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Lectures : Presentation to download

par Eric LAROSE - 30 avril 2012 ( dernière mise à jour : 5 février 2014 )


- P. Roux

Introduction to the 2013 Cargese workshop :
“Passive imaging and monitoring in wave physics : from seismology to ultrasound”

- M. Campillo

PDF - 13.5 Mo

Introduction to passive imaging and monitoring in seismology

We discuss heuristic approaches of ambient noise correlation method and give some basic mathematical results. We present the context of the use of these methods in seismology. We illustrate the evolution of the field with a few applications in imaging and monitoring.

- W. Kuperman

PDF - 14.1 Mo

Ocean Noise and Signal Processing

Ocean noise is either natural or man-made and has typically been treated as a nuisance as related to detecting desired signals. As such, many signal processing algorithms have been developed to reject or minimize noise. However, more recently, noise has itself also become a signal of interest in which, for example, ocean or geophysical properties are embedded. There is now significant ongoing research in trying to extract information from noise correlation processing. Much of the latter has utilized either own-ship noise, surface generated noise, biological noise and/or distant shipping noise. Here we review ocean noise research as it progressed from basic descriptive categorization to a more sophisticated understanding of its structure and to subsequent attempts to minimize its impact on signal detection and finally, to its utilization as an environmental descriptor.

- J. Jaffe

Sensing Sound in the Ocean With Swarms of Small Vehicles

Our group, primarily concerned with instrument design, development, and deployment, has been working on the creation of swarms (10’s) of small ocean-going floats to follow currents in 3-dimensions, to mimic the trajectories of small animals that change their buoyancy and thereby travel passively, and to measure mixing along equi-potential surfaces. Since these vehicles are equipped with hydrophones and are localized in time and space, the technology affords the measurement of the oceanic ambient noise field in clouds of kilometer dimensions that float along with the currents. The vehicles themselves are 1.5-liter self-ballasting floats that contain, in addition to the hydrophones, temperature and pressure sensors. Experiments to localize them in 3-dimensions indicates that they can be tracked with several meter accuracy over distances of kilometers at update rates of seconds, via a surface navigation array. Since they are equipped with hydrophones, they also measure the ambient acoustic environment. This has many interesting scientific ramifications. A fascinating area of research is to use them to measure the acoustic landscape in places where small animals have been attracted, presumably to increase their chances of both settling and survival. In another situation, kilometer "clouds" of localizable hydrophones that are not subject to flow noise, have potential to sense directivity and perhaps the location of the largest animals in the sea, the whales, as the floats record their vocalizations. Another application is their extremely stealth use in monitoring sounds that animals make at dusk and dawn, a potential measurement of their abundance, as, unlike underwater vehicles with motors, they do not make noise and, since they go with the flow, they have minimal hydrodynamic disturbance. The ambient oceanic noise, in itself, might actually provide a solution to our quest for global localization as the correlations of the noise field in the ocean as a function of position may be usable in determining their relative distance.

- S. Catheline

PDF - 3.5 Mo

Elastography, tribo-elastography and passive-elastography

Elastography, sometimes referred as seismology of the human body, is an imaging modality recently implemented on medical ultrasound systems. It allows to measure shear waves within soft tissues and gives a tomography reconstruction of the shear elasticity. This elasticity map is useful for early cancer detection. A general overview of this field is given in the first part of the presentation. In a second part, elastography is used in a friction experiment. Indeed, elastography is an original tool to measure elastic field inside soft solids. It results in a direct observation of friction, ruptures and waves in various regimes including slow slip and super-shear rupture. The third and last part is devoted to the application of noise correlation technique in the field of elastography. The idea, as in seismology, is to take advantage of shear waves naturally present in the human body due to muscles activities to construct shear elasticity map of the liver and the thyroid. It is thus a passive elastography approach since no shear wave sources are used.


