Geophysical Continuum Modeling from Pore to Planetary Scales

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In this proposal, I lay out a plan to advance our knowledge of Earth’s internal state and the transport of fluids inside the Earth using numerical modeling of continuum physics. The length scales involved range from planetary scales (1000s of kms) to the scales of rock pores (microns). One planetary scale phenomenon involves the segregation of porosity into band structures in porous layers where the solid can deform like a very viscous liquid when the system is subjected to an externally imposed shear. These structures may exist in Earth’s upper mantle and may provide a means for mantle melts to be extracted efficiently at mid-ocean ridges to form new oceanic crust. These bands, which are seen in laboratory experiments of sheared partially molten rocks, may also reduce the effective viscosity of Earth’s upper mantle and may therefore even be important for explaining the existence of plate tectonics on Earth. In this proposal, I describe modeling efforts to better understand the dynamics of these bands and to determine their importance for mantle melt transport and mantle dynamics. The thermal and compositional effects of melting and solidification will also be included in these studies. Also at the planetary scale, it is very important to understand the process of thermal convection that is taking place in Earth’s mantle. Mantle convection is the engine that drives plate tectonics and is responsible for the formation of Earth’s crust. Although Earth’s mantle is a solid, on long time scales it flows like a liquid. I am proposing to carry out fluid-mechanical simulations of convection with surface plates to better understand Earth’s thermal state and its heat budget over time. One effect that will be modeled will be a low viscosity layer beneath the plates which may be caused by porosity bands. I also plan to model the extraction of melt from Earth’s interior by coupling a mantle convection model with a model of porosity band formation. At the pore scale, it is crucial to understand how processes like fluid and electrical flow occur in order that we can understand processes on much larger length scales like the transport of melt in Earth’s mantle. I plan to simulate continuum phenomena like fluid flows through the pore spaces of rocks imaged with advanced imaging techniques like X-ray tomography. Using digital representations of rocks, my students and I will simulate fluid and electrical flows through the pore pathways in order to characterize the permeability and electrical formation factor. Also, we intend to incorporate effects of multiphase flows and of chemical reactions between the fluid and pore walls. These effects are important factors in, for instance, oil recovery and mineralization that may be of economic importance. Additionally, we intend to simulate the deformation of the combined pore fluid and rock matrix in order to investigate the effective elasticity and viscosity of the rock and pore fluid combination. At an intermediate (cm length) scale, I am proposing to carry out simulations related to the formation of splash-form tektites. These rocks represent frozen fluid drops that result from the splash of molten silicate rock following a large Earth impact. My students and I will couple a thermal model to describe the cooling of the rock with a model of deformation that includes the effects of rotation and surface tension in order to better understand the final shapes of these objects. I also propose to analyze high resolution images of their surfaces to study surface features like bubble pits and schlieren to gain insight into the deformation histories of these enigmatic rocks. By examining these phenomena at a range of length scales, we will better understand Earth and its evolution.