Loading Solidus Temperature Profiles¶

This example demonstrates how to load predefined solidus temperature profiles and create composite profiles spanning different depth ranges.

Background¶

The solidus defines the temperature at which rock begins to melt at a given pressure (depth). Different experimental studies have constrained solidus temperatures for different depth ranges: Hirschmann (2000) for the upper mantle, Andrault et al. (2011) and Fiquet et al. (2010) for the deep mantle. These solidus profiles are essential inputs for anelastic velocity corrections in geodynamic modelling.

This example¶

We demonstrate how to:

1. Load predefined solidus profiles from gdrift
2. Combine profiles to create a composite solidus spanning the full mantle
3. Visualise and compare different solidus models

In [1]:

import numpy as np
import gdrift
from gdrift.profile import SplineProfile

import numpy as np import gdrift from gdrift.profile import SplineProfile

Loading Predefined Solidus Models¶

gdrift provides several experimentally-derived solidus profiles as HDF5 datasets. We load them using RadialEarthModelFromFile and access the solidus temperature profile via the get_profile() method.

In [2]:

# Fiquet et al. (2010) solidus for the deep mantle
fiquet_solidus = gdrift.RadialEarthModelFromFile(
    model_name="1d_solidus_Fiquet_et_al_2010_SCIENCE",
    description="Fiquet et al 2010 Science")

# Andrault et al. (2011) solidus for the lower mantle
andrault_solidus = gdrift.RadialEarthModelFromFile(
    model_name="1d_solidus_Andrault_et_al_2011_EPSL",
    description="Andrault et al 2011 EPSL")

# Hirschmann (2000) solidus for the upper mantle (computed from pressure)
hirsch_solidus = gdrift.HirschmannSolidus()

# Fiquet et al. (2010) solidus for the deep mantle fiquet_solidus = gdrift.RadialEarthModelFromFile( model_name="1d_solidus_Fiquet_et_al_2010_SCIENCE", description="Fiquet et al 2010 Science") # Andrault et al. (2011) solidus for the lower mantle andrault_solidus = gdrift.RadialEarthModelFromFile( model_name="1d_solidus_Andrault_et_al_2011_EPSL", description="Andrault et al 2011 EPSL") # Hirschmann (2000) solidus for the upper mantle (computed from pressure) hirsch_solidus = gdrift.HirschmannSolidus()

1d_solidus_Fiquet_et_al_2010_SCIENCE:   0%|          | 0.00/6.65k [00:00<?, ?B/s]

1d_solidus_Fiquet_et_al_2010_SCIENCE: 100%|██████████| 6.65k/6.65k [00:00<00:00, 14.1kB/s]

1d_solidus_Fiquet_et_al_2010_SCIENCE: 100%|██████████| 6.65k/6.65k [00:00<00:00, 14.0kB/s]

1d_solidus_Andrault_et_al_2011_EPSL:   0%|          | 0.00/7.30k [00:00<?, ?B/s]

1d_solidus_Andrault_et_al_2011_EPSL: 100%|██████████| 7.30k/7.30k [00:00<00:00, 15.5kB/s]

1d_solidus_Andrault_et_al_2011_EPSL: 100%|██████████| 7.30k/7.30k [00:00<00:00, 15.5kB/s]

Let's examine the depth ranges of each model:

In [3]:

for name, model in [("Hirschmann", hirsch_solidus),
                    ("Andrault", andrault_solidus),
                    ("Fiquet", fiquet_solidus)]:
    profile = model.get_profile("solidus temperature")
    d_min, d_max = profile.min_max_depth()
    print(f"{name}: {d_min / 1e3:.0f} km to {d_max / 1e3:.0f} km")

for name, model in [("Hirschmann", hirsch_solidus), ("Andrault", andrault_solidus), ("Fiquet", fiquet_solidus)]: profile = model.get_profile("solidus temperature") d_min, d_max = profile.min_max_depth() print(f"{name}: {d_min / 1e3:.0f} km to {d_max / 1e3:.0f} km")

1d_prem:   0%|          | 0.00/26.2k [00:00<?, ?B/s]

1d_prem: 100%|██████████| 26.2k/26.2k [00:00<00:00, 34.5kB/s]

1d_prem: 100%|██████████| 26.2k/26.2k [00:00<00:00, 34.5kB/s]

Hirschmann: 0 km to 304 km
Andrault: 389 km to 2945 km
Fiquet: 832 km to 2908 km

Creating a Composite Solidus¶

Different solidus models are valid over different depth ranges. A common approach is to combine the Hirschmann solidus (upper mantle) with a deep mantle solidus (Andrault or Fiquet) to create a continuous profile.

