Squeezin' A Rock Around d' Clock

Changes in temperature, pressure, and stress affect fluid transport properties such as porosity and permeability. The response to this applied stress or change in pore pressure is seen as either a compaction or dilation of pore space. It is important to understand rock deformation processes because of the extremely relevant geological applications, which include the oil/gas exploration and groundwater industries. Many experiments have been conducted on sandstones and granites, however, there is a greater need for the understanding of calcite deformation. I am observing the way in which Indiana Limestone responds to various pressure and temperature conditions. Indiana Limestone is an excellent specimen in which to observe calcite deformation because it is relatively homogeneous, comprising more than 97% calcite.

Deformation can either be elastic, where the material returns to its original shape after the applied load has been removed, or inelastic, where deformation is non-recoverable. Inelastic deformation is further divided into brittle and plastic deformation. Brittle deformation is seen as fractures and plastic deformation is seen via crystal plasticity, in which one sees either dislocation slip or twinning. Previous deformation experiments have been conducted on Indiana Limestone at room temperature. Stress-strain curves (Vajdova et al., 2004) show the transition from brittle to ductile deformation; because crystal plasticity, part of the plastic deformation mechanism, is temperature dependent, I am interested in observing the effect of temperature. Additionally, the Vajdova experiments were conducted in unsaturated cores. My experiments include cores that are saturated with distilled water, so there will be an added comparison of the effect that water has on deformation.

I hypothesize that crystal plasticity behavior in calcite will affect the bulk deformation behavior as well as transport properties. The effect of dislocation slip and twinning on transport properties can be seen in appreciable amounts. I additionally hypothesize that as temperature increases, the effects of crystal plasticity will be more pronounced. This is because as rocks increase in temperature, they increasingly behave as a plastic. Current experiments follow the Vajdova data accordingly.

Further reading: Vajdova et al., 2004

Fig. 1: Prepared sample, pre-deformation. The core is jacketed with copper and has strain gages attached.

Fig. 2: Post-deformation twinning comparison between a sample that has experienced an effective pressure of 10 MPa and one that has undergone 50 MPa. The twinning is much more intense in the 50 MPa sample, leading me to believe that this twinning is most definitely deformation-induced (not natural).

Leaf vein density: The angiosperm advantage

Angiosperms are flowering plants that bear fruits and reproduce with seeds. Although angiosperms are the most diverse group of land plants today, they appear in the fossil record only 140 million years ago, during the Cretaceous Period. Since then, flowering plants have become more diverse and widely spread, transforming global ecology.

Scientists attribute the global spread of angiosperms to their increased ability to photosynthesize, or create sugars within the leaf. This unrivalled photosynthetic capacity is facilitated in flowering plants by an increased density of veins, which provide the plumbing within a leaf. Leaf vein density is projected to have increased along with angiosperm diversity throughout the fossil record. I am studying the increase in leaf vein density of the sycamore family since the Cretaceous, comparing the carbon isotope ratios of fossil and modern sycamores. Through this comparison, I will determine whether the difference in carbon isotope ratios is related to a difference in leaf vein density, and correspondingly water use within the leaf.

Leaf veins, as seen in this image of Platanus occidentalis, have evolved since the Cretaceous. The increase in leaf vein density is suggested to have enabled a major increase in the photosynthetic capacity of flowering plants. [Image source: OnlinePlantGuide]

Photosynthesis is the process by which plants use energy from sunlight to convert carbon dioxide and water into sugar and oxygen. This process occurs within the leaf, which can control how widely the stomata are open. Stomata, pore-like structures in a leaf, allow for gases to be exchanged with the atmosphere. When these pores are open, carbon dioxide can enter the leaf to facilitate photosynthesis, and oxygen is able to leave. As a downside, the leaf loses

water vapor when these pores are open. Leaf veins, which are essentially the plumbing of the leaf, provide water from the stem of the plant. The angiosperm advantage lies in the evolution of a greater density of leaf veins, allowing for more water to get to the leaf, the stomata to be open longer, and for there to be more photosynthetic activity.

