arXiv subjects

Richard F Katz

Publications and source records attributed to Richard F Katz.

5 recordsLinked to original sources

arXiv2026

How sea level paces faulting at fast-spreading mid-ocean ridges

Abyssal hills, arguably the most extensive coherent pattern in Earth's surface topography, record the spacing of normal faults formed at mid-ocean ridges. At fast-spreading ridges, high-resolution bathymetry shows a pronounced spectral peak near 41 ky, coincident with obliquity-paced Pleistocene sea-level variability. The origin of this apparent orbital imprint on seafloor structure remains unresolved. We hypothesise that glacial-interglacial sea-level variability influences fault spacing by modulating plate thickness and the flexural stresses produced during plate unbending. Sea-level change alters mantle melting rates and magma supply at ridge axes, generating variations in the properties of the accreting plate. As the plate moves off axis, it unbends from its ingrown curvature, producing tensile fibre stresses that drive normal faulting. We hypothesise that small perturbations in elastic plate thickness modulate these stresses and thereby influence fault spacing. To test this, we extend the elastic unbending theory of Buck (2001) to include spatially variable plate thickness and yield-weakening viscoplastic flexure, which localises deformation into discrete kinks interpreted as faults. Linearised analysis shows that plate-thickness perturbations generate proportional fibre-stress variations. Numerical solutions demonstrate that perturbations as small as approximately 0.1 percent can phase-lock faulting to the imposed forcing. When driven by plate-thickness perturbations derived from the Pleistocene oxygen-isotope record, the model predicts fault spacings concentrated near 41 ky in the early Pleistocene and near 100 ky in the late Pleistocene, consistent with observed abyssal-hill spectra. These results provide a quantitative mechanism by which glacial-interglacial sea-level variability can be transmitted into tectonic structure.

physics.geo-ph↗

arXiv2021

Tidal controls on the lithospheric thickness and topography of Io from magmatic segregation and volcanism modelling

Tidal heating is expected to impart significant, non-spherically-symmetric structure to Jupiter's volcanic moon Io. A signature of spatially variable tidal heating is generally sought in observations of surface heat fluxes or volcanic activity, an exploration complicated by the transient nature of volcanic events. The thickness of the lithosphere is expected to change over much longer timescales, and so may provide a robust link between surface observations and the tidal heating distribution. To predict long-wavelength lithospheric thickness variations, we couple three-dimensional tidal heating calculations to a suite of one-dimensional models of magmatic segregation and volcanic eruption. We find that the lithospheric thickness could either be correlated with the radially integrated heating rate, or weakly anti-correlated. Lithospheric thickness is correlated with radially integrated heating rate if magmatic intrusions form at a constant rate in the lithosphere, but is weakly anti-correlated if intrusions form at a rate proportional to the flux through volcanic conduits. Utilising a simple isostasy model we show how variations in lithospheric thickness can predict long-wavelength topography. The relationship between lithospheric thickness and topography depends on the difference in chemical density between the lithosphere and mantle. Assuming that this difference is small, we find that long-wavelength topography anti-correlates with lithospheric thickness. These results will allow future observations to critically evaluate models for Io's lithospheric structure, and enable their use in constraining the distribution of tidal heating.

astro-ph.EP↗

arXiv2017

Magmatic focusing to mid-ocean ridges: the role of grain size variability and non-Newtonian viscosity

Melting beneath mid-ocean ridges occurs over a region that is much broader than the zone of magmatic emplacement to form the oceanic crust. Magma is focused into this zone by lateral transport. This focusing has typically been explained by dynamic pressure gradients associated with corner flow, or by a sub-lithospheric channel sloping upward toward the ridge axis. Here we discuss a novel mechanism for magmatic focusing: lateral transport driven by gradients in compaction pressure within the asthenosphere. These gradients arise from the co-variation of melting rate and compaction viscosity. The compaction viscosity, in previous models, was given as a function of melt fraction and temperature. In contrast, we show that the viscosity variations relevant to melt focusing arise from grain-size variability and non-Newtonian creep. The asthenospheric distribution of melt fraction predicted by our models provides an improved ex- planation of the electrical resistivity structure beneath one location on the East Pacific Rise. More generally, although grain size and non-Newtonian viscosity are properties of the solid phase, we find that in the context of mid-ocean ridges, their effect on melt transport is more profound than their effect on the mantle corner-flow.

physics.geo-ph↗

arXiv2017

Volatiles beneath mid-ocean ridges: deep melting, channelised transport, focusing, and metasomatism

Deep-Earth volatile cycles couple the mantle with near-surface reservoirs. Volatiles are emitted by volcanism and, in particular, from mid-ocean ridges, which are the most prolific source of basaltic volcanism. Estimates of volatile extraction from the asthenosphere beneath ridges typically rely on measurements of undegassed lavas combined with simple petrogenetic models of the mean degree of melting. Estimated volatile fluxes have large uncertainties; this is partly due to a poor understanding of how volatiles are transported by magma in the asthenosphere. Here, we assess the fate of mantle volatiles through numerical simulations of melting and melt transport at mid-ocean ridges. Our simulations are based on two-phase, magma/mantle dynamics theory coupled to idealised thermodynamic model of mantle melting in the presence of water and carbon dioxide. We combine simulation results with catalogued observations of all ridge segments to estimate a range of likely volatile output from the global mid-ocean ridge system. We thus predict global MOR crust production of 66-73 Gt/yr (22-24 km3/yr) and global volatile output of 52-110 Mt/yr, corresponding to mantle volatile contents of 100--200~ppm. We find that volatile extraction is limited: up to half of deep, volatile-rich melt is not focused to the axis but is rather deposited along the LAB. As these distal melts crystallise and fractionate, they metasomatise the base of the lithosphere, creating rheological heterogeneity that could contribute to the seismic signature of the LAB.

physics.geo-ph↗

arXiv2014

Pipe Poiseuille flow of viscously anisotropic, partially molten rock

Laboratory experiments in which synthetic, partially molten rock is subjected to forced deformation provide a context for testing hypotheses about the dynamics and rheology of the mantle. Here our hypothesis is that the aggregate viscosity of partially molten mantle is anisotropic, and that this anisotropy arises from deviatoric stresses in the rock matrix. We formulate a model of pipe Poiseuille flow based on theory by Takei and Holtzman [2009a] and Takei and Katz [2013]. Pipe Poiseuille is a configuration that is accessible to laboratory experimentation but for which there are no published results. We analyse the model system through linearised analysis and numerical simulations. This analysis predicts two modes of melt segregation: migration of melt from the centre of the pipe toward the wall and localisation of melt into high-porosity bands that emerge near the wall, at a low angle to the shear plane. We compare our results to those of Takei and Katz [2013] for plane Poiseuille flow; we also describe a new approximation of radially varying anisotropy that improves the self-consistency of models over those of Takei and Katz [2013]. This study provides a set of baseline, quantitative predictions to compare with future laboratory experiments on forced pipe Poiseuille flow of partially molten mantle.

physics.geo-ph↗