P-wave and S-wave diagrams
image credit: http://www.physics.uiowa.edu/adventure/spr_2006/feb_18-06.html
P-waves are faster in solids than in liquids. S-waves cannot travel through liquids at all. When a body of rock is partially molten, S-waves can travel through but are slowed drastically. Based on how much the types of waves are slowed, we can determine the elastic moduli of the rock. Elastic moduli are measures of how much a wave is slowed that are changed by density and phase of the rock through which the waves travel. Using elastic moduli, geophysicists can infer the melt volume fraction, which measures how much of a rock is liquid versus solid.
At a fixed melt volume fraction, grain shape can change the elastic moduli. The shape of an area of melt between grains can be described by its dihedral angle.
Dihedral angle of a grain junction
(German, Suri, and Pavan 2008)
A new computational model that I helped Dr. Saswata Hier-Majumder develop at the University of Maryland creates idealized cross-sections of a single channel of melt, starting with the physics of the area. The paper describing the results was published in Earth and Planetary Sciences Letters in 2010 (Hier-Majumder and Abbott, 2010). The full text may be found at http://www.geol.umd.edu/~saswata/pubs.shtml for UMD students and faculty. To sum it up succinctly, the dihedral angle can be predicted by the physical model, and the dihedral angle can be used to predict how the arrangement and shape of grains affects the elastic moduli. There are a wide range of melt volume fractions possible for one set of elastic moduli, but knowing the shape allows us to eliminate much of the uncertainty.
Image of partially molten rock produced by the Laboratory for Rock Physics by Dr. Zhu
image credit: http://www.geol.umd.edu/~wzhu/
My current research is changing the code to represent a realistic body of rock instead of an idealized unit cell. This lets us take the relationship between shape, melt volume fraction, and elastic moduli out of the world of theoretical physics and into real-world scenarios. Recent advances in imaging by the University of Maryland's own Dr. Wen-lu Zhu provide an experimental result. Comparing the model to the experiments and to data from seismic studies will allow us to know if the model is doing a good job of predicting shape.
When we have the model matching experimental and real-world data, we can provide very good predictive information about melt volume, melt fraction, and microstructure shape in any area of the earth that has partially molten rock. The shape of the melt channels can also be used to determine melt focusing, which is to say the path along which melt travels most easily. In short, if the model meets our expectations we can take seismogram readings and say how much melt is in a rock and where it will go.
For a more in-depth look into the microstructure of partially molten materials, please peruse the references below:
German, RM, P Suri, and SJ Park (2008) Review: Liquid Phase Sintering. Journal of Materials Science 44:1, doi: 10.1007/s10853-008-3008-0.
Hier-Majumder, S and M Abbott (2010) The Influence of Dihedral Angle on Seismic Velocities of Partially Molten Rocks. Earth and Planetary Sciences Letters 299, doi: 10.1016/j.epsl.2010.08.007.
Yoshino, T, Y Takei, DA Wark, and B Watson (2005) Grain Boundary Wetness of Texturally Equilibriated Rocks, With Implications for Seismic Properties of the Upper Mantle. Journal of Geophysical Research 110, doi: 10.1029/2004JB003544.
