EES 215

Lecture 5

Surface waves; free oscillations

Propagation of seismic waves - tool for the study of crust; mantle and core

Snell's Law (for the interface between two media where I is the angle of incidence and r the angle of refraction): sin i / sin r = a₁ / a₂ with a_1,2 the velocities in medium 1,2
When r is 90^o, the angle of incidence is i = i_c = sin^-1 (a₁ / a₂ ), the critical angle

Reflection Seismology: Use of surface sources in order to investigate layering of near-surface crust, specifically of sedimentary formations; used frequently in oceanography and in reservoir studies.

Refraction Seismology: Distinction between direct, reflected and refracted waves allows determination of velocities and thickness of layers. Basic equations (t arrival time; x distance between source and receiver; v_1,2 velocities in layer 1,2):

Direct wave: t = x/v₁ (equation of straight line ~ 1/v₁)

Reflected wave: 1 = ((v₁t)² – x²)/4h² (equation of hyperbola; asymptote t=x/v₁; intercept t=2h/v₁)

Refracted wave: t = x/v₂ + 2h/v₁ Ö(1-v₁/v₂) (straight line ~ 1/v₂; tangent to reflected wave line)

Critical angle: q_c = v₁/v₂

x_c critical distance, first refracted arrival

x_cr cross over distance, beyond which refracted wave arrives before direct wave

Assumptions: perfect elasticity; anelastic response causes attenuation: slight so that even moderate earthquakes travel to opposite side of the earth

Homogeneous and isotropic: if true straight rays through the earth

1. Gradual changes of density and elastic constants with depth, due to effects of pressure and temperature on chemically homogeneous material
2. Sharp boundary between chemically and physically distinct media. 'Sharp' relative to wavelengths of seismic waves
3. Boundary not sharp in sense of (2) but more progressive change in properties than in (1)

All three types cause refraction of seismic waves, sharp boundaries cause also reflections and partial conversion between P and S

Behavior at boundaries: reflection - refraction;

Systematics of body waves going through the earth: Fig.1

Seismic records: Example Fig. 2

• Propagation through the earth; definition of waves; shadow zone; show seismic record; Bullard diagram; basic approach to whole earth seismology
  
  

Applications of seismic records: reflection, refraction seismology; study of the inner of the earth; body waves through the earth; shadow zone; mechanism diagrams

Whole earth seismology

source: earthquakes (nuclear explosions)

gradual change in material properties with depth (fx of p, T) -- gradual refraction -- curved paths (toward surface)

The arrival of seismic waves is a function of time and distance. The information on travel times is put together the Jeffreys-Bullen travel-time diagram Fig. 3

Velocities for both P and S waves generally increase with depth, but show abrupt changes at major boundaries such as the mantle-outer core boundary Fig. 4

Seismometers; three independent components: vertical, North-South, East-West

Reflection on major boundaries -- reflectors (phase change; composition change)

• Moho: crust - mantle
• 650 km: upper - lower mantle
• Mantle - Outer Core
• Inner - Outer Core

Approach: world-wide array of seismometers record seismic events: determination of magnitude; depth and distance of earthquake (nuclear explosion)

Travel path, attenuation etc. give information on composition of earth

P waves: P crust; mantle (pP -- first reflected from surface)

K -- outer core
I -- inner core

S waves: S crust, mantle (ScP -- S wave converted to P at core-mantle boundary)

no S wave in outer core
J --  inner core