Back to the GEOL 301 Homepage
IsostasyHandouts and Reading MaterialsIsostasyDemo of measuring gravitational acceleration.Plumb-bob DeflectionGravity with and without a mountain "root"Archimede's PrincipleThe equations of isostatic calculationsExample: Adding ice to a land surfaceExample: Filling in a lake with sedimentLinks to historical papersMeasuring Gravity (and Corrections)Topographic corrections to gravity readingsFree-air correctionBouguer correctionTerrain CorrectionThe Bouguer AnomalyThe pointThe Isostatic AnomalyOther ExamplesGlobal Gravity
Sometimes the materials linked to below will also be handed out in class in hard copy. But, for anything you need to read it will be linked to here for each "topic" we cover.
Gravity from the book Looking Into The Earth (CH 8)
Isostasy from the book Looking Into The Earth (CH 9)
Data collected in class - will be linked to here.
During historical geodetic surveys, the deflection was less than predicted (historical papers about this are linked to towards the bottom of this page):
If mountains were situated as shown below, we would expect find a gravity increase (larger with a bigger mountain) compared to the situation without a mountain:
Now think of a mountain with a low-density "root". Low-density compared to the crust surrounding it:
An actual measurement of gravity would show a much smaller increase than you would expect. This could be explained via a low-density mountain root.
This leads us to think about the crust and lithosphere as "floating" on a higher density feature (the asthenosphere) that at some depth compensates for all the weight. This is where Archimede's Principle comes into play when making a model for this phenomena. Note how the weight of the object when in equilibrium is supported by the water (or, in the earth's case, asthenosphere):
Reminder of the terms crust, lithosphere, asthenosphere:
If compensated, gravity should be approximately constant:
When "columns" (e.g. idealized mountain ranges, sedimentary basins) are in isostatic equilibrium then the pressure they exert at their compensation depth is the same (the handout I gave you refers to this aw equal weight):
Similarly you can equate heights of the columns:
Compare these equations in the context of the figure below:
Warning: Be careful with the subscripts - sometimes the subscript "a" is used for "air", sometimes it is used for "asthenosphere, or asth". So be careful you you what
After adding 2 km of ice to a continent (which wasn't all that long ago!!), what is the height of the top of the ice compared to the original surface?
Papers that discuss the history of the surveys finding the gravity anomalies near mountains, as well as the development of Airy and Pratt isostasy models.
We have seen that gravity anomalies exist (i.e. gravity varies from place to place). How large are these variations relative to the "typical" value of
Imagine a buried "density" anomaly as shown below:
At location C a measured gravity value should be larger than at location P because the density anomaly (increase in this case) is closer to the C whereas at P the the anomaly is further away.
An anomaly has the following effect on a gravity reading:
so to determine the gravity anomaly take as many closely spaced readings as you can (imagine the anomaly is a large ore body you are interested in prospecting - see Table 8.1 for how much denser ore bodies are than the surrounding shallow crust!):
See the nature of the gravity anomaly due to shallower vs deeper half sheets:
Half-sheets generated due to faulting.
We don't measure on flat surfaces!!!
Free air is ADDED.
Bouguer is SUBTRACTED.
Free-air and Bouguer can be combined:
H creates a lateral and upward pull, reducing g. V removes a downward pull, so also reduces g. Therefore these are added to the measurement of g.
Bouguer Anomaly = measured/observed value of g + free-air correction - Bouguer correction + Terrain correction - latitude correction + Eotovos correction.
Gravity survey values need modifications to isolate the subsurface anomaly from the other anomalies at the surface. This allows one to properly interpret the subsurface anomaly for geologic questions and/or resource exploration.
How can we tell if a region is in isostatic equilibrium?
Going out and testing some topographic features:
Source: Mzansi Geoscience Platform on Twitter: "Gravity model was created with data from NASA's GRACE satellite & shows variations in Earth’s gravity field. Gravity is determined by mass. Earth’s mass is not distributed equally, and it also changes over time. The colors in this image represent the gravity anomalies