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.

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

Logarithms

• Logarithms (Logs) are just exponents

• if by = x then y = logb x

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

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

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

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

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

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

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 “

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

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

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

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

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

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

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

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.

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

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

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.

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