Here we combine Hirschmann (upper mantle) with Andrault (lower mantle):

In [4]:

my_depths = []
my_solidus = []

for solidus_model in [
    hirsch_solidus.get_profile("solidus temperature"),
    andrault_solidus.get_profile("solidus temperature"),
]:
    d_min, d_max = solidus_model.min_max_depth()
    dpths = np.arange(d_min, d_max, 10e3)
    my_depths.extend(dpths)
    my_solidus.extend(solidus_model.at_depth(dpths))

# Create a new SplineProfile from the combined data
ghelichkhan_et_al = SplineProfile(
    depth=np.asarray(my_depths),
    value=np.asarray(my_solidus),
    name="solidus temperature (Ghelichkhan et al 2021)")

d_min, d_max = ghelichkhan_et_al.min_max_depth()
print(f"Composite solidus spans: {d_min / 1e3:.0f} km to {d_max / 1e3:.0f} km")

my_depths = [] my_solidus = [] for solidus_model in [ hirsch_solidus.get_profile("solidus temperature"), andrault_solidus.get_profile("solidus temperature"), ]: d_min, d_max = solidus_model.min_max_depth() dpths = np.arange(d_min, d_max, 10e3) my_depths.extend(dpths) my_solidus.extend(solidus_model.at_depth(dpths)) # Create a new SplineProfile from the combined data ghelichkhan_et_al = SplineProfile( depth=np.asarray(my_depths), value=np.asarray(my_solidus), name="solidus temperature (Ghelichkhan et al 2021)") d_min, d_max = ghelichkhan_et_al.min_max_depth() print(f"Composite solidus spans: {d_min / 1e3:.0f} km to {d_max / 1e3:.0f} km")

Composite solidus spans: 0 km to 2939 km

Visualisation¶

We plot all four solidus profiles to compare them. The composite profile (Ghelichkhan et al.) shows the smooth transition between upper and lower mantle solidus temperatures.

In [5]:

active-ipynb

%matplotlib inline

%matplotlib inline

In [6]:

active-ipynb

import matplotlib.pyplot as plt

plt.close(1)
fig = plt.figure(num=1, figsize=(8, 6))
ax = fig.add_subplot(111)

for solidus_model, marker in zip(
        [andrault_solidus.get_profile("solidus temperature"),
         hirsch_solidus.get_profile("solidus temperature"),
         fiquet_solidus.get_profile("solidus temperature"),
         ghelichkhan_et_al],
        ["-", "-.", "--", ":"]):
    d_min, d_max = solidus_model.min_max_depth()
    dpths = np.arange(d_min, d_max, 10e3)
    # Use display_name for richer legend labels
    ax.plot(solidus_model.at_depth(dpths), dpths / 1e3,
            linestyle=marker, linewidth=2, label=solidus_model.display_name)

ax.grid(alpha=0.3)
ax.invert_yaxis()
ax.set_xlabel("Solidus Temperature [K]", fontsize=12)
ax.set_ylabel("Depth [km]", fontsize=12)
ax.legend(loc="lower left")
ax.set_title("Mantle Solidus Temperature Profiles")
plt.tight_layout()
plt.show()

import matplotlib.pyplot as plt plt.close(1) fig = plt.figure(num=1, figsize=(8, 6)) ax = fig.add_subplot(111) for solidus_model, marker in zip( [andrault_solidus.get_profile("solidus temperature"), hirsch_solidus.get_profile("solidus temperature"), fiquet_solidus.get_profile("solidus temperature"), ghelichkhan_et_al], ["-", "-.", "--", ":"]): d_min, d_max = solidus_model.min_max_depth() dpths = np.arange(d_min, d_max, 10e3) # Use display_name for richer legend labels ax.plot(solidus_model.at_depth(dpths), dpths / 1e3, linestyle=marker, linewidth=2, label=solidus_model.display_name) ax.grid(alpha=0.3) ax.invert_yaxis() ax.set_xlabel("Solidus Temperature [K]", fontsize=12) ax.set_ylabel("Depth [km]", fontsize=12) ax.legend(loc="lower left") ax.set_title("Mantle Solidus Temperature Profiles") plt.tight_layout() plt.show()

Summary¶

This example demonstrated how to:

• Load predefined solidus profiles using gdrift.RadialEarthModelFromFile
• Use the HirschmannSolidus model for upper mantle solidus temperatures
• Combine multiple profiles into a composite solidus using SplineProfile
• Query solidus temperature at arbitrary depths via profile.at_depth()

The solidus profiles loaded here can be used as inputs for anelastic velocity corrections (see the anelasticity example).