The anatomy of a leaf, showing the stoma on the bottom of the diagram, which the plant can open or close to let carbon dioxide in or let oxygen out. [Image source: H. McKenna]

With more widely-opened stomata, we will expect to find a lighter isotopic composition within a leaf. For my senior thesis, I am comparing carbon isotope ratios determined from fossil and modern specimens of angiosperms to the ratios found from fossil and modern ferns. Through this comparison, we will determine if the increased leaf vein density in flowering plants correlates to differences in isotopic composition.

Further reading:

Brodribb, T.J., T.S. Feild, and G.J. Jordan, 2007, Leaf Maximum Photosynthetic Rate and Venation Are Linked by Hydraulics. Plant Physiology, 144(4): 1890-1898.

Boyce, C.K., T.J. Brodribb, T.S. Feild, and M.A. Zwieniecki, 2009, Angiosperm leaf vein evolution was physiologically and environmentally transformative. Proceedings of the Royal Society B, 276: 1771-1776.

Ice, Ice, Baby! Rifting on the Icy Satellites of the Outer Solar System

The Jovian moons of Europa and Ganymede, and the Saturnian moon Enceladus have all been shown to have prominent extensional features analogous to rifts on Earth.  For my senior thesis, I am developing numerical models in order to better understand the geodynamics of how these rifts form, and in particular, how the emplacement of magmatic dikes can affect their evolution.

“Icy satellites” is the term we use to describe most of the collected moons of the large, gaseous Jovian planets of the outer solar system (Jupiter, Saturn, Uranus and Neptune).  As the name suggests, these moons are composed primarily of ices (water ice, as well as hydrocarbon ices like ethane or methane), but are cold enough that these ices behave more like rocks here on Earth.  The mean surface temperature on Enceladus is only about 75 Kelvin, or -325 degrees Fahrenheit.  These moons range in size from bigger than planets (Ganymede is larger than Mercury) to smaller than countries (Enceladus is a mere 500 km across - smaller than Colorado).  It has also been hypothesized that many of these moons have subsurface oceans beneath their icy crusts, which could potentially be refuges for extra-terrestrial life.

Three icy satellites, along with the Earth and Moon, to scale.

Despite these geologic differences, a number of features on these worlds are identified as similar to terrestrial rifts (such as the East African Rift, or the Basin and Range in Western North America).  These rifts have been categorized based upon observed morphology as either narrow rifts with localized extension or wide rifts with extension over a larger region.  Although past geodynamic models have been able describe the formation of these rifts, they require the use of unusual initial conditions (surface temperature, ice crust thickness, etc.) that conflict with satellite observations and other geodynamic models.  Our hypothesis is that by including previously ignored effects of magmatic dikes into these geodynamic models, we will be able to rectify this conflict between model predictions and observable parameters.

Examples of the different types of rifts on the different icy satellites, along with hypothetical geologic cross sections across the rifts, displaying the different observed morphology, and hypothesized structure.

Dikes are vertical, sheet-like magmatic intrusions.  Dikes and other volcanic processes on these moons are driven by cold liquid water and hydrocarbons (as opposed to molten rock, here on Earth), in a process called “cryovolcanism.”  Dikes have been inferred to exist at least on Enceladus due to the observation of large water-ice plumes originating from rifts on the moon’s southern pole.

Cassini-Huygens image of water geysers erupting from the rifts on Enceladus.

This research can potentially provide further insight into the general processes of extension and rifting, in addition to further understanding of these strange alien worlds.

For more information about the geodynamics involved in my model, and general information on rifting on both Earth and these icy satellites, see the following two papers:

• Buck, W.R. (1991), Modes of continental lithospheric extension, J. Geophys. Res., 96 (B12), 20, 161-20, 178. (direct link)
• Nimmo, F. (2004), Dynamics of rifting and modes of extension on icy satellites, J. Geophys. Res., 109, E01003, doi: 10.1029/2003JE002168. (direct link)

-James T. Keane, 3/14/2011

Model Paints Picture of Deep Earth's Mineral Grains

Earthquakes create seismic waves of two main types: P-waves and S-waves.

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

image credit: http://www.springerimages.com/Images/Chemistry/1-10.1007_s10853-008-3008-0-7

(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.