Merge pull request #553 from bobmyhill/shearmod

add shear modulus example

Author: bobmyhill

examples/example_add_shear_modulus.py

@@ -0,0 +1,118 @@
+# This file is part of BurnMan - a thermoelastic and thermodynamic toolkit for
+# the Earth and Planetary Sciences
+# Copyright (C) 2012 - 2023 by the BurnMan team, released under the GNU
+# GPL v2 or later.
+
+
+"""
+
+example_add_shear_modulus
+-------------------------
+
+This example shows how to create a new equation of state derived
+from another in order to calculate something new. In this case, we
+seek to create an equation of state that builds on the Holland and
+Powell (2011) equation of state, adding calculations for the shear
+modulus as proposed by Hacker and Abers (2004).
+
+*Uses:*
+
+* :doc:`mineral_database`
+* :class:`burnman.Mineral`
+
+
+*Demonstrates:*
+
+* How to create a new equation of state and instantiate a mineral using it.
+* How to output thermoelastic properties from the new mineral object.
+
+"""
+from __future__ import absolute_import
+
+import numpy as np
+import matplotlib.pyplot as plt
+from copy import deepcopy
+
+from burnman import Mineral
+from burnman.minerals import HGP_2018_ds633
+from burnman.eos.hp import HP_TMT
+
+if __name__ == "__main__":
+    # First, we create a new class, derived from HP_TMT
+    # (the modified Tait equation of state derived by Holland and Powell, 2011).
+    # We overwrite just a single function; the one to calculate the shear modulus.
+    # Here we use the equations given by Hacker and Abers (2004).
+    class HP_TMT_shear(HP_TMT):
+        def shear_modulus(self, pressure, temperature, volume, params):
+            x = params["V_0"] / volume
+            phi = np.log(1.0 / x)
+            gamma = params["Gamma_0"]
+            f = 0.5 * (np.power(x, 2.0 / 3.0) - 1.0)
+            f2 = np.power(1.0 + 2.0 * f, 5.0 / 2.0)
+            G_T = params["shear_modulus_0"] * np.exp(-gamma * phi)
+            K_PT = self.isothermal_bulk_modulus(pressure, temperature, volume, params)
+            K_T = K_PT / ((1.0 - f * (5.0 - 3.0 * params["Kprime_0"])) * f2)
+            G = G_T * f2 * (1.0 - f * (5.0 - 3.0 * params["Gprime_0"] * K_T / G_T))
+            return G
+
+    # We want to create a forsterite object
+    # that uses this new equation of state. For this, we need values
+    # for the new parameters required by that equation of state.
+    # Here we create a dictionary with the values from Hacker and Abers (2004).
+    shear_params = {
+        "fo": {"shear_modulus_0": 81.6e9, "Gamma_0": 5.19, "Gprime_0": 1.82}
+    }
+
+    # One way to use the new equation of state is to first create a Mineral object
+    # from the existing forsterite class in HGP_2018_ds633, update the parameters
+    # and then use the set_method() method:
+    fo = HGP_2018_ds633.fo()
+    fo.params.update(shear_params["fo"])
+    fo.set_method(HP_TMT_shear)
+
+    # Now we can use the modified object:
+    P = 1.0e9
+    T = 500.0
+    fo.set_state(P, T)
+
+    # Print some values:
+    print(f"P: {P/1.e9:.2f} GPa, T: {T:.2f} K")
+
+    print("\nProperties from modified object:")
+    print(f"    Shear modulus: {fo.G/1.e9:.2f} GPa")
+    print(f"    V_p: {fo.v_p/1.e3:.2f} km/s, V_s: {fo.v_s/1.e3:.2f} km/s")
+
+    # This method works well if we only want one instantiation, but what if
+    # we want to create several? One way to do this is to define a new class
+    # and put the required steps into the initialisation function:
+
+    class fo_w_shear(Mineral):
+        def __init__(self):
+            tmp = HGP_2018_ds633.fo()
+            self.params = deepcopy(tmp.params)
+            name = self.params["name"]
+            self.params.update(shear_params[name])
+            Mineral.__init__(self)
+            self.set_method(HP_TMT_shear)
+
+    # Now we can create new object from the modified class
+    fo = fo_w_shear()
+    fo.set_state(P, T)
+
+    print("\nProperties from object created from modified class:")
+    print(f"    Shear modulus: {fo.G/1.e9:.2f} GPa")
+    print(f"    V_p: {fo.v_p/1.e3:.2f} km/s, V_s: {fo.v_s/1.e3:.2f} km/s")
+
+    # We can now do anything we like with this new mineral,
+    # like use the evaluate method:
+    pressures = np.linspace(1.0e5, 10.0e9, 101)
+    T = 1500.0
+    temperatures = np.ones_like(pressures) * T
+
+    v_p, v_s = fo.evaluate(["v_p", "v_s"], pressures, temperatures)
+    plt.plot(pressures / 1.0e9, v_p / 1.0e3, label=f"$V_P$ for {fo.name} at {T} K")
+    plt.plot(pressures / 1.0e9, v_s / 1.0e3, label=f"$V_S$ for {fo.name} at {T} K")
+    plt.xlabel("Pressure (GPa)")
+    plt.ylabel("Velocities (km/s)")
+    plt.legend()
+    plt.show()

misc/ref/example_add_shear_modulus.py.out

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+P: 1.00 GPa, T: 500.00 K
+
+Properties from modified object:
+    Shear modulus: 82.52 GPa
+    V_p: 8.66 km/s, V_s: 5.06 km/s
+
+Properties from object created from modified class:
+    Shear modulus: 82.52 GPa
+    V_p: 8.66 km/s, V_s: 5.06 km/s