- H. Sato

PDF - 1.1 Mo

Green’s Function Retrieval from the CCF of Random Waves and Energy Conservation for an Obstacle of Arbitrary Shape : Noise Source Distribution on the Surrounding Shell

For imaging the earth structure, the cross-correlation function (CCF) of ambient noise has been widely used for the estimation of the Green’s function. We mathematically study the constraint for the Green’s function retrieval of scalar waves in relation with energy conservation. When a single scattering obstacle of arbitrary shape is placed in a 3-D homogeneous medium, the Green’s function is written by a double series expansion using spherical harmonic functions and spherical Hankel functions of the first kind representing outgoing waves. When two receivers and the obstacle are illuminated by noise sources randomly and uniformly distributed on a closed spherical shell of a large radius surrounding them, we explicitly derive the constraint for the expansion coefficients as the sufficient condition for the Green’s function retrieval. We note that the derivation of the constraint does not assume that two receivers are in the far field of the scattering obstacle. Then, we show that the constraint is equal to the generalized optical theorem derived from the energy conservation principle. Physical meaning of the generalized optical theorem becomes clear when the expansion coefficients are transformed into scattering amplitudes in the framework of the conventional scattering theory. The derived constraint is reduced to the conventional optical theorem in the case of a spherically symmetric obstacle.

- R. van der Hilst

PDF - 38.4 Mo

Ambient noise tomography of SE Tibet and deep Earth exploration with earthquake waves



- F. Ardhuin

PDF - 9.9 Mo

Ocean waves as a source of acoustic and seismic noise at periods longer than 0.5 s.

It is well known that ocean waves are the source of a fair share of the acoustic and seismic noise measured in the oceans and on land. Noise generation theories can be formulated within the framework of wave-wave interactions as formulated by Hasselmann (Review of Geophysics 1966), which generalizes his 1962 and 1963 papers on ocean wave evolution and microseismic generation, to the general question of ocean wave nonlinear interactions and coupling to any other type of waves with effects of medium heterogeneities. To date, only the Rayleigh wave part of the main microseismic spectral peak (with periods typically between 3 and 8 s) has been convincingly explained from that theory. There are clear indications that compression body waves will soon follow (Ardhuin and Herbers, J. of Fluid Mech., 2013). There is still some work to be done for Love waves. For periods less than 1 s the variability of underwater acoustic noise is still poorly explained (Farrell and Munk, Journal of Physical Oceanography 2010 ; Ardhuin et al., J. Acoust. Soc. Amer. in press), and for very long periods we show that the theory proposed by Webb (Nature 2007) is not consistent and, when corrected, cannot explain the noise level at periods around 100 s. Many of the uncertainties in the validity of noise generation theory arise from a poor knowledge of some of the wave parameters that are relevant to noise generation. For the dominant noise peak this is mostly the directional properties encapsulated in the so-called "overlap integral". At periods around 100 s we are only beginning to discover the variability of the wave energy level (Aucan and Ardhuin, Geophys. Res. Lett. 2013). Here I will thus review the state of knowledge on ocean surface gravity wave properties from periods of 0.5 s to 200 s, the quality of numerical wave models and available databases for these, and consider the implication for seismic noise generation and how seismic noise can be used to validated models of the surface ocean waves.

- G. Prieto

PDF - 7.4 Mo

Advances and Challenges in understanding the amplitude in noise correlations

Significant advances have been made in the last few years in understanding the amplitude information obtained in correlation or correlation-like ambient field studies. Theoretical, numerical and observational studies still have discrepancies on both the ability of ambient noise studies to provide meaningful information about amplitudes (focusing, scattering and attenuation) as well as on their interpretation. I will discuss some of the recent studies and their implications, as well as possible ways in which ambient field studies can be used to obtain better, more reliable information from the noise. The main idea is that, so far, we have been focusing in correlations between two sensors (independently from its neighbors) and I will try to suggest ways in which the coherent signal between three sensors can provide better amplitude information than in the past. Extension to multiple sensors is possible, although more complicated.

- A. Le Pichon

PDF - 3.8 Mo

Infrasound for verification technology and beyond

The infrasound field, the science of low-frequency acoustic waves, has developed into a broad interdisciplinary field encompassing academic disciplines of physics and recent technical and scientific developments.
In 1996, the United Nations General Assembly adopted the Comprehensive Nuclear-Test-Ban Treaty (CTBT), prohibiting atmospheric nuclear explosions worldwide. The global International Monitoring System (IMS) infrasound network comprises 60 stations distributed over the globe. Nearly 70% of this global is now operational. All technical aspects of infrasound monitoring were re-developed for CTBT verification using all state- of-the-art advances. Highly sensitive sensors, efficient array designs and improved processing methods allow now detecting low amplitude signals within non-coherent noise. Beyond engineering sciences, also significant advances in meteorology and propagation modelling have helped to interpret the recordings.
Operational infrasound monitoring systems demonstrate the capability of the global network to detect, locate and characterize a large number of geophysical- and man-made infrasound sources. Reference events provide a unique opportunity to better understand details of propagation in relation with high-resolution atmospheric models and quantitatively assess the network performance. Systematic investigations into comprehensive reference event databases confirm that the performance of the network will fulfill the treaty verification requirements.
Recent studies have evidenced an unprecedented potential benefits of this network for useful civil by considering its use as a component in geophysical hazard warning systems. Furthermore, detailed analyses of the detected low-frequency signals point out new insights on quantitative relationships between observables and atmospheric specifications, therefore opening new fields into the mathematics of geophysical inverse problems for atmospheric remote sensing.


