Geothermal: Forward and inverse modeling of a linear change in temperature measured in a well¶

"""
Geothermal: Forward and inverse modeling of a linear change in temperature
measured in a well
"""
import numpy
from fatiando import utils
from fatiando.geothermal.climsig import linear, SingleChange
from fatiando.vis import mpl

# Generating synthetic data
amp = 5.43
age = 78.2
# along a well at these depths
zp = numpy.arange(0, 100, 1)
temp, error = utils.contaminate(linear(amp, age, zp), 0.02,
                                percent=True, return_stddev=True)

# Preparing for the inversion
data = SingleChange(temp, zp, mode='linear').config('levmarq', initial=[1, 1])
amp_, age_ = data.fit().estimate_

print "Linear change in temperature"
print "  true:      amp=%.3f age=%.3f" % (amp, age)
print "  estimated: amp=%.3f age=%.3f" % (amp_, age_)

mpl.figure(figsize=(4, 5))
mpl.title("Residual well temperature")
mpl.plot(temp, zp, 'ok', label='Observed')
mpl.plot(data.predicted(), zp, '--r', linewidth=3, label='Predicted')
mpl.legend(loc='lower right', numpoints=1)
mpl.xlabel("Temperature (C)")
mpl.ylabel("Z (m)")
mpl.ylim(100, 0)
mpl.show()