Tiny vibrations hours after large earthquakes reveal a solid, low-rigidity inner core

Tiny vibrations hours after large earthquakes reveal a solid, low-rigidity inner core

To understand the solid state of the Earth’s inner core, seismologists seek observational evidence for shear (J) waves traversing it. Shear waves are seismic waves released by earthquakes that travel exclusively through solid material. By observing inner core shear waves, we can confirm not only the inner core's solidity but also gain insights into its composition and evolution.

However, the search for J waves has been a longstanding challenge in the realm of global seismology. Direct observation of these waves is elusive because of their small amplitudes, often overwhelmed by noise and considered below the observational threshold (e.g., Shearer et al., 2011).

In a recent study in Nature Communications, our team at The Australian National University (ANU) reports unambiguous observations of J waves and measures their speed lower by 3.4% from the widely used Earth’s velocity model (PREM; Dziewoński and Anderson, 1981). Our findings enhance the understanding of the solid identity of the inner core, hitherto the least well-understood part of the Earth’s interior.

Challenging search for J waves

After the inner core was discovered (Lehmann, 1936) and its solidity hypothesized (Birch, 1940), the search for wiggles in digital seismograms corresponding to shear waves travelling through the inner core took place in seismological laboratories around the world.

In the early days, seismologists used Earth’s free oscillations or “normal modes”, the standing waves resonating the entire Earth as a musical instrument, days after large earthquakes occurred, to study the inner core’s shear properties and confirm its solidity (Dziewoński and Gilbert, 1971). The method relied on very long-period observations, weakly sensitive to the inner core’s fine structure, especially near its centre. Therefore, the detection of J waves in the direct seismic wavefield remained to be seen as the seismological proof of inner core solidity.

However, the task of finding J waves is challenging because the inner core accounts for less than 1% of the Earth’s volume, and it is surrounded by the liquid magma ocean of the outer core, which does not permit the propagation of shear waves. Thus, for J waves to exist, energy conversion at the inner core boundary from compressional waves that entered the liquid outer core to shear waves must occur.

That conversion is, nonetheless, very inefficient, which makes J waves feeble and their detection nearly impossible.

Compilation of J-wave speed estimates from seismological observations and recent mineral physics simulations. Different value of J-wave speeds obtained from multiple IC-solidity studies. Colours represent different methodologies (blue: normal modes, red: shear body waves, purple: coda-correlation wavefield, and grey: mineral physics estimates). Squares denote the averaged J-wave speeds, and the bars represent the range of J-wave speeds from the inner-core boundary (ICB) to the Earth’s centre, available in some studies. b Summary of recent mineral physics hypotheses providing possible explanations for seismologically observed low J-wave speeds. Coloured lines show different J-wave speeds as functions of temperatures at 360 GPa, the pressure at the Earth’s centre. The shaded area corresponds to the range of J-wave speeds shown in panel (a).

Observational boost

Our research group has found an innovative way to boost the weak signals carrying the footprint of the J waves (Tkalčić and Phạm, 2018). The method utilises the understanding of how the earthquake coda-correlation wavefield is formed (Phạm et al., 2018) and relies on the similarity between digital ground motion’s time series, known as seismograms. The similarity is expressed by a mathematical term known as the cross-correlation function, often used to recognise similar patterns in other fields of science and technology.

By embracing (instead of discarding) seemingly noisy portions of large earthquake seismograms from 3 to 10 hours after the event origin time, we harvest precious information from the waves reverberating like echoes from the Earth’s internal boundaries.

We achieved unprecedented clarity of the coda-correlation wavefield features sensitive to the inner core shear properties by carefully selecting earthquakes with favourably radiated energy and optimal locations of seismic stations deployed around the globe. Earthquakes of normal and thrust faulting mechanisms release seismic waves that are efficient in sampling the Earth’s interior steeply through its centre. Then, we processed thousands of seismograms and performed extensive numerical simulations on the southern hemisphere’s largest supercomputer hosted by Australia’s National Computational Infrastructure to confirm the observation of J waves and measure their absolute speed in the inner core.

Our new estimate of shear wave speed in the inner core (Costa de Lima et al., 2023) distinguishes itself from the previous estimate (Tkalčić and Phạm, 2018) because it is nearly independent of uncertainties in the velocity model of major layers of the Earth, such as the mantle, the outer core, and the inner core.

A solid but “squishy” inner core

Our team’s detection of J waves reinforces the inner core is solid. However, the shear wave speed determined from our measurements suggests these waves are slower in the inner core than the PREM model suggests. To put things into perspective, J waves traversing the inner core along the Earth’s diameter take about 699 seconds instead of PREM’s  ~ 676 seconds.

These findings indicate that the inner core is less rigid than modelled in the past. This new observation suggests that iron alloys – the inner core's main mineralogical constituent – become noticeably softer than at ambient conditions, perhaps due to their complex behaviour at high temperatures or the presence of light chemical elements.

Indeed, what happens at high pressure and temperature conditions might be a game changer in understanding the inner core’s structure and evolution.  The fact that the inner core is solid but has a low rigidity could be linked to a more complex solidification history than we think.

We believe the research community now has reliable seismological constraints on the inner core shear properties to benchmark the laboratory experiments, which could speed us up on the journey to understand better the deepest portion of our home planet.

Paving the way forward

Lying more than 5000 km beneath the surface, the inner core is inaccessible for direct sampling. Thus, most we know about it comes from studying seismic waves, conducting laboratory experiments, and computer simulations.

Here, we present an estimate of shear wave speed travelling in the inner core using tools from the coda-correlation wavefield. Our findings provide critical information for high-pressure mineral physicists, geodynamicists, and paleomagneticists, to understand the inner core composition and its influence on the Earth’s system.

Despite the recent exceptional progress in mapping the shallow Earth structures, we are making small steps toward better understanding the Earth’s deep interior, including the inner core. Our method opens new avenues for studies of the deep structure of the Earth and other planets. With our new results, we are a step closer to unearthing the remaining puzzles of our planet’s metallic core.

All details and references are reported in the paper:

Costa de Lima, T., Phạm, T.-S., Ma, X., and Tkalčić H. An estimate of absolute shear-wave speed in the Earth’s inner core.  Nat Commun 14, 4577 (2023). https://doi.org/10.1038/s41467-023-40307-9

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