# MuMaP_fwd

## Royal Holloway University of London

This module contains classes and functions relevant to calculate the effect of melting on the elastic moduli and seismic wave velocities in partially molten rocks. To run the demonstrations, a working version of Python 2.7.12 or higher, numpy, and matplotlib libraries are required.

See the Wiki pages for detailed documentation. Scroll down for a quick start guide

## Quick start guide

• Extract the files
• Open a terminal or your preferred mode of running python and type in

python demo1.py

This should execute the file and create a plot.

Go to the Project wiki pages and work through the tutorials. Each tutorial is associated with a demo file. The in-line documentation within the source files is explained in detail in the wiki file. You can also cut and paste the following code snippets into your python terminal to get a quick sample of MuMaP_fwd.

### Example1:

Plot Vinet equation of state of MORB using parameters
from Guillot and Sator(2007), run demo2.py for more plots

``````from mumap_fwd import *
import matplotlib.pylab as plt
rho1=np.linspace(2800.0,4000.0)
melt1=Melt(melt_comp=2,rho=rho1)
melt1.Melt_EOS.Vinet()
plt.plot(melt1.Melt_EOS.P/1.0e9,melt1.Melt_EOS.rho)
plt.show()
``````

### Example 2:

Plot the Vs/V0 as a function of melt fraction. In this case
all the melt resides in films of aspect ratio 0.01. This uses the formulation
of Walsh, 1969

``````from mumap_fwd import*
import matplotlib.pylab as plt
phi=np.linspace(1.0e-3,0.15)
rock=Poroelasticity(phi=phi)
rock.Melt=Melt(rho=3200.0)
rock.film(aspect=0.01)
plt.plot(rock.meltfrac,rock.vs_over_v0)
plt.show()
``````

### Example 3:

Plot Vs/V0 as a function of melt fraction. In this case, the melt geometry
is calculated from von Bargen and Waff (1986) and the effective elastic
moduli are calculated following Hier-Majumder et al. (2014). Run demo4.py

``````from mumap_fwd import *
import matplotlib.pylab as plt
phi1=np.linspace(1.0e-3,0.15)
rock=Poroelasticity(phi=phi1)
rock.tube()
plt.plot(rock.meltfrac,rock.vs_over_v0)
plt.show()
``````

Use the tutorials to try out the different features of MuMap_fwd. The tutorial progress in order of difficulty. The files corresponding to tutorials are named as demox.py, where x is the tutorial number

## To cite MuMap_fwd:

Please cite these following papers which contain much of the material involved in MuMaP_fwd. Please also see the list of references for a full list of articles or databases used in writing this code.

• Saswata Hier-Majumder. (2017, November 2). MuMap_fwd-1.0 (Version 1.0). Zenodo. http://doi.org/10.5281/zenodo.1040971
• Hier-Majumder, S., Keel, E. B., & Courtier, A. M. (2014). The influence of temperature, bulk composition, and melting on the seismic signature of the low-velocity layer above the transition zone. Journal of Geophysical Research: Solid Earth, 119(2), 971–983. https://doi.org/10.1002/2013JB010314
• Hier-Majumder, S. (2008). Influence of contiguity on seismic velocities of partially molten aggregates. Journal of Geophysical Research, 113(B12), B12205. https://doi.org/10.1029/2008JB005662

## Brief description

Detailed description for each class is provided in the wiki pages.

EOS: Contains functions for equations of state for solids and melts. This class also contains the PREM model of Dziewonski and Anderson (1984). To initiate this class for a given material known values of some paramters need to be provided. In most cases, this class will be initiated from either the Solid or the Melt class, which contain default values for the parameters.

Solid: This class contains a number of variables and functions relating to the properties of the solid. All of the parameters are provided with a default value. See the docstring for more details. By default, this class uses the PREM model to evaluate the elastic properties corresponding to the depth parameter provided during instantiation.

Melt: This class contains physical paramters for calculating the EOS of the melt. It also defaults to a dihedral angle of 15 degrees. The choice of parameters for the EOS are set by the variable melt_comp. Please see the docstring for init for a full description of the currently available choices.

Poroelasticity: This class contains functions for calculating effective elastic properties for a given melt fraction and physical properties of the solid and the melt, contained in those classes. This class contains three choices of contiguity models, see the docstrings for more information. The default model is von Bargen and Waff, which allows for variation in the dihedral angle. Do not use this model for higher melt fractions.