1. What’s seismology about?
Seismology is the study of the generation, propagation and recording of elastic waves in the Earth (and other celestial bodies) and of the sources that produce them.

3. Elastic Moduli Young’s Modulus Poisson Ratio Bulk Modulus
Shear Modulus
Lamb’s constants
Vp, Vs.

4. E = s = tensile stress = (F /A) e = tensional strain = (DL /L) s e
Young’s modulus
s = tensile stress = (F /A)
e = tensional strain = (DL /L)
… for uniaxial tension or compression s e
E =

5. E = s = tensile stress = (F /A) e = tensional strain = (DL /L) s e
Young’s modulus
s = tensile stress = (F /A)
e = tensional strain = (DL /L)
… for uniaxial tension or compression s e
E =

6. Poisson’s ratio = - (eyy / exx)
Under a stress (sxx) along the x-axis,
longitudinal strain = exx =
and transverse strain = eyy = DL L DW W
Then,
Poisson’s ratio = - (eyy / exx)

7. Bulk Modulus = (DP/Q)
… where Q = dilatation = DV/V
and P = pressure

8. m = shear stress = (DF /A) shear strain = (Dl /L) A shear stress
shear modulus
shear stress = (DF /A)
shear strain = (Dl /L)
shear stress
shear strain
m =

9. Elastic Moduli and Densities of Some Common Materials
From Lay & Wallace (1995)

10. From Lay & Wallace (1995)

11. K + ( )m l + 2m V = a = = r m V = b = 2m n E l = k - =p
4/3
V = b = m s
Where m,l are the Lamé coefficients and l is
l = k =
2m n E
( 1 + n ) ( 1 - 2n )

13. Body Waves
compressions
P-wave
dilatations
S-wave
amplitude
wavelength

21. Body wave
Amp ~ 1/x
Surface wave
Amp ~ x-1/2

29. Late homework policy
Late homework will not be accepted one week after the deadline.
Late homework will be penalized: 90% (1 day late), 80% (2 day late), 60% (3 day late), 40 % (4 day late) and 20% (5-7 day late).

30. Body Waves
compressions
P-wave
dilatations
S-wave
amplitude
wavelength

35. Seismic Rays & Geometric Ray Theory
Rays are defined as the normal to the wave fronts and thus point in the direction of propagation. Connecting the these successive directions forms a ray paths. In the case of plane wave, rays are a family of straight lines; in the case of spherical wave, rays are spokes radiating out from the seismic source. They provide a convenient means of tracking an expanding wave front.
The seismic rays corresponding to P and S waves behave very much as light does in traveling through materials of varying indices of refraction. This leads to many parallels with optics: rays bend, focus, and defocus depending on the velocity distribution. Although geometric ray theory is an approximation, it, however, simplifies the analysis and yet gives the correct answer or a good approximation.

38. Fermat’s Principle
Ray paths between two points are those for which travel time is an extremum, either a minimum or maximum, with respect to the nearby possible paths.

39. Snell’s Law and Fermat Principle
Fermat Principle: T(x) is either minimum or maximum

44. Reynolds (1997)

45. Spherical Ray Parameter
R sin i
= constant = p V

46. What control reflection and transmission?
Continuity of stress
Continuity of displacement

47. I = 1
I = 2
Reynolds (1997)