Katz Richard F.

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Richard F.

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  • Article
    The tides of Enceladus’ porous core
    (American Geophysical Union, 2022-05-02) Rovira-Navarro, Marc ; Katz, Richard F. ; Liao, Yang ; van der Wal, Wouter ; Nimmo, Francis
    The inferred density of Enceladus' core, together with evidence of hydrothermal activity within the moon, suggests that the core is porous. Tidal dissipation in an unconsolidated core has been proposed as the main source of Enceladus' geological activity. However, the tidal response of its core has generally been modeled assuming it behaves viscoelastically rather than poroviscoelastically. In this work, we analyze the poroviscoelastic response to better constrain the distribution of tidal dissipation within Enceladus. A poroviscoelastic body has a different tidal response than a viscoelastic one; pressure within the pores alters the stress field and induces a Darcian porous flow. This flow represents an additional pathway for energy dissipation. Using Biot's theory of poroviscoelasticity, we develop a new framework to obtain the tidal response of a spherically symmetric, self-gravitating moon with porous layers and apply it to Enceladus. We show that the boundary conditions at the interface of the core and overlying ocean play a key role in the tidal response. The ocean hinders the development of a large-amplitude Darcian flow, making negligible the Darcian contribution to the dissipation budget. We therefore infer that Enceladus' core can be the source of its geological activity only if it has a low rigidity and a very low viscosity. A future mission to Enceladus could test this hypothesis by measuring the phase lags of tidally induced changes of gravitational potential and surface displacements.
  • Article
    Grain-size dynamics beneath mid-ocean ridges : implications for permeability and melt extraction
    (John Wiley & Sons, 2015-03-26) Turner, Andrew J. ; Katz, Richard F. ; Behn, Mark D.
    Grain size is an important control on mantle viscosity and permeability, but is difficult or impossible to measure in situ. We construct a two-dimensional, single phase model for the steady state mean grain size beneath a mid-ocean ridge. The mantle rheology is modeled as a composite of diffusion creep, dislocation creep, dislocation accommodated grain boundary sliding, and a plastic stress limiter. The mean grain size is calculated by the paleowattmeter relationship of Austin and Evans (2007). We investigate the sensitivity of our model to global variations in grain growth exponent, potential temperature, spreading-rate, and mantle hydration. We interpret the mean grain-size field in terms of its permeability to melt transport. The permeability structure due to mean grain size may be approximated as a high permeability region beneath a low permeability region. The transition between high and low permeability regions occurs across a boundary that is steeply inclined toward the ridge axis. We hypothesize that such a permeability structure generated from the variability of the mean grain size may focus melt toward the ridge axis, analogous to Sparks and Parmentier (1991)-type focusing. This focusing may, in turn, constrain the region where significant melt fractions are observed by seismic or magnetotelluric surveys. This interpretation of melt focusing via the grain-size permeability structure is consistent with MT observation of the asthenosphere beneath the East Pacific Rise.
  • Article
    Magmatic focusing to mid-ocean ridges : the role of grain-size variability and non-Newtonian viscosity
    (John Wiley & Sons, 2017-12-06) Turner, Andrew J. ; Katz, Richard F. ; Behn, Mark D. ; Keller, Tobias
    Melting beneath mid-ocean ridges occurs over a region that is much broader than the zone of magmatic emplacement that forms 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 sublithospheric 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 covariation 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 explanation of the electrical resistivity structure beneath one location on the East Pacific Rise. More generally, we find that although grain-size and non-Newtonian viscosity are properties of the solid phase, their effect on melt transport beneath mid-ocean ridges is more profound than their effect on the mantle corner flow.