Ancient seismology and Chinese polymath Zhang Heng

Detail of linocut 'Zhang Heng' by Ele Willoughby, 2023 on 9" x 12" washi paper. 

This is a linocut print about the ancient Chinese Han Dynasty polymath and statesman Zhang Heng (78-139) who invented a device (a seismoscope, like a simplified seismometer which does not make a record of earth motions) to detect distant earthquakes and indicate their direction, 2000 years ago! I have shown him in blue with a reconstruction of his seismoscope, and a schematic of how it might have worked in bronze, as well as horizontal earthquake surface waves, and Rayleigh waves in particular, in pale pink.

A career civil servant in Nanyang, Zhang Heng (sometimes formerly written Chang Heng) was also an astronomer, mathematician, seismologist, hydraulic engineer, inventor, geographer, cartographer, ethnographer, artist, poet, philosopher, politician, and literary scholar. He was a bit of a controversial figure politically, sparing over calendar reform and with rivals amongst the palace eunuchs. But both his poetry and famous inventions are still remembered. He also improved the Chinese approximation for π and made an extensive star catalog. He understood that the Sun and Moon are spherical, and that the Moon merely reflects the light of the Sun. He also explained the nature of solar and lunar eclipses. He invented the world's first water-powered armillary sphere for astronomical observation; improved the inflow water clock by adding another tank; and, as celebrated here, he invented the world's first seismoscope, which recorded distant earthquakes and their origin (in terms of 8 cardinal directions).

China is a seismically active place, and while the cause of earthquakes remained misunderstood, in 132 Zhang Heng was able to design a device to detect seismicity from distant sources. It was named "earthquake weathervane" (hòufēng dìdòngyí 候風地動儀), and it could roughly indicate where the earthquake came from. According to the Book of Later Han (compiled by Fan Ye in the 5th century), his bronze urn-shaped device, with a swinging pendulum inside, was able to detect the direction of an earthquake hundreds of miles/kilometers away. The outside of the device was described as having 8 dragons with balls in their mouths and 8 open-mouthed frogs around the base which could catch fallen balls (and indicate direction to the source). If there was an earthquake the dragon facing its location would drop a ball into the mouth of a frog below. The Book of Later Han claims that the device was triggered by an event, which was too subtle for people to feel but that the west-facing dragon drop its ball. Officials doubted the device worked as intended, but several days later a messenger arrived from the west and reported that an earthquake had occurred in Longxi (modern Gansu Province). So, the court acknowledged it in fact worked.

Unfortunately, no ancient Chinese seismoscopes have survived and details of the mechanism are sparse. The description of the detected earthquake was written much later. So, we cannot be certain about how it worked precisely; some even doubt that it did. Later Chinese inventors were not able to reconstruct the device. However, a series of modern seismologists have put forward a series of reconstructions. There are several ways a pendulum could trigger a ball to fall. Some of the questions include: was it a regular pendulum? Was it an inverted pendulum? How was its motion transferred to the appropriate dragon and not to any other dragons? How it avoid "false positives" due to other sources of shaking? 

As a geophysicist myself, I find the contemporary reconstructions of Feng Rui and others pretty convincing, so that's what I have illustrated. These scientist argue that the device would have detected horizontal motions due to surface waves which would only be due to earthquakes, and would not be set off by vertical motions (which can be caused by earthquakes or nearby shaking, say, due to people). So they built a reconstruction which they argue is consistent with the description, but detects Rayleigh surface waves. They argue by adding a second ball inside the device, it could have avoided having two opposing dragons triggered. In their model, illustrated in my print, when there is an incoming wave, for instance, from the west, the pendulum would move from west to east. They made a hollow inside, so the pendulum would drop a ball, falling on the west side as it moves off-centre. The ball follows one of 8 radiating tracks, then pushes a lever connected to the dragon mouth and the west-side ball - and no others - would fall. This would correctly identify the direction.

They also make arguments explaining that some reconstructions are not the right style of urn or dragon, arguing that Han Dynasty dragons would have been much simpler than the fancy Ming Dynasty ones shown on some reconstructions. So my illustration tries to respect the archeology of ancient Han artifacts, as well as a mechanism which apparently avoids the pitfalls of previous reconstructions. I also included a waveform, which seismologists will recognize as a horizontal Rayleigh wave (detected by a modern seismograph).

Sources

Zhang Heng, wikipedia, accessed January 2023

Feng, Rui and Yu Yan-xiang, Zhang Heng's Seismometer and Long earthquake in AD 134, Acta Seismologica Sinica, 19, 704-719 (2006)

Feng, R., Wu, Y. Research on history of Chinese seismology. Earthq Sci 23, 243-257 (2010). https://doi.org/10.1007/s11589-010-0720-z

Hong-Sen Yan, Kuo-Hung Hsiao, Reconstruction design of the lost seismoscope of ancient China, Mechanism and Machine Theory, Volume 42, Issue 12, 2007, Pages 1601-1617, ISSN 0094-114X, https://doi.org/10.1016/j.mechmachtheory.2007.01.003.

