Tutorial 1: First steps
Welcome to this tutorial.
Importing libraries
Let’s start by importing some libraries. If you have installed meltPT correctly, this should work!
[1]:
from meltPT import *
import pyMelt as m
import matplotlib.pyplot as plt
Reading data and initialising the Suite object
Start by importing data from your csv. In this case our data are stored in a file called “PF16_UT09DV04.csv”. To keep this example simple, the input infile contains a single sample, UT09DV04, from Plank & Forsyth (2016). If necessary, please edit the path within Suite so that the csv file can be found.
[2]:
s = Suite("../Data/PF16_UT09DV04.csv", src_FeIII_totFe=0.17)
/home/mcnab/Melting/meltPT/meltPT/parse.py:79: UserWarning: Input csv does not contain a Fe2O3 column: we will try to fill it for you, or set it to zero.
warnings.warn(message)
/home/mcnab/Melting/meltPT/meltPT/parse.py:79: UserWarning: Input csv does not contain a Cr2O3 column: we will try to fill it for you, or set it to zero.
warnings.warn(message)
/home/mcnab/Melting/meltPT/meltPT/parse.py:79: UserWarning: Input csv does not contain a NiO column: we will try to fill it for you, or set it to zero.
warnings.warn(message)
/home/mcnab/Melting/meltPT/meltPT/parse.py:79: UserWarning: Input csv does not contain a CoO column: we will try to fill it for you, or set it to zero.
warnings.warn(message)
/home/mcnab/Melting/meltPT/meltPT/parse.py:79: UserWarning: Input csv does not contain a CO2 column: we will try to fill it for you, or set it to zero.
warnings.warn(message)
/home/mcnab/Melting/meltPT/meltPT/parse.py:79: UserWarning: Input csv does not contain a FeO_tot column: we will try to fill it for you, or set it to zero.
warnings.warn(message)
You have now created an instance of meltPT’s Suite class, containing the sample data. Parsing the data to the dataframe throws up a series of errors since the dataset does not contain Fe2O3, Cr2O3, NiO, CoO, CO2 or FeO_tot columns. However, since we calculate Fe2O3 and FeO_tot from our FeO column and since our chosen thermobarometric scheme does not include Cr2O3, NiO, CoO and CO2 we can ignore these warnings. Data are stored in a pandas dataframe, which you can preview by typing:
[3]:
print(s.data)
Volc Field Vent tephra/lava/MI Sample IGSN Latitude \
0 SCVF Diamond V tephra/MI UT-09 DV04 TAP00001C 37.2571
Longitude SiO2 TiO2 Al2O3 ... U Fe2O3 Cr2O3 \
0 -113.6243 47.666258 1.85866 15.292146 ... 1.6 2.095933 0.030731
NiO CoO CO2 FeO_tot src_FeIII_totFe src_Fo Total
0 0.020911 0.0 0.0 11.28 0.17 0.9 100.0
[1 rows x 49 columns]
Note that the Suite class includes various other options that we don’t need for this example. To see all these options, and some more information about exactly what Suite does, you can access the docstring by typing:
[4]:
Suite?
in the terminal. All of meltPT’s classes and functions have detailed docstrings that you can access in this way.
Backtrack compositions
The next step is backtracking the sample’s composition. The aim here is to account for the effects of fractional crystallisation of olivine and estimate the sample’s “primary” composition: i.e., its composition when it last equilibrated with the mantle. To do so, we first set up a backtracker class instance. Here we correct for olivine fractionation, follwing the method of Lee et al. (2009, EPSL); the only option currently implemented in meltPT. We specify a fixed value for the partition coefficient, Kd, and set “verbose” to True, so that the program prints updates during the process.
[5]:
b = BacktrackOlivineFractionation(Kd=0.3, verbose=True)
We then pass this class to the backtrack_compositions method of the suite class, to be applied to our data.
[6]:
s.backtrack_compositions(backtracker=b)
Backtracking sample UT-09 DV04 to primary composition:
- 0.05% olivine added, melt Fo = 0.8498, Kd = 0.3000.
- 0.10% olivine added, melt Fo = 0.8501, Kd = 0.3000.
- 0.15% olivine added, melt Fo = 0.8503, Kd = 0.3000.
- 0.20% olivine added, melt Fo = 0.8505, Kd = 0.3000.
- 0.25% olivine added, melt Fo = 0.8507, Kd = 0.3000.
- 0.30% olivine added, melt Fo = 0.8510, Kd = 0.3000.
- 0.35% olivine added, melt Fo = 0.8512, Kd = 0.3000.
- 0.40% olivine added, melt Fo = 0.8514, Kd = 0.3000.
- 0.45% olivine added, melt Fo = 0.8517, Kd = 0.3000.
- 0.50% olivine added, melt Fo = 0.8519, Kd = 0.3000.
- 0.55% olivine added, melt Fo = 0.8521, Kd = 0.3000.
- 0.60% olivine added, melt Fo = 0.8523, Kd = 0.3000.
- 0.65% olivine added, melt Fo = 0.8526, Kd = 0.3000.
- 0.70% olivine added, melt Fo = 0.8528, Kd = 0.3000.
- 0.74% olivine added, melt Fo = 0.8530, Kd = 0.3000.
- 0.79% olivine added, melt Fo = 0.8532, Kd = 0.3000.
- 0.84% olivine added, melt Fo = 0.8535, Kd = 0.3000.
- 0.89% olivine added, melt Fo = 0.8537, Kd = 0.3000.
- 0.94% olivine added, melt Fo = 0.8539, Kd = 0.3000.
- 0.99% olivine added, melt Fo = 0.8541, Kd = 0.3000.
- 1.04% olivine added, melt Fo = 0.8543, Kd = 0.3000.
- 1.09% olivine added, melt Fo = 0.8546, Kd = 0.3000.
- 1.14% olivine added, melt Fo = 0.8548, Kd = 0.3000.
- 1.19% olivine added, melt Fo = 0.8550, Kd = 0.3000.
- 1.23% olivine added, melt Fo = 0.8552, Kd = 0.3000.
- 1.28% olivine added, melt Fo = 0.8554, Kd = 0.3000.
- 1.33% olivine added, melt Fo = 0.8556, Kd = 0.3000.
- 1.38% olivine added, melt Fo = 0.8558, Kd = 0.3000.
- 1.43% olivine added, melt Fo = 0.8561, Kd = 0.3000.
- 1.48% olivine added, melt Fo = 0.8563, Kd = 0.3000.
- 1.53% olivine added, melt Fo = 0.8565, Kd = 0.3000.
- 1.57% olivine added, melt Fo = 0.8567, Kd = 0.3000.
- 1.62% olivine added, melt Fo = 0.8569, Kd = 0.3000.
- 1.67% olivine added, melt Fo = 0.8571, Kd = 0.3000.
- 1.72% olivine added, melt Fo = 0.8573, Kd = 0.3000.
- 1.77% olivine added, melt Fo = 0.8575, Kd = 0.3000.
- 1.82% olivine added, melt Fo = 0.8578, Kd = 0.3000.
- 1.86% olivine added, melt Fo = 0.8580, Kd = 0.3000.
- 1.91% olivine added, melt Fo = 0.8582, Kd = 0.3000.
- 1.96% olivine added, melt Fo = 0.8584, Kd = 0.3000.
- 2.01% olivine added, melt Fo = 0.8586, Kd = 0.3000.
- 2.06% olivine added, melt Fo = 0.8588, Kd = 0.3000.
- 2.10% olivine added, melt Fo = 0.8590, Kd = 0.3000.
- 2.15% olivine added, melt Fo = 0.8592, Kd = 0.3000.
- 2.20% olivine added, melt Fo = 0.8594, Kd = 0.3000.
- 2.25% olivine added, melt Fo = 0.8596, Kd = 0.3000.
- 2.30% olivine added, melt Fo = 0.8598, Kd = 0.3000.
- 2.34% olivine added, melt Fo = 0.8600, Kd = 0.3000.
- 2.39% olivine added, melt Fo = 0.8602, Kd = 0.3000.
- 2.44% olivine added, melt Fo = 0.8604, Kd = 0.3000.
- 2.49% olivine added, melt Fo = 0.8606, Kd = 0.3000.
- 2.53% olivine added, melt Fo = 0.8608, Kd = 0.3000.
- 2.58% olivine added, melt Fo = 0.8610, Kd = 0.3000.
- 2.63% olivine added, melt Fo = 0.8612, Kd = 0.3000.
- 2.68% olivine added, melt Fo = 0.8614, Kd = 0.3000.
- 2.72% olivine added, melt Fo = 0.8616, Kd = 0.3000.
- 2.77% olivine added, melt Fo = 0.8618, Kd = 0.3000.
- 2.82% olivine added, melt Fo = 0.8620, Kd = 0.3000.
- 2.87% olivine added, melt Fo = 0.8622, Kd = 0.3000.
- 2.91% olivine added, melt Fo = 0.8624, Kd = 0.3000.
- 2.96% olivine added, melt Fo = 0.8626, Kd = 0.3000.
- 3.01% olivine added, melt Fo = 0.8628, Kd = 0.3000.
- 3.05% olivine added, melt Fo = 0.8630, Kd = 0.3000.
- 3.10% olivine added, melt Fo = 0.8632, Kd = 0.3000.
- 3.15% olivine added, melt Fo = 0.8634, Kd = 0.3000.
- 3.19% olivine added, melt Fo = 0.8636, Kd = 0.3000.
- 3.24% olivine added, melt Fo = 0.8638, Kd = 0.3000.
