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Geology 2112 – Principles and Applications of Geophysical Methods WEEK 5
1
Lecture Notes – Week 5 PART 2
SHAPE OF THE EARTH: GRAVITY
The Geoid
Reading: Fowler Chapter 5.4, 5.6.2
Objectives: Discuss the concept of the ‘Geoid’ and how we use it to describe the shape of the earth.
The Reference Ellipsoid (or Oblate Spheroid):
• So far we’ve seen the evolution of our understanding o f the shape of the earth from flat, to round (spherical) to the ‘oblate spheroid’ or ellipsoid
• A ‘perfect’ ellipsoid can be characterized (relative to a sphere) by a ‘flattening parameter:
Where f is flattening, RE is the equatorial (longest) radius, and RP is the polar (shortest) radius
• Flattening of the earth spheroid is approximately 1/298
[ Note that Fowler introduces latitude corrections here, but we’ve already seen the concept with Richer’s clock, and we’ll return to the actual correction later]
BUT, the earth is not a perfect ellipsoid either – think of mountains, valleys, subduction zones, even small hills – these are all departures from the perfect ellipsoid
And we also still need a ‘reference surface’ or zero elevation to use as a starting point – traditionally we’ve used the mean or average sea‐level, which should be a perfect equipotential surface because it the water surface can flow and adjust to gravity
Equipotential Surfaces:
• We can simplify the shape of the earth down to perfect or reference ellipsoid
• On the surface of that ellipsoid – or any imaginary concentric ellipsoid we choose – the force of gravity should be equal everywhere, and should be directed straight down (perpendicular to the surface) everywhere
• That makes the surface of a perfect ellipsoid an ‘equipotential surface’ because gravity (gravitational potential) is the same everywhere
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Geology 2112 – Principles and Applications of Geophysical Methods WEEK 5
3
Geology 2112 – Principles and Applications of Geophysical Methods WEEK 5
4
Isostasy:
• 1737‐1740 Pierre Bouger noticed that his plumb‐bob vertical wasn’t deflected as much as expected by the mass of some big mountains in the Andes
• 1806‐1843 George Everest compared triangulated distances with those determined astronomically (comparing plumb‐bob vertical with astronomical vertical, as Bouger did) and noticed the same effect as Bouger
• Vertical (local gravity or the geoid surface) was only deflected about 1/3 of what was expected by all the extra mass above the ground
• G.B. Airy in 1855 and J.H. Pratt in 1859 tried to explain the observations
• The basically said that yes, there was a mass excess above the surface (above sea‐level or the reference ellipsoid), but there was also a mass defecit below somewhere
• This led to the idea of deep mountain roots, and requires that the lithosphere is somehow ‘floating’ on a flowing mantle (asthenosphere)
• The floating means that the lithosphere is less dense than the mantle, and that if we add a bunch of mass above the ‘surface’ (by thrusting or glaciations) the whole area must sink to compensate, and so less dense material is pushed into the mantle
• Alternatively, if we remove a bunch of mass from a given location (e.g. melt the glaciers), the less dense material below floats up to a new equilibrium
• Parts of the lithosphere that are out of equilibrium (being forced down or pushed up) will have gravity anomalies that don’t quite match the surface expression, and a positive or negative geoid anomaly results