Stability of the Epidemic-Type Aftershock Sequence Model with Tapered Gutenberg–Richter Distributed Seismic Moments

ABSTRACT The epidemic-type aftershock sequence model with tapered Gutenberg–Richter (ETAS-TGR)-distributed seismic moments is a modification of the classical ETAS-GR (without tapering) proposed by Kagan in 2002 to account for the finiteness of the deformational energy in the earthquake process. In this article, I analyze the stability of the ETAS-TGR model by explicitly computing the relative branching ratio ηTGR: it has to be set less than 1 for the process not to explode, in fact in the ETAS-TGR model, the critical parameter equals the branching ratio as it happens for the ETAS-GR, due to the rate separability in the seismic moments component. When the TGR parameter βk=23ln10β is larger than the fertility parameter αk=23ln10α, respectively obtained from the GR and the productivity laws by translating moment magnitudes into seismic moments, the ETAS-TGR model results to have less restrictive nonexplosion conditions than in the ETAS-GR case. Furthermore, differently from the latter case in which it must hold β>α for ηGR to exist finite, any order relation for βk and αk (equivalently, for β,α) is admissible for the stability of the ETAS-TGR process; indeed ηTGR is well defined and finite for any βk,αk. This theoretical result is strengthened by a simulation analysis I performed to compare three ETAS-TGR synthetic catalogs generated with βk⋚αk. The branching ratio ηTGR is shown to decrease as the previous parameter difference increases, reflecting: (1) a lower number of aftershocks, among which a lower percentage of first generation shocks; (2) a lower corner seismic moment for the moment–frequency distribution; and (3) a longer temporal window occupied by the aftershocks. The less restrictive conditions for the stability of the ETAS-TGR seismic process represent a further reason to use this more realistic model in forecasting applications.

The influence of detachment strength on the evolving deformational energy budget of physical accretionary prisms

Tracking the evolution of the deformational energy budget within accretionary systems provides insight into the driving mechanisms that control fault development. To quantify the impact of these mechanisms on overall system efficiency, we estimate energy budget components as the first thrust fault pair develops in dry-sand accretion experiments. We track energy budget components in experiments that include and exclude a basal layer of glass beads in order to investigate the influence of detachment strength on work partitioning. We use the measurements of normal force exerted on the backwall to estimate external work, and measurements of strain observed on the sides of the sand packs to estimate the internal work, frictional work and work against gravity done within increments of each experiment. Thrust fault development reduces the incremental external work and incremental internal work, and increases the incremental frictional work and incremental gravitational work. The faults that develop within higher-friction detachment experiments produce greater frictional work than the faults in experiments with glass bead detachments because the slip distribution along the detachments remains the same, while the effective friction coefficient of the detachment differs between the experiments. The imbalance of the cumulative work budget suggests that additional deformational processes that are not fully captured in our measurements of the energy budget, such as acoustic energy, consume work within the deforming wedge.

The influence of detachment strength on the evolving deformational energy budget of physical accretionary prisms

Tracking the evolution of the deformational energy budget within accretionary systems provides insight into the driving mechanisms that control fault development. To quantify the impact of these mechanisms on overall system efficiency, we estimate energy budget components as the first thrust fault pair develops in dry sand accretion experiments. We track energy budget components in experiments that include and exclude a basal layer of glass beads in order to investigate the influence of detachment strength on work partitioning. We use the measurements of normal force exerted on the backwall to estimate external work, and measurements of strain observed on the sides of the sandpacks to estimate the internal work, frictional work and work against gravity done within increments of each experiment. Thrust fault development reduces the incremental external work and incremental internal work, and increases the incremental frictional work and incremental gravitational work. The faults that develop within higher friction detachment experiments produce greater frictional work than the faults in experiments with glass bead detachments because the slip distribution along the detachments remain the same while the effective friction coefficient of the detachment differs between the experiments. The imbalance of the cumulative work budget suggests that additional deformational processes that are not fully captured in our measurements of the energy budget, such as acoustic energy, consume work within the deforming wedge.