Zhang Heng Seismoscope, Atlas Obscura 

Jamie Rigg, The ancient earthquake detector that puzzled modern historians, engaged, September 28, 2018

Andrew Robinson, The world's first seismometer used a toad to catch an earthquake, New Scientist, 30 November 2016

Seismologist Inge Lehmann for Ada Lovelace Day

Inge Lehmann, linocut on Japanese washi, 8" x 8" by Ele Willoughby

Today is the 9th annual international day of blogging to celebrate the achievements of women in technology, science and math, Ada Lovelace Day 2017 (ALD17). I'm sure you'll all recall, Ada, brilliant proto-software engineer, daughter of absentee father, the mad, bad, and dangerous to know, Lord Byron, she was able to describe and conceptualize software for Charles Babbage's computing engine, before the concepts of software, hardware, or even Babbage's own machine existed! She foresaw that computers would be useful for more than mere number-crunching. For this she is rightly recognized as visionary - at least by those of us who know who she was. She figured out how to compute Bernouilli numbers with a Babbage analytical engine. Tragically, she died at only 36. Today, in Ada's name, people around the world are blogging about women in STEM.

You can find my previous Ada Lovelace Day posts here. 

This year, to celebrate Ada Lovelace Day (ALD17), I'm writing about a great a Danish (or, as she put it the only Danish) seismologist who was at the forefront of the field in the early twentieth century, the one and only Inge Lehmann (1888-1993). She was a pioneer woman in science, a brilliant seismologist and lived to be 104. In 1936 she wrote an earth-shattering paper, with an astonishingly succinct title: P' in which she laid out her arguments supporting her discovery of the inner core of the earth.

We now know, as she first postulated, that the earth has roughly three equal concentric sections: mantle, liquid outer core and solid inner core. The crust, on which we live is merely a thin, um, scum really, on top of this slowly boiling pot. The only way to probe deep into the earth's core is to employ massive earthquakes, the waves they generate and the paths they follow. There are two main types of seismic waves used for studies of the globe, unimaginatively named Primary (or P, which are known as pressure waves or compressional waves) and Secondary (or S, which are shear waves). “P is used to denote longitudinal or ‘pressure’ seismic waves. Those that travel in the Earth’s mantle and crust only are represented by P; P’ represents P-waves that pass through the mantle into the core, and then pass through the mantle again,” she explained. The paths these waves can follow through the Earth depend on their nature, and the materials through which they travel.

Even if you don't regularly think about waves, you will be familiar with a type of compressional wave, namely sound. Read this aloud and the air molecules between your mouth and the ears of any listener (including your own) will compress and rarefy in a wave pattern as the sound is transmitted. Shear waves are different, and as the name implies, they are excited by a shearing motion (like you make with scissors, also known as shears). I can't describe a shear wave in air, or any other fluid, for the same reason you can't cut air with your scissors: fluids do not support shear.

Lehmann's 1936 paper presented this (simplified) three-shell model of the Earth.
She argued that P-waves recorded within the shadow zone are caused by
their interaction with a solid inner core. Today we know that in reality,
seismic waves curve as they travel through the layers of Earth.
Credit: Kathleen Cantner, AGI, based on Lehmann’s original figure, redrawn in 2001.

Imagine a glass of water with a straw; the straw will appear broken at the air-water interface, because light bends as it enters the water. Just like light travelling through different media, these seismic waves can bend, reflect or be transmitted at any boundary. The difference in physical properties between the mantle and outer core causes a P-wave shadow, due to diffractions at the boundary (like in the straw in water analogy). For S-waves, the shadow zone is absolute because liquids, like the outer core, do not support shear. Thus, no shear waves can make it through the outer core, and thus we can be certain the outer core is fluid. The faster moving compressional waves can move through fluids, but they refract at the boundary, which causes the shadow zone for seismic stations beyond 105° from an epicentre. Lehmann found that there were some late-arriving P-waves are much larger angles (142° to 180°) which had been vaguely labelled 'diffractions' (shown in orange on the diagram). These were P' waves which had travelled right through the Earth's core, then out through the mantle again to the other side. Some appeared stronger amplitude than expected (red lines, between the two shadow zones). There were also waves inexplicably arriving within the P-wave shadow, where no one expected compressional waves to arrive. She showed that these could be explained instead by deflections of the waves which travelled through the outer core at her postulated inner core boundary. These weird P' waves could only be explained by if there was another interface within the core, between an outer fluid core and an inner solid core!