- 3.29% olivine added, melt Fo = 0.8640, Kd = 0.3000.
- 3.33% olivine added, melt Fo = 0.8641, Kd = 0.3000.
- 3.38% olivine added, melt Fo = 0.8643, Kd = 0.3000.
- 3.43% olivine added, melt Fo = 0.8645, Kd = 0.3000.
- 3.47% olivine added, melt Fo = 0.8647, Kd = 0.3000.
- 3.52% olivine added, melt Fo = 0.8649, Kd = 0.3000.
- 3.57% olivine added, melt Fo = 0.8651, Kd = 0.3000.
- 3.61% olivine added, melt Fo = 0.8653, Kd = 0.3000.
- 3.66% olivine added, melt Fo = 0.8655, Kd = 0.3000.
- 3.71% olivine added, melt Fo = 0.8657, Kd = 0.3000.
- 3.75% olivine added, melt Fo = 0.8658, Kd = 0.3000.
- 3.80% olivine added, melt Fo = 0.8660, Kd = 0.3000.
- 3.85% olivine added, melt Fo = 0.8662, Kd = 0.3000.
- 3.89% olivine added, melt Fo = 0.8664, Kd = 0.3000.
- 3.94% olivine added, melt Fo = 0.8666, Kd = 0.3000.
- 3.98% olivine added, melt Fo = 0.8668, Kd = 0.3000.
- 4.03% olivine added, melt Fo = 0.8670, Kd = 0.3000.
- 4.08% olivine added, melt Fo = 0.8671, Kd = 0.3000.
- 4.12% olivine added, melt Fo = 0.8673, Kd = 0.3000.
- 4.17% olivine added, melt Fo = 0.8675, Kd = 0.3000.
- 4.21% olivine added, melt Fo = 0.8677, Kd = 0.3000.
- 4.26% olivine added, melt Fo = 0.8679, Kd = 0.3000.
- 4.31% olivine added, melt Fo = 0.8681, Kd = 0.3000.
- 4.35% olivine added, melt Fo = 0.8682, Kd = 0.3000.
- 4.40% olivine added, melt Fo = 0.8684, Kd = 0.3000.
- 4.44% olivine added, melt Fo = 0.8686, Kd = 0.3000.
- 4.49% olivine added, melt Fo = 0.8688, Kd = 0.3000.
- 4.53% olivine added, melt Fo = 0.8690, Kd = 0.3000.
- 4.58% olivine added, melt Fo = 0.8691, Kd = 0.3000.
- 4.63% olivine added, melt Fo = 0.8693, Kd = 0.3000.
- 4.67% olivine added, melt Fo = 0.8695, Kd = 0.3000.
- 4.72% olivine added, melt Fo = 0.8697, Kd = 0.3000.
- 4.76% olivine added, melt Fo = 0.8698, Kd = 0.3000.
- 4.81% olivine added, melt Fo = 0.8700, Kd = 0.3000.
- 4.85% olivine added, melt Fo = 0.8702, Kd = 0.3000.
- 4.90% olivine added, melt Fo = 0.8704, Kd = 0.3000.
- 4.94% olivine added, melt Fo = 0.8705, Kd = 0.3000.
- 4.99% olivine added, melt Fo = 0.8707, Kd = 0.3000.
- 5.03% olivine added, melt Fo = 0.8709, Kd = 0.3000.
- 5.08% olivine added, melt Fo = 0.8711, Kd = 0.3000.
- 5.12% olivine added, melt Fo = 0.8712, Kd = 0.3000.
- 5.17% olivine added, melt Fo = 0.8714, Kd = 0.3000.
- 5.21% olivine added, melt Fo = 0.8716, Kd = 0.3000.
- 5.26% olivine added, melt Fo = 0.8717, Kd = 0.3000.
- 5.30% olivine added, melt Fo = 0.8719, Kd = 0.3000.
- 5.35% olivine added, melt Fo = 0.8721, Kd = 0.3000.
- 5.39% olivine added, melt Fo = 0.8723, Kd = 0.3000.
- 5.44% olivine added, melt Fo = 0.8724, Kd = 0.3000.
- 5.48% olivine added, melt Fo = 0.8726, Kd = 0.3000.
- 5.53% olivine added, melt Fo = 0.8728, Kd = 0.3000.
- 5.57% olivine added, melt Fo = 0.8729, Kd = 0.3000.
- 5.62% olivine added, melt Fo = 0.8731, Kd = 0.3000.
- 5.66% olivine added, melt Fo = 0.8733, Kd = 0.3000.
- 5.70% olivine added, melt Fo = 0.8734, Kd = 0.3000.
- 5.75% olivine added, melt Fo = 0.8736, Kd = 0.3000.
- 5.79% olivine added, melt Fo = 0.8738, Kd = 0.3000.
- 5.84% olivine added, melt Fo = 0.8739, Kd = 0.3000.
- 5.88% olivine added, melt Fo = 0.8741, Kd = 0.3000.
- 5.93% olivine added, melt Fo = 0.8743, Kd = 0.3000.
- 5.97% olivine added, melt Fo = 0.8744, Kd = 0.3000.
- 6.02% olivine added, melt Fo = 0.8746, Kd = 0.3000.
- 6.06% olivine added, melt Fo = 0.8748, Kd = 0.3000.
- 6.10% olivine added, melt Fo = 0.8749, Kd = 0.3000.
- 6.15% olivine added, melt Fo = 0.8751, Kd = 0.3000.
- 6.19% olivine added, melt Fo = 0.8752, Kd = 0.3000.
- 6.24% olivine added, melt Fo = 0.8754, Kd = 0.3000.
- 6.28% olivine added, melt Fo = 0.8756, Kd = 0.3000.
- 6.32% olivine added, melt Fo = 0.8757, Kd = 0.3000.
- 6.37% olivine added, melt Fo = 0.8759, Kd = 0.3000.
- 6.41% olivine added, melt Fo = 0.8761, Kd = 0.3000.
- 6.45% olivine added, melt Fo = 0.8762, Kd = 0.3000.
- 6.50% olivine added, melt Fo = 0.8764, Kd = 0.3000.
- 6.54% olivine added, melt Fo = 0.8765, Kd = 0.3000.
- 6.59% olivine added, melt Fo = 0.8767, Kd = 0.3000.
- 6.63% olivine added, melt Fo = 0.8769, Kd = 0.3000.
- 6.67% olivine added, melt Fo = 0.8770, Kd = 0.3000.
- 6.72% olivine added, melt Fo = 0.8772, Kd = 0.3000.
- 6.76% olivine added, melt Fo = 0.8773, Kd = 0.3000.
- 6.80% olivine added, melt Fo = 0.8775, Kd = 0.3000.
- 6.85% olivine added, melt Fo = 0.8776, Kd = 0.3000.
- 6.89% olivine added, melt Fo = 0.8778, Kd = 0.3000.
- 6.93% olivine added, melt Fo = 0.8780, Kd = 0.3000.
- 6.98% olivine added, melt Fo = 0.8781, Kd = 0.3000.
- 7.02% olivine added, melt Fo = 0.8783, Kd = 0.3000.
- 7.06% olivine added, melt Fo = 0.8784, Kd = 0.3000.
- 7.11% olivine added, melt Fo = 0.8786, Kd = 0.3000.
- 7.15% olivine added, melt Fo = 0.8787, Kd = 0.3000.
- 7.19% olivine added, melt Fo = 0.8789, Kd = 0.3000.
- 7.24% olivine added, melt Fo = 0.8790, Kd = 0.3000.
- 7.28% olivine added, melt Fo = 0.8792, Kd = 0.3000.
- 7.32% olivine added, melt Fo = 0.8793, Kd = 0.3000.
- 7.36% olivine added, melt Fo = 0.8795, Kd = 0.3000.
- 7.41% olivine added, melt Fo = 0.8796, Kd = 0.3000.
- 7.45% olivine added, melt Fo = 0.8798, Kd = 0.3000.
- 7.49% olivine added, melt Fo = 0.8799, Kd = 0.3000.
- 7.54% olivine added, melt Fo = 0.8801, Kd = 0.3000.
- 7.58% olivine added, melt Fo = 0.8802, Kd = 0.3000.
- 7.62% olivine added, melt Fo = 0.8804, Kd = 0.3000.
- 7.66% olivine added, melt Fo = 0.8805, Kd = 0.3000.
- 7.71% olivine added, melt Fo = 0.8807, Kd = 0.3000.
- 7.75% olivine added, melt Fo = 0.8808, Kd = 0.3000.
- 7.79% olivine added, melt Fo = 0.8810, Kd = 0.3000.
- 7.83% olivine added, melt Fo = 0.8811, Kd = 0.3000.
- 7.88% olivine added, melt Fo = 0.8813, Kd = 0.3000.
- 7.92% olivine added, melt Fo = 0.8814, Kd = 0.3000.
- 7.96% olivine added, melt Fo = 0.8816, Kd = 0.3000.
- 8.00% olivine added, melt Fo = 0.8817, Kd = 0.3000.
- 8.05% olivine added, melt Fo = 0.8819, Kd = 0.3000.
- 8.09% olivine added, melt Fo = 0.8820, Kd = 0.3000.
- 8.13% olivine added, melt Fo = 0.8822, Kd = 0.3000.
- 8.17% olivine added, melt Fo = 0.8823, Kd = 0.3000.
- 8.21% olivine added, melt Fo = 0.8825, Kd = 0.3000.
- 8.26% olivine added, melt Fo = 0.8826, Kd = 0.3000.
