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  1. Free, publicly-accessible full text available December 9, 2024
  2. Abstract

    The Hawaiian Ridge has long been a focus site for studying lithospheric flexure due to intraplate volcano loading, but crucial load and flexure details remain unclear. We address this problem using wide‐angle seismic refraction and reflection data acquired along a ∼535‐km‐long profile that intersects the ridge between the islands of Maui and Hawai'i and crosses 80–95 Myr‐old lithosphere. A tomographic image constructed using travel time data of several seismic phases reveals broad flexure of Pacific oceanic crust extending up to ∼200–250 km either side of the Hawaiian Ridge, and vertically up to ∼6–7 km. TheP‐wave velocity structure, verified by gravity modeling, reveals that the west flank of Hawaii is comprised of extrusive lavas overlain by volcanoclastic sediments and a carbonate platform. In contrast, the Hāna Ridge, southeast of Maui, contains a high‐velocity core consistent with mafic or ultramafic intrusive rocks. Magmatic underplating along the seismic line is not evident. Reflectors at the top and bottom of the pre‐existing oceanic crust suggest a ∼4.5–6 km crustal thickness. Simple three‐dimensional flexure modeling with an elastic plate thickness,Te, of 26.7 km shows that the depths to the reflectors beneath the western flank of Hawai'i can be explained by volcano loading in which Maui and the older islands in the ridge contribute ∼43% to the flexure and the island of Hawai'i ∼51%. Previous studies, however, revealed a higherTebeneath the eastern flank of Hawai'i suggesting that isostatic compensation may not yet be complete at the youngest end of the ridge.

     
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    Free, publicly-accessible full text available December 1, 2024
  3. Free, publicly-accessible full text available November 1, 2024
  4. Abstract

    The Hawaiian Ridge, a classic intraplate volcanic chain in the Central Pacific Ocean, has long attracted researchers due to its origin, eruption patterns, and impact on lithospheric deformation. Thought to arise from pressure‐release melting within a mantle plume, its mass‐induced deformation of Earth's surface depends on load distribution and lithospheric properties, including elastic thickness (Te). To investigate these features, a marine geophysical campaign was carried out across the Hawaiian Ridge in 2018. Westward of the island of O'ahu, a seismic tomographic image, validated by gravity data, reveals a large mass of volcanic material emplaced on the oceanic crust, flanked by an apron of volcaniclastic material filling the moat created by plate flexure. The ridge adds ∼7 km of material to pre‐existing ∼6‐km‐thick oceanic crust. A high‐velocity and high‐density core resides within the volcanic edifice, draped by alternating lava flows and mass wasting material. Beneath the edifice, upper mantle velocities are slightly higher than that of the surrounding mantle, and there is no evidence of extensive magmatic underplating of the crust. There is ∼3.5 km of downward deflection of the sediment‐crust and crust‐mantle boundaries due to flexure in response to the volcanic load. At Ka'ena Ridge, the volcanic edifice's height and cross‐sectional area are no more than half as large as those determined at Hawai'i Island. Together, these studies confirm that volcanic loads to the west of Hawai'i are largely compensated by flexure. Comparisons to the Emperor Seamount Chain confirm the Hawaiian Ridge's relatively stronger lithospheric rigidity.

     
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  5. We consider the Ising perceptron model with N spins and M = N*alpha patterns, with a general activation function U that is bounded above. For U bounded away from zero, or U a one-sided threshold function, it was shown by Talagrand (2000, 2011) that for small densities alpha, the free energy of the model converges in the large-N limit to the replica symmetric formula conjectured in the physics literature (Krauth–Mezard 1989, see also Gardner–Derrida 1988). We give a new proof of this result, which covers the more general class of all functions U that are bounded above and satisfy a certain variance bound. The proof uses the (first and second) moment method conditional on the approximate message passing iterates of the model. In order to deduce our main theorem, we also prove a new concentration result for the perceptron model in the case where U is not bounded away from zero. 
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