GG 652 Homework 6: Gravity Anomalies Read Blakely Ch 7, Due Fri. 2/22

1) Use Matlab to plot the total gravity described by Eq. 7.5 that would be measured along a transect going from the equator ( = 0) to the north pole ( = 90º) by a high-altitude balloon that maintains a constant radial distance of r = a from the Earth’s center (a is the equatorial radius of Earth). Show your answer in mGal. Explain why g varies as it does.

2) Plot the total gravity that would be measured along a transect going from equator ( = 0) to the north pole ( = 90º) on the surface of Earth’s reference ellipsoid. Show your answer in mGal. What is the difference in weight of a 50 kg person between London (53°N) and Hawaii (21.25°N)?

3) Four main factors influence the strength of Earth’s “normal” gravity (plotted in (2) above) and its latitudinal variation. What are they and how does each affect the variation from the equator to the poles?

Imagine you have done a gravity survey perpendicular to a very long (hence 2D) topographic ridge. To keep things simple, this ridge is more like a long plateau with steep sides as illustrated below. Your measurement points are shown as asterisks (diagram not to scale). The file "data.hw6” contains the data collected in 3 columns: (i) horizontal position from the center of the ridge (x, in m), (ii) altitude (in m) above sea level of your measurements, and (iii) observed gravity (in mGal). Type “load data.hw6”, then “x=data(:,1)”, then “h=data(:,2)”, then “gobs =data(:,3);” and you will have 3 vectors ready to plot and manipulate.

4) First plot the observed gravity versus distance (using “subplot(411)”) and then plot elevation (h) versus distance on the same figure (using “subplot(414)”). Why is the observed gravity high where topography is low and why is the gravity low were topography is high?

5) A free-air gravity anomaly gfa is the observed gravity minus the attraction of the Earth as a spheroid (i.e. gn), and corrected for the effects of elevation above sea level (see Eq. 7.14). Compute free-air gravity anomaly for each of your measurement points using the IGF 1984 model (p. 136)—the latitude of your survey is 21.5N. Then in “subplot(412)”, plot your results as a function of distance x. Why is

gfa high over the topographic high and low over the topographic low?

6) Next let’s produce a simple Bouguer gravity anomaly. From the free-air gravity anomaly, remove the effects of the crust between the observation point and sea level by apply the “Bouguer plate correction”

(Eq. 7.16). Plot the resulting simple Bouguer gravity anomaly gsb below your plot of free-air anomaly (“subplot(413)”). Interpret what you see in terms of the density structure of the Earth beneath your survey profile.