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Seismology 1936

P′

Inge Lehmann

Read the shadow earthquakes cast, and find a core inside the core.

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In depth · the introduction

Earthquakes ring the whole planet like a struck bell — and by timing the echoes, one woman found a hidden core inside Earth's core.

A core within the core

When an earthquake strikes, it sends waves racing through the whole Earth. P waves — the fast, push-pull kind — travel all the way through, and they bend as the rock they pass through changes. By the 1920s seismologists knew Earth had a dense core about halfway to the centre, and that its outer part was liquid: it refused to pass the side-to-side S waves.

But there was a puzzle. A liquid core bends P waves so sharply that it leaves a "shadow" — a band of the globe, roughly a third to two-fifths of the way around from any quake, where no direct P should arrive. Yet faint P waves kept turning up in the shadow. In 1936 Inge Lehmann explained them: there must be a second, inner core, where the waves speed up again and get bent back out into the shadow. Earth's core was two nested balls, not one.

Reading Greenland's seismographs

Lehmann was a Danish seismologist who ran the seismograph stations of the Royal Danish Geodetic Institute, two of them in Greenland. Her work was the patient craft of reading squiggles on smoked paper and timing each wave's arrival to the second. Poring over records of large, well-recorded earthquakes — among them a big 1929 quake near Murchison, New Zealand — she kept finding P arrivals where the textbooks said there should be silence.

Rather than dismiss them, she built the simplest model that could produce them: she imagined a small core at the very centre, with waves moving faster inside it, and worked out by hand where its refracted rays would surface. They landed exactly in the shadow. She published the idea in a paper with the shortest title in the history of science — a single character, "P′" — and within a few years the inner core was part of every model of the Earth.

Why it mattered

Lehmann found the last great layer of the planet's gross structure — and showed off a method. You cannot dig to the centre of the Earth; the deepest borehole barely scratches the crust. But earthquake waves go everywhere and report back in their timing. Her inner core proved how much of the unreachable interior can be reconstructed from those reports — and the inner core turned out to be central to a deeper story, since its slow freezing helps drive the churning outer core that generates Earth's protective magnetic field.

Like ringing a glass to feel for a flaw

Tap a wine glass and listen: the ring tells you about the glass without your ever seeing inside it. Now imagine a marble were frozen at its centre — the timing of the ring would change, and a careful listener could deduce the marble is there. Lehmann was that listener for the whole Earth. She "heard" an inner core in the timing of waves that arrived where silence was expected, and reasoned her way back to the hidden ball that had sent them.

A cross-section of the Earth with mantle, liquid outer core and a small inner core, and an earthquake at the top. A slider moves a station around the globe; a checkbox turns the inner core on or off. A ray is drawn to the station and the readout says what arrives: direct P near the quake, nothing in the 103°–143° shadow band, PKP far around the globe, and — with the inner core on — a faint PKIKP refracted into the shadow.

Where it sits

Lehmann's inner core completed a relay of discovery that read the deep Earth from its tremors: Richard Oldham first found the core in 1906, Beno Gutenberg measured how deep it lay, Harold Jeffreys showed its outer part was liquid — and Lehmann found the solid heart within. It sits beside the other ways this Library's scientists learned to read the planet, from Hutton and Lyell in the rocks to Wegener and Hess in the moving sea floor. The inner core she found is now known to spin a little out of step with the rest of the world — a hidden clock at the centre of the Earth.

The original document
Original source text
Inge Lehmann · “P′” · Publications du Bureau Central Séismologique International, Série A, Travaux Scientifiques, 14: 87–115 · 1936
A title of one character
Lehmann's paper carries the shortest title in the literature of science: P′ ("P-prime"), the seismologist's name for P waves that have travelled through the Earth's core. The paper asks what those waves reveal about the core's interior.
The puzzle: P waves in the shadow
A liquid core bends P waves so sharply that direct P fades out near 103° from an earthquake and does not reappear until about 143°; the band between is the core's shadow zone. Yet seismograms — including those of the large 1929 Buller (Murchison) earthquake in New Zealand — recorded faint but real P arrivals inside that shadow.
The model: a core within the core
We take it that, as before, the earth consists of a core and a mantle, but that inside the core there is an inner core in which the velocity is larger than the outer one.
Adopting a deliberately simple Earth — constant velocities, so that rays are straight lines and travel times follow from elementary trigonometry — Lehmann showed that such an inner core refracts a branch of P outward into the shadow zone, matching the anomalous arrivals. She estimated the inner core's radius at roughly 1400 km; the modern value is about 1221 km.
[ … ]
Lehmann claimed a discontinuity in velocity, not a change of state; the inner core's solidity was established only later. The full paper, with its travel-time curves and station data, is at the source below.
Geodetical Institute · Copenhagen · 1936