Sustained eruptions on Enceladus explained by turbulent dissipation in tiger stripes

Spacecraft observations suggest that the plumes of Saturn's moon Enceladus draw water from a subsurface ocean, but the sustainability of conduits linking ocean and surface is not understood. Observations show sustained (though tidally modulated) fissure eruptions throughout each orbit, and since the 2005 discovery of the plumes. Peak plume flux lags peak tidal extension by $\sim$1 radian, suggestive of resonance. Here we show that a model of the tiger stripes as tidally-flexed slots that puncture the ice shell can simultaneously explain the persistence of the eruptions through the tidal cycle, the phase lag, and the total power output of the tiger stripe terrain, while suggesting that the eruptions are maintained over geological timescales. The delay associated with flushing and refilling of \emph{O}(1) m-wide slots with ocean water causes erupted flux to lag tidal forcing and helps to buttress slots against closure, while tidally pumped in-slot flow leads to heating and mechanical disruption that staves off slot freeze-out. Much narrower and much wider slots cannot be sustained. In the presence of long-lived slots, the 10$^6$-yr average power output of the tiger stripes is buffered by a feedback between ice melt-back and subsidence to \emph{O}(10$^{10}$) W, which is similar to the observed power output, suggesting long-term stability. Turbulent dissipation makes testable predictions for the final flybys of Enceladus by the \emph{Cassini} spacecraft. Our model shows how open connections to an ocean can be reconciled with, and sustain, long-lived eruptions. Turbulent dissipation in long-lived slots helps maintain the ocean against freezing, maintains access by future Enceladus missions to ocean materials, and is plausibly the major energy source for tiger stripe activity

Self-similar slip pulses during rate-and-state earthquake nucleation

For a wide range of conditions, earthquake nucleation zones on rate- and state-dependent faults that obey either of the popular state evolution laws expand as they accelerate. Under the “slip” evolution law, which experiments show to be the more relevant law for nucleation, this expansion takes the form of a unidirectional slip pulse. In numerical simulations these pulses often tend to approach, with varying degrees of robustness, one of a few styles of self-similar behavior. Here we obtain an approximate self-similar solution that accurately describes slip pulses growing into regions initially sliding at steady state. In this solution the length scale over which slip speeds are significant continually decreases, being inversely proportional to the logarithm of the maximum slip speed V_(max), while the total slip remains constant. This slip is close to D_c(1−a/b)^(−1), where D_c is the characteristic slip scale for state evolution and a and b are the parameters that determine the sensitivity of the frictional strength to changes in slip rate and state. The pulse has a “distance to instability” as well as a “time to instability,” with the remaining propagation distance being proportional to (1−a/b)^(−2) [ln(V_(max)Θ_(bg)/D_c)]^(−1), where Θ_(bg) is the background state into which the pulse propagates. This solution provides a reasonable estimate of the total slip for pulses growing into regions that depart modestly from steady state

The transition from diapirism to dike intrusion: Implications for planetary volcanism

Magma transport processes influence the rate of magma transport and how far the magma travels before it freezes, the degree to which the magma communicates chemically with the host rock, the morphology of volcanic landforms on planetary surfaces, the interplay between magmatism and regional tectonics, and even the direction the magma moves. The primary question motivating this research is: How does magma rheology influence the mechanisms by which it is transported through planetary lithospheres? It is widely recognized that on Earth basaltic intrusions typically take the form of narrow dikes, while granites are typically found in more equidimensional plutons. Several explanations for this observation were offered over the last 50 years. While basalts and rhyolites vary somewhat in temperature and density, the major difference is the 2 to 8 orders of magnitude contrast in viscosity. The significant ductile strains associated with many granitic plutons has led to the statement that the occurrence of granites in diapirs rather than dikes results from the fact that there is insufficient viscosity contrast between the magma and wall rock for the granite to intrude narrow cracks. A second explanation states that granites are so viscous that they cannot propagate far before freezing. Despite the length of time these explanations have been around, there has been relatively little effort to investigate them quantitatively. My goal has been to evaluate these explanations through a series of well-posed numerical models. These models can be tested by the decades of field data collected by structural geologists that have yet to be integrated into any coherent theory, and the results should have important implications for volcanism on the terrestrial planets

Earthquake nucleation on rate and state faults – Aging and slip laws

We compare 2-D, quasi-static earthquake nucleation on rate-and-state faults under both “aging” and “slip” versions of the state evolution law. For both versions mature nucleation zones exhibit 2 primary regimes of growth: Well above and slightly above steady state, corresponding respectively to larger and smaller fault weakening rates. Well above steady state, aging-law nucleation takes the form of accelerating slip on a patch of fixed length. This length is proportional to b^−1 and independent of a, where a and b are the constitutive parameters relating changes in slip speed and state to frictional strength. Under the slip law the nucleation zone is smaller and continually shrinks as slip accelerates. The nucleation zone is guaranteed to remain well above steady state only for values of a/b that are low by laboratory standards. Near steady state, for both laws the nucleation zone expands. The propagating front remains well above steady state, giving rise to a simple expression for its effective fracture energy G c . This fracture energy controls the propagation style. For the aging law G c increases approximately as the square of the logarithm of the velocity jump. This causes the nucleation zone to undergo quasi-static crack-like expansion, to a size asymptotically proportional to b/(b−a)^2. For the slip law G c increases only as the logarithm of the velocity jump, and crack-like expansion is not an option. Instead, the nucleation zone grows as an accelerating unidirectional slip pulse. Under both laws the nucleation front propagates at a velocity larger than the slip speed by roughly μ′/bσ divided by the logarithm of the velocity jump, where μ′ is the effective elastic shear modulus. For this prediction to be consistent with observed propagation speeds of slow slip events in subduction zones appears to require effective normal stresses as low as 1 MPa

