1. Seismic tomography
Tomography attempts to determine anomalous structures within the Earth as revealed by deviations from “average” seismic properties at depth.
Average is usually determined by one of the simple “radial” structural models of the Earth. PREM (Anderson and Dziewonski, 1981) is the most commonly used reference Earth model.
Thanks and/or apologies to Barbara Romanowicz, UC Berketey some of whose slides have been used liberally in this presentation.

3. PREM
Anderson and Dziewonski (1981) determined a spherical shell model of the Earth that was most consistent with the observed travel times from seismic sources to seismic stations that had been accumulated in the previous 80 years of seismology.
Recall that the model is “layered” and laterally averaged over the whole Earth within layers and so no lateral variations in structure are modelled.

4. P-wave velocity

5. S-wave velocity

6. Preliminary Reference Earth Model

7. What are we missing?

8. What are we seeking?

9. Crust and Mantle Structures

10. What we would like to see...

11. Body and surface waves 𝑻 Δ = 𝒙 𝒗(𝒙) 𝒅𝒙 along path
Seismic waves integrate the seismic velocities experienced point-by-point along their paths:
𝑻 Δ = 𝒙 𝒗(𝒙) 𝒅𝒙 along path

12. Seismic wave paths

13. A tomographic slice
Over a diametrical slice through the Earth, we look for regions that are anomalously slow or fast compared to the PREM average for that depth within the Earth.

14. Basic concept Each of these 3 paths is the same distance.
S1-A: no variation
S2-B: encounters a fast region
S1-C: encounters a slow region

15. Earthquakes and seismographs
Earthquakes and seismographs are not uniformly or even with uniform randomness distributed over the world. We only have biased data sets.

16. Density of paths transiting a region of between 660 and 870km
Sample bias -- 1
Density of paths transiting a region of between 660 and 870km

17. Density of paths transiting a region of between 2670km and CMB
Sample bias -- 2
Density of paths transiting a region of between 2670km and CMB
Vasco and Johnson, 1998

18. The Scripps SB4L18 model
Seismic tomography is very fashionable, now, and most major seismic laboratories are presenting mantle velocity anomaly models. This one, the Scripps SB4L18 model, presents results as depth layers over the Earth. What is plotted is slow S-wave and fast S-wave velocities.
Laske, Masters and Reif, AGU 2001

19. Example results
Van der Hilst, et al., 1998

20. (Lawrence-Livermore National Labs)
Layer-by-layer model
(Lawrence-Livermore National Labs)

21. North American transect

22. Image of subducted Farallon plate (3D)

23. Modelled solutions vary
Berkeley vs. CalTech
Modelled solutions vary
Laske, Masters and Reif, AGU 2001