Welcome to Let’s Talk Outcrop, a weekly newsletter delivered every Tuesday where I explain Earth Science topics such as interesting geologic formations, Earth’s structure, physical Earth processes, or natural disasters (earthquakes or volcanoes). Other topics include famous geologic maps, minerals, or interplanetary science.
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Earth’s Shape
Earth is broadly defined as a sphere, a 3-D ball floating through the vast space circling our Sun. Generally, this is a pretty good assumption and the Earth is basically a ball.
A ball makes for the most representative shape for our planet, and any variations from a sphere aren’t going to make much of a difference in day-to-day life for most people.
However, we know that Earth isn’t a perfect sphere. Long-term effects of the rapid spinning of our planet have led to a larger diameter at the equator than at the poles due to the inertial motion of the planet. Technically, Earth has a bulge at the equator about 27 miles (43 kilometers) greater in diameter than at the poles. The shape of a sphere that has been stretched at the equator is called an ‘oblate spheroid’.
Perhaps classifying the Earth as an oblate spheroid satisfies our want to adequately describe our planet’s shape. This explanation seems to more than suffice for pretty much everyone. But if we look closer at small-scale features, our planet is covered with incredible mountain peaks, deep canyons, and valleys, creating a rough undulating surface. These topographic features have varying effects on the actual surface level of the Earth’s crust, but also the gravitational effects on the surface of the planet.
If we include all the topographic features on Earth, we would quickly realize that a smooth sphere, ellipse, or oblate spheroid doesn’t accurately represent Earth’s surface.
Attempting to include the undulating topography on Earth’s surface is where the discussion of a new shape began.
Why We Need A Better Model
For geographers, navigators, and astronomers, the description of Earth as a sphere or ellipse usually does a good job for their purposes. Other scientists who study Earth’s surface or subsurface and create highly accurate topographic maps and geophysical surfaces, understanding Earth’s interior and gravitational field care deeply about the small variations in surface topography. A description of the shape as a smooth ellipsoid or oblate spheroid just doesn’t cut it.
In that case, mathematicians, geophysicists, cartographers, and hydrographers have gone to great lengths to create the most accurate representation of Earth’s crust surface. A highly representative model is necessary for length and elevation measurements, and internal studies of the Earth.
Also perhaps unsurprisingly, true approximations of Earth’s surface are necessary for military purposes. Describing Earth’s topography and gravitational strength is necessary for ballistic missile trajectory designs. The inertial guidance systems in missiles rely on knowing the force of gravity and topography for precise target locations.
Advances in GPS and satellite technologies also rely on accurate surface measurements.
The Geoid
The reasons above state the rationale for a better approximation than a smooth shape.
Enter Johann Carl Friedrich Gauss.
Gauss was a mathematician, geodesist, physicist, and astronomer who contributed extensively to many fields with mathematical and physical equations and models.
Gauss first described the surface of the Earth with a mathematical model that was a smooth but irregular surface that arose from the irregular distribution of mass within the Earth. The surface that Gauss created began to define the ‘Geoid’, which has been continually updated over time and is the shape now used to describe Earth.
The geoid is defined as the geopotential surface on Earth which coincides with global mean sea levels. This means that if the Earth was covered with water, the geoid would be the surface that would track sea levels. Sea level is the reference because liquids precisely follow topography and are "flat" along lines of equal gravity. (Flat is a broad term as the surface levels are curved around our ellipsoidal Earth') The geoid also includes the bulge at Earth’s equator due to its rotation, called the ‘equatorial bulge'.
In other words, the geoid surface is the approximated topographic surface of the Earth that is directly perpendicular to the downward force of gravity. The geoid is a combination of a reference ellipsoid that smoothly defines Earth and includes deviations caused by distributions of mass on or below Earth’s surface. Geoid deviations from the reference ellipsoid are on the order of +/- 330 feet (100 meters) or less.
In the above photo, you can see the model of the geoid as it is defined today. regions above the theoretical model are colored red, and regions below the model are colored blue. Topographic differences are heavily vertically exaggerated to highlight the geoid structure.
These differences in the geoid of 10's of feet are dwarfed by the diameter of the Earth, which is approximately 7,900 miles (12,700 kilometers). The small differences are why, in general, the description of Earth as an oblate spheroid, ellipsoid, or even sphere usually suffice. However, the minuscule differences in the geoid height are then small, but very important to geophysicists interested in precisely understanding Earth's interior structure. Small-scale topographic changes also matter to volcanologists who can use surface elevation changes of less than one inch (millimeters or centimeters) to monitor and study volcanic deformation.
