Evolution of attached and detached slabs and their associated mantle dynamics

Over the two years of the NASA grant, this project has produced a significant amount of research results related to the plate subduction process and the surface crustal deformation at convergent boundaries (i.e., above subduction zones). While some research objectives are completely accomplished, other research tasks remain active and continue to be investigated at present. A steady state analytic thermal model for subducting slabs was used to examine the torques acting on a descending slab. It is found that gravitational torque vanishes when a slab is dipping either vertically or horizontally, unlike previous studies indicating that the magnitude of gravitational torque decreases as dip angle increases. Subsequently, a new time-dependent, analytic thermal model for a subducting slab was developed. The new model enables us to study transient phenomena associated with plate subduction analytically. On the basis of this model, the nature of slab dip angles was evaluated. Slab dip angles are found to be transient features. As they penetrate into the mantle and increase their lengths, the associated gravitational torque also increases resulting in a downward pulling of the slab to the steeper dip angle. This is especially true once a slab penetrates the olivine-spinel phase boundary at about 400 km depth. However, if the phase transformation does not follow the equilibrium condition, the gravitational torque may have a different behavior. This problem was investigated. Except for fast descending slabs, non-equilibrium phase transformation can only slow down the transient increase of slab dip angles discussed earlier. Its effect is not sufficiently strong to reverse the downward pulling for most of the slabs. However, when slabs subducting at 10 cm/yr or faster, a sufficient amount of metastable olivine can exist beneath 400 km. Because of its low density compared with the surrounding spinel, an upward buoyancy is produced resulting in an upward bending of the slab and possibly an upward rotation of the slab such that smaller dip angles are formed. Seismic studies of the Japanese Slab seem to support this interpretation. The development of oroclinal geometries at convergent boundaries was also examined to study plate obduction which is an important ingredient to the initiation of plate subduction. Although the study suggests that surface features are better modeled by block models, the large scale deformation can be adequately studied by viscous models. Such a model is now under development to complete our original objective to study the initiation of plate subduction. Finally, a three-dimensional, finite element, spherical convective model is developed to study dynamic plate subductions. The model development is now complete and it is being tested to ensure its proper operation. The model is able to generate convection results with a viscosity contrast of about 100. Our research continues to push the viscosity contrast to a level that is appropriate for a subducting slab

Thermal History and Mantle Dynamics of Venus

One objective of this research proposal is to develop a 3-D thermal history model for Venus. The basis of our study is a finite-element computer model to simulate thermal convection of fluids with highly temperature- and pressure-dependent viscosities in a three-dimensional spherical shell. A three-dimensional model for thermal history studies is necessary for the following reasons. To study planetary thermal evolution, one needs to consider global heat budgets of a planet throughout its evolution history. Hence, three-dimensional models are necessary. This is in contrasts to studies of some local phenomena or local structures where models of lower dimensions may be sufficient. There are different approaches to treat three-dimensional thermal convection problems. Each approach has its own advantages and disadvantages. Therefore, the choice of the various approaches is subjective and dependent on the problem addressed. In our case, we are interested in the effects of viscosities that are highly temperature dependent and that their magnitudes within the computing domain can vary over many orders of magnitude. In order to resolve the rapid change of viscosities, small grid spacings are often necessary. To optimize the amount of computing, variable grids become desirable. Thus, the finite-element numerical approach is chosen for its ability to place grid elements of different sizes over the complete computational domain. For this research proposal, we did not start from scratch and develop the finite element codes from the beginning. Instead, we adopted a finite-element model developed by Baumgardner, a collaborator of this research proposal, for three-dimensional thermal convection with constant viscosity. Over the duration supported by this research proposal, a significant amount of advancements have been accomplished

