Plate tectonics and mathematics

SUMMARY: Tectonic plate movement is measured and analyzed using mathematics. 

The ideas of plate tectonics and continental drift have been theorized by many scientists for decades. For example, in the early twentieth century, Alfred Wegener publicly presented theories regarding the existence of a supercontinent called “Pangea” that eventually formed all the known continents. He supported centrifugal force as an explanation for drift. A few years later, Arthur Holmes supported thermal convection as an explanation. At the time, there was insufficient mathematical and scientific evidence to support these theories and they were largely dismissed. This was, in part, because seeing into the depths of the oceans and into the Earth itself was often a more difficult venture than seeing galaxies at the far reaches of the universe. By the latter half of the twentieth century, discoveries such as mid-Atlantic underwater volcanic chains and the mapping and mathematical analysis of seismic activity suggested the existence of large, mobile plates in the Earth’s crust. 

In the twenty-first century, scientists and mathematicians developed new and innovative ways to collect data, model, visualize, and simulate the Earth’s inner structure. For example, geophysicist Robert van der Hilst and mathematician Maarten Van de Hoop used a mathematical technique known as “micro-local analysis,” as well as statistical methods, such as confidence intervals, to explore the geometry of the layers near the boundary of the Earth’s core and mantle. This technique extended existing methods for analyzing noisy seismic data. It produced not only an image, but also an estimate of the probability that a true layer has been discovered. Ongoing collaboration between mathematicians and geophysical scientists was crucial to address the massively scaled problems that arise in geoscience, such as continental drift. This was true not only for data collection in the field, but also for computer simulation, which was increasingly an avenue of exploration and cross-validation for theories and data. These simulations often required combining many scales of data, both macro and micro, as well as observations collected over different periods of time. Further, much of the data was noisy, incomplete, or difficult to directly measure. Mathematics was also involved in the increasingly sophisticated tools that allowed scientists to visit the depths of the oceans and begin to look at some previously impenetrable layers of the Earth. 

The Spreading Sea Floor

As an officer in the U.S. Navy, Harry Hess’s curiosity led him to measure the ocean floor using sounding gear and magnetometers during World War II. Once the war ended, Hess developed the theory of sea floor spreading to explain his data. He proposed that magma oozed up between the plates along the ridges in the ocean floor, pushing them apart and causing the plates to move. 

Strips of rock parallel to the ridges provided evidence for sea floor spreading. Strips closest to the ridge had the same polarity as the Earthmagnetic north pointing to the north pole. However, the strips moving out away from the ridge on opposite sides mirrored each other and alternated between current polarity and reversed polarity as the Earth’s magnetic field reversed over time. These alternating strips suggested that new rock was created along the ridges over geologic time. 

Continents Adrift

Until 1912, scientists assumed that the continents were fixed in place. In that year, Alfred Wenger suggested that the continents were adrift, originally part of one large landmass. Wegner cited evidence such as matching geological formations and fossils from South America and Africa. It was not until the late 1960s that discoveries were made and measuring techniques improved to the extent that the theory of plate tectonics emerged and became widely accepted. Scientists now recognized that the continents were attached to plates and moved with them rather than moving independently. Scientists also now know that the plates that made up Earth’s crust and the continents attached to them moved several centimeters per year on average as they collided, moved apart, and brushed up against each other. 

Plate Movement

Muawia Barazangi and James Dorman (1969) charted the locations of all earthquakes occurring from 1961 to 1967 and found that most occurred in a narrow band of seismic activity. This band of high earthquake and volcanic activity, commonly called the “Pacific Ring of Fire,” defines many plate boundaries around the Pacific Ocean. 

Most plate movement occurred along the edges of the plates. Scientists could measure the velocityspeed and directionof plate movement and determine how that relates to earthquake and volcanic activity. For historical information, scientists turn to ocean floor magnetic striping data and geological dating of rock formations. 

Measurement techniques have improved since Hess’s measurements. The most common technique for measuring plate movement in the early twenty-first century was the Global Positioning System (GPS). As satellites continuously transmitted radio signals to Earth, each GPS ground site simultaneously received signals from at least four satellites. By recording the exact time and location of each satellite when its signal was received, it was possible to determine the precise position of the GPS ground site on Earth, measuring exact longitude, latitude, and elevation. Regularly measuring distances between specific points allowed scientists to determine if there had been active movement between plates on a scale of millimeters. Using time-series graphs and plotting vectors, it was possible to learn how the plates move. 

While scientists knew that most earthquakes and volcanoes occurred along plate boundaries, they still could not predict exactly when and where they would occur. By monitoring plate movement, scientists hoped to learn more about the events building up to earthquakes and volcanic eruptions. 

In 2024, a consensus formed among many researchers that the Earth had shown similar patterns of plate tectonics throught its entire history. This thought was informed from the study of the mineral zircon. Zircon is an important substance found in the Earth's crust. Zircons are resistant from chemical alterations, even after billions of years. In studying zircons of different eras, the studies showed consistencies and not progressions in the development of the earth's crust.

Scientists, such as a team lead by the University of Wisconsin-Madison, suggested the same styles of zircons that exist in contemporary times similarly could be found much earlier in the earth's history. This suggested that the earth's plates had been in constant movement for most of its existence. Scientists also suggested that evidence of similar patterns of plate tectonics on other planets could be an indicator that other planets may be hospitable to life.

Bibliography

Barazangi, Muawia, and James Dorman. “World Seismicity Maps Compiled from ESSA, Coast and Geodetic Survey, Epicenter Data, 1961–1967.” Bulletin of the Seismological Society of America, vol. 59, 1969.

"Four Billion Years Ago, but Not So Different: Plate Tectonics Likely Looked Closer to What We Experience Today." National Science Foundation, 26 Sept. 2024, phys.org/news/2024-09-billion-years-plate-tectonics-closer.html. Accessed 7 Oct. 2024.

Marshall, Michael. "Geology’s Biggest Mystery: When Did Plate Tectonics Start to Reshape Earth?" Nature, 14 Aug. 2024, www.nature.com/articles/d41586-024-02602-3. Accessed 7 Oct. 2024.

Mixon, Emily E., et al. "Zircon Geochemistry from Early Evolved Terranes Records Coeval Stagnant- and Mobile-Lid Tectonic Regimes." Proceedings from the National Academy of Sciences, 16 Sept. 2024, Accessed 7 Oct. 2024.

Preskes, Naomi. Plate Tectonics: An Insider’s History of the Modern Theory of the Earth. Westview Press, 2003.