A physical model for seismic noise generation by turbulent flow in rivers

Previous studies suggest that the seismic noise induced by rivers may be used to infer river transport properties, and previous theoretical work showed that bedload sediment flux can be inverted from seismic data. However, the lack of a theoretical framework relating water flow to seismic noise prevents these studies from providing accurate bedload fluxes and quantitative information on flow processes. Here we propose a forward model of seismic noise caused by turbulent flow. In agreement with previous observations, modeled turbulent flow-induced noise operates at lower frequencies than bedload-induced noise. Moreover, the differences in the spectral signatures of turbulent flow-induced and bedload-induced forces at the riverbed are significant enough that these two processes can be characterized independently using seismic records acquired at various distances from the river. In cases with isolated turbulent flow noise, we suggest that riverbed stress can be inverted. Finally, we validate our model by comparing predictions to previously reported observations. We show that our model captures the spectral peak located around 6–7 Hz and previously attributed to water flow at Hance Rapids in the Colorado River (United States); we also show that turbulent flow causes a significant part of the seismic noise recorded at the Trisuli River in Nepal, which reveals that the hysteresis curve previously reported there does not solely include bedload, but is also largely influenced by turbulent flow-induced noise. We expect the framework presented here to be useful to invert realistic bedload fluxes by enabling the removal of the turbulent flow contribution from seismic data

Limit Synchronization in Markov Decision Processes

Markov decision processes (MDP) are finite-state systems with both strategic and probabilistic choices. After fixing a strategy, an MDP produces a sequence of probability distributions over states. The sequence is eventually synchronizing if the probability mass accumulates in a single state, possibly in the limit. Precisely, for 0 <= p <= 1 the sequence is p-synchronizing if a probability distribution in the sequence assigns probability at least p to some state, and we distinguish three synchronization modes: (i) sure winning if there exists a strategy that produces a 1-synchronizing sequence; (ii) almost-sure winning if there exists a strategy that produces a sequence that is, for all epsilon > 0, a (1-epsilon)-synchronizing sequence; (iii) limit-sure winning if for all epsilon > 0, there exists a strategy that produces a (1-epsilon)-synchronizing sequence. We consider the problem of deciding whether an MDP is sure, almost-sure, limit-sure winning, and we establish the decidability and optimal complexity for all modes, as well as the memory requirements for winning strategies. Our main contributions are as follows: (a) for each winning modes we present characterizations that give a PSPACE complexity for the decision problems, and we establish matching PSPACE lower bounds; (b) we show that for sure winning strategies, exponential memory is sufficient and may be necessary, and that in general infinite memory is necessary for almost-sure winning, and unbounded memory is necessary for limit-sure winning; (c) along with our results, we establish new complexity results for alternating finite automata over a one-letter alphabet

Sea ice inertial oscillations in the Arctic Basin

International audienceAn original method to quantify the amplitude of inertial motion of oceanic and ice drifters, through the introduction of a non-dimensional parameter M defined from a spectral analysis, is presented. A strong seasonal dependence of the magnitude of sea ice inertial oscillations is revealed, in agreement with the corresponding annual cycles of sea ice extent, concentration, thickness, advection velocity, and deformation rates. The spatial pattern of the magnitude of the sea ice inertial oscillations over the Arctic Basin is also in agreement with the sea ice thickness and concentration patterns. This argues for a strong interaction between the magnitude of inertial motion on one hand, the dissipation of energy through mechanical processes, and the cohesiveness of the cover on the other hand. Finally, a significant multi-annual evolution towards greater magnitudes of inertial oscillations in recent years, in both summer and winter, is reported, thus concomitant with reduced sea ice thickness, concentration and spatial extent

Predicting short-period, wind-wave-generated seismic noise in coastal regions

Substantial effort has recently been made to predict seismic energy caused by ocean waves in the 4–10 s period range. However, little work has been devoted to predict shorter period seismic waves recorded in coastal regions. Here we present an analytical framework that relates the signature of seismic noise recorded at 0.6–2 s periods (0.5–1.5 Hz frequencies) in coastal regions with deep-ocean wave properties. Constraints on key model parameters such as seismic attenuation and ocean wave directionality are provided by jointly analyzing ocean-floor acoustic noise and seismic noise measurements. We show that 0.6–2 s seismic noise can be consistently predicted over the entire year. The seismic noise recorded in this period range is mostly caused by local wind-waves, i.e. by wind-waves occurring within about 2000 km of the seismic station. Our analysis also shows that the fraction of ocean waves traveling in nearly opposite directions is orders of magnitude smaller than previously suggested for wind-waves, does not depend strongly on wind speed as previously proposed, and instead may depend weakly on the heterogeneity of the wind field. This study suggests that wind-wave conditions can be studied in detail from seismic observations, including under specific conditions such as in the presence of sea ice

Computer aided synthesis: a game theoretic approach

In this invited contribution, we propose a comprehensive introduction to game theory applied in computer aided synthesis. In this context, we give some classical results on two-player zero-sum games and then on multi-player non zero-sum games. The simple case of one-player games is strongly related to automata theory on infinite words. All along the article, we focus on general approaches to solve the studied problems, and we provide several illustrative examples as well as intuitions on the proofs.Comment: Invitation contribution for conference "Developments in Language Theory" (DLT 2017

