Evolving pressure-temperature conditions during metamorphism drive changes in the stable mineral assemblage, mineral proportions and mineral compositions in rocks. These changes are achieved via the diffusion of components between minerals, fluid and melt, the driving force for diffusion being the gradients in chemical potential of the components developed spatially within the rock. This study utilises recent developments in the software THERMOCALC THERMOCALC to investigate quantitatively chemical potential relationships in rocks, with the phases involved being (solid) solutions. Phase diagrams with chemical potentials as axes are used to understand better the spatial rearrangement of components during the metamorphic evolution of rocks and the metamorphic textures that result. In contrast to qualitative chemical potential diagrams, quantitative diagrams can be contoured for mineral composition, allowing consideration of chemical zoning in minerals. Furthermore, the amount of material required to diffuse to equalise chemical potentials can be calculated. We start by demonstrating the approach via an example of retrograde corona development in an ultra-high-temperature granulite. Whereas the use of chemical potentials to consider the retrograde development of corona textures is well known, they are also significant in considering the prograde history. The role of chemical potentials in prograde metamorphic textural evolution is highlighted in consideration of the consumption and growth of aluminosilicates during the kyanite-to-sillimanite reaction, and the growth of garnet porphyroblasts.

[1] The reason for the survival of mountainous topography in ancient orogenic belts is a long-standing problem in geomorphology and geodynamics. We explore the geomorphologic controls on the timescale for the postorogenic decay of topography to address the question of whether there is a viable geomorphologic explanation for the persistence of topography in ancient orogenic belts or whether alternative geodynamic explanations must be sought. Using both approximate analytical solutions and numerical simulations, we show that the standard detachment-limited stream power river incision model predicts, for reasonable initial topographies, relatively short postorogenic decay times of 1-10 Myr. Additional layers of complexity are introduced to this simplest model including isostasy and flexural strength, a transition to transport-limited conditions during decline, and the incorporation of the combined effects of a critical threshold for erosion and the stochastic variability of flood magnitudes. Each of these additional factors acts to lengthen the decay timescale. Pure Airy isostatic rebound of a thick crustal root results in decay times that are at most a factor of 6 longer than the detachmentlimited result. The transition to transport-limited conditions involves partial protection of the bed by a thin layer of alluvium, which inhibits erosion and therefore increases decay times by a factor of 2-3 in our analysis. Finally, including critical shear stress results increases decay time by approximately a factor of 20 for the parameter values in our example calculation. More importantly, however, a significant portion of topography remains after predicted lowering rates have dropped to values less than measured rates of denudation in weathering-limited, low-relief environments. Thus a model combining isostasy, a transition to transport-limited conditions, and a critical shear stress for erosion could account for the presence of residual topography for hundreds of million years. All three of these factors can be expected to play a role in natural settings. INDEX TERMS:1815 Hydrology: Erosion and sedimentation; 1824 Hydrology: Geomorphology (1625); 8110 Tectonophysics: Continental tectonics-general (0905); KEYWORDS: topography, erosion, relief, postorogenic, geomorphology Citation: Baldwin, J. A., K. X. Whipple, and G. E. Tucker, Implications of the shear stress river incision model for the timescale of postorogenic decay of topography,

A new quantitative approach to constraining mineral equilibria in sapphirine-bearing ultrahightemperature (UHT) granulites through the use of pseudosections and compatibility diagrams is presented, using a recently published thermodynamic model for sapphirine. The approach is illustrated with an example from an UHT locality in the Ana´polis-Itauc¸u Complex, central Brazil, where modelling of mineral equilibria indicates peak metamorphic conditions of about 9 kbar and 1000°C. The early formed, coarse-grained assemblage is garnet-orthopyroxene-sillimanite-quartz, which was subsequently modified following peak conditions. The retrograde pressure-temperature (P-T) path of this locality involves decompression across the FeO-MgO-Al 2 O 3 -SiO 2 (FMAS) univariant reaction orthopyroxene + sillimanite ¼ garnet + sapphirine + quartz, resulting in the growth of sapphirine-quartz, followed by cooling and recrossing of this reaction. The resulting microstructures are modelled using compatibility diagrams, and pseudosections calculated for specific grain boundaries considered as chemical domains. The sequence of microstructures preserved in the rocks constrains a two-stage isothermal decompression-isobaric cooling path. The stability of cordierite along the retrograde path is examined using a domainal approach and pseudosections for orthopyroxene-quartz and garnet-quartz grain boundaries. This analysis indicates that the presence or absence of cordierite may be explained by local variation in a H 2 O . This study has important implications for thermobarometric studies of UHT granulites, mainly through showing that traditional FMAS petrogenetic grids based on experiments alone may overestimate P-T conditions. Such grids are effectively constant a H 2 O sections in FMAS-H 2 O (FMASH), for which the corresponding a H 2 O is commonly higher than that experienced by UHT granulites. A corollary of this dependence of mineral equilibria on a H 2 O is that local variations in a H 2 O may explain the formation of cordierite without significant changes in P-T conditions, particularly without marked decompression.

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