GG413 Geological Data Analysis
Homework #1: Error Analysis and Exploratory Data Analysis
Reading: Swan & Sandilands Handout, and Wessel 1.1-1.3
Due Tue. Sept 2, 2014
For this and your future homework assignments, please explain your thought process for each problem thoroughly
and concisely. A well-described and correct reasoning process but wrong answer is better than the right answer with
inadequate explanation. Please also be sure to label units and give your answers in the appropriate significant figures.
All plots should be easy to understand with the axes labelled, the symbols clearly distinguishable, and the meaning of
each part of the plot clearly labelled (by hand is ok). Include a copy of your Matlab code when requested as it is in
this assignment. The code is supporting information only; it should not be used for explaining and giving your
solutions. Homework can be turned in as a hard copy or electronic file.
Exploratory Data Analysis (EDA)
1) Based on what you have learned so far, perform EDA on 2 out of the 4 data sets provided on the course web page:
“seismicity.txt” has four columns containing longitude, latitude, depth (in km), and magnitude for significant
earthquake hypocenters in the Tonga-Kermadec region.
“hi ages.txt” contains longitude, latitude, radiometric age (in Myr), and distance from Kilauea (in km) for the
Hawaiian seamount chain.
“v3312.txt” contains distance (km) and bathymetry (i.e., seafloor topography in m) along a ship track (Vema 3312)
going from from Japan to Guam.
“lat_lon_depth_temp.txt” contains latitude, longitude, depth (in ft), and fluid temperature (C) from borehole
measurements on the Big Island.
Produce 2 plots for each of the 2 data sets chosen (i.e., 4 plots total) that illuminate the features you are exploring.
Provide commentary on what you see as being significant for each plot and data set, especially note any outliers or
peculiarities about the data sets. You may use the Matlab functions demonstrated in the lectures.
Error Analysis
2) Explorations for minerals concentrated in dense ore bodies can be done by using gravity measurements, which
sense density variations in the underlying rock. The peak gravity anomaly measured over a buried spherical ore
body having a volume of V, depth of z (i.e., to the center of the sphere), and density excess relative to the host rock
of  is
GV 
g=
,
z2
where and G = 6.673 x 10-6 is Newton’s gravitational constant in units of kg-1 m2 mGal (1 mGal = 10-5 m/s2).
Suppose you measure a gravity anomaly of g = 2 ±0.2 mGal, and other information gives you a depth estimate of z
= 200 ± 10m and volume estimate of V = 1.4±0.2 x107 m3. An estimate of  pertains to the concentration of or in
the body. What is your estimate of  and its uncertainty?
3) The depth z of the seafloor due to cooling of the underlying lithosphere has been shown to approximately increase
with the square-root of seafloor t age according to
2  m Tm  t
z = zr +
.
 m  w  
With thermal diffusivity = 1.00±0.04 x 10-6 m2s-1, water density w = 1000±1 kg/m3, mantle density m = 3300 ±
10 kg/m3, coefficient of thermal expansion  = 3.00 ± 0.02 x 10-5K-1, average mid-ocean ridge depth zr = 2500 ±
200 m, and mantle temperature Tm = 1300 ± 25 K, what is the predicted seafloor depth with its uncertainty at an age
of t = 29 Myr?
GG413 Geological Data Analysis
Extra Credit:
Use Matlab to plot the predicted seafloor depth and its uncertainty as a function of seafloor age for t = 0 to 80 Myr.
To plot the predicted seafloor depth you can do the following:
>>kap=1e-6; rhom=3300; rhow=1000; alpha=3e-5; zr=2500; Tm=1300; %First define variables
>>seconds_per_My=60*60*24*365.25*1e6; sqkm_per_sqm = 1e-3*1e-3;
>>kap=kap*sqkm_per_sqm.*seconds_per_Myr; %Convert kap in m2/s to km2/Myr
>> t= [0:2:80]’;
%Create a column vector from 0 to 80 by increments of 2
>> z=zr + 2*rhom*alpha*Tm/(rhom-rhow).*sqrt(kap.*t./pi); % use “.*” for multiplying individual values of t
>>Figure 1; clf;
>>plot(t,z,’k-‘,’Linewidth’,1); %plot z vs t with a black solid line with a thickness of 1 pt
>> hold on; grid on; %allow additions to the current plot and draw a grid
>>set(gca,’YDIR’,’reverse’); %show the depth increasing downward
>>xlabel(‘seafloor age (Myr)’); ylabel(‘Depth (m)’);
Next you should plot z ± its error as a function of age (due to the uncertainties in the above parameters). Be sure to
check your units and make sure your answer makes sense.