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GEO 5/6690 Geodynamics 24 Oct 2014 Last Time: Flexural Isostasy Isostasy is a stress balance resulting in ~consistent pressure at “asthenospheric” depth. Airy isostasy balances vertical stress (in columns) only; flexural isostasy balances vertical + horizontal & is governed by a 4th order PDE: D w P w gw q 2 2 2 ETe3 For a perfectly elastic plate, D 121 2 and for multiple layers: D D1 D2 Tetot 3 Te31 Te32 For top-loading, the PDE has linear solution (in amplitudes of sines/cosines) of theform: WT k 0 D k 4 g Read for Fri 31 Oct: T&S 105-130 HT k © A.R. Lowry 2014 Next Journal Article(s) Reading: For Monday Nov 3: Audet & Bürgmann (2011) Dominant role of tectonic inheritance in supercontinent cycles. Nature Geosci. 4 184-187. Important to think about: What are the possible reasons for a directional dependence of Te? Also, read the abstract and conclusions (and look at the figures) of: Kirby & Swain (2014) On the robustness of spectral methods that measure anisotropy in the effective elastic thickness. Geophys. J. Int. 199(1) 391-401. Problem: What if loads are both surface and internal? • Total isostatic balance includes surface (topographic) mass plus internal mass variations plus lithospheric stress • Surface loads are undercompensated by subsurface mass because of flexural strength of the lithosphere • Internal loads are undercompensated by surface topographic response If rigidity D and mean profile density of the lithosphere are known, can solve for two unknowns (surface and internal load mass) from two observations (gravity and topography fields) Separation of loads is useful for: • Estimation of lithospheric strength and rheology (parameterized by effective elastic thickness Te) • Understanding processes of mass redistribution in/on the Earth Surface loading processes: Internal loading processes: • Erosion/exhumation • Deposition • Normal faulting (footwall uplift) • Reverse faulting (hanging-wall thrust) • Volcanic construction • Thermal mass variations • Compositional mass variations • Crustal thickening or thinning by lower crustal flow • Cooled igneous intrusions Example Applications of Isostatic Analysis: • Monday’s paper used separation of surface and internal loads for the western US • More commonly, Te is used to model surface processes (e.g., surface response to some “known” load such as basin deposition or erosional mass removal) • And of course Te has implications for strength & rheology Implications For Mass Flux Processes: Surface Loads • Erosion • Deposition • Fault Displacement • Volcanic Construction Subsurface Loads • Thermal Variations • Lithologic Variations • Crustal Thickness (Lower Crustal Flow) Gravity & Topography reflect a complicated mix of all mass flux processes… But if we can separate the loads from their isostatic response, it narrows the field of candidate processes. METHOD: Using equations for observed topography h and Bouguer gravity anomaly b plus: the definition of surface load gravity due to internal mass variation flexure of a thin elastic plate gives 2 eqns in 2 unknowns: Then search for Te (& perhaps other parameters) that minimize the difference between observed & predicted coherence Or equivalently, that minimize correlation of the load fields Elevation of the Western U.S. Cordillera? Elevation of the actively extending Basin and Range province in the western United States is anomalously high (average ~1650 m) given the anomalously thin (30–35 km) crust. Why? Possible reasons include: • Hot lithosphere due to rifting (stretching) • Hot asthenosphere (e.g., introduced by the Yellowstone hotspot). Lowry et al. JGR 2000 Surface Load Topography: • Dominated by normal and thrust fault uplift features, stress-supported rift flank uplift, volcanically constructed topo • Uncertainties reflect uncertainties in the estimate of Te, uncertainties in reference density structure, measurement error in the original topo and gravity But mostly instability of the matrix solution for loading! Crustal Mass Contribution: • Used “old” seismic refraction data and estimated mass variations for both crustal thickness variations and internal density variations • Note we need to know Te to turn mass variation (loading) into elevation! • Uncertainties reflect interpolation error, uncertainties in seismic velocity structure, errors in regression of seismic velocities to density Conductive Thermal Contribution: • Note error (neglected crust): Really should be ~30-50% larger. • Thinning of the thermal boundary layer does contribute to high elevation but only partly explains total elevation Uncertainties: interpolation error, heat flow measurement error, heat production model, thermal conductivity, coefficient of thermal expansion Take: Minus: Equals: Minus: Minus: Possibility we considered at the time: Example: Tharsis Rise, Mars: Martian topography is dominated by (1) a north-south hemispheric “crustal dichotomy” and (2) the Tharsis rise, average elevation 5000 m covering 20% of the planet The geoid is the shape of the gravity field. The 2000 m geoid anomaly over Tharsis is the largest in the solar system! The Tharsis Rise Loading Controversy: Surface topography constructed by volcanism? [e.g., Willemann & Turcotte, 1982; Solomon & Head, 1982] Thermal/chemical buoyancy of a single mantle plume? [e.g., Sleep & Phillips, 1979; Harder & Christensen, 1996; Harder, 2000] Probably some combination of both!