- 8.30% olivine added, melt Fo = 0.8827, Kd = 0.3000.
- 8.34% olivine added, melt Fo = 0.8829, Kd = 0.3000.
- 8.38% olivine added, melt Fo = 0.8830, Kd = 0.3000.
- 8.42% olivine added, melt Fo = 0.8832, Kd = 0.3000.
- 8.47% olivine added, melt Fo = 0.8833, Kd = 0.3000.
- 8.51% olivine added, melt Fo = 0.8835, Kd = 0.3000.
- 8.55% olivine added, melt Fo = 0.8836, Kd = 0.3000.
- 8.59% olivine added, melt Fo = 0.8838, Kd = 0.3000.
- 8.63% olivine added, melt Fo = 0.8839, Kd = 0.3000.
- 8.68% olivine added, melt Fo = 0.8840, Kd = 0.3000.
- 8.72% olivine added, melt Fo = 0.8842, Kd = 0.3000.
- 8.76% olivine added, melt Fo = 0.8843, Kd = 0.3000.
- 8.80% olivine added, melt Fo = 0.8845, Kd = 0.3000.
- 8.84% olivine added, melt Fo = 0.8846, Kd = 0.3000.
- 8.88% olivine added, melt Fo = 0.8847, Kd = 0.3000.
- 8.93% olivine added, melt Fo = 0.8849, Kd = 0.3000.
- 8.97% olivine added, melt Fo = 0.8850, Kd = 0.3000.
- 9.01% olivine added, melt Fo = 0.8852, Kd = 0.3000.
- 9.05% olivine added, melt Fo = 0.8853, Kd = 0.3000.
- 9.09% olivine added, melt Fo = 0.8854, Kd = 0.3000.
- 9.13% olivine added, melt Fo = 0.8856, Kd = 0.3000.
- 9.17% olivine added, melt Fo = 0.8857, Kd = 0.3000.
- 9.21% olivine added, melt Fo = 0.8858, Kd = 0.3000.
- 9.26% olivine added, melt Fo = 0.8860, Kd = 0.3000.
- 9.30% olivine added, melt Fo = 0.8861, Kd = 0.3000.
- 9.34% olivine added, melt Fo = 0.8863, Kd = 0.3000.
- 9.38% olivine added, melt Fo = 0.8864, Kd = 0.3000.
- 9.42% olivine added, melt Fo = 0.8865, Kd = 0.3000.
- 9.46% olivine added, melt Fo = 0.8867, Kd = 0.3000.
- 9.50% olivine added, melt Fo = 0.8868, Kd = 0.3000.
- 9.54% olivine added, melt Fo = 0.8869, Kd = 0.3000.
- 9.58% olivine added, melt Fo = 0.8871, Kd = 0.3000.
- 9.62% olivine added, melt Fo = 0.8872, Kd = 0.3000.
- 9.67% olivine added, melt Fo = 0.8873, Kd = 0.3000.
- 9.71% olivine added, melt Fo = 0.8875, Kd = 0.3000.
- 9.75% olivine added, melt Fo = 0.8876, Kd = 0.3000.
- 9.79% olivine added, melt Fo = 0.8877, Kd = 0.3000.
- 9.83% olivine added, melt Fo = 0.8879, Kd = 0.3000.
- 9.87% olivine added, melt Fo = 0.8880, Kd = 0.3000.
- 9.91% olivine added, melt Fo = 0.8881, Kd = 0.3000.
- 9.95% olivine added, melt Fo = 0.8883, Kd = 0.3000.
- 9.99% olivine added, melt Fo = 0.8884, Kd = 0.3000.
- 10.03% olivine added, melt Fo = 0.8885, Kd = 0.3000.
- 10.07% olivine added, melt Fo = 0.8887, Kd = 0.3000.
- 10.11% olivine added, melt Fo = 0.8888, Kd = 0.3000.
- 10.15% olivine added, melt Fo = 0.8889, Kd = 0.3000.
- 10.19% olivine added, melt Fo = 0.8890, Kd = 0.3000.
- 10.23% olivine added, melt Fo = 0.8892, Kd = 0.3000.
- 10.27% olivine added, melt Fo = 0.8893, Kd = 0.3000.
- 10.31% olivine added, melt Fo = 0.8894, Kd = 0.3000.
- 10.35% olivine added, melt Fo = 0.8896, Kd = 0.3000.
- 10.39% olivine added, melt Fo = 0.8897, Kd = 0.3000.
- 10.43% olivine added, melt Fo = 0.8898, Kd = 0.3000.
- 10.47% olivine added, melt Fo = 0.8900, Kd = 0.3000.
- 10.51% olivine added, melt Fo = 0.8901, Kd = 0.3000.
- 10.55% olivine added, melt Fo = 0.8902, Kd = 0.3000.
- 10.59% olivine added, melt Fo = 0.8903, Kd = 0.3000.
- 10.63% olivine added, melt Fo = 0.8905, Kd = 0.3000.
- 10.67% olivine added, melt Fo = 0.8906, Kd = 0.3000.
- 10.71% olivine added, melt Fo = 0.8907, Kd = 0.3000.
- 10.75% olivine added, melt Fo = 0.8908, Kd = 0.3000.
- 10.79% olivine added, melt Fo = 0.8910, Kd = 0.3000.
- 10.83% olivine added, melt Fo = 0.8911, Kd = 0.3000.
- 10.87% olivine added, melt Fo = 0.8912, Kd = 0.3000.
- 10.91% olivine added, melt Fo = 0.8913, Kd = 0.3000.
- 10.95% olivine added, melt Fo = 0.8915, Kd = 0.3000.
- 10.99% olivine added, melt Fo = 0.8916, Kd = 0.3000.
- 11.03% olivine added, melt Fo = 0.8917, Kd = 0.3000.
- 11.07% olivine added, melt Fo = 0.8918, Kd = 0.3000.
- 11.11% olivine added, melt Fo = 0.8920, Kd = 0.3000.
- 11.15% olivine added, melt Fo = 0.8921, Kd = 0.3000.
- 11.19% olivine added, melt Fo = 0.8922, Kd = 0.3000.
- 11.23% olivine added, melt Fo = 0.8923, Kd = 0.3000.
- 11.27% olivine added, melt Fo = 0.8925, Kd = 0.3000.
- 11.31% olivine added, melt Fo = 0.8926, Kd = 0.3000.
- 11.35% olivine added, melt Fo = 0.8927, Kd = 0.3000.
- 11.39% olivine added, melt Fo = 0.8928, Kd = 0.3000.
- 11.43% olivine added, melt Fo = 0.8929, Kd = 0.3000.
- 11.47% olivine added, melt Fo = 0.8931, Kd = 0.3000.
- 11.50% olivine added, melt Fo = 0.8932, Kd = 0.3000.
- 11.54% olivine added, melt Fo = 0.8933, Kd = 0.3000.
- 11.58% olivine added, melt Fo = 0.8934, Kd = 0.3000.
- 11.62% olivine added, melt Fo = 0.8935, Kd = 0.3000.
- 11.66% olivine added, melt Fo = 0.8937, Kd = 0.3000.
- 11.70% olivine added, melt Fo = 0.8938, Kd = 0.3000.
- 11.74% olivine added, melt Fo = 0.8939, Kd = 0.3000.
- 11.78% olivine added, melt Fo = 0.8940, Kd = 0.3000.
- 11.82% olivine added, melt Fo = 0.8941, Kd = 0.3000.
- 11.86% olivine added, melt Fo = 0.8943, Kd = 0.3000.
- 11.89% olivine added, melt Fo = 0.8944, Kd = 0.3000.
- 11.93% olivine added, melt Fo = 0.8945, Kd = 0.3000.
- 11.97% olivine added, melt Fo = 0.8946, Kd = 0.3000.
- 12.01% olivine added, melt Fo = 0.8947, Kd = 0.3000.
- 12.05% olivine added, melt Fo = 0.8949, Kd = 0.3000.
- 12.09% olivine added, melt Fo = 0.8950, Kd = 0.3000.
- 12.13% olivine added, melt Fo = 0.8951, Kd = 0.3000.
- 12.17% olivine added, melt Fo = 0.8952, Kd = 0.3000.
- 12.20% olivine added, melt Fo = 0.8953, Kd = 0.3000.
- 12.24% olivine added, melt Fo = 0.8954, Kd = 0.3000.
- 12.28% olivine added, melt Fo = 0.8956, Kd = 0.3000.
- 12.32% olivine added, melt Fo = 0.8957, Kd = 0.3000.
- 12.36% olivine added, melt Fo = 0.8958, Kd = 0.3000.
- 12.40% olivine added, melt Fo = 0.8959, Kd = 0.3000.
- 12.43% olivine added, melt Fo = 0.8960, Kd = 0.3000.
- 12.47% olivine added, melt Fo = 0.8961, Kd = 0.3000.
- 12.51% olivine added, melt Fo = 0.8962, Kd = 0.3000.
- 12.55% olivine added, melt Fo = 0.8964, Kd = 0.3000.
- 12.59% olivine added, melt Fo = 0.8965, Kd = 0.3000.
- 12.63% olivine added, melt Fo = 0.8966, Kd = 0.3000.
- 12.66% olivine added, melt Fo = 0.8967, Kd = 0.3000.
- 12.70% olivine added, melt Fo = 0.8968, Kd = 0.3000.
- 12.74% olivine added, melt Fo = 0.8969, Kd = 0.3000.
- 12.78% olivine added, melt Fo = 0.8970, Kd = 0.3000.
