Exam 1 Review Flashcards
What are the compositional layers of the earth?
Crust Upper Mantle (includes transition zone) Lower Mantle (includes D'') Outer Core Inner Core
Crust
- thicknesses
- chemical composition
Continental Crust
~20-70 km thick
-mainly granitoid
Oceanic Crust
~7 km thick
-gabbro (basalt)
Upper Mantle
- thicknesses
- chemical composition
70-660 km
Peridotite (~75% olivine (olivine structure), ~25% pyroxine)
Transition Zone
- thicknesses
- chemical composition
410-660 km
Mg2SiO4 (spinel structure)
Lower Mantle
- thicknesses
- chemical composition
660-2891 km
Solid - perovskite
D’’
- thicknesses
- chemical composition
~2741-2541 - 2891 km
Solid - Denser post-perovskite
Outer Core
- thicknesses
- chemical composition
2891-5150 km
Liquid - Fe, some lighter elements (S , Ni)
Inner Core
- thicknesses
- chemical composition
5150 - 6371 km
Solid - Mostly Fe, Some Ni
What are the mechanical layers of the earth?
Lithosphere Asthenosphere Mesosphere Outer Core Inner Core
Lithosphere
- thickness
- Mechanical Behavior
- Includes what compositional layers?
Upper 100 km
Hard Solid
Crust and some of the upper mantle
Asthenosphere
- thickness
- Mechanical Behavior
- Includes what compositional layers?
100-350 km
Soft Solid
In the upper mantle
Mesosphere
- thickness
- Mechanical Behavior
- Includes what compositional layers?
350 - 2891 km
Hard Solid
Some of the upper mantle, transition zone, and lower mantle including the D’’ layer.
Outer Core
- thickness
- Mechanical Behavior
- Includes what compositional layers?
2891 - 5150 km
Liquid
Outer Core
Inner Core
- thickness
- Mechanical Behavior
- Includes what compositional layers?
5150 - 6371 km
Hard Solid
Inner Core
What are the boundaries within the earth?
- MOHO
- D’’ discontinuity
- Core mantle boundary
- Inner core boundary
MOHO
- type of boundary
- location
compositional
Between crust and mantle
D’’ discontinuity
- type of boundary
- location
compositional
Between ‘lower mantle’ and D’’
Core mantle boundary
- type of boundary
- location
compositional and mechanical
Between mantle and core
Inner core boundary
- type of boundary
- location
compositional and mechanical
Between outer core and inner core
What are the types of seismic waves?
Body waves and Surface Waves
Define Seismic Wave
Disturbances in the Earth, propagate as waves
Define Body Wave
Propagate within a medium (travel through body of the earth)
Define Surface Wave
Propagate along the surficial boundary of a medium (confined to surface of earth, created by constructive interference of body waves at the surface)
What are the types of body waves?
P-waves and S-waves
What is a P-wave?
Primary (P or compressional waves)
Why are they called P-waves?
They are called primary because they arrive first.
How do P-waves propagate?
They propagate by a series of compressions or dilations of a material.
What is the particle motion of a P-wave?
The particle displacement is parallel to the direction of propagation.
What can P-waves travel through?
Both Solids and Liquids
DRAW A DIAGRAM FOR P-WAVE PARTICLE MOTION
SEE HANDOUT L04
Give an analogy as to how P-waves move
Like a slinky
What is the equation for the velocity of a P-wave?
Vp = sqrt((k + 4u/3)/p) (see study guide)
Fill in the blank: The more incompressible or rigid the material is, then the __________ the P-wave will travel through it.
FASTER
What is an S-wave?
Secondary (S or shear) wave
Why are they called S-waves?
These are called secondary because they arrive behind the P-waves.
How do S-waves propagate?
These propagate by shearing the material back and forth.
What is the particle motion of an S-wave?
Particle displacement is perpendicular to the direction of propagation.
What can S-waves travel through?
only solids
Why don’t S-waves travel through liquids?
S waves are dependent on shear modulus and in liquids the shear modulus is zero.
Why can S-waves be divided into two components? What are they?