Research Letter

Water that pressurizes the base of glaciers and ice sheets enhances glacier velocities and modulates glacial erosion. Predicting ice flow and erosion therefore requires knowledge of subglacial channel evolution, which remains observationally limited.Water that pressurizes the base of glaciers and ice sheets enhances glacier velocities and modulates glacial erosion. Predicting ice flow and erosion therefore requires knowledge of subglacial channel evolution, which remains observationally limited. Here we demonstrate that detailed analysis of seismic ground motion caused by subglacial water flow at Mendenhall Glacier (Alaska) allows for continuous measurement of daily to subseasonal changes in basal water pressure gradient, channel size, and sediment transport. We observe intermittent subglacial water pressure gradient changes during the melt season, at odds with common assumptions of slowly varying, low-pressure channels. These observations indicate that changes in channel size do not keep pace with changes in discharge. This behavior strongly affects glacier dynamics and subglacial channel erosion at Mendenhall Glacier, where episodic periods of high water pressure gradients enhance glacier surface velocity and channel sediment transport by up to 30% and 50%, respectively. We expect the application of this framework to future seismic observations acquired at glaciers worldwide to improve our understanding of subglacial processes.This study was funded by NSF grant EAR-1453263. We thank Flavien Beaud and an anonymous reviewer for thorough reviews that improved the manuscript. We also thank Michael Lamb, Olivier Gagliardini, Jean-Philippe Avouac, Gael Durand and Adrien Gilbert for fruitful discussions.Ye

Distributed Synthesis in Continuous Time

We introduce a formalism modelling communication of distributed agents strictly in continuous-time. Within this framework, we study the problem of synthesising local strategies for individual agents such that a specified set of goal states is reached, or reached with at least a given probability. The flow of time is modelled explicitly based on continuous-time randomness, with two natural implications: First, the non-determinism stemming from interleaving disappears. Second, when we restrict to a subclass of non-urgent models, the quantitative value problem for two players can be solved in EXPTIME. Indeed, the explicit continuous time enables players to communicate their states by delaying synchronisation (which is unrestricted for non-urgent models). In general, the problems are undecidable already for two players in the quantitative case and three players in the qualitative case. The qualitative undecidability is shown by a reduction to decentralized POMDPs for which we provide the strongest (and rather surprising) undecidability result so far

Subseasonal changes observed in subglacial channel pressure, size, and sediment transport

Water that pressurizes the base of glaciers and ice sheets enhances glacier velocities and modulates glacial erosion. Predicting ice flow and erosion therefore requires knowledge of subglacial channel evolution, which remains observationally limited. Here we demonstrate that detailed analysis of seismic ground motion caused by subglacial water flow at Mendenhall Glacier (Alaska) allows for continuous measurement of daily to subseasonal changes in basal water pressure gradient, channel size, and sediment transport. We observe intermittent subglacial water pressure gradient changes during the melt season, at odds with common assumptions of slowly varying, low-pressure channels. These observations indicate that changes in channel size do not keep pace with changes in discharge. This behavior strongly affects glacier dynamics and subglacial channel erosion at Mendenhall Glacier, where episodic periods of high water pressure gradients enhance glacier surface velocity and channel sediment transport by up to 30% and 50%, respectively. We expect the application of this framework to future seismic observations acquired at glaciers worldwide to improve our understanding of subglacial processes

Symbolic Backwards-Reachability Analysis for Higher-Order Pushdown Systems

Higher-order pushdown systems (PDSs) generalise pushdown systems through the use of higher-order stacks, that is, a nested "stack of stacks" structure. These systems may be used to model higher-order programs and are closely related to the Caucal hierarchy of infinite graphs and safe higher-order recursion schemes. We consider the backwards-reachability problem over higher-order Alternating PDSs (APDSs), a generalisation of higher-order PDSs. This builds on and extends previous work on pushdown systems and context-free higher-order processes in a non-trivial manner. In particular, we show that the set of configurations from which a regular set of higher-order APDS configurations is reachable is regular and computable in n-EXPTIME. In fact, the problem is n-EXPTIME-complete. We show that this work has several applications in the verification of higher-order PDSs, such as linear-time model-checking, alternation-free mu-calculus model-checking and the computation of winning regions of reachability games

Seismic Mapping of Subglacial Hydrology Reveals Previously Undetected Pressurization Event

Understanding the dynamic response of glaciers to climate change is vital for assessing water resources and hazards, and subglacial hydrology is a key player in glacier systems. Traditional observations of subglacial hydrology are spatially and temporally limited, but recent seismic deployments on and around glaciers show the potential for comprehensive observation of glacial hydrologic systems. We present results from a high-density seismic deployment spanning the surface of Lemon Creek Glacier, Alaska. Our study coincided with a marginal lake drainage event, which served as a natural experiment for seismic detection of changes in subglacial hydrology. We observed glaciohydraulic tremor across the surface of the glacier that was generated by the subglacial hydrologic system. During the lake drainage, the relative changes in seismic tremor power and water flux are consistent with pressurization of the subglacial system of only the upper part of the glacier. This event was not accompanied by a significant increase in glacier velocity; either some threshold necessary for rapid basal motion was not attained, or, plausibly, the geometry of Lemon Creek Glacier inhibited speedup. This pressurization event would have likely gone undetected without seismic observations, demonstrating the power of cryoseismology in testing assumptions about and mapping the spatial extent of subglacial pressurization.This work was made possible in part by hard work in the field by Margot Vore, Daniel Bowden, Galen Kaip, and the students and staff of the 2017 Juneau Icefield Research Program. We especially thank Matt Beedle for provision of the photogrammetrically-produced DEM of Lake Linda, following lake drainage. This work was also aided by the advice of Mike Gurnis and Rob Clayton. We thank Paul Winberry and two anonymous reviewers for their helpful feedback, which improved this paper greatly. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1745301. This work was made possible in part by a University of Idaho seed grant, #FY18-01. DEM provided by the Polar Geospatial Center under NSF-OPP awards 1043681, 1559691, and 1542736.Ye