- 12.82% olivine added, melt Fo = 0.8972, Kd = 0.3000.
- 12.85% olivine added, melt Fo = 0.8973, Kd = 0.3000.
- 12.89% olivine added, melt Fo = 0.8974, Kd = 0.3000.
- 12.93% olivine added, melt Fo = 0.8975, Kd = 0.3000.
- 12.97% olivine added, melt Fo = 0.8976, Kd = 0.3000.
- 13.01% olivine added, melt Fo = 0.8977, Kd = 0.3000.
- 13.04% olivine added, melt Fo = 0.8978, Kd = 0.3000.
- 13.08% olivine added, melt Fo = 0.8979, Kd = 0.3000.
- 13.12% olivine added, melt Fo = 0.8981, Kd = 0.3000.
- 13.16% olivine added, melt Fo = 0.8982, Kd = 0.3000.
- 13.19% olivine added, melt Fo = 0.8983, Kd = 0.3000.
- 13.23% olivine added, melt Fo = 0.8984, Kd = 0.3000.
- 13.27% olivine added, melt Fo = 0.8985, Kd = 0.3000.
- 13.31% olivine added, melt Fo = 0.8986, Kd = 0.3000.
- 13.34% olivine added, melt Fo = 0.8987, Kd = 0.3000.
- 13.38% olivine added, melt Fo = 0.8988, Kd = 0.3000.
- 13.42% olivine added, melt Fo = 0.8989, Kd = 0.3000.
- 13.46% olivine added, melt Fo = 0.8990, Kd = 0.3000.
- 13.49% olivine added, melt Fo = 0.8992, Kd = 0.3000.
- 13.53% olivine added, melt Fo = 0.8993, Kd = 0.3000.
- 13.57% olivine added, melt Fo = 0.8994, Kd = 0.3000.
- 13.61% olivine added, melt Fo = 0.8995, Kd = 0.3000.
- 13.64% olivine added, melt Fo = 0.8996, Kd = 0.3000.
- 13.68% olivine added, melt Fo = 0.8997, Kd = 0.3000.
- 13.72% olivine added, melt Fo = 0.8998, Kd = 0.3000.
As you can see, the sample started with a Forsterite number of c. 0.85. The program then added olivine in equilibrium with the melt, until, after adding c. 14% olivine, it reached a Forsterite number of 90%, which we assumed for the mantle source.
You have now created a new dataframe within the suite class containing the sample’s primary composition:
[7]:
print(s.primary)
Al2O3_primary_wt CO2_primary_wt CaO_primary_wt CoO_primary_wt \
0 13.044663 0.0 7.382189 0.0
Cr2O3_primary_wt Fe2O3_primary_wt FeO_primary_wt H2O_primary_wt \
0 0.026214 1.787895 9.582655 1.174439
K2O_primary_wt MgO_primary_wt MnO_primary_wt Na2O_primary_wt \
0 0.939551 14.481938 0.150999 2.885765
NiO_primary_wt P2O5_primary_wt SiO2_primary_wt TiO2_primary_wt ol_added
0 0.017838 0.327165 46.613197 1.585493 0.137187
Compute pressures & temperatures
Now we can calculate pressures and temperatures at which the sample was last in equilibrium with the mantle. Use Suite’s compute_pressure_temperature method:
[8]:
s.compute_pressure_temperature(method="PF16")
The results are stored in a new dataframe:
[9]:
print(s.PT)
P P_err T T_err
0 2.069507 0.24 1370.081495 39.0
The calculated pressure of 2.07 GPa and temperature of 1370 oC are the same as those from Plank & Forsyth (2016, their Table S8), which is good!
Fit a melting path
Next we would like to link our estimate equilibration pressure and temperature to a model geotherm. In meltPT, we make use of the pyMelt package to compute adiabatic decompression melting paths. For this example we use pyMelt’s implientation of Katz et al.’s (2003) lherzolite melting model to set up the mantle object.
[10]:
lz = m.lithologies.katz.lherzolite()
mantle = m.mantle([lz], [1], ['Lz'])
We can now pass our mantle object to Suite’s find_individual_potential_temperatures method. This will take a few seconds!
[11]:
s.find_individual_potential_temperatures(mantle)
This will create a new dataframe, called individual_potential_temperatures which contains information about the result and a copy of the best-fitting pyMelt path object:
[12]:
print(s.individual_potential_temperatures)
F P T Tp misfit \
0 0.035642 2.069514 1370.082558 1346.651898 0.00004
path
0 <pyMelt.meltingcolumn_classes.meltingColumn ob...
Variable Kd
In the above example we used a fixed value for the partition coefficient that describes partitioning between olivine and melt, Kd. There is also an option to allow this value to vary as a function of melt Mg#, after Tamura et al. (2020, JoP). Let’s repeat the steps above with this option.
[13]:
# Read the csv, create a new Suite object.
s_varKd = Suite("../Data/PF16_UT09DV04.csv", src_FeIII_totFe=0.17)
# Backtrack. Variable Kd is the default option, so we can simply miss out that
# flag. Notice that in this case, we need to add more olivine, about 17%, to
# reach our target forsterite content.
b = BacktrackOlivineFractionation(verbose=True)
s_varKd.backtrack_compositions(backtracker=b)
# Compute pressure and temperature. The result is hotter and deeper than the
# fixed Kd case.
s_varKd.compute_pressure_temperature(method="PF16")
print(s.PT)
# Find the best fitting potential temperature.
s_varKd.find_individual_potential_temperatures(mantle)
Backtracking sample UT-09 DV04 to primary composition:
- 0.05% olivine added, melt Fo = 0.8505, Kd = 0.2984.
- 0.10% olivine added, melt Fo = 0.8507, Kd = 0.2985.
- 0.15% olivine added, melt Fo = 0.8509, Kd = 0.2986.
- 0.20% olivine added, melt Fo = 0.8511, Kd = 0.2987.
- 0.25% olivine added, melt Fo = 0.8513, Kd = 0.2987.
- 0.30% olivine added, melt Fo = 0.8515, Kd = 0.2988.
- 0.35% olivine added, melt Fo = 0.8517, Kd = 0.2989.
- 0.40% olivine added, melt Fo = 0.8519, Kd = 0.2990.
- 0.45% olivine added, melt Fo = 0.8521, Kd = 0.2991.
- 0.50% olivine added, melt Fo = 0.8522, Kd = 0.2992.
- 0.55% olivine added, melt Fo = 0.8524, Kd = 0.2992.
- 0.60% olivine added, melt Fo = 0.8526, Kd = 0.2993.
- 0.65% olivine added, melt Fo = 0.8528, Kd = 0.2994.
- 0.70% olivine added, melt Fo = 0.8530, Kd = 0.2995.
- 0.74% olivine added, melt Fo = 0.8532, Kd = 0.2996.
- 0.79% olivine added, melt Fo = 0.8534, Kd = 0.2996.
- 0.84% olivine added, melt Fo = 0.8536, Kd = 0.2997.
- 0.89% olivine added, melt Fo = 0.8538, Kd = 0.2998.
- 0.94% olivine added, melt Fo = 0.8540, Kd = 0.2999.
- 0.99% olivine added, melt Fo = 0.8541, Kd = 0.3000.
- 1.04% olivine added, melt Fo = 0.8543, Kd = 0.3000.
- 1.09% olivine added, melt Fo = 0.8545, Kd = 0.3001.
- 1.14% olivine added, melt Fo = 0.8547, Kd = 0.3002.
- 1.19% olivine added, melt Fo = 0.8549, Kd = 0.3003.
- 1.23% olivine added, melt Fo = 0.8551, Kd = 0.3004.
- 1.28% olivine added, melt Fo = 0.8552, Kd = 0.3004.
- 1.33% olivine added, melt Fo = 0.8554, Kd = 0.3005.
- 1.38% olivine added, melt Fo = 0.8556, Kd = 0.3006.
- 1.43% olivine added, melt Fo = 0.8558, Kd = 0.3007.
- 1.48% olivine added, melt Fo = 0.8560, Kd = 0.3008.
- 1.53% olivine added, melt Fo = 0.8562, Kd = 0.3008.
- 1.57% olivine added, melt Fo = 0.8563, Kd = 0.3009.
- 1.62% olivine added, melt Fo = 0.8565, Kd = 0.3010.
- 1.67% olivine added, melt Fo = 0.8567, Kd = 0.3011.
- 1.72% olivine added, melt Fo = 0.8569, Kd = 0.3012.
- 1.77% olivine added, melt Fo = 0.8570, Kd = 0.3012.
- 1.82% olivine added, melt Fo = 0.8572, Kd = 0.3013.
- 1.86% olivine added, melt Fo = 0.8574, Kd = 0.3014.
- 1.91% olivine added, melt Fo = 0.8576, Kd = 0.3015.
- 1.96% olivine added, melt Fo = 0.8577, Kd = 0.3016.
- 2.01% olivine added, melt Fo = 0.8579, Kd = 0.3016.
- 2.06% olivine added, melt Fo = 0.8581, Kd = 0.3017.
- 2.10% olivine added, melt Fo = 0.8583, Kd = 0.3018.
- 2.15% olivine added, melt Fo = 0.8584, Kd = 0.3019.
- 2.20% olivine added, melt Fo = 0.8586, Kd = 0.3020.
- 2.25% olivine added, melt Fo = 0.8588, Kd = 0.3020.
- 2.30% olivine added, melt Fo = 0.8590, Kd = 0.3021.