Finite amplitude thermal convection with variable gravity

Finite amplitude thermal convection is studied in a horizontal layer of infinite Prandtl number fluid with a variable gravity. For the present study, gravity is restricted to vary quadratically with respect to the vertical variable. A perturbation technique based on a small parameter, which is a measure of the ratio of the vertical to horizontal dimensions of the convective cells, is employed to determine the finite amplitude steady solutions. These solutions are represented in terms of convective modes whose amplitudes can be either small or of order unity. Stability of these solutions is investigated with respect to three dimensional disturbances. A variable gravity function introduces two non-dimensional parameters. For certain range of values of these two parameters, double or triple cellular structure in the vertical direction can be realized. Hexagonal patterns are preferred for sufficiently small amplitude of convection, while square patterns can become dominant for larger values of the convective amplitude. Variable gravity can also affect significantly the wavelength of the cellular pattern and the onset condition of the convective motion

Tube Wave Attenuation and In-Situ Permeability

The measurement of in-situ permeability is very important in exploration and production logging. Observed data show that tube wave attenuation in full waveform acoustic logs is correlated with formation permeability. It is postulated that attenuation is due to fluid flowing away from the borehole into the formation. In this paper we investigate the theoretical relationship between tube wave attenuation and permeability using two different models. The first is a simple model of a borehole with absorbing walls, and the second is a borehole with a Biot porous medium in the formation. Both models give qualitatively similar results. Tube wave attenuation increases with increasing permeability. Attenuation also increases with increasing frequency and porosity. We have also investigated the relative effects of intrinsic formation attenuation (anelasticity) and permeability on the attenuation of tube waves. Intrinsic attenuation was introduced into the models by means of complex velocities. It is found that in rocks with low to medium permeability (less than 100 millidarcies), intrinsic attenuation is the major contributor to tube wave attenuation. However, in high permeability (greater than 100 millidarcies) rocks, fluid flow associated with in-situ permeability is as important as intrinsic attenuation in controlling tube wave attenuation. In either case, if one can estimate the intrinsic formation attenuation from the other parts of the full waveform (such as the P wave or the psuedo-Rayleigh wave), an estimate of the permeability of the formation can be obtained. We tested the models using published data on core permeability and tube wave amplitudes. By assuming an average value of intrinsic attenuation appropriate to the formations under study, we obtained a good agreement between theory and data.Massachusetts Institute of Technology. Full Waveform Acoustic Logging Consortiu

On similarity waves in compacting media

Compaction generally refers to the relative motion of fluid with respect to the deformable surroundings in a two-phase system. It has many geophysical and engineering applications, including liquefaction, formation of magma chamber, genesis of igneous rocks, foam drainage, and flow in sediments. In this paper, we followed McKenzie's two-phase flow formulation (1984) to study the flow through a porous medium, which is a commonly used model for compaction study. Using the same approach as Barcilon and Lovera (1989), we studied the wave solution with and without melting effect, under the assumption that the ambient porosity is small. Similarity waves were of particular interest here. We discussed the necessary conditions for a specific class of similarity waves to exist, followed by the general behavior of such waves and numerical determination of the solution for several cases. Parametric studies were also carried out to invstiage the dependence of the solution on factors such as the melting rate, the density ratio, and the permeability of the solid matrix, etc.published or submitted for publicatio

A stability analysis and some numerical computations for thermal convection with a variable buoyancy factor

Linear and nonlinear analyses of thermal convection with a variable "buoyancy factor", which is defined as the product of thermal expansion coefficient and gravitational acceleration, are investigated for a fluid layer between two infinite horizontal plates. An isothermal boundary condition is applied for both boundaries, and the buoyancy factor throughout the fluid layer is chosen to be a function of depth. For various profiles of variable buoyancy factor, the associated eigenvalue problem for the linear regime is solved numerically using a spectral method. It is found that for the case of buoyancy factor gain, where the vertical rate of change of the buoyancy factor is positive, the results are reversed. A formula for the critical Rayleigh number as a function of the statistical features of the buoyancy factor is developed. For the nonlinear regime, computations based on a spectral Fourier-Chebyshev collocation method are carried out for six parabolic profiles of buoyancy factor. Flow patterns are found to be dominated by two-dimensional rolls for the Rayleigh numbers considered. The computed Nusselt numbers indicate that buoyancy factor deficit (gain) yields lower (higher) heat flux when compared with the corresponding constant buoyancy factor case. When the buoyancy factor deficit is sufficiently large to produce sign changes in the profile, our numerical simulations show that multiple layering in the vertical direction can be produced.published or submitted for publicationis peer reviewe