Because particle motion is perpendicular to the propagation direction.
SH-motion
SV-motion
What is SH-motion?
Parallel to the horizontal axis
What is SV-motion?
Perpendicular to SH-motion.
DRAW A DIAGRAM FOR S-WAVE PARTICLE MOTION
See handout L04
What is the equation for S-wave velocity?
Vs=sqrt(u/p) see study guide handout
What happens to the velocity of P and S waves with increasing depth?
With increasing depth, the pressure increases and most materials become more compact.
As this happens generally k and u increase, which implies that Vp and Vs also increase.
BUT an increase in depth usually is accompanied by an increase in density.
This causes Vp and Vs to decrease.
In general, the increase in k and u is much greater than the decrease in p.
So we get an overall INCREASE in Vp and Vs.
What are the two types of surface waves?
Rayleigh Waves (ground roll) Love Waves
What creates Rayleigh Waves?
Created by a combination of P- and Sv- wave motion (created by constructive interference of P and SV waves at the surface)
What is the particle motion of Rayleigh Waves?
Particle displacement is retrograde elliptical.
DRAW A DIAGRAM FOR RAYLEIGH WAVE MOTION
See L04 and class review notes
What is the velocity of Rayleigh Waves?
Vr=0.9Vs
What creates Love Waves?
Created by SH waves at the subsurface (created by constructive interference of SH waves at the free surface)
What is the particle motion of Love Waves?
Particle Displacement is transverse to the direction of propagation.
(Particle motion is in and out of the board perpendicular to propagation direction)
DRAW A DIAGRAM FOR LOVE WAVE MOTION
See L04 and class review notes
What is the difference between mechanical and compositional layers of the earth?
Mechanical layers have to do with how each layer behaves (mainly due to pressure/temperature and depth) whereas compositional layers have to do with what each section is actually made up of.
Why do the layers in the earth exist?
The mechanical layers exist due to the increasing pressure and temperature as depth increases and how it affects the minerals at that depth.
The compositional layers sort themselves in this manner due to differentiation, which is when more dense minerals sink and start to form ‘core’ and ‘mantle’
What happens when a ray strikes a boundary with increasing velocity? (relationship between theta and layer velocities, essentially)
When a ray strikes a boundary with increasing velocity the refracted ray transmits through to the next layer wit a larger angle than the incidence angle.
Theta 2 > Theta 1 for V2 > V1
For larger and larger velocity contrasts (V2»V1), what happens to theta 2?
Also gets bigger
What happens to theta 2 if theta 1 gets larger?
theta 2 also increases
Can theta be forever increasing through layer after layer?
NO. Eventually, we will get to a point where the refracted ray travels horizontally along the interface boundary.
At what angle does the refracted ray need to be to travel horizontally across a boundary?
theta = 90°
What is the critical angle (THETAc) (or theta critical)?
Theta critical = sin^-1(v1/v2)
What layer does the critically refracted ray travel with? At what velocity?
This critically refracted ray travels in the top of the lower layer, so travels with the velocity of the lower layer.
Define headwaves, why?
Critically refracted rays, they travel at faster velocities and arrive before direct waves at larger distances.
What is an analogy for a wave front?
Like dropping a stone in water and watching the ripples radiate out.
Define ray path
The path the energy takes (trajectory seismic energy travels)
What is the relationship between ray paths and wave fronts?
Ray paths are always perpendicular to the wave fronts.
DRAW A RAY PATH WAVE FRONT DIAGRAM
See L04-9
How does wave speed change with depth?
The speed increases as depth increases
What does it mean for something to be elastic or in the elastic regime?
If we remove the stress the object returns to its normal shape.
What happens to the material of the Earth when a seismic wave passes through it?
When a seismic wave passes through the Earth it stresses the material, but once that disturbance passes the material returns to its normal shape.
In what regime are seismic waves? (think stress strain diagram)
Seismic waves stay permanently in the elastic regime
Define Bulk Modulus (k)
The bulk modulus (or incompressibility) is a materials ability to resist being compressed under a pressure equal in all directions.