The influence of a model subglacial lake on ice dynamics and internal layering

As ice flows over a subglacial lake, the drop in bed resistance leads to an increase in ice velocities and a draw down of isochrones and cold ice. The ice surface flattens as it adjusts to the lack of resisting forces at the base. The rapid transition in velocity induces changes in ice viscosity and releases deformation energy that can raise the temperature locally. Recent studies of Antarctic subglacial lakes indicate that many lakes experience very fast and possibly episodic drainage, during which the lake size is rapidly reduced as water flows out. Questions that arise are what effect this would have on internal layers within the ice and whether such past drainage events could be inferred from isochrone structures downstream. Here, we study the effect of a subglacial lake on ice dynamics as well as the influence that such short timescale drainage would have on the internal layers of the ice. To this end, we use a full Stokes, polythermal ice flow model. An enthalpy-gradient method is used to account for the evolution of temperature and water content within the ice. We find that a rapid transition between slow-moving ice outside the lake, and full sliding over the lake, can release considerable amounts of deformational energy, with the potential to form a temperate layer at depth in the transition zone. In addition, we provide an explanation for a characteristic surface feature commonly seen at the edges of subglacial lakes, a hummocky surface depression in the transition zone between little to full sliding. We also conclude that rapid changes in the horizontal extent of subglacial lakes and slippery patches, compared to the average ice column velocity, can create a traveling wave at depth within the isochrone structure that transfers downstream with the advection of ice, thus indicating the possibility of detecting past drainage events with ice penetrating radar.

The influence of a model subglacial lake on ice dynamics and internal layering

As ice flows over a subglacial lake, the drop in bed resistance leads to an increase in ice velocities and a subsequent draw-down of isochrones and cold ice from the surface. The ice surface flattens as it adjusts to the lack of resisting forces at the base. The rapid transition in velocity induces changes in temperature and ice viscosity, releasing deformation energy which raises the temperature locally. Recent studies of Antarctic subglacial lakes indicate that many lakes experience very fast and possibly episodic drainage, during which the lake size is rapidly reduced as water flows out. A question is what effect this would have on internal layers within the ice, and whether such past events could be inferred from isochrone structures downstream. Here, we study the effect of a subglacial lake on the dynamics of a model ice stream as well as the influence that such short timescale drainage would have on the internal layers of the ice. To this end, we use a Full–Stokes, polythermal ice flow model. An enthalpy gradient method is used to account for the evolution of temperature and water content within the ice. We find that the rapid transition between slow-moving ice outside the lake, and full sliding over the lake, releases large amounts of deformational energy, which has the potential to form a temperate layer at depth in the transition zone. In addition, we provide an explanation for a characteristic surface feature, commonly seen at the edges of subglacial lakes, a hummocky surface depression in the transition zone between little to full sliding. We also conclude that rapid changes in lake geometry or basal friction create a travelling wave at depth within the isochrone structure that transfers downstream with the advection of ice, thus indicating the possibility of detecting past events with ice penetrating radar.

Evaluation of Thermal and Mechanical Filler Gas Influence on Honeycomb Structures Behavior

In this paper the behavior of hexagonal honeycombs under dynamic in-plane loading is described. Additionally, the presence and influence of the filler gas inside the honeycomb cells is considered. Such structures are subjected to very large deformation during an impact, where the filler gas might strongly affect their behavior and the capability of deformational energy absorption, especially at very low relative densities. The purpose of this research was therefore to evaluate the influence of filler gas on the macroscopic cellular structure behavior under dynamic uniaxial loading conditions by means of computational simulations. The LS-DYNA code has been used for this purpose, where a fully coupled interaction between the honeycomb structure and the filler gas was simulated. Different relative densities, initial pore pressures and strain rates have been considered. The computational results clearly show the influence of the filler gas on the macroscopic behavior of analyzed honeycomb structures. Because of very large deformation of the cellular structure, the gas inside the cells is also enormously compressed which results in very high gas temperatures and contributes to increased crash energy absorption capability. The evaluated results are valuable for further research considering also the heat transfer in honeycomb structures and for investigations of variation of the base material mechanical properties due to increased gas temperatures under impact loading conditions.