1
-1 0 +2
F=3
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Pressure = StressPressure = Stress
• Pressure is Force per unit Area
• So Pressure must have units of kg . m
sec2 m2
• 1 kg . m is called a Pascal (Pa)
sec2 m2
For solid-solid systems, Pressure is called “stress”For solid-solid systems, Pressure is called “stress”
Pressure (stress) = density x gravity x depth ρgz
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DensityDensity• Density is the mass contained in a unit volume
• Thus density must have SI units kg/m3
• The symbol for density is pronounced “rho”
• Very important is not a p, it is an r• It is NOT the same as pressure
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Chaining Conversion FactorsChaining Conversion Factors
Suppose you need the density of water in kg/m3. You may recall that 1 cubic centimeter (cm3) of water has a mass of 1 gram.
1 gram water x (100 cm)3 x 1 kilogram = 1000 kg / m3
(centimeter)3 (1 meter)3 1000 grams
water = 1000 kg / m3
Don’t forget to cube the 100
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EnergyEnergy• Energy is the ability to do work, and work and
energy have the same units• Work is the product of Force times distance, • W = Fd
• 1 kg . m2 is called a N.m or Joule (J)
sec2
• Energy in an isolated system is conserved • KE + PE + P/v + Heat = constant
N.m is pronounced Newton meter, Joule sounds like Jewel. KE is Kinetic Energy, PE is Potential Energy, P/v is Pressure, v is unit volumeAn isolated system, as contrasted with an open system, is a physical system that does not interact with its surroundings.
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Kinetic EnergyKinetic Energy
• Kinetic Energy (KE) is the energy of motion
• KE = 1/2 mass . Velocity 2 = 1/2 mV2
• SI units for KE are 1/2 . kg . m . m• sec2Note the use of m both for meters and for mass. The context will tell you which.
That’s the reason we study units.Note that the first two units make a Newton (force) and the remaining unit is meters, so the units of KE are indeed Energy
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Potential EnergyPotential Energy
• Potential energy (PE) is the energy possible if an object is released within an acceleration field, for example above a solid surface in a gravitational field.
• The PE of an object at height h is
PE = mgh Units are kg . m . m
sec2
Note that the first two units make a Newton (force) and the remaining unit is meters, so the units of PE are indeed EnergyNote also, these are the same units as for KE
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KE and PE exchangeKE and PE exchange• An object falling under gravity loses
Potential Energy and gains Kinetic Energy.• A pendulum in a vacuum has potential
energy PE = mgh at the highest points, and no kinetic energy because it stops
• A pendulum in a vacuum has kinetic energy KE = 1/2 mass.V2 at the lowest point h = 0, and no potential energy.
• The two energy extremes are equal
Stops v=0 at high point, fastest but h = 0 at low point.Without friction, the kinetic energy at the lowest spot (1) equals the potential energy at the highest spot, and the pendulum will run forever.
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OverburdenOverburden
• Stress caused by gravity is called overburden.
• Pressure (stress) = density x gravity x depth
• Stress ρgz
= 2.7 g/cm3 x 9.81 m/sec2 x 1000 m
ρ = 2.7 g x 1003 cm3 x 1 kg = 2700 kg/m3
cm3 1 m3 1000 g
= 2700 kg/m3 x 9.81 m/sec2 x 1000 m• The normal stress (pressure) at 1 km depth is about
26487000 Pa ~25 MPa in the upper crust.
The upper crust has an average density of 2.7 g/cm3
we need to convert units for density