- 2.34% olivine added, melt Fo = 0.8591, Kd = 0.3022.
- 2.39% olivine added, melt Fo = 0.8593, Kd = 0.3023.
- 2.44% olivine added, melt Fo = 0.8595, Kd = 0.3024.
- 2.49% olivine added, melt Fo = 0.8596, Kd = 0.3024.
- 2.53% olivine added, melt Fo = 0.8598, Kd = 0.3025.
- 2.58% olivine added, melt Fo = 0.8600, Kd = 0.3026.
- 2.63% olivine added, melt Fo = 0.8601, Kd = 0.3027.
- 2.68% olivine added, melt Fo = 0.8603, Kd = 0.3028.
- 2.72% olivine added, melt Fo = 0.8605, Kd = 0.3028.
- 2.77% olivine added, melt Fo = 0.8606, Kd = 0.3029.
- 2.82% olivine added, melt Fo = 0.8608, Kd = 0.3030.
- 2.87% olivine added, melt Fo = 0.8610, Kd = 0.3031.
- 2.91% olivine added, melt Fo = 0.8611, Kd = 0.3032.
- 2.96% olivine added, melt Fo = 0.8613, Kd = 0.3032.
- 3.01% olivine added, melt Fo = 0.8615, Kd = 0.3033.
- 3.05% olivine added, melt Fo = 0.8616, Kd = 0.3034.
- 3.10% olivine added, melt Fo = 0.8618, Kd = 0.3035.
- 3.15% olivine added, melt Fo = 0.8620, Kd = 0.3036.
- 3.19% olivine added, melt Fo = 0.8621, Kd = 0.3036.
- 3.24% olivine added, melt Fo = 0.8623, Kd = 0.3037.
- 3.29% olivine added, melt Fo = 0.8624, Kd = 0.3038.
- 3.33% olivine added, melt Fo = 0.8626, Kd = 0.3039.
- 3.38% olivine added, melt Fo = 0.8628, Kd = 0.3040.
- 3.43% olivine added, melt Fo = 0.8629, Kd = 0.3040.
- 3.47% olivine added, melt Fo = 0.8631, Kd = 0.3041.
- 3.52% olivine added, melt Fo = 0.8632, Kd = 0.3042.
- 3.57% olivine added, melt Fo = 0.8634, Kd = 0.3043.
- 3.61% olivine added, melt Fo = 0.8636, Kd = 0.3043.
- 3.66% olivine added, melt Fo = 0.8637, Kd = 0.3044.
- 3.71% olivine added, melt Fo = 0.8639, Kd = 0.3045.
- 3.75% olivine added, melt Fo = 0.8640, Kd = 0.3046.
- 3.80% olivine added, melt Fo = 0.8642, Kd = 0.3047.
- 3.85% olivine added, melt Fo = 0.8643, Kd = 0.3047.
- 3.89% olivine added, melt Fo = 0.8645, Kd = 0.3048.
- 3.94% olivine added, melt Fo = 0.8647, Kd = 0.3049.
- 3.98% olivine added, melt Fo = 0.8648, Kd = 0.3050.
- 4.03% olivine added, melt Fo = 0.8650, Kd = 0.3051.
- 4.08% olivine added, melt Fo = 0.8651, Kd = 0.3051.
- 4.12% olivine added, melt Fo = 0.8653, Kd = 0.3052.
- 4.17% olivine added, melt Fo = 0.8654, Kd = 0.3053.
- 4.21% olivine added, melt Fo = 0.8656, Kd = 0.3054.
- 4.26% olivine added, melt Fo = 0.8657, Kd = 0.3055.
- 4.31% olivine added, melt Fo = 0.8659, Kd = 0.3055.
- 4.35% olivine added, melt Fo = 0.8660, Kd = 0.3056.
- 4.40% olivine added, melt Fo = 0.8662, Kd = 0.3057.
- 4.44% olivine added, melt Fo = 0.8663, Kd = 0.3058.
- 4.49% olivine added, melt Fo = 0.8665, Kd = 0.3058.
- 4.53% olivine added, melt Fo = 0.8666, Kd = 0.3059.
- 4.58% olivine added, melt Fo = 0.8668, Kd = 0.3060.
- 4.63% olivine added, melt Fo = 0.8669, Kd = 0.3061.
- 4.67% olivine added, melt Fo = 0.8671, Kd = 0.3062.
- 4.72% olivine added, melt Fo = 0.8672, Kd = 0.3062.
- 4.76% olivine added, melt Fo = 0.8674, Kd = 0.3063.
- 4.81% olivine added, melt Fo = 0.8675, Kd = 0.3064.
- 4.85% olivine added, melt Fo = 0.8677, Kd = 0.3065.
- 4.90% olivine added, melt Fo = 0.8678, Kd = 0.3066.
- 4.94% olivine added, melt Fo = 0.8680, Kd = 0.3066.
- 4.99% olivine added, melt Fo = 0.8681, Kd = 0.3067.
- 5.03% olivine added, melt Fo = 0.8682, Kd = 0.3068.
- 5.08% olivine added, melt Fo = 0.8684, Kd = 0.3069.
- 5.12% olivine added, melt Fo = 0.8685, Kd = 0.3069.
- 5.17% olivine added, melt Fo = 0.8687, Kd = 0.3070.
- 5.21% olivine added, melt Fo = 0.8688, Kd = 0.3071.
- 5.26% olivine added, melt Fo = 0.8690, Kd = 0.3072.
- 5.30% olivine added, melt Fo = 0.8691, Kd = 0.3073.
- 5.35% olivine added, melt Fo = 0.8693, Kd = 0.3073.
- 5.39% olivine added, melt Fo = 0.8694, Kd = 0.3074.
- 5.44% olivine added, melt Fo = 0.8695, Kd = 0.3075.
- 5.48% olivine added, melt Fo = 0.8697, Kd = 0.3076.
- 5.53% olivine added, melt Fo = 0.8698, Kd = 0.3077.
- 5.57% olivine added, melt Fo = 0.8700, Kd = 0.3077.
- 5.62% olivine added, melt Fo = 0.8701, Kd = 0.3078.
- 5.66% olivine added, melt Fo = 0.8702, Kd = 0.3079.
- 5.70% olivine added, melt Fo = 0.8704, Kd = 0.3080.
- 5.75% olivine added, melt Fo = 0.8705, Kd = 0.3080.
- 5.79% olivine added, melt Fo = 0.8707, Kd = 0.3081.
- 5.84% olivine added, melt Fo = 0.8708, Kd = 0.3082.
- 5.88% olivine added, melt Fo = 0.8709, Kd = 0.3083.
- 5.93% olivine added, melt Fo = 0.8711, Kd = 0.3084.
- 5.97% olivine added, melt Fo = 0.8712, Kd = 0.3084.
- 6.02% olivine added, melt Fo = 0.8713, Kd = 0.3085.
- 6.06% olivine added, melt Fo = 0.8715, Kd = 0.3086.
- 6.10% olivine added, melt Fo = 0.8716, Kd = 0.3087.
- 6.15% olivine added, melt Fo = 0.8718, Kd = 0.3087.
- 6.19% olivine added, melt Fo = 0.8719, Kd = 0.3088.
- 6.24% olivine added, melt Fo = 0.8720, Kd = 0.3089.
- 6.28% olivine added, melt Fo = 0.8722, Kd = 0.3090.
- 6.32% olivine added, melt Fo = 0.8723, Kd = 0.3091.
- 6.37% olivine added, melt Fo = 0.8724, Kd = 0.3091.
- 6.41% olivine added, melt Fo = 0.8726, Kd = 0.3092.
- 6.45% olivine added, melt Fo = 0.8727, Kd = 0.3093.
- 6.50% olivine added, melt Fo = 0.8728, Kd = 0.3094.
- 6.54% olivine added, melt Fo = 0.8730, Kd = 0.3094.
- 6.59% olivine added, melt Fo = 0.8731, Kd = 0.3095.
- 6.63% olivine added, melt Fo = 0.8732, Kd = 0.3096.
- 6.67% olivine added, melt Fo = 0.8734, Kd = 0.3097.
- 6.72% olivine added, melt Fo = 0.8735, Kd = 0.3097.
- 6.76% olivine added, melt Fo = 0.8736, Kd = 0.3098.
- 6.80% olivine added, melt Fo = 0.8737, Kd = 0.3099.
- 6.85% olivine added, melt Fo = 0.8739, Kd = 0.3100.
- 6.89% olivine added, melt Fo = 0.8740, Kd = 0.3101.
- 6.93% olivine added, melt Fo = 0.8741, Kd = 0.3101.
- 6.98% olivine added, melt Fo = 0.8743, Kd = 0.3102.
- 7.02% olivine added, melt Fo = 0.8744, Kd = 0.3103.
- 7.06% olivine added, melt Fo = 0.8745, Kd = 0.3104.
- 7.11% olivine added, melt Fo = 0.8747, Kd = 0.3104.
- 7.15% olivine added, melt Fo = 0.8748, Kd = 0.3105.
- 7.19% olivine added, melt Fo = 0.8749, Kd = 0.3106.
- 7.24% olivine added, melt Fo = 0.8750, Kd = 0.3107.
- 7.28% olivine added, melt Fo = 0.8752, Kd = 0.3108.
- 7.32% olivine added, melt Fo = 0.8753, Kd = 0.3108.
- 7.36% olivine added, melt Fo = 0.8754, Kd = 0.3109.
- 7.41% olivine added, melt Fo = 0.8755, Kd = 0.3110.
- 7.45% olivine added, melt Fo = 0.8757, Kd = 0.3111.
