Tuesday, October 10, 2017

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.

Women in Science and Engineering Trading cards starter pack
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.

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