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Motivation Sputnik Planitia Flexural Modeling Plans for GEOL

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Motivation Sputnik Planitia Flexural Modeling Plans for GEOL Motivation Sputnik Planitia Flexural modeling Sputnik Planitia Flexure model • Large teardrop-shaped basin The flexure of an elastic plate in two dimensions obeys Equation 1 located on Pluto at 20°N 180°E 푑4푤 퐷 + 푚 − 푐 푔푤 = 푉0 Equation 1. • Size: 1300 km by 900 km 푑푥4 4퐷 1/4 퐸∗ℎ3 • Depth: 3-4 km (basin) where 훼 = is the flexural parameter, 퐷 = is the flexural rigidity, is the 휌 −휌 12(1−푣2) 푚 • 푚 푐 Deposit of nitrogen ice density of the underlying layer of the ice shell, is the density of the ice shell. g is the gravity on • 푐 Water ice basement Pluto, E is the Young’s modulus of water ice, h is the elastic thickness, and 휈 is Poisson’s ratio 푑3푤 1 푑푤 For a single vertical load at 푥 = 0 , the boundary conditions are 퐷 = 푉 and = 0 Formation Hypotheses 푑푥3 2 0 푑푥 • An ancient impact basin created The deflection due to several line loads is found by superposition: 푉 훼3 푥−푥 푥−푥 푥−푥 by an impactor later filled with 푤 = σ 푖 sin 푖 + cos 푖 exp − 푖 Equation 2. 푖 8퐷 훼 훼 훼 N2 ice. The feature would have moved to the current location Where {푉푖} is the magnitude of the loads at position {푥푖} through polar wander. • Runaway deposition of N2 ice Inversion due to albedo feedback at the The load vector 퐕 that produces topography 퐰, is found by least squares optimization: ±30°. The depression is due to 퐕 = 퐌′퐌 + 퐂 −1 퐌′퐰 elastic flexure under the load of 풎 where M is the operator matrix that links a load at position 푥푗 to deflection at a point 푥푖 a thick N2 ice cap. Most of the 3 훼 푥푖 − 푥푗 푥푖 − 푥푗 푥푖 − 푥푗 cap has since sublimated away. 퐌 = sin + cos exp − 푖푗 8퐷 훼 훼 훼 and 퐂 = −2 훿 is the covariance matrix, whose components are linked to the noise of the Hypothesis 푚 푡 푖푗 topographic data, • The topography of Pluto around Sputnik Planitia matches the prediction of an 푡 elastic plate flexed by a large load. Synthetic Model The inversion method was tested using two synthetic profiles generated by Dr. Montesi. I inverted Expected results and implications the profiles using many test values of and recorded the misfit. The smallest misfit was found for 훼 = • What elastic thickness would explain the observe topography around Sputnik Planitia? 45 ± 32 (1 value) when the synthetic profile was built with 훼 = 45 and for 훼 = 224 ± 160 (1 • Was the interior relatively warm or cold? Did the deformation happen early or late value) when the synthetic profile was built with 훼 = 225 (shown in figure below). in the history of Pluto? • Was the ice as flexible as expected if there is a water ocean? • What load distribution and amplitude can explain the observed topography? • Is there evidence of a much larger N2 ice layer as inferred today? Example of plate flexure on Earth • The Hawaiian islands act as line load on the Pacific Plate. • Flexure is expressed as a moat around False-color elevation map of Sputnik Planitia with twenty 600 km long tracks approximately the islands surrounded by a bulge. perpendicular to the edge of the basin. • A similar signal may be present around Sputnik Planitia. • Topographic map and profile taken from GeoMapApp. Left image. The top panel displays an elastic flexure signal under a line load along with the curve of best fit that was produced with the misfit test. The bottom panel displays the mass distribution. The model is unitless. Right image. The flexural parameter, alpha, and misfit values displayed as a graph with the best misfit value highlight with a dot. Theoretical model of elastic flexure Plans for GEOL 394 • An elastic plate subjected to a line • Conduct the analysis of the inverse theory on the 20 profiles tracked for Sputnik Planitia and its load is deflected downward, forming surrounding. a moat. • Find if the elastic thicknesses and load magnitude for all 20 profiles are consistent. • A bulge develop due to the restoring • Time permitting, create a 2D finite element model that uses the geometry of Sputnik Planitia to force acting against the deflected also find the best elastic thickness and load magnitude. plate. • The values for elastic thickness and load size will indicate if the interior is warm or cold, which helps constrain the timing of the load. This model may also allow the evaluation if a subsurface Selected topographic profiles across the edge of Sputnik Planitia. Each profile is offset for clarity. ocean is needed as that will change the flexibility of Pluto’s ice shell. Some profiles show a clear topographic bulge while others show apparently random variations..
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