- 7.49% olivine added, melt Fo = 0.8758, Kd = 0.3111.
- 7.54% olivine added, melt Fo = 0.8759, Kd = 0.3112.
- 7.58% olivine added, melt Fo = 0.8760, Kd = 0.3113.
- 7.62% olivine added, melt Fo = 0.8762, Kd = 0.3114.
- 7.66% olivine added, melt Fo = 0.8763, Kd = 0.3114.
- 7.71% olivine added, melt Fo = 0.8764, Kd = 0.3115.
- 7.75% olivine added, melt Fo = 0.8765, Kd = 0.3116.
- 7.79% olivine added, melt Fo = 0.8767, Kd = 0.3117.
- 7.83% olivine added, melt Fo = 0.8768, Kd = 0.3118.
- 7.88% olivine added, melt Fo = 0.8769, Kd = 0.3118.
- 7.92% olivine added, melt Fo = 0.8770, Kd = 0.3119.
- 7.96% olivine added, melt Fo = 0.8771, Kd = 0.3120.
- 8.00% olivine added, melt Fo = 0.8773, Kd = 0.3121.
- 8.05% olivine added, melt Fo = 0.8774, Kd = 0.3121.
- 8.09% olivine added, melt Fo = 0.8775, Kd = 0.3122.
- 8.13% olivine added, melt Fo = 0.8776, Kd = 0.3123.
- 8.17% olivine added, melt Fo = 0.8778, Kd = 0.3124.
- 8.21% olivine added, melt Fo = 0.8779, Kd = 0.3124.
- 8.26% olivine added, melt Fo = 0.8780, Kd = 0.3125.
- 8.30% olivine added, melt Fo = 0.8781, Kd = 0.3126.
- 8.34% olivine added, melt Fo = 0.8782, Kd = 0.3127.
- 8.38% olivine added, melt Fo = 0.8784, Kd = 0.3127.
- 8.42% olivine added, melt Fo = 0.8785, Kd = 0.3128.
- 8.47% olivine added, melt Fo = 0.8786, Kd = 0.3129.
- 8.51% olivine added, melt Fo = 0.8787, Kd = 0.3130.
- 8.55% olivine added, melt Fo = 0.8788, Kd = 0.3130.
- 8.59% olivine added, melt Fo = 0.8789, Kd = 0.3131.
- 8.63% olivine added, melt Fo = 0.8791, Kd = 0.3132.
- 8.68% olivine added, melt Fo = 0.8792, Kd = 0.3133.
- 8.72% olivine added, melt Fo = 0.8793, Kd = 0.3134.
- 8.76% olivine added, melt Fo = 0.8794, Kd = 0.3134.
- 8.80% olivine added, melt Fo = 0.8795, Kd = 0.3135.
- 8.84% olivine added, melt Fo = 0.8796, Kd = 0.3136.
- 8.88% olivine added, melt Fo = 0.8798, Kd = 0.3137.
- 8.93% olivine added, melt Fo = 0.8799, Kd = 0.3137.
- 8.97% olivine added, melt Fo = 0.8800, Kd = 0.3138.
- 9.01% olivine added, melt Fo = 0.8801, Kd = 0.3139.
- 9.05% olivine added, melt Fo = 0.8802, Kd = 0.3140.
- 9.09% olivine added, melt Fo = 0.8803, Kd = 0.3140.
- 9.13% olivine added, melt Fo = 0.8804, Kd = 0.3141.
- 9.17% olivine added, melt Fo = 0.8806, Kd = 0.3142.
- 9.21% olivine added, melt Fo = 0.8807, Kd = 0.3143.
- 9.26% olivine added, melt Fo = 0.8808, Kd = 0.3143.
- 9.30% olivine added, melt Fo = 0.8809, Kd = 0.3144.
- 9.34% olivine added, melt Fo = 0.8810, Kd = 0.3145.
- 9.38% olivine added, melt Fo = 0.8811, Kd = 0.3146.
- 9.42% olivine added, melt Fo = 0.8812, Kd = 0.3146.
- 9.46% olivine added, melt Fo = 0.8814, Kd = 0.3147.
- 9.50% olivine added, melt Fo = 0.8815, Kd = 0.3148.
- 9.54% olivine added, melt Fo = 0.8816, Kd = 0.3149.
- 9.58% olivine added, melt Fo = 0.8817, Kd = 0.3149.
- 9.62% olivine added, melt Fo = 0.8818, Kd = 0.3150.
- 9.67% olivine added, melt Fo = 0.8819, Kd = 0.3151.
- 9.71% olivine added, melt Fo = 0.8820, Kd = 0.3152.
- 9.75% olivine added, melt Fo = 0.8821, Kd = 0.3152.
- 9.79% olivine added, melt Fo = 0.8822, Kd = 0.3153.
- 9.83% olivine added, melt Fo = 0.8823, Kd = 0.3154.
- 9.87% olivine added, melt Fo = 0.8825, Kd = 0.3155.
- 9.91% olivine added, melt Fo = 0.8826, Kd = 0.3155.
- 9.95% olivine added, melt Fo = 0.8827, Kd = 0.3156.
- 9.99% olivine added, melt Fo = 0.8828, Kd = 0.3157.
- 10.03% olivine added, melt Fo = 0.8829, Kd = 0.3158.
- 10.07% olivine added, melt Fo = 0.8830, Kd = 0.3158.
- 10.11% olivine added, melt Fo = 0.8831, Kd = 0.3159.
- 10.15% olivine added, melt Fo = 0.8832, Kd = 0.3160.
- 10.19% olivine added, melt Fo = 0.8833, Kd = 0.3161.
- 10.23% olivine added, melt Fo = 0.8834, Kd = 0.3161.
- 10.27% olivine added, melt Fo = 0.8835, Kd = 0.3162.
- 10.31% olivine added, melt Fo = 0.8836, Kd = 0.3163.
- 10.35% olivine added, melt Fo = 0.8837, Kd = 0.3164.
- 10.39% olivine added, melt Fo = 0.8839, Kd = 0.3164.
- 10.43% olivine added, melt Fo = 0.8840, Kd = 0.3165.
- 10.47% olivine added, melt Fo = 0.8841, Kd = 0.3166.
- 10.51% olivine added, melt Fo = 0.8842, Kd = 0.3167.
- 10.55% olivine added, melt Fo = 0.8843, Kd = 0.3167.
- 10.59% olivine added, melt Fo = 0.8844, Kd = 0.3168.
- 10.63% olivine added, melt Fo = 0.8845, Kd = 0.3169.
- 10.67% olivine added, melt Fo = 0.8846, Kd = 0.3170.
- 10.71% olivine added, melt Fo = 0.8847, Kd = 0.3170.
- 10.75% olivine added, melt Fo = 0.8848, Kd = 0.3171.
- 10.79% olivine added, melt Fo = 0.8849, Kd = 0.3172.
- 10.83% olivine added, melt Fo = 0.8850, Kd = 0.3173.
- 10.87% olivine added, melt Fo = 0.8851, Kd = 0.3173.
- 10.91% olivine added, melt Fo = 0.8852, Kd = 0.3174.
- 10.95% olivine added, melt Fo = 0.8853, Kd = 0.3175.
- 10.99% olivine added, melt Fo = 0.8854, Kd = 0.3176.
- 11.03% olivine added, melt Fo = 0.8855, Kd = 0.3176.
- 11.07% olivine added, melt Fo = 0.8856, Kd = 0.3177.
- 11.11% olivine added, melt Fo = 0.8857, Kd = 0.3178.
- 11.15% olivine added, melt Fo = 0.8858, Kd = 0.3179.
- 11.19% olivine added, melt Fo = 0.8859, Kd = 0.3179.
- 11.23% olivine added, melt Fo = 0.8860, Kd = 0.3180.
- 11.27% olivine added, melt Fo = 0.8861, Kd = 0.3181.
- 11.31% olivine added, melt Fo = 0.8862, Kd = 0.3182.
- 11.35% olivine added, melt Fo = 0.8863, Kd = 0.3182.
- 11.39% olivine added, melt Fo = 0.8864, Kd = 0.3183.
- 11.43% olivine added, melt Fo = 0.8865, Kd = 0.3184.
- 11.47% olivine added, melt Fo = 0.8866, Kd = 0.3185.
- 11.50% olivine added, melt Fo = 0.8867, Kd = 0.3185.
- 11.54% olivine added, melt Fo = 0.8868, Kd = 0.3186.
- 11.58% olivine added, melt Fo = 0.8869, Kd = 0.3187.
- 11.62% olivine added, melt Fo = 0.8870, Kd = 0.3188.
- 11.66% olivine added, melt Fo = 0.8871, Kd = 0.3188.
- 11.70% olivine added, melt Fo = 0.8872, Kd = 0.3189.
- 11.74% olivine added, melt Fo = 0.8873, Kd = 0.3190.
- 11.78% olivine added, melt Fo = 0.8874, Kd = 0.3191.
- 11.82% olivine added, melt Fo = 0.8875, Kd = 0.3191.
- 11.86% olivine added, melt Fo = 0.8876, Kd = 0.3192.
- 11.89% olivine added, melt Fo = 0.8877, Kd = 0.3193.
- 11.93% olivine added, melt Fo = 0.8878, Kd = 0.3193.
- 11.97% olivine added, melt Fo = 0.8879, Kd = 0.3194.
- 12.01% olivine added, melt Fo = 0.8880, Kd = 0.3195.
- 12.05% olivine added, melt Fo = 0.8881, Kd = 0.3196.
