What’s seismology about?

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

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

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

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

44. Reynolds (1997)

45. Spherical Ray Parameter R sini = constant = p V

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

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