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 whose slides have
been used liberally in this presentation.

2. 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.
Note that the model is “layered” and laterally averaged over the whole Earth within layers and so no lateral variations in structure are modelled.

3. P-wave velocity

4. S-wave velocity

5. Preliminary Reference Earth Model

6. IASPEI91
Kennett et al. (1991) obtained another 1-D Earth model that is often used in reference.

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
Seismic waves integrate the seismic velocities experienced point-by-point along their paths:
T() = 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. Example results
Van der Hilst, et al., 1998

19. 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

20. Berkeley vs. CalTech
Laske, Masters and Reif, AGU 2001

21. 3D DNA09
Regional tomographic model of structure beneath the Western US.
Note the P-wave and S-wave velocity anomalies, especially below Yellowstone. Is the Yellowstone “plume” so restricted to the upper mantle.

22. PNW10-S Cascadia subduction zone
Figure 1. Transect S-N along the subduction interface.
Figure 2. Transect following the spine of the Cascades mountains chain and heat flow profile.

23. So, what do we really know?
Layered Structure
Seismology finds global radial variations in physical properties α and β at many nearly fixed depths within the Earth.
~5-70 km
410 km
660 km
~2700 km ±
2890 km
5150 km 23 23 23 23

24. Rheological hack: eshear = (t/2η + 1/2μ)σshear
Rheology from Tectonics
Isostatic recovery from glacial loading and lateral tectonic plate motions suggest a different layering, especially of the outer regions.
0 – 200 km (~elastic)
to ~400 km (~low viscosity fluid)
to ~2900 km (~higher viscosity)
to ~5100 km (very low viscosity)
to 6375 km (~soft elastic)
Rheological hack: eshear = (t/2η + 1/2μ)σshear 24 24 24 24

25. Seismic provisos
Seismic technologies are not as powerful as we might like you to believe... geologists and mantle petrologists want to believe in seismic tomography
What Lies Deep in the Mantle Below?
“Teleseismic tomography, although sensitive to horizontal variations in seismic wave speed, has virtually no ability to determine depth variations.”
...but still
“Were it not for seismology, we would be almost totally ignorant of the structure of the deep interior of Earth.” 25 25 25 25