Modern depiction of the Lehmann discontinuity where there's a
kink in the speed of mantle P waves for three different settings -
TNA = Tectonic North America, SNA = Shield North America
and ATL = North Atlantic. [*]

She later discovered a discontinuity in the mantle (confusingly also called the Lehmann discontinuity). She did important work well into her 70s and lived to be 105.

When she received the Bowie medal in 1971 (she was the first woman to receive the highest honour of the American Geophysical Union), her citation noted that the "Lehmann discontinuity was discovered through exacting scrutiny of seismic records by a master of a black art for which no amount of computerization is likely to be a complete substitute..." (*).

I think her accomplishments are downright astonishing. To have the exactitude to work with the data and the daring to neglect the irrelevant and offer up a simple, elegant - correct! - explanation is a rare and marvellous thing. To be the top of her field in 1936, when she was a pioneer for women in science and had to "compete in vain with incompetent men" (her words *) is heroic.

You can find my portrait of Inge Lehmann here. Both Lehmann and Ada, Countess Lovelace are among the portaits I contributed to the Phylo Women in STEM trading cards (which can be found at the link). The set can be downloaded and printed for free or you can purchase your own set as illustrated.

There are a grand total of three easily found photographs of Lehmann I was able to find on the internet. I based my portrait one of the earlier ones, to match the date of her phenomenal P' paper. I also show her model of the earth (as she herself presented it in 1936) in red-orange ink, complete with mantle, inner and outer core, and travel paths for rays through the layers, including into the shadow zone. One of the great geophysicists - one of the great scientists of the 20th century, Inge Lehmann should be remembered.

Earthquake seismology great Inge Lehmann

The Mad Scientists of Etsy theme for the month of April is Earthquake Seismology. This was inspired to honour the victims of the Japanese earthquake and tsunami. I decided I did not want to make art about the destructive power of earthquakes. (I'm offering a copy of my moku hanga woodblock print with all proceeds to the Canadian Red Cross for relief of those effected by the disaster. I hope this is more constructive an approach.).

I had been thinking, rather, for some time, of doing a portrait of Inge Lehmann (1888-1993), a Danish (or, as she put it the Danish) seismologist who was at the forefront of the field in the early twentieth century. In 1936, she wrote a paper, entitled simply P', in which she laid out her arguments supporting her discovery of the inner core of the earth.



We now know, as she first postulated, that the earth has roughly three equal concentric sections: mantle, liquid outer core and solid inner core. The crust, on which we live is merely a thin, um, scum really, on top of this slowly boiling pot. The only way to probe deep into the earth's core is to employ massive earthquakes, the waves they generate and the paths they follow. There are two main types of seismic waves used for studies of the globe, unimaginatively named Primary (or P, or compressional) and Secondary (or S, or shear). Imagine a glass of water with a straw; the straw will appear broken at the air-water interface, because light bends as it enters the water. Just like light travelling through different media, these seismic waves can bend, reflect or be transmitted at any boundary. The difference in physical properties between the mantle and outer core causes a P-wave shadow. (For S-waves, the shadow zone is absolute because liquids, like the outer core, do not support shear - imagine trying to cut water with a pair of shears and you can see this for yourself. Thus, no shear waves can make it through the outer core, and thus we can be certain the outer core is fluid). That means, the compressional waves from an earthquake can be recorded at seismic stations out to 105^o from an epicentre and then there is a zone which is in the core's shadow. Lehmann found that there were some late-arriving P-waves are much larger angles (142^o to 180^o) which had been vaguely labelled 'diffractions'. She showed that these could be explained instead by deflections of the waves which travelled through the outer core at her postulated inner core boundary.

She later discovered a discontinuity in the mantle (confusingly also called the Lehmann discontinuity). She did important work well into her 70s and lived to be 105.

When she received the Bowie medal in 1971 (she was the first woman to receive the highest honour of the American Geophysical Union), her citation noted that the "Lehmann discontinuity was discovered through exacting scrutiny of seismic records by a master of a black art for which no amount of computerization is likely to be a complete substitute..." (1, 2).

I think her accomplishment is downright astonishing. To have the exactitude to work with the data and the daring to neglect the irrelevant and offer up a simple, elegant - correct! - explanation is a rare and marvellous thing. To be the top of her field in 1936, when she was a pioneer for women in science and had to compete in vain with incompetent men (her words,1) is heroic.

There are a grand total of two easily found photographs of Lehmann I was able to find on the internet. I based my portrait on the earlier one, to match the date of her phenomenal P' paper. I also show her model of the earth in red-orange ink, complete with mantle, inner and outer core, and travel paths for rays through the layers, including into the shadow zone.