- J. Meunier

PDF - 11.4 Mo

Seismic Reservoir Monitoring : Active, Passive, or Both ?

The interest of the oil and gas industry in seismic reservoir monitoring was first documented in the early 1980s. The basic idea was to record a measurement at various time intervals and analyze the differences between the first and successive values. In those days, 3D seismic migration was a new technique that provided adequate images of the subsurface. Along with the relatively low resolution of seismic images, a major difficulty was the poor accuracy of most seismic measurements. The modest results of the first experiments turned into a new field of seismic activity : Time Lapse, 4D, and Reservoir Monitoring. Great efforts were dedicated to improving seismic resolution and measurement accuracy, resulting in significantly clearer 4D seismic images. The increased number of simultaneous recording channels used to generate a seismic image (currently 100,000+) and enhanced computing power are among the most critical enablers of this progress.
The use of microearthquakes generated by oil and gas production to enhance reservoir knowledge started slightly later. Geophones were deployed downhole in the vicinity of the production. Besides the technological challenges associated with downhole geophone deployment, the difficulty of this technique was the poor geometrical recording configuration (usually several three-component receivers in a single well). Shale gas production, which relies on (artificial) rock fracturation, gave a significant boost to these techniques at the beginning of the 21st century. In particular, the search for richer geometrical configurations led to microseismic recording directly at the surface of the earth or within its vicinity. As in 4D, the same enablers triggered similar progress in the knowledge extracted from microseismic measurements.
Combining geophysical methods in oil and gas exploration is an old dream that has really never come true. There are many reasons for this failure. One of them is that different methods image different features that may not be easy to associate with one another. Reservoir monitoring provides a possible bridge between these methods. The bridge is the reservoir itself. The changes occur in the reservoir. Of course, there are changes outside the reservoir, which must be separated from the changes in the reservoir, but the association problem loses one dimension and becomes easier to solve. This must be true for the combination of active and passive seismic monitoring.

- A. Curtis

PDF - 5.7 Mo

Source-Receiver Interferometry (SRI)

Seismic Interferometry allows seismic tomography of the Earth’s subsurface to be performed using only background vibrational noise. Seismometers can be turned into virtual (imagined) sources of energy that produce real seismograms, and real energy sources (e.g., earthquakes or active-source seismic shots) to be turned into virtual seismometers perhaps deep inside the solid Earth without the need for invasive drilling - i.e., we can use one earthquake as a seismometer to record seismograms from another earthquake. Interferometry also provides novel schemas for computational modelling of acoustic, elastic and electromagnetic phenomena, and embodies completely new Optical Theorems of Physics. In this talk I will introduce some of the most recent interferometric advances using the theory of Source-Receiver Interferometry (SRI : Curtis and Halliday, 2010). SRI allows us to record earthquake seismograms on seismometers that were installed (perhaps years) after the earthquake occurred - a result that can be generalised to acoustic, electromagnetic, diffusive and a range of other phenomena. SRI provides new generalised, nonlinear methods to form seismic images of the Earth’s interior using active sources. SRI leads to data-driven methods to decompose observed multiply-scattered wavefields into their constituent inter-scatterer components. I will introduce the theory of SRI, then these various results, and will discuss their applications and implications.

- J. Garnier

PDF - 1.1 Mo

Role of scattering in virtual source array imaging

We consider the problem of sensor array imaging through a randomly scattering medium. The source array is far from the reflector to be imaged but the receiver array is close. In this situation it is known that the cross correlations of the incoherent signals recorded on the receiver array can be used to image reflectors. In this talk we study the role of scattering in this imaging technique when the source array has limited aperture. In particular we show that random scattering enhances the resolution properties of the imaging function in the weakly scattering paraxial regime but it reduces them in strongly scattering layered media.


