Earth Structure

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Earth Structure

• Using seismic waves

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Waves Propagate with a Wide Range of
Velocities
Disturbances that Move through Space as Time
Progresses

• Seismic Waves 100s m/s to 10s km/s
• Sound Waves 100s m/s
• Radio Waves 299,800,000 m/s
• Light Waves 299,800,000 m/s
• Water Waves 100s m/s

Propagation Velocity
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Attributes of a Propagating Wave

• Arrive Time and Velocity
• Location (hazards, monitoring for nukes)
• Determine structure (oil, gas, water, formation
  of Earth)
• Amplitude
• Magnitude (hazards)
• Discrimination (EQ or nuke?)
• Frequency/Period (used in all above applications)
• Frequency 1/Period
• Wavelength

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Using Propagating Waves
Using Our Description of Propagating Waves
V X / T Velocity is defined as distance divided
by time (ft/s) material property
determination X V ??T Distance traveled
calculated from material velocity and travel
time distance to lightning distance to
earthquake depth to layers in earth T X / V
Travel time determined by distance from
source to receiver and velocity time of
arrival of ground shaking time of arrival of
tsunami time of arrival of sonic bomb
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Outline

• Refraction Seismology
• Reflection Seismology
• Seismic Waves in a Spherical Earth
• Body Wave Travel Time Studies
• Anisotropy
• Attenutation
• Deep earth

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Earth Structure

• In general, travel times used to study structure
• Body waves
• Ray approximation travel time
• T travel time S source r receiver 1/v
  slowness
• Surface waves can be used (tomography), but
  usually based on group and phase velocity
  measurements

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Ray Theory Basics

• Rays bent when they reach an impedance contrast
  refraction
• Rays turned back at interface reflection

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Snells Law

• Snells Law controls what direction (angle) the
  rays are bent

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Critical Angle
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Critical Angle and Huygens Principle

• Incident angle where the bent ray becomes
  horizontal
• Called a head wave travels along interface
• Huygens Principle generating a head wave along
  the interface as a series of point sources

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Huygens Principles

• Head wave point sources along boundary

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Basic Ray Paths
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Travel Time Curve

• Crossover distance
• Refracted wave overtakes direct wave
• Critical distance
• Refracted wave begins

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Travel Times for Basic Paths

• Direct wave
• Reflected
• Refracted

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How do we use this to determine Earth structure?

• What can we do?
• Refraction experiment
• Reflection experiment
• What else?
• Body wave and surface wave tomography

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Reflection and Refraction

• Seismic refraction survey
• Each wiggle is a recording
• Evenly spaced recordings
• Notice change in slope of arrival time

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Seismic Refraction Survey

• Components
• SOURCE
• PROPAGATION THROUGH EARTH
• RECEIVER

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Seismic Refraction Survey 1. SOURCE
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Seismic Refraction Survey 2. PROPAGATION
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Seismic Refraction Survey 3. RECEIVER
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Seismic Refraction Survey
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Wave Propagation for Shallow Structure
Refraction Seismology
h
Soil V1
Rock V2
Direct wave travels directly through
soil Refracted wave travels through soil,
refracts and Travels in the rock and then
refracts back to surface
V2 gt V1
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Resulting Travel Time Curve
?t2
?x2
td
V2 ?x2 / ?t2
?t1
Time (seconds)
V1 ?x1 / ?t1
h ( xc/2) (V2 - V1)/(V2 V1)1/2
?x1
?
Xc (Crossover Distance)
?
Distance (feet)
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Rays and Travel Times
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A Local Experiment

• What is the crossover distance?
• What is V1? V2?

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• A large experiment

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More complicated structure

• Travel times

• Ray paths

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Blind Zone

• Layer too thin

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Dipping Structure
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• Travel time

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Real data!
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Low Velocity Zones

• Rays bent away
• Questions
• Would you generate a head wave?
• What would a raypath look like?
• What might a travel time plot look like?
• Can you image the LVZ with refraction?

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Advanced Methods

• Modeling amplitudes and times

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Crustal Structure

• Forward modeling to get structure
• Simple 1-D velocity model

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Wavelength and Structure

• Velocity
• V w/k f l l/T
• Period
• T 2p/w 1/f l/v
• Wavelength
• l 2p/k v/f vT
• Wavenumber
• K 2p/l w/v 2pf/v
• Resolution
• Body waves?
• Surface waves?

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Crustal Velocity Models Western U.S.
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Crustal Thickness
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Pn Velocity
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Global Thickness
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What is the Moho?
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Rocks and Velocity
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Travel Time Curve for Reflections

• Travel time
• Hyperbola
• Slope of hyperbola gives velocity
• Flatter higher
• Normal Moveout (NMO)
• Difference between travel times from some
  distance and zero offset

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Ray Parameter

• Relationship between ray path and travel time
  curves
• Slope of travel time curves
• Ray parameter is constant along ray

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Multiple layers

• Multiple layers result in multiple reflections
• Will get different travel time curves
• Hyperbolic approximation good for large offsets
• Get layer velocities from travel time curves

• Derive Dixs equation (interval velocity)

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Travel Time Curves for Multiple Layers

• The deeper the layer, the flatter the curves
• Becomes difficult to resolve

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Reflections and Dippling Structure

• Hyperbola will be offset

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Slowness

• Useful to think in terms of v(z)
• p sin(i)/v(z) constant along ray
• For a ray, total travel time is given as T(p),
  where u(z)1/v(z) is called the slowness

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Constant Ray Parameter
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Vertical and Horizontal Slowness

• Lets derive on the board the intercept-slowness
  formulation for travel times

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