A Semi-classical calculus of correlations

The method of passive imaging in seismology has been developped recently in order to image the earth crust from recordings of the seismic noise. This method is founded on the computation of correlations of the seismic noise. In this paper, we give an explicit formula for this correlation in the "semi-classical" regime. In order to do that, we define the power spectrum of a random field as the ensemble average of its Wigner measure, this allows phase-space computations: the pseudo-differential calculus and the ray theory. This way, we get a formula for the correlation of the seismic noise in the semi-classcial regime with a source noise which can be localized and non homogeneous. After that, we show how the use of surface guided waves allows to image the earth crust.Comment: To appear in a special issue "Imaging and Monitoring with Seismic Noise" of the series "Comptes Rendus G\'eosciences", from the French "Acad\'emie des sciences

Quantum control by von Neumann measurements

A general scheme is presented for controlling quantum systems using evolution driven by non-selective von Neumann measurements, with or without an additional tailored electromagnetic field. As an example, a 2-level quantum system controlled by non-selective quantum measurements is considered. The control goal is to find optimal system observables such that consecutive non-selective measurement of these observables transforms the system from a given initial state into a state which maximizes the expected value of a target operator (the objective). A complete analytical solution is found including explicit expressions for the optimal measured observables and for the maximal objective value given any target operator, any initial system density matrix, and any number of measurements. As an illustration, upper bounds on measurement-induced population transfer between the ground and the excited states for any number of measurements are found. The anti-Zeno effect is recovered in the limit of an infinite number of measurements. In this limit the system becomes completely controllable. The results establish the degree of control attainable by a finite number of measurements

Is ambient noise tomography across ocean basins possible?

International audienceBased on year-long cross-correlations of broad-band seismic records obtained at sixty-six stations within or adjacent to the Pacific Basin, we show that broad-band ambient noise is observed to propagate coherently between island stations and between island and continent stations. For many station pairs, high signal-to-noise ratio (SNR) fundamental mode Rayleigh wave Green functions are observed, which establishes the physical basis for ambient noise tomography across the Pacific. Similar trends for continental and oceanic stations are observed in the relationship between the ambient noise level at a station and the ''noise coherence distance'' – the longest distance at which a high SNR cross-correlation signal is observed for a station. Because locally generated noise obscures long distance coherent noise, situating stations at quiet locations on islands is necessary for the success of ambient noise tomography. Local noise poses a particular challenge at atoll sites and, on the basis of analysis of data from station H2O, at ocean bottom sites at periods above $25 sec

Slopes instability of the Dolomieu crater in La Reunion from seismological observations and numerical modeling.

International audienceThe intensity of volcanic activity and seasonal rains associated with the instability of the natural slopes has caused many rockfalls in the Dolomieu crater located on top of the volcano Piton de la Fournaise in La Reunion Island. These phenomena, that involve individual blocks up to larger volumes, are expected to be related to the volcanic activity. The unpredictable nature and destructive power of gravitational flows make in-situ measurements extremely difficult. The seismic signal generated by these slope instabilities provides thus a unique tool to trace back these events and retrieve their characteristics (volume, duration, localization, . . . ). The permanent seismic network set on Le Piton de la Fournaise volcano is particularly well suited to the study of seismic signals related to gravitational collapse and of their relation to volcanic activity. Using this network and the new seismic broadband stations recently installed, the seismic signals generated by slope instabilities have been acquired and analyzed. In a first step, signal processing techniques have been developed to distinguish the seismic signal generated by rockfalls from that generated by other seismological events that affect the Piton de la Fournaise Volcano. A localization method has been developed based on inversion of waves arrival time. We focus on the 2006-2007 period, during which the crater has undergone a major collapse. This event has considerably destabilized the Dolomieu crater edges, providing a good opportunity to study the evolution in time of the rockfall activity. Analysis of the seismic signal and simple scaling laws for granular flows made it possible to derive interesting relations between the energy of the seismic waves and the characteristics of rockfalls. The role of the local topography in these relations has been investigated using numerical modeling of dry granular flows and the Digital Elevation Model of the Dolomieu crater constructed by photogrammetric techniques. Good agreement is found between the scaling laws obtained theoretically and those derived from seismic observation providing insight into the effect of the source parameters on the generated seismic signal. The detection methods and the scaling laws developed here provide useful tools for monitoring of rockfall activity, in particular in relation with the volcanic activity. These works were conducted within UNDERVOLC project

Monitoring volcanoes using seismic noise correlations Surveillance des volcans à partir du bruit de fond sismique

International audienceIn this article, we summarize some recent results of measurements of temporal changes of active volcanoes using seismic noise cross-correlations. We first present a novel approach to estimate volcano interior temporal seismic velocity changes. The proposed method allows to measure very small velocity changes (≈ 0.1%) with a time resolution as small as one day. The application of that method to Piton de la Fournaise Volcano (La Réunion Island) shows velocity decreases preceding eruptions. Moreover, velocity changes from noise cross-correlations over 10 years allow to detect transient velocity changes that could be due to long-lasting intrusions of magma without eruptive activity or to pressure buildup associated to the replenishing of the magma reservoir. We also present preliminary results of noise cross-correlation waveform perturbation associated with the occurrence of dike injection and volcanic eruption. We show that such an analysis leads us to locate the areas of dike injection and eruptive fissures at Piton de la Fournaise Volcano. These recent results suggest that monitoring volcanoes using seismic noise correlations should improve our ability to forecast eruptions, their intensity and thus potential environmental impact

The feeder system of the Toba supervolcano from the slab to the shallow reservoir

The Toba Caldera has been the site of several large explosive eruptions in the recent geological past, including the world’s largest Pleistocene eruption 74,000 years ago. The major cause of this particular behaviour may be the subduction of the fluid-rich Investigator Fracture Zone directly beneath the continental crust of Sumatra and possible tear of the slab. Here we show a new seismic tomography model, which clearly reveals a complex multilevel plumbing system beneath Toba. Large amounts of volatiles originate in the subducting slab at a depth of ∼150 km, migrate upward and cause active melting in the mantle wedge. The volatile-rich basic magmas accumulate at the base of the crust in a ∼50,000 km3 reservoir. The overheated volatiles continue ascending through the crust and cause melting of the upper crust rocks. This leads to the formation of a shallow crustal reservoir that is directly responsible for the supereruptions

Toward Forecasting Volcanic Eruptions using Seismic Noise

During inter-eruption periods, magma pressurization yields subtle changes of the elastic properties of volcanic edifices. We use the reproducibility properties of the ambient seismic noise recorded on the Piton de la Fournaise volcano to measure relative seismic velocity variations of less than 0.1 % with a temporal resolution of one day. Our results show that five studied volcanic eruptions were preceded by clearly detectable seismic velocity decreases within the zone of magma injection. These precursors reflect the edifice dilatation induced by magma pressurization and can be useful indicators to improve the forecasting of volcanic eruptions.Comment: Supplementary information: http://www-lgit.obs.ujf-grenoble.fr/~fbrengui/brenguier_SI.pdf Supplementary video: http://www-lgit.obs.ujf-grenoble.fr/~fbrengui/brenguierMovieVolcano.av