- M. Fink

PDF - 4 Mo

From time-reversal to passive imaging : complex media and super-resolution.


- P. Johnson

PDF - 15.9 Mo

Non-linear elasticity : new observations and implications

The elastic behavior of rocks and other earth materials can be highly complex and cannot described by classical theories. In this presentation I provide an overview of the topic. I’ll include laboratory observations of dynamic acousto-elasticity, unconsolidated granular material, and creep-like recovery processes. I will relate laboratory observations to field observations, and link the application of passive noise imaging to extract elastic changes in earth. I’ll also devote a portion of the presentation to recent observations of precursors to slip in sheared granular media, as well as a short discussion of dynamic earthquake triggering in the context of elastic nonlinear processes. Here again I will link the application of passive noise to study elastic changes induced by seismic waves.

- E. Moulin

PDF - 2 Mo

Exploitation of acoustic reverberation for parameter estimation and imaging in plate-shaped structures.

This talk is intended to illustrate the possibility of extracting quantitative information from a limited number of sensors by exploiting the averaging properties of the acoustic reverberation in a solid plate. It will be explained how the multiple reflections are conveniently described through a nonstationary random process based on the image-sources method and taking into account the dispersive nature of the propagated waves. The statistical model thus developed has the advantages of allowing the prediction of a general behaviour (in the form of mathematical expectations) from a limited set of experimentally accessible parameters. This offers an original way of extracting useful structural parameters (such as material properties, dimensions, source localisation and defect characteristics) from reverberant signals triggered by either known or unknown (possibly ambient) excitation sources. Then, it will be shown that correlating such signals and working in a differential mode (after defect minus before defect) could allow detection and imaging of a localised defect despite non-perfect convergence towards the Green’s functions.

- J. de Rosny

PDF - 3.5 Mo

Green’s function retrieval from electromagnetic noise

Experimental demonstration of electromagnetic Green’s function retrieval from noise in anechoic and reverberant cavities is presented. Especially, in this talk we show that the Green’s function between two antennas can be extracted by cross-correlating milliseconds of decimeter wavelength thermal noise. The temperature dependence of the cross-correlation amplitude is well predicted by the black body theory in the Rayleigh-Jeans limit. Because thermal noise level is very weak, care is given to identify all the noise sources that contribute to the correlation. The effect of a non-uniform temperature distribution on the cross-correlation time symmetry is also explored. Finally we apply these results to image a metallic scatterer.

- A. Aubry

PDF - 3.3 Mo

Propagation of waves in complex media under a random matrix approach

This work is devoted to the study of the ultrasonic wave propagation operator in random media. The experimental set up consists in a multi-element array placed in front of a random medium. The inter-element responses between each couple of transducers form the array response matrix. Whereas the propagation operator exhibits a random behavior in the mutiple scattering regime, single scattered echoes keep a deterministic coherence despite disorder. This phenomenon is closely related to the memory effect studied in optics. This difference of behaviour has led to the design of a smart radar which separates single and multiple scattered echoes. This approach is applied here to two different issues.

The first one is very practical and deals with the detection of flaws in coarse grain steels commonly found in nuclear power plants. Whereas the detection capabilities of common ultrasonic techniques suffer from multiple scattering at high frequencies and large depths, our smart radar allows to go beyond these limits. We are able to detect and image flaws which used to be hidden by the multiple scattering noise with classical imaging techniques.

The second issue is more fundamental and concerns the Anderson localization of ultrasound in brazed aluminium beads demonstrated few years ago by John Page and his team. Interestingly, the deterministic coherence displayed by the backscattering matrix in weakly scattering media arises again in this strongly scattering regime. This is due to the occurrence of recurrent scattering paths or loops whose probability dramatically increases at the mobility edge. Our smart radar allows to filter this contribution which directly yields the probability for a wave to come back at its starting spot. The time decay of this quantity is shown to drastically change near the Anderson localization transition. The dynamic evolution of the coherent backscattering cone also shows a substantial deviation from the diffusive behavior at the Anderson localization transition.