What is the equation for bulk modulus?
k = stress/strain = (DeP)/((DeV)/V)) See notes L03?
where P is the pressure (force/area) applied to a volume of material given by V.
What is a good visual for Bulk Modulus?
Imagine a box, compress on all sides, now the box is proportionally still the same, its just an overall smaller box
DRAW BULK MODULUS DIAGRAM
See L03-09
DRAW BULK MODULUS PLOT
See L03-09
What happens as the bulk modulus gets smaller?
As the bulk modulus gets smaller, the material has less ability to resist compression and we get larger volume changes or strains for the same applied stress.
Define Shear Modulus (u) where u is actually ‘mu’
The Shear modulus (or rigidity) is the ability of a material to resist shearing
What is the equation for shear modulus?
u = (DeF/A) / (DeL/L) see notes L03?
What is a good visual for Shear Modulus?
Imagine a cube pushed on sides so now the front and back are parallelograms
What happens as the shear modulus gets smaller?
The smaller the shear modulus (u) the less resistance to shearing the material has
What is the shear modulus for a fluid?
For a fluid, there is no resistance to shearing so u = 0.
Define Young’s Modulus
Young’s Modulus is how much a wire will extend under tension or buckle under compression
What is the equation for Young’s Modulus?
E = (F/A) / (DeL/L) See notes L03?
What is a good visual for Young’s Modulus?
Rod getting longer in one direction
What is the equation for Poisson ratio?
v = (DeW/W) / (DeL/L) see notes L03?
Why is Poisson ratio important?
When a material is stretched in one direction it usually contracts in other directions.
What material properties do we need to know to relate how fast seismic waves travel to actual rock samples?
Bulk Modulus (k) Shear Modulus (u) Density (p)
What is the easiest to measure for crustal materials?
For crustal materials it is easier to measure Young’s Modulus (E) and Poisson ratio (v)
What is the relationship equation for shear modulus, Young’s modulus and Poisson ratio?
Shear modulus = u = E/ (2(1+v)) See L03
What is the relationship equation for Bulk Modulus, Young’s Modulus and Poisson ratio?
Bulk Modulus = k = E / (3(1-2v)) See L03
What is the easiest to measure at higher pressure? What is it more challenging to measure? What is the least constrained parameter in the deeper portions of the Earth?
At higher pressure it is easier to measure the bulk modulus (k) directly.
But it is more challenging to measure any of the other elastic moduli.
Hence, in the deeper portions of the Earth, the shear modulus is the least well constrained parameter.
Define Hooke’s Law
Force is linearly proportional to the extension.
In seismology, stress is linearly proportional to strain.
General Equation of Hooke’s Law
F(x) = -kx
Seismology Equation of Hooke’s Law
Sigma = ce
Where sigma = stress (F/A) measured in Pascals
c is elastic modual used in seismology
e is strain, relative measure of deformation
Where is Hooke’s Law followed on the stress/strain diagram?
It is the linear part of the stress/strain diagram.
Define Stress
Force per unit area (F/A) (measured in Pascals) acting on a volume element of material in some continuous medial.
Define Strain
the fractional change in dimensions of a volume element due to an applied stress (unitless)
DRAW THE GRAPH ON L03-06
SEE L03-06
DRAW THE DIAGRAM L03-06
SEE L03-06
What is an elastic wave?
When a seismic wave passes through the Earth it stresses the material, but once that disturbance passes the material returns to its normal shape.
MEMORIZE DIAGRAM L05-10
SEE L05-10
What is the critical distance?
For any critically refracted arrival, there must be some minimum distance (CRITICAL DISTANCE) before which you don’t see the arrival - because it doesn’t exist yet.
Equation for critical distance
Xc=2b=2htan(thetaC)
Define crossover distance (Xcr)
The distance where the refracted arrival overtakes the direct arrival (where the two lines intersect on the graph)
What is the equation for crossover distance?
Xcr = 2h*sqrt((v2+v1) / (v2-v1))
What is the problem when trying to detect a low velocity layer?
When we have a low velocity layer the ray gets bent backward and no critically refracted ray can be initiated
How does a low velocity layer effect the travel time graph?
