Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Geology 6600/7600 Signal Analysis 16 Nov 2015 Last time: Deconvolution in Flexural Isostasy • Flexural isostasy reflects convolution of mass load distributions with lithospheric response (a function of mass density and flexural rigidity D): HT = HI + WT • Using relations to observable signals (gravity, topography) can express as a system of linear equations and solve for the loads (e.g, SHD relations for Mars areoid and shape): • Densities and flexural rigidity must be independently determined… © A.R. Lowry 2015 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! A Tricky-Bit: If Tharsis results from plume dynamics, this analysis must examine loading depths in the flow field! And it does. The l parameter in equation 3 is the surface deformation response kernel for an instantaneous viscous flow model with appropriate thickness, density and viscosity for the assumed planetary model… Mars Earth Another Tricky-Bit: What if the matrix is singular? In the presence of membrane stress (as here), these equations are not automatically ~singular at long wavelengths (but they will be singular given some choice of load depth!) By algebraically evaluating the determinant of the matrix and setting it = 0, find that: Another Tricky-Bit: What if the matrix is singular? Singularity happens when the geoid/topography ratio predicted for pure surface loading is identical to that predicted for pure internal loading. Max surface load 400 km load depth 100 km load depth Max surface load Test criterion Reduce the problem by “capping” load amplitudes when matrix is nearsingular… Effects of lithosphere thickness and internal load depth on the estimate of internal load contribution Effects of crustal density and crustal thickness on the estimate of internal load contribution Constraining Parameter Space: • Correlation of the load estimates is very sensitive to parameter-induced error, because errors in one load must be balanced by error in the other • Hence we assume surface and internal load fields are uncorrelated, and search for model params that minimize the correlation of the two! Using the model parameterization that minimizes load coherence, the “best” estimate of surface loading has an average thickness of 17 km within the Tharsis rise, and average flexure is 12 km. The averaged internal load is buoyant but small. Anomalous elevation of the western U.S. Cordillera (Lowry, Ribe & Smith, JGR 2000) Researchers have long noted that 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. Hypotheses include hot lithosphere due to rifting (stretching) and hot asthenosphere introduced by the Yellowstone hotspot.