- J.P. Montagner

PDF - 24.5 Mo

Seismic anisotropy and passive onitoring of seismogenic zones

Seismic anisotropy, in spite of its inherent complexity is becoming an important ingredient for explaining various kinds of seismic data. Different physical processes (lattice preferred orientation of crystals, cracks or fluid inclusions, fine layering...) related to strain field and/or stress field, give rise to observable seismic anisotropy (S-wave splitting, surface wave radial and azimuthal anisotropies), which makes its interpretation sometimes difficult and non-unique. But the determination of anisotropy provides invualable information on the state of stress and/or strain fields in the solid Earth.

Measuring significant and systematic temporal variations of physical parameters is a major goal of seismologists for monitoring seismogenic zones. Seismic anisotropy is a good candidate for this purpose. In that case, it is primarily induced by the crack distribution within the continental crust, and it is very sensitive to stress-field changes. To date, anisotropy has been investigated through shear-wave splitting (SWS) measurements of local earthquakes. To avoid the erratic occurrence and spatial uncertainties of these events, we have measured the effects of anisotropy on surface waves recovered from the cross-correlation tensor of the ambient seismic noise. We find that the polarization angles of the retrieved surface waves provide a very sensitive parameter for monitoring stress changes in seismogenic zones.

We processed data continuously recorded by the High Resolution Seismic Network (HRSN) located around the San Andreas Fault (SAF), Southern California, USA. We focused on a two-year period, from 2004, when the Parkfield earthquake occurred (28 September, 2004 ; Mw 6.0), to 2005, with no significant seismic activity. We identified and separated out two main contributions from temporal changes of surface wave polarization : (1) slow and weak variations due to seasonal changes of seismic noise incident direction ; and (2) strong and fast rotations of quasi-Rayleigh and quasi-Love wave polarization angles at the moment of the Parkfield event. After removing part (1), the strong polarization shift may be related to changes in crack properties induced by the co-seismic stress. More precisely, it is observed that the polarization directions began to rotate several months before the earthquake and even continue after it. Contrarily to the SWS, polarization of surface waves is more sensitive to crack distribution rotation than travel-times or phase velocity.

Synthetic experiments are exploring how an anisotropic medium with a horizontal symmetry axis mimicking the crack distribution, affects the polarization of surface waves as a function of azimuth. This new technique can be implemented on a routine basis for monitoring stress changes in seismogenic zones.


- Y. Ben-Zion

PDF - 12.2 Mo

Multi-scale 4D imaging of fault zone Environments

I review multi-signal multi-scale seismic imaging studies of fault zones with information on bimaterial interfaces and hierarchical damage structures that become reactivated at shallow depth during earthquakes. The studies use earthquake data to image the seismogenic sections of faults and ambient noise to image the shallower structures. The fault damage zones follow overall a flower-type structure with pronounced damage generally limited to the section above the seismicity. In places with across-fault velocity contrast, the damage zones are offset to the side with higher velocity at depth. These features are evident in earthquake traveltime and noise tomography of the San Jacinto fault zone with low velocity zones at scales of 3-6 km [1], and waveform modeling of trapped and diffracted waves within internal damage zones at a scale of 100 m [2] A similar sense of damage asymmetry is observed at various locations with multiple geological signals [3]. Anisotropy signals provide evidence for low velocity zones at scales from several km to 100 m with predominance of fault-parallel cracks [4]. Polarization analysis at near fault stations also indicates predominance of fault-parallel cracks in fault damage zones [5]. At sections of the San Andreas and North Anatolian faults there is evidence for bimaterial interfaces with considerable along-strike and depth extent. These are seen most clearly with fault zone head waves [6], and are also indicated by teleseismic data [7] and local tomographic images [1]. Various monitoring techniques reveal co- and post-seismic temporal changes of seismic properties. Analyses based on ambient noise use relatively long time scales (>day) and indicate typically <1% temporal changes [8]. Analyses based on earthquake waveforms resolve time scales of seconds and show considerably larger changes. Results associated with local network around the North Anatolian fault indicate clear regional changes of seismic velocities produced by the M7.1 Duzce earthquake, with 20-50% reduction of S velocity at the top 100-500 m of the fault-zone followed by log(t) recovery [9]. These observations are consistent with laboratory experiments with different materials [10] and recent observations following the 2011 M9.0 Tohoku earthquake in Japan [11].

