Seismology and the Earth's Interior

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  • Created on: 23-05-15 19:59

Seismology and the Earth's Interior

Notes from Lecture 2 of LEC 171. Can also relate to LEC 172 and LEC 185

Sources:

Kresan & Mencke, 2014

Grotzinger & Jordan, 2014

Holden, 2012

http://www.tulane.edu/~sanelson/geol111/earthint.htm

http://www.gg.uwyo.edu/content/laboratory/earthquakes/snells_law/critical.asp?callNumber=33714&color=006600&unit=quakes1

Seismic Waves (Grotzinger & Jordan, 2014. pg 355) images: http://www.sms-tsunami-warning.com/pages/seismic-waves#.VWC36_lViko 

Types of waves:

Body Waves

P and S waves (http://www.sms-tsunami-warning.com/theme/tsunami/img/p-and-s-waves.jpg)

  • P Waves 
    • Arrive first
    • Any medium (Slower in Liquid
    • Compress the rock
  • S Waves
    • Arrive Second
    • Cannot shear (travel through) liquid or gas. Can only travel through solids.
    • Bend the rock in a wave-like fashion

Surface Waves

Love and Rayleigh waves (http://www.sms-tsunami-warning.com/theme/tsunami/img/love-and-rayleigh-waves.jpg)

  • Love Wave 
    • Shakes ground sideways
    • Faster at surface (3.5km/s)
  • Rayleigh Waves
    • 'Rolls' the ground

Adams-Williamson Equation 

Velocity is subject to density, and elasticity of the material it is going through.

Vp = Ö [(K + 4/3m )/r ]

Vs = Ö [( m )/r ]

  • K = incompressibility
  • m = rigidity
  • r = density

Reflection, Refraction and Transformation of Seismic Waves.

Seismic discontinuity: is a boundary between 2 differect layes with different properties. (different seismic wave velocities)

when a wave reaches this area different things can happen together or separately;

  • Reflection- wave bounces back through the layer it is in.
  • Refraction - wave speeds up or slows down
  • Transformation - wave is transformed. eg S  --> P or visa versa. 

image: http://www.tulane.edu/~sanelson/geol111/earthint.htm

(http://www.tulane.edu/~sanelson/images/reflrefr.gif)

Snell's Law of refractionhttp://en.wikipedia.org/wiki/Snell%27s_law

\frac{\sin\theta_1}{\sin\theta_2} = \frac{v_1}{v_2} = \frac{n_2}{n_1} (http://upload.wikimedia.org/math/2/0/a/20aa1e3d192ecb3164ac4f2095c86cd3.png)

when V1>V2 waves are refracted towards the centre of the earth (towards the normal)

When V1<V2, waves are refracted away from the centre of the earth (away from the normal)

Critical Angle (Reflection)

The behavior of the seismic wave largely depends upon the relation of the incidence angle to the critical angle. 

(http://www.gg.uwyo.edu/media/earthquakes/diagrams/critical_angle.gif)

image and explanation: http://www.gg.uwyo.edu/content/laboratory/earthquakes/snells_law/critical.asp?callNumber=33714&color=006600&unit=quakes1

At the critical angle, the wave is refracted along the interface between the two layers. Seismic waves incident to the interface at angles greater or less than the critical angle behave very differently.

  • The critical angle varies with the seismic velocities. because of this s- and p-waves traveling through the same layers will have different critical angles.
  • This angle can be calculated using Snell's law by setting angle of refraction equal to 90 degrees, i.e. the angle a ray will be refracted along the layer interface.

Sin ic =V1/V2

when i < ic the wave is reflected back into the upper layer and refracted

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