Dynamic tensile-failure-induced velocity deficits in rock

Planar impact experiments were employed to induce dynamic tensile failure in Bedford limestone. Rock discs were impacted with aluminum and polymethyl methacralate (PMMA) flyer plates at velocities of 10 to 25 m/s. Tensile stress magnitudes and duration were chosen so as to induce a range of microcrack growth insufficient to cause complete spalling of the samples. Ultrasonic P- and S-wave velocities of recovered targets were compared to the velocities prior to impact. Velocity reduction, and by inference microcrack production, occurred in samples subjected to stresses above 35 MPa in the 1.3 μs PMMA experiments and 60 MPa in the 0.5 μs aluminum experiments. Using a simple model for the time-dependent stress-intensity factor at the tips of existing flaws, apparent fracture toughnesses of 2.4 and 2.5 MPa m^(½) are computed for the 1.3 and 0.5 μs experiments. These are a factor of ∼ 2 to 3 greater than quasi-static values. The greater dynamic fracture toughness observed may result from microcrack interaction during tensile failure. Data for water-saturated and dry targets are indistinguishable

Impact-induced tensional failure in rock

Planar impact experiments were employed to induce dynamic tensile failure in Bedford limestone. Rock discs were impacted with aluminum and polymethyl methacralate flyer plates at velocities of 10 to 25 m/s. This resulted in tensile stresses in the range of ∼11 to 160 MPa. Tensile stress durations of 0.5 and 1.3 μs induced microcrack growth which in many experiments were insufficient to cause complete spalling of the samples. Ultrasonic P and S wave velocities of recovered targets were compared to the velocities prior to impact. Velocity reduction, and by inference microcrack production, occurred in samples subjected to stresses above 35 MPa in the 1.3-μs PMMA experiments and 60 MPa in the 0.5-μs aluminum experiments. Apparent fracture toughnesses of 2.4 and 2.5 MPa m^(1/2) are computed for the 1.3- and 0.5-μs experiments. These are a factor of ∼2 to 6 greater than quasi-static determinations. Three-dimensional impact experiments were conducted on 20 cm-sized blocks of Bedford limestone and San Marcos gabbro. Compressional wave velocity deficits up to 50–60% were observed in the vicinity of the crater. These damage levels correspond to O'Connell and Budiansky damage parameters of 0.4 as compared to the unshocked rock. The damage decreases as ∼r^(−1.5) from the crater indicating a dependence on the magnitude and duration of the tensile pulse. Using the observed variation in damage with tensile stress from the one-dimensional experiments, and estimates of the variation of peak dynamic tensile stress and tensile stress duration with distance from an impact on an elastic half-space, the observed dependence of damage with radius in the three-dimensional experiments are theoretically predicted and compare favorably to experimental data

Shock wave equation of state of muscovite

Shock wave data to provide an equation of state of muscovite (initial density: 2.835 g/cm^3) were determined up to a pressure of 141 GPa. The shock velocity (Us) versus particle velocity (Up) data are fit with a single linear relationship: U_s=4.62(±0.12) +1.27(±0.04)U_p (km/s). Third-order Birch-Murnaghan equation of state parameters (isentropic bulk modulus and isentropic pressure derivative of bulk modulus) are K_(os)=52±4GPa and K'_(os)=3.2±0.3. The pressure-temperature relation along the Hugoniot suggests that muscovite may dehydrate to KAlSi_3O_8 (hollandite), corundum, and water, with a small volume change, above 80 GPa. Thermodynamic calculations of the equilibrium pressure for the dehydration yields a significantly lower value. Observed unloading paths from shock pressures up to about 80 GPa are steeper in a density-pressure plane than the Hugoniot and become shallower with increasing shock pressure above that pressure. The changing slope may indicate that devolatilization occurs during unloading above 80 GPa. The present equation of state data for muscovite are compared with results of previously reported recovery experiments

Aftershock asymmetry on a bimaterial interface

To better understand the asymmetric distribution of microearthquake aftershocks along the central San Andreas fault, we study dynamic models of slip-weakening ruptures on an interface separating differing elastic half-spaces. Subshear ruptures grow as slightly asymmetric bilateral cracks, with larger propagation velocities, slip velocities, and normal stress changes at the rupture front moving in the direction of slip of the medium with the lower shear wave speed (the southeast front, in the context of the San Andreas). When the SE front encounters a stress barrier, the tensile stress perturbation behind the rupture front continues forward and for a wide range of barrier strengths nucleates a dying slip pulse. This slip pulse smooths the stress field and reduces the static stress change beyond the SE front. Furthermore, because the tensile stress that carried the slip pulse into the barrier is a purely dynamic phenomenon, the SE rupture front can be left far below the failure threshold, while the NW front remains quite close to failure. Both mechanisms could contribute to the observed aftershock asymmetry. Formation of a robust slip pulse requires a peak tensile stress perturbation that approaches the nominal strength drop of the slip-weakening law. To achieve this while minimizing off-fault damage requires either substantial velocity contrasts or small reductions in friction. The simulations also show a pronounced asymmetry in the timescales over which barriers to the SE and NW experience increasing stresses, a result that has implications for the asymmetric distribution of subevents in compound earthquakes