- P. Gueguen

PDF - 28.6 Mo

Experimental testing of structures using ambient vibrations

Knowing the integrity of a structure and monitoring its evolution are essential information involved in decision-making, such as after extreme events (earthquake, tornado...) or at the end of the structure lifetime. The main purpose of this research is to improve the detection, localisation and amplitude of changes observed in structure, using numerical modelling, laboratory experiments and real data. Since the variability of the experimental modal parameters (frequency, damping, mode shapes) is directly related to the structural health, changes in buildings may be due to natural aging, the impact of extreme events such as earthquakes or the variations of the boundary conditions (i.e., soil-structure interaction, air temperature...). The main questions are : - (1) What are the smallest variations in modal parameters that can be detected by ambient vibrations and related to structural changes ?

- M. Todorovska

PDF - 10.1 Mo

Wave methods for structural system identification and health monitoring of buildings.

The nature of seismic wave propagation in buildings is discussed through analyses of simple models and recorded acceleration response in full-scale buildings during earthquakes. The discussion is from the perspective of structural health monitoring and damage detection. The models include uniform and piecewise uniform shear beams and plates, uniform Timoshenko beam, and a soil-structure interaction model with coupled horizontal and rocking response.

Several algorithms for identification of the wave velocities (direct and iterative) are presented and discussed, all of which involve fitting of pulses in the structure impulse response functions. The advantages of the waveform inversion algorithm are demonstrated on examples. The issues of greatest importance for structural health monitoring are discussed, such as the spatial resolution and accuracy of the identification, the presence of dispersion, and the ability to identify the building properties in the more realistic, as well as more challenging, case when there is coupling of the building horizontal and rocking response due to soil-structure interaction. Results of identification are presented for several buildings, and the ability to detect damage is demonstrated on case studies of real buildings that have suffered light or severe damage during the earthquake. The advantages of this wave method for structural health monitoring are highlighted.

- E. Larose

PDF - 12.8 Mo

Detecting and Locating changes with ambient noise and diffuse waves

The first part of the talk concerns landslide monitoring. To detect the partial deconsolidation of clay material (toward liquefaction), we analyze continuous seismic noise acquired at two distant sensors on an active landslide. We find that the apparent seismic velocity drops by 5% several days before the slope failure, which points toward a possible precursory signal. Analyzing the dispersion characteristics of the ambient noise records also allows to locate the change at the base of the sliding layer.
The second part of the talk concerns an original imaging procedure (Locadiff) that uses the decorrelation of diffuse records obtained for fixed receivers but at to different dates, to locate the change. To perform the imaging procedure, we follow a probabilistic approach based on the transfer of the wave intensity throughout the medium. Application to numerical simulations and ultrasound in concrete will be discussed. A perspective toward volcano monitoring will terminate the talk (to be continued during next talk by Brenguier).

- F. Brenguier

PDF - 6.1 Mo

What can we learn about volcanoes from passive seismic noise monitoring ?

Volcanoes are among the most dynamic geological entities, and their eruptions provide a dramatic manifestation of the Earth’s internal activity. However, strong eruptions are only short episodes in the history of volcanoes, which remain quiescent most of the time. During these inter-eruption periods, slow processes such as changes in the magma supply to the reservoir and changes in the physical or chemical properties of magma lead to perturbations of the reservoir pressure and thus prime the volcano for a new eruption. It is, therefore, very important to better describe these processes to fully understand the functioning of active magmatic systems and to improve our ability to forecast volcanic eruptions.
Within volcanoes, magma pressure buildup and transport induces high stress-strain perturbations of the surrounding volcanic edifice which cause changes of seismic wave velocities. Monitoring seismic velocity changes on volcanoes thus provides information about the unrest of volcanic activity. Recently, the development of noise-based seismic monitoring has drastically improved our ability to detect small changes of seismic velocities continuously in time. We are now able to detect relative seismic velocity changes as small as 10-4 with a temporal resolution of 1 day.
With this approach on Piton de la Fournaise volcano (La Réunion island) we are able to detect clear precursors to volcanic eruptions that we interpret as being linked to magma pressure buildup within the magmatic storage area at depth. The obtained measurements of seismic velocity changes also help to identify strong deformation associated with volcanic flank movements that is crucial for improving volcanic hazard assessment.
Finally, we study how the changes in noise source properties may biased our measurements. We are also interested in studying the effects of external perturbations such as rainfall, or barometric and air temperature changes on seismic velocity changes. Correcting these effects is necessary to extract the internal magmatic contribution to the observed velocity changes.

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