structural geology basics

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Structural Geology Structural Geology Basics Basics We need to review fundamental We need to review fundamental information about physical information about physical properties and their units. properties and their units.

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Structural Geology Basics. We need to review fundamental information about physical properties and their units. Exponents. Suppose m and n are rational numbers. a m a n = a m+n a m /a n = a m-n - PowerPoint PPT Presentation

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Page 1: Structural Geology Basics

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.

Page 2: Structural Geology Basics

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

Page 3: Structural Geology Basics

Logarithms

• Logarithms (Logs) are just exponents

• if by = x then y = logb x

Page 4: Structural Geology Basics

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

Page 5: Structural Geology Basics

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

Page 6: Structural Geology Basics

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

Page 7: Structural Geology Basics

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

Page 8: Structural Geology Basics

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

Page 9: Structural Geology Basics

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

Page 10: Structural Geology Basics

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 “

Page 11: Structural Geology Basics

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

Page 12: Structural Geology Basics

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

Page 13: Structural Geology Basics

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

Page 14: Structural Geology Basics

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

Page 15: Structural Geology Basics

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

Page 16: Structural Geology Basics

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

Page 17: Structural Geology Basics

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

Page 18: Structural Geology Basics

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.

Page 19: Structural Geology Basics

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

Page 20: Structural Geology Basics

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

Page 21: Structural Geology Basics

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.

Page 22: Structural Geology Basics

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