- 12.09% olivine added, melt Fo = 0.8882, Kd = 0.3196.
- 12.13% olivine added, melt Fo = 0.8883, Kd = 0.3197.
- 12.17% olivine added, melt Fo = 0.8884, Kd = 0.3198.
- 12.20% olivine added, melt Fo = 0.8885, Kd = 0.3199.
- 12.24% olivine added, melt Fo = 0.8886, Kd = 0.3199.
- 12.28% olivine added, melt Fo = 0.8887, Kd = 0.3200.
- 12.32% olivine added, melt Fo = 0.8888, Kd = 0.3201.
- 12.36% olivine added, melt Fo = 0.8889, Kd = 0.3202.
- 12.40% olivine added, melt Fo = 0.8890, Kd = 0.3202.
- 12.43% olivine added, melt Fo = 0.8891, Kd = 0.3203.
- 12.47% olivine added, melt Fo = 0.8892, Kd = 0.3204.
- 12.51% olivine added, melt Fo = 0.8893, Kd = 0.3204.
- 12.55% olivine added, melt Fo = 0.8894, Kd = 0.3205.
- 12.59% olivine added, melt Fo = 0.8894, Kd = 0.3206.
- 12.63% olivine added, melt Fo = 0.8895, Kd = 0.3207.
- 12.66% olivine added, melt Fo = 0.8896, Kd = 0.3207.
- 12.70% olivine added, melt Fo = 0.8897, Kd = 0.3208.
- 12.74% olivine added, melt Fo = 0.8898, Kd = 0.3209.
- 12.78% olivine added, melt Fo = 0.8899, Kd = 0.3210.
- 12.82% olivine added, melt Fo = 0.8900, Kd = 0.3210.
- 12.85% olivine added, melt Fo = 0.8901, Kd = 0.3211.
- 12.89% olivine added, melt Fo = 0.8902, Kd = 0.3212.
- 12.93% olivine added, melt Fo = 0.8903, Kd = 0.3213.
- 12.97% olivine added, melt Fo = 0.8904, Kd = 0.3213.
- 13.01% olivine added, melt Fo = 0.8905, Kd = 0.3214.
- 13.04% olivine added, melt Fo = 0.8906, Kd = 0.3215.
- 13.08% olivine added, melt Fo = 0.8907, Kd = 0.3215.
- 13.12% olivine added, melt Fo = 0.8907, Kd = 0.3216.
- 13.16% olivine added, melt Fo = 0.8908, Kd = 0.3217.
- 13.19% olivine added, melt Fo = 0.8909, Kd = 0.3218.
- 13.23% olivine added, melt Fo = 0.8910, Kd = 0.3218.
- 13.27% olivine added, melt Fo = 0.8911, Kd = 0.3219.
- 13.31% olivine added, melt Fo = 0.8912, Kd = 0.3220.
- 13.34% olivine added, melt Fo = 0.8913, Kd = 0.3221.
- 13.38% olivine added, melt Fo = 0.8914, Kd = 0.3221.
- 13.42% olivine added, melt Fo = 0.8915, Kd = 0.3222.
- 13.46% olivine added, melt Fo = 0.8916, Kd = 0.3223.
- 13.49% olivine added, melt Fo = 0.8916, Kd = 0.3223.
- 13.53% olivine added, melt Fo = 0.8917, Kd = 0.3224.
- 13.57% olivine added, melt Fo = 0.8918, Kd = 0.3225.
- 13.61% olivine added, melt Fo = 0.8919, Kd = 0.3226.
- 13.64% olivine added, melt Fo = 0.8920, Kd = 0.3226.
- 13.68% olivine added, melt Fo = 0.8921, Kd = 0.3227.
- 13.72% olivine added, melt Fo = 0.8922, Kd = 0.3228.
- 13.76% olivine added, melt Fo = 0.8923, Kd = 0.3229.
- 13.79% olivine added, melt Fo = 0.8924, Kd = 0.3229.
- 13.83% olivine added, melt Fo = 0.8924, Kd = 0.3230.
- 13.87% olivine added, melt Fo = 0.8925, Kd = 0.3231.
- 13.90% olivine added, melt Fo = 0.8926, Kd = 0.3231.
- 13.94% olivine added, melt Fo = 0.8927, Kd = 0.3232.
- 13.98% olivine added, melt Fo = 0.8928, Kd = 0.3233.
- 14.02% olivine added, melt Fo = 0.8929, Kd = 0.3234.
- 14.05% olivine added, melt Fo = 0.8930, Kd = 0.3234.
- 14.09% olivine added, melt Fo = 0.8931, Kd = 0.3235.
- 14.13% olivine added, melt Fo = 0.8931, Kd = 0.3236.
- 14.16% olivine added, melt Fo = 0.8932, Kd = 0.3236.
- 14.20% olivine added, melt Fo = 0.8933, Kd = 0.3237.
- 14.24% olivine added, melt Fo = 0.8934, Kd = 0.3238.
- 14.27% olivine added, melt Fo = 0.8935, Kd = 0.3239.
- 14.31% olivine added, melt Fo = 0.8936, Kd = 0.3239.
- 14.35% olivine added, melt Fo = 0.8937, Kd = 0.3240.
- 14.38% olivine added, melt Fo = 0.8937, Kd = 0.3241.
- 14.42% olivine added, melt Fo = 0.8938, Kd = 0.3241.
- 14.46% olivine added, melt Fo = 0.8939, Kd = 0.3242.
- 14.49% olivine added, melt Fo = 0.8940, Kd = 0.3243.
- 14.53% olivine added, melt Fo = 0.8941, Kd = 0.3244.
- 14.57% olivine added, melt Fo = 0.8942, Kd = 0.3244.
- 14.60% olivine added, melt Fo = 0.8943, Kd = 0.3245.
- 14.64% olivine added, melt Fo = 0.8943, Kd = 0.3246.
- 14.68% olivine added, melt Fo = 0.8944, Kd = 0.3246.
- 14.71% olivine added, melt Fo = 0.8945, Kd = 0.3247.
- 14.75% olivine added, melt Fo = 0.8946, Kd = 0.3248.
- 14.78% olivine added, melt Fo = 0.8947, Kd = 0.3249.
- 14.82% olivine added, melt Fo = 0.8948, Kd = 0.3249.
- 14.86% olivine added, melt Fo = 0.8948, Kd = 0.3250.
- 14.89% olivine added, melt Fo = 0.8949, Kd = 0.3251.
- 14.93% olivine added, melt Fo = 0.8950, Kd = 0.3252.
- 14.97% olivine added, melt Fo = 0.8951, Kd = 0.3252.
- 15.00% olivine added, melt Fo = 0.8952, Kd = 0.3253.
- 15.04% olivine added, melt Fo = 0.8953, Kd = 0.3254.
- 15.07% olivine added, melt Fo = 0.8953, Kd = 0.3254.
- 15.11% olivine added, melt Fo = 0.8954, Kd = 0.3255.
- 15.15% olivine added, melt Fo = 0.8955, Kd = 0.3256.
- 15.18% olivine added, melt Fo = 0.8956, Kd = 0.3256.
- 15.22% olivine added, melt Fo = 0.8957, Kd = 0.3257.
- 15.25% olivine added, melt Fo = 0.8957, Kd = 0.3258.
- 15.29% olivine added, melt Fo = 0.8958, Kd = 0.3259.
- 15.33% olivine added, melt Fo = 0.8959, Kd = 0.3259.
- 15.36% olivine added, melt Fo = 0.8960, Kd = 0.3260.
- 15.40% olivine added, melt Fo = 0.8961, Kd = 0.3261.
- 15.43% olivine added, melt Fo = 0.8961, Kd = 0.3261.
- 15.47% olivine added, melt Fo = 0.8962, Kd = 0.3262.
- 15.50% olivine added, melt Fo = 0.8963, Kd = 0.3263.
- 15.54% olivine added, melt Fo = 0.8964, Kd = 0.3264.
- 15.58% olivine added, melt Fo = 0.8965, Kd = 0.3264.
- 15.61% olivine added, melt Fo = 0.8965, Kd = 0.3265.
- 15.65% olivine added, melt Fo = 0.8966, Kd = 0.3266.
- 15.68% olivine added, melt Fo = 0.8967, Kd = 0.3266.
- 15.72% olivine added, melt Fo = 0.8968, Kd = 0.3267.
- 15.75% olivine added, melt Fo = 0.8969, Kd = 0.3268.
- 15.79% olivine added, melt Fo = 0.8969, Kd = 0.3269.
- 15.82% olivine added, melt Fo = 0.8970, Kd = 0.3269.
- 15.86% olivine added, melt Fo = 0.8971, Kd = 0.3270.
- 15.90% olivine added, melt Fo = 0.8972, Kd = 0.3271.
- 15.93% olivine added, melt Fo = 0.8973, Kd = 0.3271.
- 15.97% olivine added, melt Fo = 0.8973, Kd = 0.3272.
- 16.00% olivine added, melt Fo = 0.8974, Kd = 0.3273.
- 16.04% olivine added, melt Fo = 0.8975, Kd = 0.3273.
- 16.07% olivine added, melt Fo = 0.8976, Kd = 0.3274.
- 16.11% olivine added, melt Fo = 0.8977, Kd = 0.3275.
- 16.14% olivine added, melt Fo = 0.8977, Kd = 0.3276.
- 16.18% olivine added, melt Fo = 0.8978, Kd = 0.3276.
- 16.21% olivine added, melt Fo = 0.8979, Kd = 0.3277.