You’ll have a line for direct and 2nd refraction, but 2nd refraction will look like 1st refraction, however, the slope for this line will not be 1/v2, it will be 1/v3, leading to an interpretation of a 2 layer structure, not a 3 layer structure.
How can a low velocity layer be detected?
The trick is to look at the critical distance. Consider the critical distances for the measured structure vs. the true structure.
The critical distance calculated is larger than observed.
What is the problem when dealing with a thin layer?
The arrival from the critically diffracted ray along the v2-v3 boundary could always arrive ahead of the arrival from the critically diffracted ray along the v1-v2 boundary.
This is because the velocity in layer 3 is higher than the velocity in layer 2.
How does a thin layer affect the travel time curve? And thus lead to what wrong interpretation?
The travel-time curve for the first critically refracted arrival never shows up as the 1st arrival.
Hence it way be hidden and may result in an over estimation in thickness of the next layer.
How do you determine if a layer is dipping?
Look at forward and reverse shots and compare slopes, differences in slopes means one took longer so it must be a dipping bed.
Shortest travel time=down dip direction
What are some popular geophysical techniques?
Gravity Resistivity Magnetics Seismic Electromagnetic Waves Heat Flow
Geophysical Technique: Gravity
What’s Measured?
Property:
Geophysical Technique: Gravity
What’s Measured? - Measures the minute variations in Earth’s gravity field. Based on these variations, subsurface density and thereby composition can be inferred.
Property: Density
Geophysical Technique: Resistivity
What’s Measured?
Property:
Geophysical Technique: Resistivity
What’s Measured? - Measurement of differences in electric potential at Earth’s surface in response to injection of electric current.
Property: Electrical resistivity
Geophysical Technique: Magnetics
What’s Measured?
Property:
Geophysical Technique: Magnetics
What’s Measured? - Measure disturbances in Earth’s natural magnetic field. These disturbances are caused by ferromagnetic materials, either magnetic rocks or man made objects containing iron or steel.
Property: Magnetic susceptibility and magnetic remanence
Geophysical Technique: Seismic
What’s Measured?
Property:
Geophysical Technique: Seismic
What’s Measured? - Measurement of travel-times and amplitudes of seismic waves at various distances from a seismic source (ex. earthquake or explosion)
Property: Seismic wave velocity, density, interfaces
Geophysical Technique: Electromagnetic Waves
What’s Measured?
Property:
Geophysical Technique: Electromagnetic Waves
What’s Measured? - Many different techniques exist (ex. ground penetrating radar, magnetotelluric surveying)
Property: Electrical capacitance, conductivity, inductance
Geophysical Technique: Heat flow
What’s Measured?
Property:
Geophysical Technique: Heat Flow
What’s Measured? - The change in temperature can be measured from the surface downward in drill-holes. This gives the geothermal gradient (dT/dZ)
Property: Thermal conductivity
What are the two categories of geophysical techniques?
Passive
Active
What is a Passive geophysical technique?
Measurements taken from naturally occurring phenomena (gravity field, magnetic field, earthquake generated seismic waves, etc.)
What is an Active geophysical technique?
Transmit a signal into the subsurface and record what comes back.
What are five limitations to geophysical techniques?
1) Methods Require a Contrast in Physical Properties
2) Resolution is determined by wavelength of the signal
3) Nonuniqueness of solution
4) Noise prevents recovery of low amplitude signal
5) Resolution may diminish with distance
What is it meant by resolution is determined by wavelength of the signal?
If the structure is smaller than the wavelength of the wave we are using it becomes difficult to see the object
What is the forward modeling of nonuniqueness of solution?
Forward Modeling: Calculate the result of a specific structure. We can vary some subsurface physical property and then calculate what the geophysical anomaly produced would be. We start out with an estimate of the Earth model and predict what the observations should look like. If our predictions don’t look like our observations we change our input model and try again.
What is the inverse modeling of nonuniqueness of solution?
Inverse Modeling: This is the opposite direction from forward modeling. Here we measure the geophysical anomaly and use a mathematical technique to “invert” for the variation of the physical property.
