1. Geology 5640/6640 Introduction to Seismology 13 Apr 2015 © A.R. Lowry 2015 Read for Wed 15 Apr: S&W 177-184 (§3.6) Last time: Ray-Tracing in a Spherical Earth In a spherical geometry, the angle of incidence for a ray at the top of a uniform-velocity layer is slightly different than the angle at the bottom. We account for this by re-writing Snell’s law to account for the change in angle of incidence, as: Instead of units of slowness, the ray parameter p = dT/d  has units of time per angle in radians The ray-tracing relations become (for  = r/v ):

2. Note that part of the T vs  slope in a spherical geometry is just geometry, while part reflects the change in velocity with depth…

3. And note that our early understanding of travel-times for the various phases in the Earth (and hence structure of the Earth’s interior) relied on ray theory in a spherical Earth!

4. RegionDepth (km)Description A B C D D’ D” E F 33 413 670 2898 1000-2700 2700-2900 4982 6371 Crust Upper mantle Transition region Lower mantle 2-3% velocity jump Outer Core Inner Core Structure of the Deep Earth’s Interior Recent additions to knowledge of the deep Earth’s interior (in the last several decades) from seismology include recognition of phase boundaries at ~410 and 670 km depths, and phase and/or compositional boundary(ies?) in the lowermost mantle 1940 1991

5. Understanding the velocities observed at these depths requires a combination of high P-T lab measurements, geodynamical modeling and geochemical measurements of surface magmas

6. Getting this kind of information is of course easier at the shallower depths…

7. Schmandt et al., Science, 2014

8. Colors are flow model predictions of upwelling (red)/ downwelling (blue) for two different global shear wave velocity models… White squares indicate where Ps converted waves suggest very low v S just below the transition zone!

9. Measurements of P-T conditions for formation of post- perovskite are a bit uncertain, and the existence or not of this phase depends on the (poorly known) geotherm at the core-mantle boundary…

10. Tomograms at 2811 km depth The combination of geodynamical modeling and geochemistry with the seismic data suggests thermochemical convection (plumes arise from a thin, compositionally distinct layer near CMB) modulated by slabs which may enter PPv phase nearby

11. Practical note: Travel- time T & distance  depend on source depth! But how did we get this info?

12. Body Wave Studies use the various P and S body wave paths through crust, mantle and core to image variations… with emphasis on lateral perturbations.

13. A quick reminder of seismic phase designations: Each path provides a slightly different piece of information…

14. Most body waves are minimum travel-time phases… But surface reflections in a spherical Earth are called “maximum time” because they take longer to arrive than would any other travel path reflected off the surface! Consider a ray reflected from a point  away:

15. We can use a Taylor series expansion to write: and summing: The travel-time curve is concave-down So all other paths would be faster!

16. Core phases: Reflections off the core-mantle boundary also can be useful for imaging lateral variations in mantle velocity… We denote with a “c”, e.g. PcP, ScS As the liquid outer core cannot transmit S, all SH motion is reflected (both at the CMB and at the surface) resulting in a particularly strong ScS phase (relative e.g. to PcS and PcP).

17. Much of the P wave energy by contrast is transmitted. Consider: From 0-98°, rays refract within the mantle Rays with slightly smaller angle of incidence are refracted downward (and the large decrease in velocity results in some unusual moveout in PKP! With increasing  i get C  B  A).

18. As angle of incidence and ray parameter p decrease the reflection off the inner core (PKiKP) is retrograde Rays with even smaller angle of incidence transmit through the inner core (PKIKP) in a progressive direction The diffracted core phase is also strongly observed (P d or P diff ).