how we know the earth has a solid inner core

The Mechanism

*Inge Lehmann* (born Østerbro, Copenhagen, 13 May 1888; died Copenhagen, 21 February 1993, aged 104) was a Danish mathematician and seismologist who, in 1925, was hired by the *Royal Danish Geodetic Institute* in Copenhagen to set up and operate the new Danish seismic stations — at *Copenhagen*, *Ivigtut* in Greenland, *Scoresbysund* in East Greenland, and *Tórshavn* in the Faroe Islands. From the records sent in from the four stations she and her small team catalogued every seismic event that registered above the noise floor, indexed each station's tracings by event-time on filing cards kept in a series of old oatmeal-and-laundry-soap cardboard boxes in her Copenhagen office. By 1936 the standard model of the Earth's interior — built up since *Richard Dixon Oldham*'s 1906 identification of a *liquid outer core* (from the observation that primary seismic *P-waves* were sharply attenuated and refracted, and that secondary *S-waves* — which cannot propagate through a liquid — were entirely missing, in a circular *shadow zone* on the opposite side of the Earth from the earthquake's epicentre) and *Beno Gutenberg*'s 1914 refinement of the core-mantle boundary depth (2,900 km) — described the Earth as a *solid mantle* enclosing a *single liquid core* of nickel-iron. The model was geometrically simple and accounted for the missing-S-wave shadow zone. It did not account for what Lehmann began seeing in 1929. On *17 June 1929* a magnitude-7.3 earthquake struck the *Buller (Murchison)* district of New Zealand's South Island. The seismograms from the Danish stations — and from European and Asian stations sharing data through the *International Seismological Summary* — showed clean *P-waves* arriving on the direct path through the mantle and clean attenuated P-waves on the path through the liquid core, just as the Oldham–Gutenberg model predicted. But the records also showed *additional faint P-wave arrivals* at stations *deep inside the shadow zone* — at Sverdlovsk and Irkutsk in Siberia, and at Kew Observatory in London — small clean signals about three minutes after the predicted shadow-zone silence, arriving at angles the standard model declared impossible. The signals had been seen before — *Harold Jeffreys* at Cambridge had noted them in 1926 — and dismissed as either noise or as P-waves diffracted around the edge of the liquid core (a marginal effect that was at most a tenth of the observed amplitude). Lehmann did not dismiss them. Over the following six years she worked through her index-card catalogue of every quake whose seismograms reached the stations she ran, building a ray-trace diagram of P-wave paths through the Earth's interior for a series of hypothetical core structures. In the late summer of 1935 she tested a model in which the *single liquid core* was replaced by a *two-layered core*: a *liquid outer core* extending from the mantle boundary down to a new internal discontinuity at a depth she initially estimated at about *5,000 km* below the surface, and a *solid inner core* below that boundary down to the centre of the Earth at 6,371 km. In her ray-trace, a P-wave entering the liquid outer core at the right angle from a surface earthquake would refract once at the mantle–outer-core boundary, refract again at the new outer-core–inner-core boundary, *speed up* across the solid inner core (because P-wave velocity is higher in a solid than in a liquid of the same composition), and refract a fourth time on the way out — depositing the wave on the surface inside what the single-core model called the shadow zone, at exactly the angles and exactly the relative amplitudes she was seeing in the records. Three minutes late. Faint. Real. She wrote the result up over the autumn of 1935 and the winter of 1935-36 and published in 1936 in *Publications du Bureau Central Séismologique International, Série A, Travaux Scientifiques* (volume 14, pages 87-115) — a journal of the international seismology consortium based in Strasbourg. The paper had a one-character title: *P′* (the standard seismological notation for a P-wave that has traveled through the core; the prime marks the core-traversing branch). It was three pages of text and twelve pages of ray-trace diagrams and arrival-time tables. The conclusion: *the Earth has a solid inner core surrounded by a liquid outer core, and the boundary between them lies at a depth of approximately 5,000 kilometres*. The paper was received quietly. *Beno Gutenberg* and *Harold Jeffreys* both accepted Lehmann's interpretation within a year; *Charles Richter* described it as the most significant seismological inference of the decade. The fully quantitative confirmation came in 1971, when *Adam Dziewonski* at Harvard inverted the global seismic-wave travel-time dataset (assembled across the 1960s by the *World-Wide Standardized Seismograph Network* set up under the U.S. nuclear-test-detection programme) and recovered a sharp inner-core–outer-core boundary at a depth of *5,150 km* — within 3% of Lehmann's 1936 estimate. The boundary is now called the *Lehmann discontinuity*. Lehmann was elected to the Royal Society of London as a Foreign Member in 1969, awarded the Bowie Medal of the American Geophysical Union in 1971, and the William Bowie Medal of the AGU in 1975. She continued to publish into her ninety-third year. As of 2026, the standard textbook model of the Earth's interior — a solid silicate mantle, a liquid iron–nickel outer core, and a *solid iron–nickel inner core* about the size of the Moon at the centre — rests on the inference Inge Lehmann drew alone, in a Copenhagen office heated by a coal stove, from a catalogue of seismogram filing cards kept in old oatmeal boxes, in the winter of 1935-36.