Geology of Mars

This website, authored by Albert T. Hsui of the University of Illinois at Urbana-Champaign, provides information about the six geological processes that are either currently operating on Mars or have operated during Martian history. These include the aeolian, cratering, hydro, landslides, tectonic, and volcanic processes. Example images of the results of these processes are provided. This is a wonderfully comprehensive overview of different geologic aspects of the Martian surface

Finite amplitude thermal convection with variable gravity

Finite amplitude thermal convection is studied in a horizontal layer of infinite Prandtl number fluid with a variable gravity. For the present study, gravity is restricted to vary quadratically with respect to the vertical variable. A perturbation technique based on a small parameter, which is a measure of the ratio of the vertical to horizontal dimensions of the convective cells, is employed to determine the finite amplitude steady solutions. These solutions are represented in terms of convective modes whose amplitudes can be either small or of order unity. Stability of these solutions is investigated with respect to three dimensional disturbances. A variable gravity function introduces two non-dimensional parameters. For certain range of values of these two parameters, double or triple cellular structure in the vertical direction can be realized. Hexagonal patterns are preferred for sufficiently small amplitude of convection, while square patterns can become dominant for larger values of the convective amplitude. Variable gravity can also affect significantly the wavelength of the cellular pattern and the onset condition of the convective motion

Observations of Li isotopic variations in the Trinity Ophiolite : evidence for isotopic fractionation by diffusion during mantle melting

Author Posting. © The Authors, 2004. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Geochimica et Cosmochimica Acta 69 (2005) 735-751, doi:10.1016/j.gca.2004.08.004.The Trinity peridotite (northern CA) contains numerous lithologic sequences consisting of dunite to harzburgite to spinel lherzolite to plagioclase lherzolite. Previous workers have documented geochemical gradients in these sequences consistent with melt-rock reaction processes occurring around dunites, interpreted to reflect conduits for melt ascent. We have undertaken a study of Li isotope compositions of clinopyroxene and some olivine within these sequences using ion probe techniques in order to test the hypothesis that the geochemical gradients are related to diffusive fluxing of alkali elements into or away from the melt conduit. Results show large variations in 7Li/6Li occurring in a consistent pattern across three transects from dunite to plagioclase lherzolite within the Trinity peridotite. Specifically, measurements of average δ7Li for single thin sections along the traverse reveal a low in δ7Li in the harzburgite adjacent to the dunite returning to higher values farther from the dunite with a typical offset of ~10 per mil in the low δ7Li trough. This pattern is consistent with a process whereby Li isotopes are fractionated during diffusion through a melt either from the dunite conduit to the surrounding peridotite, or from the surrounding peridotite into the dunite conduit. The patterns in 7Li/6Li occur over a length scale similar to the decrease in REE concentration in these same samples. Explaining both the trace element and Li isotopic gradients requires a combined process of alkali diffusion and melt extraction. We develop a numerical model and examine several scenarios of the combined diffusion-extraction process. Using experimentally constrained values for the change in Li diffusion coefficient with isotope mass, large changes in δ7Li as a function of distance can be created in year to decade time scales. The addition of the melt extraction term allows larger Li concentration gradients to be developed and thus produces larger isotopic fractionations than diffusion only models. The extraction aspect of the model can also account for the observed decrease in rare earth element concentrations across the transects.UIUC SIMS analyses were carried out in the Center for Microanalysis of Materials, University of Illinois, which is partially supported by the U.S. Department of Energy under grant DEFG02-91-ER45439. This work was supported by NSF OCE0096533