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2313de8 Apr 30, 2014
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'''
Created on Apr 28, 2014
@author: nick touran
Reads in actual meteorite and terrestrial Pb isotopics and computes the age of earth.
Data source: Murthy, Patterson, "Primary Isochron of Zero Age for Meteorites and the Earth,"
J. Geophysical Research, 67, 1, (1962).
Created to be featured on whatisnuclear.com's Age of Earth page at
http://www.whatisnuclear.com/physics/age_of_earth.html
'''
import itertools
import math
from scipy.stats import linregress
import scipy.optimize
import pylab
# decay constants of Uranium isotopes
dec_235=9.8485e-10
dec_238=1.55125e-10 # /yr
def loadData(fName='lead_data.txt'):
"""
read lead isotopic data from text file
Returns
-------
leadData : dict
dataType : [(name, pb206, pb207, pb208)] ratio values (over pb204)
"""
leadData = {}
with open(fName) as f:
for line in f:
line=line.strip()
if not line:
continue
elif ',' not in line:
dataType=line
leadData[dataType]=[]
else:
name, pb206, pb207, pb208 = line.split(',')
leadData[dataType].append((name, float(pb206), float(pb207), float(pb208)))
return leadData
def plotData(leadData):
"""
Plot the data from the table and fit a linear regression. return the slope
"""
markers=itertools.cycle(['o','v','s']) # different types of markers for the plot
allX,allY=[],[]
for dataType, vals in leadData.items():
xy = [(pb206, pb207) for (name, pb206, pb207, pb208) in vals]
x,y = zip(*xy)
pylab.plot(x,y,markers.next(),label=dataType)
allX.extend(x)
allY.extend(y) # for regression
# compute the best linear regression
slope, intercept, rval,pval,stderr = linregress(pylab.array(allX),
pylab.array(allY))
# plot the regression line
xi = pylab.linspace(min(allX),max(allX),100)
yi = [slope*xii+intercept for xii in xi]
pylab.plot(xi,yi,'-',label='Best fit ($R^2$={0:.4f})'.format(rval))
# add some labels to the axes, etc.
pylab.grid(color='0.7')
pylab.legend(loc='upper left',numpoints=1)
pylab.xlabel('Pb206/Pb204')
pylab.ylabel('Pb207/Pb204')
pylab.savefig('pb-pb-isochron.png')
return slope
def slopeEqn(t,slope):
"""
Evaluate the isochron equation for any time or slope.
This is needed as a helper function to the numerical root finder in calcAge.
"""
# 137.88 is the current abundance ratio of U238/U235.
return slope-1.0/137.88*(math.exp(dec_235*t)-1)/(math.exp(dec_238*t)-1)
def calcAge(slope):
"""
Numerically solve for the age of the Earth given a slope of the geochron."""
val=scipy.optimize.brentq(slopeEqn,100,10e9,args=(slope,))
return val
if __name__ == '__main__':
ld = loadData()
slope = plotData(ld)
age = calcAge(slope)
print('Slope of Geochron is {0}'.format(slope))
print('Age of earth is: {0:.2f} billion years'.format(age/1e9))