The geoid level is influenced by the existence or absence of dense bodies of mass beneath the Earth’s surface or large mountain ranges. Large and dense bodies of mass have higher gravity than smaller bodies of mass.
Large bodies of mass next to a point of measurement can influence the downward force of gravity and pull the normally downward force left or right. The presence or absence of extra mass bodies is what creates the wavy geoid surface used as Earth’s estimated topographic surface.
To better picture what the geoid surface is, remember that the geoid surface is a surface where gravity is the same, so any object placed on this surface should not move, and the force of gravity is directly perpendicular to this surface and not necessarily straight down toward Earth's center.
(For more information, read about Pratt and Airy isostatic compensation models to try and understand more about the role of densities with topographic heights. Or, check out my past article on Glacial Rebound where I discuss isostasy and crust flexure in more detail!)
A mountain range for example on land is an example of extra mass on the Earth’s surface, creating a stronger pull of gravity in this particular region. To counteract this extra gravity, to create a surface of equal gravity across the mountain range, the geoid height would actually go down, to maintain a level of equal gravity through the mountain range. A region of mass absence, such as a large cave or upwelling molten rock (which is less dense than surrounding solid rocks) would create a gravitational deficit and the resulting geoid height over this mass deficit would be higher than the surrounding regions.
The geoid then is a theoretical model of Earth's topography that would show sea levels if Earth was covered in water, and is lowered where gravity is low, and rises where gravity is high.
Geoid Anomalies
The geoid follows beneath continents and tracks sea level heights across the globe, and estimates where sea levels would be across continents incorporating their densities and masses. These measurements are made by complex mathematical calculations, surveys from land crews, airborne readings, and satellite measurements.
Geoid anomalies are any deviations from this theoretical sea-level model over the globe. These anomalies have given researchers insight into mantle structure and mantle properties. The geoid is directly related to the gravitational strength of the Earth beneath the crust, which depends on the densities and accumulation of mass below.
The largest variation from the geoid surface is in the Indian Ocean. Deviations above or below the geoid are known as ‘geoid anomalies’. The large negative anomaly in the Indian Ocean is referred to as the Indian Ocean Geoid Low (IOGL). This anomaly spans over ~1250 miles (2000 kilometers) and is ~350 feet (106 meters) below the geoid surface.
Several hypotheses for the cause of the IOGL have been proposed for the cause of the massive negative anomaly, including a depression at the Core-Mantle Boundary at the base of the mantle, a graveyard of dense slabs at the base of the mantle that are still solid, or a large body of low-velocity materials (and lower densities) in the mantle.
Other anomalies ranging from 20-70 feet (5-20 meters) from the geoid surface are proposed to be due to small-scale convection currents circulating partial melt and upper-mantle material of different temperatures. These small-scale convection currents also influence tectonic plate motions, magma upwelling, volcanism, and oceanic crust structure.
Understanding the true shape of the Earth has seemingly little effect on many day-to-day activities, but has a high impact on the effectiveness of GPS systems, surveying precise distances on Earth, and use for global navigation and ballistics tracking systems.
The use of the geoid also has very high impacts on map making and truly understanding the subsurface dynamics and structure of our planet.
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References
Jet Propulsion Laboratory. (2007, December 11). Global gravity: Africa and Europe. NASA. https://www.jpl.nasa.gov/images/pia12104-global-gravity-africa-and-europeNational Oceanic and Atmospheric Administration. (n.d.). What is the geoid? NOAA. https://oceanservice.noaa.gov/facts/geoid.html
Pandey, D., Tiwari, V. M., Steinberger, B. (2023). Understanding the geodynamics of the largest geoid low in the Indian Ocean. Tectonophysics, 847(20), 229692. https://www.sciencedirect.com/science/article/abs/pii/S0040195122004863
Ramillien, G., Frappart, F., Seoane, L. (2016). Space Gravimetry Using GRACE Satellite Mission: Basic Concepts. In Microwave Remote Sensing of Land Surface (pp. 285-302). Elsevier. https://www.sciencedirect.com/science/article/abs/pii/B9781785481598500062
Xiong Li and Hans‐Jürgen Götze, (2001), "Ellipsoid, geoid, gravity, geodesy, and geophysics," GEOPHYSICS 66: 1660-1668. https://doi.org/10.1190/1.1487109
U.S. Geological Survey. (n.d.). What is a geoid? Why do we use it and where does its shape come from? U.S. Geological Survey. https://www.usgs.gov/faqs/what-a-geoid-why-do-we-use-it-and-where-does-its-shape-come
Thanks! That hit the (hot) spot of my curiosity.