Whole Earth Imaging

By the end of this lecture, you will be able to:

• [LO-11.1] Describe how global travel-time observations probe Earth's radial structure.
• [LO-11.2] Read a global travel-time diagram and identify the major body-wave phases (P, S, PP, PcP, PKP, PKIKP, SKS).
• [LO-11.3] Explain the shadow-zone reasoning behind the three canonical discoveries: fluid outer core (Oldham 1906), depth to CMB (Gutenberg 1914), and solid inner core (Lehmann 1936).

Prerequisites: Snell's law (Lec 3), ray-wavefront duality (Lec 4), forward/inverse problem framing (Module 2 intro).

The motivating claim

No one has ever been more than 12.3 km below the surface.

That is roughly 1/500th of the way to the centre.

Yet seismologists report the radius of the core to within a kilometre,
the depth to the CMB to a few kilometres, and the speed of sound in the core
to three significant figures.

How?

Answer: by reading the times at which seismic waves arrive at stations around the globe.

The reasoning arc for today

A seismic wave at has sampled the entire mantle.
A wave at has passed through the core twice and the inner core once.

Each travel time is a line integral of slowness along a path through the planet.

Collect enough — invert — and a 1-D Earth emerges.

Physics: why rays curve

Snell's law at each infinitesimal interface bends the ray toward the slower side.
The shape of encodes the depth dependence of velocity.

Both shadow zones start at 103° — for different reasons

• 103° is geometric — the epicentral distance at which a direct mantle ray just grazes the CMB
• S shadow → antipode: fluid outer core, , shear cannot propagate
• P shadow → 143°: P refracts into core ( km/s → km/s); PKP fills in beyond the caustic

Discovery 1 · Oldham 1906

S-waves do not arrive at stations more than ~103° from the source.

Inference: the Earth has a fluid outer core, a zone where shear waves cannot propagate.

The reasoning required nothing more than absence-of-observation plus the physics of shear in fluids.

Discovery 2 · Gutenberg 1914

A band of missing P arrivals exists between ~103° and ~143°.

Inference: a sharp velocity drop at the CMB refracts P-rays strongly.
Depth estimate: ~2900 km → within a few percent of modern PREM value (2891 km).

The reasoning required Snell's law applied at a single global interface.

Discovery 3 · Lehmann 1936

Weak P-wave energy arrives inside the predicted P shadow, at ~150°–160°.

Inference: there must be a solid inner core with higher than the outer core, reflecting/refracting waves back into the shadow band.

The reasoning required reading anomalies in the P-shadow — a detail-driven result.

Global travel-time curves — the AK135 inversion

Each curve is the forward prediction of a named phase. Every curve is also a teaching tool for phase identification.

Phase nomenclature — the grammar

P/S = mantle K = outer core (P) I/J = inner core (P/S)
c = reflection at CMB i = reflection at ICB

Worked example — CMB depth from

At (AK135):

• min
• min
• s

With average mantle km/s:

→ CMB at ~2900 km. Modern value: 2891 km.

The 1-D answer: PREM

Dziewonski & Anderson 1981.
Still the reference — 45 years on.
Note in the outer core.

Key equation — travel time as integral of slowness

For a spherically symmetric Earth, depends only on ray parameter and the radial profile .

Inversion of many for → PREM.

Cascadia anchor

Every teleseismic first arrival recorded at a PNSN station is compared to AK135.

The residual — positive or negative by a few seconds — is a direct measurement of 3-D mantle structure beneath our feet.

That residual is the data of Lecture 12.

Research horizon

• Inner-core rotation: Vidale et al. 2024 (Nature) — still debated.
• Comparative planetology: Mars (InSight, Stähler et al. 2021), Moon (Apollo, Weber et al. 2011).
• CMB texture: ULVZs, D″ phase transitions mapped with ScS precursors.
• AI-assisted picking: PhaseNet/EQTransformer — 10× catalog completeness in 5 years.

AI Literacy — Epistemics (LO-7)

Try this prompt: "List the seismic phases that pass through Earth's inner core and their typical travel times at ."

What to check

1. Is each named phase valid under P/S/K/I/J/c/i?
2. Has it been observationally confirmed? (PKJKP: contested.)
3. Do the travel times match obspy.taup AK135 predictions?

The rule: never treat AI-generated scientific lists as primary sources. Cross-check.

Concept checks

1. If km/s everywhere, what is at ? Compare to PKIKP (~20 min). Sign of the difference?
2. A seismogram at unknown shows P at 7 min, S at 13 min. Estimate from the curves. What phases come next?
3. Why does the existence of PKIKP inside the P shadow require a solid inner core?

Summary

• Why: Travel times of body waves at global distances probe the deep Earth.
• What: Three discoveries — fluid outer core, CMB depth, solid inner core — from shadow-zone reasoning alone.
• How: Global curves inverted for the radial profile , , → PREM.
• Next: Residuals from PREM become the data for 3-D tomography. Lecture 12.

Further reading

• Kennett et al. 1995, GJI — AK135 model. (Open access.)
• Stein & Wysession 2003, Ch. 3.3–3.5. (UW Libraries.)
• IRIS/EarthScope Global Stacks: https://ds.iris.edu/spud/eventplot
• Lowrie & Fichtner 2020, Ch. 3.5–3.6. (UW Libraries — primary text.)
• obspy.taup — TauPyModel(model="ak135") — reproduce every figure.