Jupyter Notebook problems in the Essentials of Paleomagnetism Textbook by L. Tauxe

Problems in Chapter 6

Problem 6.1



In [18]:

    
from IPython.display import Image
Image(filename='ps6_prob1.png')









    Out[18]:

A: is hematite and B is magnetite.

Problem 2a

Start with the function dir2cart.py from Problem set # 2:



In [2]:

    
import numpy as np
import pandas as pd
def dir2cart(data):
    """ Converts data array with [Declination, Inclination, Intensity] 
        to cartesian coordinates, X=North, Y=East, Z=Down
        Returns array with [X,Y,Z]
    """
    # convert degrees to radians for declination and inclination
    decs,incs,ints=np.radians(data[0]),np.radians(data[1]),data[2]
    X=ints*np.cos(decs)*np.cos(incs)
    Y=ints*np.sin(decs)*np.cos(incs)
    Z=ints*np.sin(incs)
    cart=np.array([X,Y,Z]).transpose()
    return cart

Read in the datafile demag.dat in the Chapter_6 directory and convert the dec, inc, int data into X,Y,Z.



In [3]:

    
data=np.loadtxt('Chapter_6/demag.dat').transpose()
# Put Temperature in Ts and Ints, Decs Incs into their own lists
Ts,Ints,Decs,Incs=data[0],data[1],data[2],data[3]
print (dir2cart([Decs,Incs,Ints])) # package up and send to our function









    



[[ 0.56726641  2.22547481  0.12438127]
 [ 0.52539356  1.82026868  0.12583757]
 [ 0.46138597  1.49049726  0.16674533]
 [ 0.3331374   1.27893419  0.17164718]
 [ 0.35435714  1.05906186  0.13514433]
 [ 0.30617847  0.81457462  0.13938613]
 [ 0.22860964  0.61144425  0.11041008]
 [ 0.20406515  0.41471514  0.09655915]
 [ 0.14246211  0.2538645   0.09178533]
 [ 0.08424191  0.07505681  0.07871011]
 [ 0.0563417   0.03008367  0.07168645]
 [ 0.03534411  0.01121181  0.0527592 ]
 [ 0.01391931  0.00476565  0.0224831 ]]

Problem 2b

For this we just have to normalize Ints to the first step and re-run dir2cart.



In [4]:

    
Ints=Ints/Ints[0] # This will normalize by the first step.



In [6]:

    
cart=dir2cart([Decs,Incs,Ints]).transpose() # get X,Y,Zs
print (cart) # need to transpose so X is cart[0], etc.









    



[[ 0.24663757  0.22843198  0.2006026   0.14484235  0.15406832  0.13312107
   0.09939549  0.08872398  0.06194005  0.03662692  0.02449639  0.015367
   0.00605187]
 [ 0.96759774  0.79142117  0.64804229  0.55605834  0.46046168  0.35416288
   0.26584533  0.18031093  0.11037587  0.03263339  0.01307986  0.0048747
   0.00207202]
 [ 0.05407881  0.05471199  0.07249797  0.07462921  0.05875841  0.06060266
   0.04800438  0.04198224  0.03990667  0.03422179  0.03116802  0.02293878
   0.00977526]]

Problem 2c

Now plot X and Y components versus Temperature



In [9]:

    
import matplotlib.pyplot as plt
%matplotlib inline
plt.plot(Ts,cart[0],'ro') # plot X versus T as red circles
plt.plot(Ts,cart[0],'r-') # and as red line
plt.plot(Ts,cart[1],'bs') # plot Y versus T as blue squares
plt.plot(Ts,cart[1],'b-') # and as blue line
plt.xlabel('Temperature $^{\circ}$C') # add X label using latex syntax
plt.ylabel('Magnetization'); # and Y label

The strong field component (2 T) was along X and it is the red line. This survives until way above 600$^{\circ}$C and is probably hematite. The lower coercivity component (0.4 T) was along Y (the blue line). It and dies between 550 and 600$^{\circ}$C. It is probably the magnetite component.

Problem 3a



In [24]:

    
Image(filename='microprobe.png')









    Out[24]:

A Curie temperature of 420$^{\circ}$C could indicate a titanomagnetite of composition x $\simeq$ 0.25 (Figure 6.4c) or a titanohematite with composition x $\simeq$ 0.3 (Figure 6.6b in book). But the observation that the coercivity spectrum indicates $\mu_oH_c < $ 30 mT indicates that you are dealing with titanomagnetite rather than Ti-poor titanohematite which would have $\mu_oH_c > $ 30 mT. This ferromagnetic mineral must be a titanomagnetite with x $\simeq$ 0.25.

Problem 3b

A Curie temperature of 200$^{\circ}$C could indicate a titanomagnetite of composition x $\simeq$ 0.6 (Figure 6.4c) or a titanohematite with composition x $\simeq$ 0.55 (Figure 6.6b). The microprobe data indicate a TiO:(Fe2O3+FeO) ratio which is higher than any titanomagnetite, but is consistent with a titanohematite with composition y$\simeq$ 0.55. The ferromagnetic mineral must be a titanohematite with y $\simeq$ 0.55.