- 16.25% olivine added, melt Fo = 0.8980, Kd = 0.3278.
- 16.28% olivine added, melt Fo = 0.8980, Kd = 0.3278.
- 16.32% olivine added, melt Fo = 0.8981, Kd = 0.3279.
- 16.35% olivine added, melt Fo = 0.8982, Kd = 0.3280.
- 16.39% olivine added, melt Fo = 0.8983, Kd = 0.3281.
- 16.42% olivine added, melt Fo = 0.8983, Kd = 0.3281.
- 16.46% olivine added, melt Fo = 0.8984, Kd = 0.3282.
- 16.49% olivine added, melt Fo = 0.8985, Kd = 0.3283.
- 16.53% olivine added, melt Fo = 0.8986, Kd = 0.3283.
- 16.56% olivine added, melt Fo = 0.8987, Kd = 0.3284.
- 16.60% olivine added, melt Fo = 0.8987, Kd = 0.3285.
- 16.63% olivine added, melt Fo = 0.8988, Kd = 0.3285.
- 16.67% olivine added, melt Fo = 0.8989, Kd = 0.3286.
- 16.70% olivine added, melt Fo = 0.8990, Kd = 0.3287.
- 16.74% olivine added, melt Fo = 0.8990, Kd = 0.3288.
- 16.77% olivine added, melt Fo = 0.8991, Kd = 0.3288.
- 16.81% olivine added, melt Fo = 0.8992, Kd = 0.3289.
- 16.84% olivine added, melt Fo = 0.8993, Kd = 0.3290.
- 16.87% olivine added, melt Fo = 0.8993, Kd = 0.3290.
- 16.91% olivine added, melt Fo = 0.8994, Kd = 0.3291.
- 16.94% olivine added, melt Fo = 0.8995, Kd = 0.3292.
- 16.98% olivine added, melt Fo = 0.8996, Kd = 0.3292.
- 17.01% olivine added, melt Fo = 0.8996, Kd = 0.3293.
- 17.05% olivine added, melt Fo = 0.8997, Kd = 0.3294.
- 17.08% olivine added, melt Fo = 0.8998, Kd = 0.3294.
- 17.12% olivine added, melt Fo = 0.8999, Kd = 0.3295.
P P_err T T_err Fit_Tp
0 2.069507 0.24 1370.081495 39.0 True
/home/mcnab/Melting/meltPT/meltPT/parse.py:79: UserWarning: Input csv does not contain a Fe2O3 column: we will try to fill it for you, or set it to zero.
warnings.warn(message)
/home/mcnab/Melting/meltPT/meltPT/parse.py:79: UserWarning: Input csv does not contain a Cr2O3 column: we will try to fill it for you, or set it to zero.
warnings.warn(message)
/home/mcnab/Melting/meltPT/meltPT/parse.py:79: UserWarning: Input csv does not contain a NiO column: we will try to fill it for you, or set it to zero.
warnings.warn(message)
/home/mcnab/Melting/meltPT/meltPT/parse.py:79: UserWarning: Input csv does not contain a CoO column: we will try to fill it for you, or set it to zero.
warnings.warn(message)
/home/mcnab/Melting/meltPT/meltPT/parse.py:79: UserWarning: Input csv does not contain a CO2 column: we will try to fill it for you, or set it to zero.
warnings.warn(message)
/home/mcnab/Melting/meltPT/meltPT/parse.py:79: UserWarning: Input csv does not contain a FeO_tot column: we will try to fill it for you, or set it to zero.
warnings.warn(message)
Plotting
Now let’s make a nice plot of our result!
[14]:
# Initialise seperate plots for the fixed and variable Kd axes.
fig, axs = plt.subplots(1, 2, sharex=True, sharey=True, figsize=(14,5))
# Set up pressure array.
P = np.arange(1., 3.5, 0.01)
# Plot the solidus.
axs[0].plot(lz.TSolidus(P), P, c="0.75", label="Solidus")
axs[1].plot(lz.TSolidus(P), P, c="0.75", label="Solidus")
# Plot an adiabat corresponding to the best-fitting potential temperature
adiabat_label = r"Adiabat: $T_p$ = %i $^{\circ}$C" % s.individual_potential_temperatures.iloc[0]['Tp']
axs[0].plot(
mantle.adiabat(
P,
s.individual_potential_temperatures.iloc[0]['Tp']),
P, ":", label=adiabat_label)
adiabat_label = r"Adiabat: $T_p$ = %i $^{\circ}$C" % s_varKd.individual_potential_temperatures.iloc[0]['Tp']
axs[1].plot(
mantle.adiabat(
P,
s_varKd.individual_potential_temperatures.iloc[0]['Tp']),
P, ":", label=adiabat_label)
# Plot melt path corresponding to best-fitting potential temperature
melt_label = r"Melting path: $T_p$ = %i $^{\circ}$C" % s.individual_potential_temperatures.iloc[0]['Tp']
axs[0].plot(
s.individual_potential_temperatures.iloc[0].path.T,
s.individual_potential_temperatures.iloc[0].path.P,
label=melt_label)
melt_label = r"Melting path: $T_p$ = %i $^{\circ}$C" % s_varKd.individual_potential_temperatures.iloc[0]['Tp']
axs[1].plot(
s_varKd.individual_potential_temperatures.iloc[0].path.T,
s_varKd.individual_potential_temperatures.iloc[0].path.P,
label=melt_label)
# Plot our sample!
sample_label = r"UT09DV04, $F$ = %.2f%%" % (s.individual_potential_temperatures.iloc[0]['F']*100.)
axs[0].plot(s.PT['T'], s.PT['P'], "o", label=sample_label)
sample_label = r"UT09DV04, $F$ = %.2f%%" % (s_varKd.individual_potential_temperatures.iloc[0]['F']*100.)
axs[1].plot(s_varKd.PT['T'], s_varKd.PT['P'], "o", label=sample_label)
# Do some formatting and reveal
for ax in axs:
ax.set_xlabel(r"Temperature [$^{\circ}$C]")
ax.set_xlim(1300., 1500.)
ax.set_ylim(1., 3.5)
ax.legend()
ax.invert_yaxis()
axs[0].set_ylabel(r"Pressure [GPa]")
plt.show()
Testing different thermobarometric schemes
meltPT includes several different thermobarometric schemes, which are simple to interchange. Here we will quickly show you how to do this. In Tutorial 4, we test out the different schemes more systematically, and in Tutorial 6, you can see how to implement your own scheme.
To see a list of the available options, we can look at the compute_presssure_temperature method’s doc string. Type the following into the prompt:
[15]:
s.compute_pressure_temperature?
This time, we will estimate melt CO2, for use with the Sun & Dasgupta (2020) thermometer. We will also miss out the verbose flag in backtracking.
[16]:
s = Suite("../Data/PF16_UT09DV04.csv", src_FeIII_totFe=0.17, param_co2=True)
b = BacktrackOlivineFractionation(Kd=0.3)
s.backtrack_compositions(backtracker=b)
/home/mcnab/Melting/meltPT/meltPT/parse.py:79: UserWarning: Input csv does not contain a Fe2O3 column: we will try to fill it for you, or set it to zero.
warnings.warn(message)
/home/mcnab/Melting/meltPT/meltPT/parse.py:79: UserWarning: Input csv does not contain a Cr2O3 column: we will try to fill it for you, or set it to zero.
warnings.warn(message)
/home/mcnab/Melting/meltPT/meltPT/parse.py:79: UserWarning: Input csv does not contain a NiO column: we will try to fill it for you, or set it to zero.
warnings.warn(message)
/home/mcnab/Melting/meltPT/meltPT/parse.py:79: UserWarning: Input csv does not contain a CoO column: we will try to fill it for you, or set it to zero.
warnings.warn(message)
/home/mcnab/Melting/meltPT/meltPT/parse.py:79: UserWarning: Input csv does not contain a CO2 column: we will try to fill it for you, or set it to zero.
warnings.warn(message)
/home/mcnab/Melting/meltPT/meltPT/parse.py:79: UserWarning: Input csv does not contain a FeO_tot column: we will try to fill it for you, or set it to zero.
warnings.warn(message)
First let’s define a list of the schemes we would like to use. We will take a subset for now.
[17]:
schemes = ["PF16", "L09", "P08", "BK21", "SD20"]
schemesT = ["B93", "P07_2", "P07_4", "HA15"]
Loop over the schemes saving the result in a separate list.
[18]:
PT = {}
T = {}
for scheme in schemes:
s.compute_pressure_temperature(method=scheme)
PT[scheme] = s.PT.copy()
for scheme in schemesT:
s.compute_temperature(method=scheme, P=PT['PF16']['P'])
T[scheme] = s.PT.copy()
Plot the results.
[19]:
plt.plot(lz.TSolidus(P), P, c="0.75", label="Solidus")
for scheme in schemes:
plt.errorbar(float(PT[scheme]['T']), float(PT[scheme]['P']), xerr=float(PT[scheme]['T_err']), yerr=float(PT[scheme]['P_err']), label=scheme, marker="o")
for scheme in schemesT:
plt.errorbar(float(T[scheme]['T']), float(T[scheme]['P']), xerr=float(T[scheme]['T_err']), label=scheme, marker="^")
plt.legend()
plt.xlim(1300., 1550.)
plt.ylim(1., 4.5)
plt.xlabel(r"Temperature [$^{\circ}$C]")
plt.ylabel(r"Pressure [GPa]")
plt.gca().invert_yaxis()
plt.show()
